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```									                             TABLE OF CONTENTS

Sl No           DESCRIPTION OF THE EXPERIMENT                      PAGE NO.

1      Study of Vibration- Two and Multi degree Freedom Systems     1- 61

2      Study of Quality Circle Concepts                            62 - 80
Study of Numerical Control Machines And Programmable
3                                                                  81 - 142
Logic Controllers
4      Study of Tolerance Charting Techniques                      143-194

5      Study of Horizontal Surface Grinder And Grinding Wheels     195-210

6      Study of Shaping Machine

7      Study of Slotting Machine

8      Study of Radial Drilling Machine and Drill Tools

9      Shaper Operation- Female Dove Tail

10     Slotter Operation-Male Dove Tail

11     Drilling Operation

12     Horizontal Surface Grinder Operation
M 608 ADVANCED MACHINE TOOL LABORATORY

Ex No.1: STUDY OF VIBRATION OF TWO AND
MULTI-DEGREE FREEDOM SYSTEMS

OBJECTIVE:

To study about Vibration of two and multi-degree freedom systems.

THEORY
The simplest vibratory system can be described by a single mass connected to a spring
(and possibly a dashpot). The mass is allowed to travel only along the spring elongation
direction. Such systems are called Single Degree-of-Freedom (SDOF) systems and are
shown in the following figure,

Equation of Motion for SDOF Systems:

SDOF vibration can be analyzed by Newton's second law of motion, F = m*a. The
analysis can be easily visualized with the aid of a free body diagram,

The resulting equation of motion is a second order, non-homogeneous, ordinary
differential equation:

with the initial conditions,

3
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

The solution to the general SDOF equation of motion is shown in the damped SDOF.

Definition of an Un-damped SDOF System

If there is no external force applied on the system,        , the system will experience
free vibration. Motion of the system will be established by an initial disturbance (i.e.
initial conditions).

Furthermore, if there is no resistance or damping in the system,      , the oscillatory
motion will continue forever with a constant amplitude. Such a system is termed
undamped and is shown in the following figure,

Time Solution for Un-damped SDOF Systems

The equation of motion derived on the introductory page can be simplified to,

with the initial conditions,

This equation of motion is a second order, homogeneous, ordinary differential equation
(ODE). If the mass and spring stiffness are constants, the ODE becomes a linear
homogeneous ODE with constant coefficients and can be solved by the Characteristic
Equation method. The characteristic equation for this problem is,

which determines the 2 independent roots for the undamped vibration problem. The final
solution (that contains the 2 independent roots from the characteristic equation and
satisfies the initial conditions) is,

4
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

n   is defined by,

and depends only on the system mass and the spring stiffness (i.e. any damping will not
change the natural frequency of a system).

Alternatively, the solution may be expressed by the equivalent form,

where the amplitude A0                        0   are given by,

Sample Time Behaviour

The displacement plot of an undamped system would appear as,

Please note that an assumption of zero damping is typically not accurate. In reality, there
almost always exists some resistance in vibratory systems. This resistance will damp the
vibration and dissipate energy; the oscillatory motion caused by the initial disturbance
will eventually be reduced to zero.
5
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Free vibration (no external force) of a single degree-of-freedom system with viscous
damping can be illustrated as,

Damping that produces a damping force proportional to the mass's velocity is commonly
referred to as "viscous damping", and is denoted graphically by a dashpot.

Time Solution for Damped SDOF Systems

For an unforced damped SDOF system, the general equation of motion becomes,

with the initial conditions,

This equation of motion is a second order, homogeneous, ordinary differential equation
(ODE). If all parameters (mass, spring stiffness and viscous damping) are constants, the
ODE becomes a linear ODE with constant coefficients and can be solved by the
Characteristic Equation method. The characteristic equation for this problem is,

which determines the 2 independent roots for the damped vibration problem. The roots to
the characteristic equation fall into one of the following 3 cases:

   If            < 0, the system is termed under damped. The roots of the
characteristic equation are complex conjugates, corresponding to oscillatory
motion with an exponential decay in amplitude.

   If            = 0, the system is termed critically-damped. The roots of the
characteristic equation are repeated, corresponding to simple decaying motion
with at most one overshoot of the system's resting position.

   If            > 0, the system is termed overdamped. The roots of the characteristic
equation are purely real and distinct, corresponding to simple exponentially
decaying motion.

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DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

To simplify the solutions coming up, we define the critical damping cc, the damping ratio
ζ, and the damped vibration frequency ωd as,

where the natural frequency of the system ωn is given by,

Note that ωd will equal ωn when the damping of the system is zero (i.e. undamped). The
time solutions for the free SDOF system is presented below for each of the three case
scenarios.

Under damped Systems

When             < 0 (equivalent to < 1 or     < ), the characteristic equation has a
pair of complex conjugate roots. The displacement solution for this kind of system is,

An alternate but equivalent solution is given by,

The displacement plot of an under damped system would appear as,

7
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Note that the displacement amplitude decays exponentially (i.e. the natural logarithm of
the amplitude ratio for any two displacements separated in time by a constant ratio is a
constant; long-winded!),

Where                            is the period of the damped vibration.

Critically-Damped Systems

When              = 0 (equivalent to = 1 or      = ), the characteristic equation has
repeated real roots. The displacement solution for this kind of system is,

The critical damping factor cc can be interpreted as the minimum damping that results in
non-periodic motion (i.e. simple decay).

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DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

The displacement plot of a critically-damped system with positive initial displacement
and velocity would appear as,

The displacement decays to a negligible level after one natural period, Tn. Note that if the
initial velocity v0 is negative while the initial displacement x0 is positive, there will exist
one overshoot of the resting position in the displacement plot.

Overdamped Systems

When               > 0 (equivalent to > 1 or     > ), the characteristic equation has
two distinct real roots. The displacement solution for this kind of system is,

The displacement plot of an overdamped system would appear as,

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DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

The motion of an over damped system is non-periodic, regardless of the initial conditions.
The larger the damping, the longer the time to decay from an initial disturbance.

If the system is heavily damped,         , the displacement solution takes the approximate
form,

SDOF Systems under Harmonic Excitation

When a SDOF system is forced by f(t), the solution for the displacement x(t) consists of
two parts: the complimentary solution, and the particular solution. The complimentary
solution for the problem is given by the free vibration discussion. The particular solution
depends on the nature of the forcing function.

When the forcing function is harmonic (i.e. it consists of at most a sine and cosine at the
same frequency, a quantity that can be expressed by the complex exponential eiωt), the
method of Undetermined Coefficients can be used to find the particular solution. Non-
harmonic forcing functions are handled by other techniques.

Consider the SDOF system forced by the harmonic function f(t),

The particular solution for this problem is found to be,

The general solution is given by the sum of the complimentary and particular solutions
multiplied by two weighting constants c1 and c2,

The values of c1 and c2 are found by matching x(t = 0) to the initial conditions.
Undamped SDOF Systems under Harmonic Excitation

For an undamped system (cv = 0) the total displacement solution is,

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DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

If the forcing frequency is close to the natural frequency,       , the system will exhibit
resonance (very large displacements) due to the near-zeros in the denominators of x(t).

When the forcing frequency is equal to the natural frequency, we cannot use the x(t)
given above as it would give divide-by-zero. Instead, we must use L'Hôspital's Rule to
derive a solution free of zeros in the denominators,

To simplify x(t), let's assume that the driving force consists only of the cosine function,
,

The displacement                                                    solution reduces to,

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DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

This solution contains one term multiplied by t. This term will cause the displacement
amplitude to increase linearly with time as the forcing function pumps energy into the
system, as shown in the following displacement plot,

The maximum displacement of an undamped system forced at its resonant frequency will
increase unbounded according to the solution for x(t) above. However, real systems will
physics (nonlinear plastic deformation, heat transfer, buckling, etc.) will serve to limit the
maximum displacement exhibited by the system, and allow one to escape the "sudden
death" impression that such systems will immediately fail.

TERMS AND DEFINITIONS

Beat Phenomenon

When a two degree-of-freedom system has two closely spaced natural frequencies, ωn1
and ωn2, vibration kinetic energy will transfer from one degree-of-freedom to the other in
a periodic fashion. The frequency of this transfer is known as the beat frequency, given
by (ωn1 - ωn2) / 2.

Critical Damping

The minimum damping that results in non-periodic motion of a system under free
vibration.

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DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Damping Ratio

The ratio of a system's actual damping to its critical damping. When less than 1, the
system in underdamped and will exhibit ringing when disturbed. When larger than 1, the
system is overdamped and disturbances will die out without ringing.

Degree-of-Freedom

In the simplest of cases, a degree-of-freedom is an independent displacement or rotation
that a system may exhibit. A degree-of-freedom for a system is analogous to an
independent variable for a mathematical function. All system degrees-of-freedom must be
specified to fully characterize the system at any given time.

Free Body Diagram

A schematic isolating an object (or part of an object) from its environment for the
purpose of revealing all external forces and moments acting on the object. Free body
diagrams are helpful in applying Newton‘s 2nd Law of motion to objects.

Maxwell's Reciprocity Theorem

For two identically-sized forces applied at the distinct points A and B on a linear
structure, Maxwell‘s Reciprocity Theorem states that the displacement at A caused by the
force at B is the same as the displacement at B caused by the force at A. As a result, the
flexibility matrix (and its inverse, the stiffness matrix) of linear systems is symmetric.

Natural Frequency

A frequency where a system resonance exists. If excited at this frequency, the system will
exhibit very large displacements (for low damping levels). If the system is undamped,
then vibrations can occur at the natural frequency without any external excitation
indefinitely.

Resonance

A condition where very little energy input into a structure results in a very large
displacement (for low damping levels). By definition, resonances occur at the natural
frequencies of a system.

Multiple Degree-of-Freedom Example

Consider the 3 degree-of-freedom system,

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DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

There are 3 degrees of freedom in this problem since to fully characterize the system we
must know the positions of the three masses (x1, x2, and x3).

Three free body diagrams are needed to form the equations of motion. However, it is also
possible to form the coefficient matrices directly, since each parameter in a mass-
dashpot-spring system has a very distinguishable role.

Equations of Motion from Free Body Diagrams

The equations of motion can be obtained from free body diagrams, based on the Newton's
second law of motion,

F = m*a.

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DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

The equations of motion can therefore be expressed as,

Equations of Motion From Direct Matrix Formation

Observing the above coefficient matrices, we found that all diagonal terms are positive
and contain terms that are directly attached to the corresponding elements.

Further r more, all non-diagonal terms are negative and symmetric. They are symmetric
since they are attached to two elements and the effects are the same in these two elements
(a condition known as Maxwell's Reciprocity Theorem). They are negative due to the
relative displacements/velocities of the two attached elements.

In summary,

   Determine the number of degrees of freedom for the problem; this determines the
size of the mass, damping, and stiffness matrices. Typically, one degree of
freedom can be associated with each mass.

   Enter the mass values (if associated with a degree of freedom) into the diagonals
of the mass matrix; the exact ordering does not matter. All other values in the
mass matrix are zero.

In matrix form the equations become,

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DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

   For each mass (associated with a degree of freedom), sum the damping from all
dashpots attached to that mass; enter this value into the damping matrix at the
diagonal location corresponding to that mass in the mass matrix.

   Identify dashpots that are attached to two masses; label the masses as m and n.
Write down the negative dashpot damping at the (m, n) and (n, m) locations in the
damping matrix. Repeat for all dashpots. Any remaining terms in the damping
matrix are zero.

   For each mass                                          (associated with a degree of
freedom), sum the stiffness from all springs attached to that mass; enter this value
into the stiffness matrix at the diagonal location corresponding to that mass in the
mass matrix.

   Identify springs that are attached to two masses; label the masses as m and n.
Write down the negative spring stiffness at the (m, n) and (n, m) locations in the
stiffness matrix. Repeat for all springs. Any remaining terms in the stiffness
matrix are zero.

16
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

   Sum the external forces applied on each mass (associated with a degree of
freedom); enter this value into the force vector at the row location corresponding
to the row location for that mass (in the mass matrix).

The resulting matrix equation of motion is,

Vehicle Travelling over a Bumpy Road

Consider a simple model of a vehicle moving over a bumpy road as illustrated in the
following figure. Assume that the vehicle vibrates only in the vertical direction, the
stiffness and damping effects of the tire can be neglected, and the tire has good traction
and never leaves the road surface.

The free body diagram of this moving-base system can be illustrated as,

17
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

The equation of motion is thus,

Suppose that the vehicle is traveling at a constant speed, v, and the road roughness can be
approximated by the equation,

The road roughness can then be rewritten in terms of time (instead of position),

The harmonic moving base system is then equivalent to a harmonic vibration
excitation with the equation of motion,

Since we seek the steady state solution for this problem (there are no "initial conditions"
to prescribe), the displacement solution is just the particular solution for this problem,

Note that if we had initial conditions, then we would need to also find the complimentary
solution and weight the sum of the complimentary and particular solutions such that the
initial conditions were satisfied. However, due to the damping in this system, the
complimentary solution would die away exponentially and after a period of time only the
particular solution (i.e. steady state solution) would remain.

18
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Degree
s of
Freedo
m

It is
import
ant to
apprec
iate the
concep
t of
"degre
es of
freedo
m".
The
numbe
r of
"degre
es of
freedo
m"
that a
vibrati
ng
system
has
will
greatly
affect
how it
vibrate
s.

A
simple
definiti
on of
"degre
es of
freedo
m" is -
the
numbe
r of
coordi
nates
19
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

that it
takes
to
unique
ly
specify
the
positio
n of a
system
.
Consid
er a
rigid
block
that is
free to
move
in 3
dimens
ional
space.
As
shown
in the
diagra
m it
may
move
withou
t
rotatio
n in
each of
the
three
directi
ons x,
y and
z.
these
are
called
the
three
degree
s of

20
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

transla
tion.

The
block
may
also
rotate
each of
the
axes,
these
are
called
the
three
degree
s of
rotatio
n.

Thus
to
unique
ly
define
the
positio
n of
the
block
in
space
we
need to
define
six
coordi
nates,
three
transla
tion
and
three
rotatio
n.

21
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

It
should
be
noted
that
each of
the
coordi
nates
would
be
define
d with
respect
to
some
fixed
referen
ce.
The
origin
of the
x. y
and z
axes
would
be a
fixed
positio
n with
respect
to
earth
and the
directi
ons of
the 3
axes
would
also be
fixed.

It is
possibl
e to
reduce
the

22
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

numbe
r of
degree
s of
freedo
m of
such a
rigid
block
by
introdu
cing
constra
ints

One
degree
of
freedo
m

In this
first
case
we
have
constra
ined
the
block
23
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

to have
only
one
degree
of
freedo
m by,

Using
a rigid
rod
which
is
fixed
to
earth
(not
shown
for
clarity)
Thus
the
block
may
move
along
the rod
in the
y
directi
on
only.

Also
becaus
e the
rod has
a
square
section
the
block
cannot
rotate
the
axis of
the
24
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

rod.

There
is
therefo
re only
one
degree
of
freedo
m.
Knowi
ng the
positio
n of
the
fixed
and
rigid
rod we
only
need
one
coordi
nate -
in this
case
the y
coordi
nate -
to
unique
ly
specify
the
positio
n of
the
block.

25
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Two
degree
s of
freedo
m

In this
second
case
we
have
allowe
d the
block a
second
degree
of
freedo
m by
giving
the
rigid
rod a
circula
r
section
.

This
means
that
the
block
may
rotate

26
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

the
axis of
the
rod.
To
unique
ly
define
the
positio
n of
the
block
now
require
s that
we
specify
the
positio
n
along
the rod
(the y
coordi
nate)
and
also
the
rotatio
n of
the
block
the rod

coordi
nate).

The
block
thus
has
two
degree
s of
freedo
27
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

m.

Some
skill is
require
d in
more
compl
ex
system
s to
determ
ine the
numbe
r of
degree
s of
freedo
m.

Introduction

A system may vibrate when it is possible for energy to be converted from one form to
another and back again. In mechanical systems this is usually from the kinetic energy of
motion to the stored energy in for example a spring.

The simplest vibrating system consists of a rigid mass attached by a massless spring to a
fixed abutment. The animation shows the energy stored in the spring (black) and the
kinetic energy of the mass (red). The total energy of the system is constant, energy is
continuously converted from one form to another.

If there is an energy dissipation source, such as a viscous damper, then the vibration will
gradually decay as energy is converted to heat. However more of this later.

28
DEPARTMENT OF MECHANICAL ENGINEERING
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Transient

Vibration is often considered as "transient" or "forced" vibration.

A transient vibration is one that dies away with time due to energy dissipation (the source
of the energy dissipation is not shown in the animation). Usually there is some initial
disturbance as illustrated in the animation. Following this initial disturbance the system
vibrates without any further input. This is called the transient vibration.

A forced vibration is usually defined as being one that is kept going by an external
excitation. Thus the animation can be considered as a forced vibration as there is a
continuing input from the abutment.

A better (and clearer?) definition of "transient" and "forced" vibration is provided by
considering the equation of motion and its mathematical solution.

Undamped

Consider the motion of the spring/mass system when it is initially disturbed and then
allowed to vibrate freely.

The displacement of the mass with time, x(t), is measured from the static equilibrium
position, i.e. the rest position.

If the spring has a linear stiffness k, then P=kx.

If at some time t the mass is displaced an amount x(t) in the positive direction shown.
Then there will be a force on the mass from the spring of -kx(t).

Thus from Newton's second law of motion using a free-body diagram,

Equation (1) is called the equation of motion. The equation is unchanged if gravity effects
are included

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DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
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The solution of the equation of motion gives,

where x(0) is the initial displacement from the equilibrium position;
x'(0) is the initial velocity.
The frequency is called the undamped natural frequency and

Thus for an initial displacement but with no initial velocity the motion is sinusoidal with
an amplitude x(0) and a frequency ,

NOTE:
The undamped natural frequency does not depend on the initial conditions or the
amplitude of motion. It only depends on the mass and stiffness.

Damped

Real vibration systems have a source of energy dissipation and it is convenient to
represent this by a mass less viscous damper as shown. This produces a drag force
opposing the motion and which depends on the velocity of the mass.

Thus the damping coefficient c, of the damper, results in an additional force -cx'(t) on the
mass. Thus from Newton's second law of motion using a free-body diagram, the equation
of motion is,

It is useful to divide equation (2) by m so that rearranging we obtain,

30
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
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Where is the undamped natural frequency as before and
the viscous damping ratio is defined as

The solution of equation (3) has a different form depending on the value of   . If the
initial conditions are x(0) and x'(0) then

for

31
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
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NOTE:

The damped natural frequency is

and when         there is no vibration

Log decrement

When the damping ratio     < 1.0 then vibration will occur and the motion is defined by

and looks like

It can be shown that, if the amplitudes on any two successive peaks are measured, the ratio of
these amplitudes is constant. For any value of m, the log decrement will be

This equation can be rearranged to give,

NOTE:
The two peaks used to find the log decrement must be on the same side of the axis.

The log decrement will be found to be the same for any two successive peaks.

The damping ratio obtained by using the log decrement does not depend on how the oscillation
was started

External force

We now come to look at the vibration of a one degree of freedom system when there is an
externally applied force.

32
DEPARTMENT OF MECHANICAL ENGINEERING
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The system will respond to the force. The response will depend on the particular forcing
function. As shown the vibration dies away with time due to energy dissipation (the source of
the energy dissipation is not shown in the animation).

We will look at two forcing functions that illustrate most of the main effects resulting from
external forces.

The first is a force of constant magnitude acting for a set time.

The second is a sinusoidal varying force that has a particular frequency.

General force input

We may represent a general force input by F(t) as shown in the diagram. Using Newton II and a
free body diagram we obtain the equation of motion as,

The solution of this equation consists of two parts, the complimentary function (a transient
component) and the particular integral [the response to F(t)].

A typical excitation and response are shown above. There are various mathematical methods
available for solving x(t) for particular examples of F(t). It is also possible to use numerical
methods and an example program has been written using the Runge-Kutta method.

The number of possible force inputs is infinite. However a good understanding of the forced
vibration response of a system can be obtained by applying a force that varies sinusoidal.

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Sinusoidal force

The equation of motion when the force input f(t) is F sinwt is

Typical motion resulting from such an exciting force is shown below.

However if c>0 the motion will after some time settle down to be sinusoidal as shown below.

The mathematical solution of the equation of motion may be achieved in various ways. It will
be found that after an initial transient (depending on initial conditions and start up effects from
applying the sinusoidally varying force) the motion becomes a steady sinusoidal displacement.
This situation is known as the steady state.

The equation of motion with a sinusoidal excitation force is

Typical steady state motion is as shown below.

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The steady state solution for x(t) can be shown to be

X is the displacement amplitude and f is the phase angle between displacement and force.

The response curve has a resonance. The resonance is at a frequency

There is thus no resonance (i.e. no peak in the response) when

At resonance the response peak equals 1/2x for small x. The value of x may be determined from
the response curve for small x.

The phase f varies from 0 to -180 degrees, i.e the displacement lags the force.

It is common to non-dimensionalise these equations so that

These equations may be presented in graphical form,

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Out-of-balance

A common source of excitation force is a rotating system with an out of balance mass. As
shown in the diagram this is a mass m' at a radius r rotating with an angular velocity w. To be
realistic it is also important to include an angular acceleration a as the steady angular velocity is
not achieved instantly.

It can be shown that the force F(t) that acts on the mass m as a result of the rotating out of
balance mass m' is

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and the equation of motion becomes

and rearranging

NOTE:

There will be a force on the mass perpendicular to the x direction. However as this is a one
degree-of-freedom system, this force does not produce any motion.

In practice the constraint, that only allows motion in the x direction, will be subject to a force
that is perpendicular to the x direction.

If disturbed the system will vibrate with a decaying motion.

If there is no damping the vibration does not decay and the frequency of vibration is called
the undamped natural frequency.

The damping ratio is important as if it is equal to or greater than 1.0 then there is no
oscillation.

If there is an oscillation then the damping ratio can be found from the amplitude on
successive peaks.

Even when there is a steady excitation there is a transient at the start of the motion.

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An external force will produce a response in the system. The force is often sinusoidal and after a
period of time when there is an initial transient a steady state solution is achieved. The system
then vibrates at the same frequency as the forcing fequency of.

In the steady state it is common to record the amplitude and phase of the response. These are
then plotted as graphs against forcing frequency.

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NOTE:

The response curve has a resonance when the response is a maximum. The resonance is at a
frequency

At resonance the response peak equals 1/2for small x. The value of x may be determined
from the response curve for small x.

A rotating out-of-balance mass produces an exciting force and hence there is a response
similar BUT not the same as for a constant magnitude oscillating force. The steady state
response curves are shown below.

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NOTE:

As there is no rotation there would be no exciting force and hence no steady state motion.

This is the condition for the centre of mass of m and m' not to be moving.
The resonance is at a frequency

(Which is greater than the undamped natural frequency!) There is no resonance (i.e. no peak
in the response) when

Abutment excitation produces a response similar to the above BUT not the same. The
steady state response curves are shown below.

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NOTE:

The resonance is at a frequency

There is thus always a resonance. At resonance the response peak equals 1/2 for small x.
The phase f varies in a range from 0 to -180 degrees, i.e the displacement lags the input.
However note that at high frequency the phase lag tends to 90 degrees.

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Preventive Maintenance
Historically, maintenance activities have been regarded as a necessary evil by the various
management functions in an organization. However, in recent years this attitude has
increasingly been replaced by one which recognizes maintenance as a strategic issue in the
organization. The developments which contributed to this change include: environmental
concerns, safety issues, warranty and liability factors, regulatory matters, ageing plant and
equipment, drive for cost reduction and the like. To live up to the new expectations demanded
of maintenance activities, maintenance programes have to be developed to ensure that physical
assets will continue to fulfill their intended functions at a minimum expenditure of resources.
Obviously, maintenance activities which do not contribute to preserving or restoring the
intended functions of assets should be eliminated.

Maintenance activities fall into two broad categories, namely corrective maintenance and
preventive maintenance. Corrective maintenance (CM), also known as breakdown maintenance,
is performed when action is taken to restore the functional capabilities of failed or
malfunctioned equipment or systems. This is a reactive approach to maintenance because the
action is triggered by the unscheduled event of an equipment failure. With this kind of
maintenance policy, the maintenance related costs are usually high due to the following
reasons:

l. The high cost of restoring equipment to an operable condition under crisis
situation;
2. The secondary damage and safety/health hazards inflicted by the failure;
3. The penalty associated with lost production.

Preventive maintenance (PM), on the other hand, is the approach developed to avoid this kind of
waste. Traditionally, PM takes mainly the form of equipment overhaul or item replacement at
fixed intervals. This practice is known as time directed (TD) maintenance. When only TD
maintenance is performed, however, to exploit the full potential of PM, the reasons for
Should be recognized. The reasons are
 to prevent failure;
 to detect the onset of failure;
 to discover hidden failure.

These reasons give rise to three types of PM task. The first and most common type of PM task
is time directed (TD). TD tasks, performed to prevent or retard failures, are done at hard time
intervals regardless of other information that may be available when the preset time occurs. A
TD task also requires an intrusion into the equipment, thereby rendering it out of service until
The second type of PM task is condition-based maintenance (CBM), which is also known as on-
condition maintenance, condition-directed maintenance, or predictive maintenance. CBM is
designed to detect the onset of a failure. It is an appropriate option for PM when the following
conditions apply:

1. Either failure prevention is not feasible, or how it can be achieved is not

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yet known, as in cases where the event leading to failure occurs in a predominantly random
manner;
2. A measurable parameter which correlates with the onset of failure has
been identified, for example, the solids content in the lubricant is an
indicator of the machine‘s wearing condition;
3. It is possible to identify a value of that parameter when action may be taken before full failure
occurs, such as the setting of warning limits for the solids content of the lubricant.
CBM is similar to TD maintenance in that the task is performed at preset intervals. However,
unlike TD tasks, CBM does not normally involve an intrusion into the equipment and the actual
preventive action is taken only when it is believed that an incipient failure has been detected.
Standby units, protective devices, or infrequently used equipment create special problems in
preventive maintenance. Failures in this type of equipment are known as hidden failures
because they are not evident until the time when the proper function of the item is needed.
Hidden failures cause operational surprises which may give rise to accidents. To reduce the risk
exposed to hidden failures, fault-finding (FF) tasks are performed at scheduled intervals to
check the state of items with dormant functions.

The risk of failure

There is a widespread belief that corrective maintenance is always less economical than
preventive maintenance, and all failures can be prevented. As a result, time-directed
maintenance becomes the norm of preventive maintenance action, motivating the indiscriminate
use of overhaul or preventive replacement procedures in PM programmes. Experience,
judgment, vendor recommendations and ―the more the better‖ syndrome are the common bases
for determining the content and frequency of a TD task. This approach to PM
wastes a lot of resources in doing unnecessary tasks which will not improve equipment or
system availability. Furthermore, PM tasks which involve intrusion into the equipment
(overhaul tasks) are potentially risky. According to a study on fossil power plants, 56 per cent of
the forced outages occurred within one week after an intrusive type of maintenance task has
been performed.
The failure rate of equipment measures the risk of its failure. It is defined as

h(t) =f(t)/R(t)

where f(t) is the failure density, and R(tp) = º°
tp f(t)dt is the reliability of an item at age tp.

According to the ―bathtub model‖, the failure rate, h (·), decreases with
age or usage when the equipment is new – the time during which this applies is
known as the infant mortality period, and it is usually relatively short. This is
followed by a period of constant failure rate (the useful life period), and then a
―wear-out‖ period. The latter is characterized by a failure rate which is an
increasing function of age or usage. TD tasks are effective in preventing failures
when the equipment is operating within the wear-out region. In such cases, an
overhaul or preventive replacement task will revert the equipment to the ―asnew‖
condition and, after a brief run-in period, the risk of failure will be
significantly reduced. If the goal of performing TD tasks is to minimize the total

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maintenance-related costs, the decision model for determining the optimal
interval between TD tasks is shown below[3]:
where Cp is the total cost of a TD task, Cf is the total cost of a corrective
maintenance task, M(tp) is the mean time to failure given that the failure
occurred before time tp, and C(tp) is the total cost per unit time if the TD task is
performed when an item is of age tp.
Obviously, performing a TD task will be a waste of resources when:
l h(·) is a non-increasing function of age;
l the cost penalty of a corrective maintenance task, Cf, is not greater than
that of a TD task, Cp.
According to an extensive study conducted in the airline industry, the ―bathtub
curve‖ is not a universal model that applies to all items, as most people have
believed. In fact, as much as 89 per cent of all the airline equipment items do not
have a noticeable wear-out region throughout their service life, and hence these
items will not benefit from TD tasks[4].

Vibration monitoring

Vibration monitoring techniques can be used to detect fatigue, wear, imbalance,
misalignment, loosened assemblies, turbulence, etc. in systems with rotational
or reciprocating parts, such as bearings, gear boxes, shafts, pumps, motors,
engines and turbines. The operation of such mechanical systems releases
energy in the form of vibration with frequency components which can be traced
to specific parts in the system. The amplitude of each distinct vibration
component will remain constant unless there is a change in the operating
dynamics of the system.
Vibration can be characterized in terms of three parameters, namely,
amplitude, velocity and acceleration. The sensitivity of senors used for
measuring these parameters varies with frequency of the vibration. The
general selection guideline is to use amplitude senors to pick up low frequency
signals, velocity senors in the middle ranges, and accelerometers at higher
frequencies.
In one form of vibration monitoring, readings of the overall vibration energy
between 10 to 10,000Hz are taken from selected points on a machine. These data
are compared to baseline readings taken from a new machine. Alarm limits are
established on the basis of the baseline readings. A fault diagnosis will be
triggered when a reading exceeds its alarm limit. Alternatively, vibration
readings are compared to vibration severity charts to determine the relative
condition of the machine. This approach is known as broadband vibration
trending, and it monitors only the overall machine conditions. The common
microprocessor-based instrumentation for this procedure monitors the rootmean-
square (RMS) level of the vibration.
In the narrowband trending technique, the total energy across a specific
bandwidth of vibration frequencies is tracked to monitor the health condition of
specific machine components or failure modes.
The process of scanning vibration signals across a bandwidth captures
vibration data on the time domain. Such data can be transformed into the

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frequency domain so that the vibration at each frequency component can be
measured. The frequency plot that provides a visual representation of each
frequency component generated by a machine is known as the machine‘s
vibration signature.

AUTOMATED PROCESS PLANNING

INTRODUCTION

Process planning translates design information into the process steps and instructions to
efficiently and effectively manufacture products. As the design process is supported by many
computer-aided tools, computer-aided process planning (CAPP) has evolved to simplify and
improve process planning and achieve more effective use of manufacturing resources.

PROCESS PLANNING

Process planning encompasses the activities and functions to prepare a detailed set of plans and
instructions to produce a part. The planning begins with engineering drawings, specifications,
parts or material lists and a forecast of demand. The results of the planning are:

     Routings which specify operations, operation sequences, work centers, standards,
tooling and fixtures.This routing becomes a major input to the manufacturing resource
planning system to define operations for production activity control purposes and define
required resources for capacity requirements planning purposes.
     Process plans which typically provide more detailed,step-by-step work instructions
including dimensions related to individual operations, machining parameters, set-up
instructions, and quality assurance checkpoints.
     Fabrication and assembly drawings to support manufacture (as opposed to engineering
drawings to define the part).

Manual process planning is based on a manufacturing engineer's experience and knowledge of
production facilities,equipment, their capabilities, processes, and tooling. Process planning is
very time-consuming and the results vary based on the person doing the planning.

COMPUTER-AIDED PROCESS PLANNING

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Manufacturers have been pursuing an evolutionary path to improve and computerize
process planning.

Prior to CAPP, manufacturers attempted to overcome the problems of manual process planning
by basic classification of parts into families and developing somewhat standardized process
plans for parts families (Stage I). When a new part was introduced, the process plan for that
family would be manually retrieved, marked-up and retyped. While this improved productivity,
it did not improve the quality of the planning of processes and it did not easily take into account
the differences between parts in a family nor improvements in production processes.

Computer-aided process planning initially evolved as a means to electronically store a process
plan once it was created, retrieve it, modify it for a new part and print the plan (Stage II). Other
capabilities of this stage are table-driven cost and standard estimating systems.

This initial computer-aided approach evolved into what is now known as "variant" CAPP.
However, variant CAPP is based on a Group Technology (GT) coding and classification
approach to identify a larger number of part attributes or parameters. These attributes allow the
system to select a baseline process plan for the part family and accomplish about ninety percent
of the planning work. The planner will add the remaining ten percent of the effort modifying or
fine-tuning the process plan. The baseline process plans stored in the computer are manually
entered using a super planner concept,that is, developing standardized plans based on the
accumulated experience and knowledge of multiple planners and manufacturing engineers
(Stage III).

The next stage of evolution is toward generative CAPP (Stage IV). At this stage, process
planning decision rules are built into the system. These decision rules will operate based on a
part's group technology or features technology coding to produce a process plan that will require
minimal manual interaction and modification (e.g., entry of dimensions).

While CAPP systems are moving more and more towards being generative, a pure generative
system that can produce a complete process plan from part classification and other design data
is a goal of the future. This type of purely generative system (in Stage V) will involve the use of
artificial intelligence type capabilities to produce process plans as well as be fully integrated in a
CIM environment. A further step in this stage is dynamic, generative CAPP which would
consider plant and machine capacities, tooling availability, work center and equipment loads,
and equipment status (e.g., maintenance downtime) in developing process plans.

The process plan developed with a CAPP system at Stage V would vary over time depending on
the resources and workload in the factory. For example, if a primary work center for an
operation(s) was overloaded, the generative planning process would evaluate work to be
released involving that work center, alternate processes and the related routings. The decision
rules would result in process plans that would reduce the overloading on the primary work
center by using an alternate routing that would have the least cost impact. Since finite
scheduling systems are still in their infancy, this additional dimension to production scheduling
is still a long way off.

Dynamic, generative CAPP also implies the need for online display of the process plan on a

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workorder oriented basis to insure that the appropriate process plan was provided to the floor.
Tight integration with a manufacturing resource planning system is needed to track shop floor
status and load data and assess alternate routings vis-a-vis the schedule.Finally, this stage of
CAPP would directly feed shop floor equipment controllers or, in a less automated
environment,display assembly drawings online in conjunction with process plans.

CAPP PLANNING PROCESS

The system logic involved in establishing a variant process planning system is relatively straight
forward - it is one of matching a code with a pre-established process plan maintained in the
system. The initial challenge is in developing the GT classification and coding structure for the
part families and in manually developing a standard baseline process plan for each part family.

The first key to implementing a generative system is the development of decision rules
appropriate for the items to be processed. These decision rules are specified using decision
trees, computer languages involving logical "if-then" type statements, or artificial intelligence
approaches with object-oriented programming.

The nature of the parts will affect the complexity of the decision rules for generative planning
and ultimately the degree of success in implementing the generative CAPP system.The majority
of generative CAPP systems implemented to date have focused on process planning for
fabrication of sheet metal parts and less complex machined parts. In addition, there has been
significant recent effort with generative process planning for assembly operations, including
PCB assembly.

A second key to generative process planning is the available data related to the part to drive the
planning. Simple forms of generative planning systems may be driven by GT codes. Group
technology or features technology (FT) type classification without a numeric code may be used
to drive CAPP. This approach would involve a user responding to a series of questions about a
part that in essence capture the same information as in a GT or FT code. Eventually when
features-oriented data is captured in a CAD system during the design process, this data can
directly drive CAPP.

A frequently overlooked step in the integration of CAD/CAM is the process planning that must
occur. CAD systems generate graphically oriented data and may go so far as graphically
identifying metal, etc. to be removed during processing. In order to produce such things as NC
instructions for CAM equipment, basic decisions regarding equipment to be used, tooling and
operation sequence need to be made. This is the function of CAPP. Without some element of
CAPP, there would not be such a thing as CAD/CAM integration. Thus CAD/CAM systems
that generate tool paths and NC programs include limited CAPP capabilities or imply a certain
approach to processing.

CAD systems also provide graphically-oriented data to CAPP systems to use to produce
assembly drawings, etc. Further, this graphically-oriented data can then be provided to
manufacturing in the form of hardcopy drawings or work instruction displays. This type of
system uses work instruction displays at factory workstations to display process plans

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graphically and guide employees through assembly step by step. The assembly is shown on the
screen and as a employee steps through the assembly process with a footswitch, the components
to be inserted or assembled are shown on the CRT graphically along with text instructions and
warnings for each step.

If NC machining processes are involved, CAPP software exists which will select tools, feeds,
and speeds, and prepare NC programs.

CAPP BENEFITS

Significant benefits can result from the implementation of CAPP. In a detailed survey of
twenty-two large and small companies using generative-type CAPP systems, the following
estimated cost savings were achieved:

     58% reduction in process planning effort
     10% saving in direct labour
     4% saving in material
     10% saving in scrap
     12% saving in tooling
     6% reduction in work-in-process

In addition, there are intangible benefits as follows:

     Reduced process planning and production leadtime; faster response to engineering
changes
     Greater process plan consistency; access to up-to-date information in a central database
     Improved cost estimating procedures and fewer calculation errors
     More complete and detailed process plans
     Improved production scheduling and capacity utilization
     Improved ability to introduce new manufacturing technology and rapidly update process
plans to utilize the improved technology

Process planning consists of preparing a set of instructions that describe how to fabricate a
part or build an assembly which will satisfy engineering design specifications. The resulting
set of instructions may include any or all of the following:
Operation sequence, machines, tools, materials, tolerances, notes, cutting parameters,
processes (such as how to heat-treat), jigs, fixtures, methods, time standards, setup details,
inspection criteria, gauges, and graphical representations of the part in various stages of
completion. It is obvious that process planning can be a very complex and time-consuming
job requiring a large amount of data. In addition, several people may participate in developing
a process plan, because no one person may have the broad expertise required. This is further
complicated by the fact that the plan is a critical element in making the part correctly and
economically.
Process planning received little attention until the latter 1970s. Informally, process planning
has been performed for hundreds of years ever since someone first developed instructions to
make something. However, the industrial revolution fostered a need to formalize process
planning in the manufacturing environment. Initially, manufactured parts had few components
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and were made by a small number of people. In this setting, formal process plans were not
required. As the number of parts and complexities increased, a need for formal process plans
was recognized. Nevertheless, until the 1970s the importance of process planning was
understood primarily by those closely involved in making the individual parts. Consequently,
little was done to automate this process.
Today‘s manufacturing environment has become very competitive and complex. This
complexity is a function of more intricate parts and factors, such as machining technologies
that permit making a part several different ways, small lot sizes that neither support long setup
times nor provide frequent learning reinforcement for the machine operator, increased
government regulation that requires documentation of process plans, many types of materials
that may require special tools and/or processes, and less skilled machinists. These factors
combined with increased emphasis on reducing manufacturing costs have affirmed the
significance of process planning, and corroborated that substantial savings can be achieved by
automating the preparation of process plans. Consequently, this function has been receiving
The benefits that have been reported from successful applications of auto mating some of the
process planning functions are impressive and have one of the shortest payback periods of all
CAD/CAM technologies. Some typical benefits include:
1. 50% increase in process planner productivity
2. 40% increase in capacity of existing equipment
3. 25% reduction in setup costs
4. 12% reduction in tooling
5. 10% reduction in scrap and rework
6. 10% reduction in shop labour
7. 6% reduction in work in process
IE 447 CIM Lecture Notes – Chapter 7: Process Planning - 69
8. 4% reduction in material
Some of these benefits may not appear to be related to the automation of process planning.
However, consider what can happen if the process planner‘s productivity is significantly
improved:
1. More time can be spent on methods improvements and cost-reduction activities.
2. Routings can be consistently optimized.
3. Manufacturing instructions can be provided in greater detail.
4. Preproduction lead times can be reduced.
5. Responsiveness to engineering changes can be increased.
Benefits such as these are not going unnoticed.

Key Definitions

Computer Managed Process Planning (CMPP) A generative process planning system
developed by United Technologies and the U.S. Army.

Decision table A tabular method for expressing the actions that should follow if certain
conditions exist. The table is composed of four major components: condition stubs, condition
entries, action stubs, and action entries.

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Design and Classification Information Retrieval (DCLASS) A general-purpose computer
system for processing classification and decision-making logic.

Decision tree A graphical method for expressing decision-making logic (the actions that
should follow if certain conditions exist). The graph is composed of a root, branches, and
nodes.

Generative process planning A process planning system, including a data base and decision
logic that will automatically generate a process plan from graphical and textual engineering
specifications of the part.

Geometric Modelling Applications Interface Program (GMAP) A project funded by the
U.S. Air Force to expand upon the results obtained in the Product Definition Data Interface
(PDDI) project. PDDI is extended to cover two new part types (turbine disks and blades), and
applications in inspection, analysis, and product support.

Hierarchical tree A method for expressing decision information and logic as a graphical tree.

Initial Graphics Exchange Specification (IGES) A standard sequential file format for
interchanging product definition data (wire frame edge-vertex geometry, annotations, and

Operation code (op code) An alphanumeric code used to represent a series of operations
performed at one machine or one work station.

Operation plan (op plan) A detailed description of operations represented by an op code. All
operations performed at a machine or work station may not be described, only those deemed
necessary to concisely and clearly describe what tasks are to be performed.

Part family matrix A matrix used to represent the group technology codes for parts in a
family. The columns of the matrix represent character positions in the group technology code,
and the rows represent the number of characters that can be assigned to any one position in the
code.

Process planning The preparation of a set of instructions that describe how to fabricate a part
or build an assembly which will satisfy engineering design specifications.
IE 447 CIM Lecture Notes – Chapter 7: Process Planning - 70

Product Data Exchange Specification (PDES) A project initiated by the IGES organization to
develop specifications that will facilitate transferring a complete product model with sufficient
information as to be interpretable by advanced CAD/CAM applications, such as process
planning. The product model includes data relative to the entire life cycle of a product,
encompassing design to field support.

Product Definition Data Interface (PDDI) A project funded by the U.S. Air Force to define
and demonstrate a prototype system that replaces the engineering drawing as the interface

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between design and all manufacturing functions, including process planning, numerical control
programming, quality assurance, tool design, and production planning and control. This concept
is based on a neutral file exchange format that can be used to translate data among dissimilar

Standard for Transfer and Exchange of Product Model Data (STEP) A world wide
standard being defined by the International Standards Organization (ISO) to capture the
information comprising a computerized product model in a neutral format that can be used
throughout the life cycle of the product.

Standard process plan A sequence of op codes representing all operations included in a
process plan for any part in a particular part family.

Tolerance chart A procedure for calculating the dimensions and associated tolerances that
must be maintained for each cut so that the finished part will satisfy blueprint specifications.

Variant process planning Computer-aided process planning involving a library of standard
process plans; interactive editing programs; and storage, retrieval, and documentation
capabilities. The plan for a new part is created by retrieving and modifying the standard process
plan for a given part family.

The role of Process Planning in CAD/CAM Integration

With the emergence of CAD/CAM integration as a predominant thrust in discrete parts
industries, the communication between design engineering and manufacturing engineering has
become a very important consideration. Most firms are using CAD techniques extensively to
design their products; similarly, they are using some CAM techniques, such as computerized
numerical control (CNC) machines, to manufacture products. However, in many of these firms
there is very little communication between design and manufacturing. As was noted in the
previous chapter, the norm is well described by engineering designs the product and then throws
the drawings over the wall for manufacturing to make the product.‖ Process planning emerges
as a key factor in CAD/CAM integration because it is the link between CAD and CAM. After
engineering designs are communicated to manufacturing, either on paper or electronic media,
the process planning function converts the designs into instructions used to make the specified
part. CIM cannot occur until this process is automated; consequently, automated process
Group technology is an important element in CAD/CAMintegration, because it provides a basis
and a methodology for engineering and manufacturing communications. Automated process
planning provides a means to facilitate this communication and remove the ―wall‖ between
engineering and manufacturing. The significance of group technology to this integration will be
reinforced in this chapter with the realization that most CAPP systems utilize group technology
concepts. As a result, it is easy to understand why process planning and group technology has
received a great deal of attention as CAD and CAM technologies are implemented and
integrated.

Approaches to Process Planning

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Traditionally, process planning has been performed manually by most companies.
As companies seek to automate this function, two approachesare considered: variant and
generative. Each of these approaches will be discussed in this
section.
Manual Approach

Under the manual approach, a skilled individual, often a former machinist examines a part
drawing to develop the necessary instructions for the process plan. This requires knowledge of
the manufacturing capabilities of the factory: machine and process (such as heat-treat)
capabilities, tooling, materials, standard practices, and associated costs. Very little of this
information is documented; often this information exists only in the minds of the process
planners. When a process plan is being prepared, if the planner has a good memory, a process
plan for a similar part might be retrieved and modified. In a more organized company, some
―workbooks‖ might be used to store and provide limited retrieval capabilities. This approach
relies almost entirely on the knowledge of the individual planner. Consequently, process plans
developed for the same part by different planners will usually differ unless the part is simple to
make.
The same planner may develop a different process plan for the same part if there is a
long time lag between the analyses for that part, because the planner‘s experience may change
during the time interval and/or shop conditions may change significantly. For instance, a critical
machine might have been under repair and because the part was needed as soon as possible, a
different machine might have been specified, even though the cost to make the part might be
considerably greater. In this case, when the critical machine is repaired, the process plan
probably will not be modified because of the manual effort involved. Manual preparation
involves subjective judgments that reflect the personal preferences and experiences of the
planner; consequently, plans prepared by different planners for similar parts can vary
significantly. Furthermore, as much as 40% of the task involves the preparation of
documentation for the plan. As a result, this approach is very labor-intensive, timeconsuming,
and tedious. For example, it is not uncommon for a process plan for one part in the aerospace
industry to contain more than 100 pages. Despite these disadvantages, the manual approach is
generally preferred by small firms that have few process plans to prepare. However, as the
volume of the plans to be prepared increases, a point is reached where some type of
computerized system should be considered to assist in this task. The exact point will depend on
the cost of the system and the benefits that can be realized. These factors are rapidly changing
as the cost of computing decreases and process planning system capabilities increase with
changes in technology.

Variant Approach

The variant approach is one of two approaches, the other being generative, used to develop a
CAPP system. A variant system is much simpler than a generative approach, but it can require
more human interaction. It is important to realize that all CAPP systems in use outside research
environments require someone to input the specifications (shape, features, dimensions,
tolerances, instructions, etc.) of Variant CAPP systems are designed to utilize the fast storage
and retrieval capabilities of a computer, and to provide an interactive environment between the
planner and the computer. This type of system is developed so that a planner with limited

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DEPARTMENT OF MECHANICAL ENGINEERING
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M 608 ADVANCED MACHINE TOOL LABORATORY

computer knowledge can effectively prepare a process plan. Thus, the planner is prompted for
the necessary data, and the inputs are edited. If errors are detected, the user is prompted to
correct the erroneous entry.
A variant system requires a data base containing standard process plans. A standard
process plan for a family consists of all instructions (such as operations, tools, and notes) that
would be included in a process plan for any part in that family. Initially, group technology
concepts are usually applied to form families of parts. Then a standard process plan is created
for each of these families and stored in the computer.
The process planning task for a new part starts with coding and classifying the part
into a part family using group technology. The standard process plan for this family can then be
retrieved from the computer. Since this plan contains instructions for all parts in this family,
some editing may be required for a specific part. Therefore, variant systems provide editing
programs to facilitate this procedure. Often, very little editing is required, because the new plan
is a variation (variant) of the standard process plan. As a result, considerable time is saved in
preparation of the plan, and a significantly greater consistency in plans is obtained. After
editing, the plan can be stored and/or printed out.
If the part being planned cannot be classified into an existing family of parts, the planner can
develop a new standard process plan using interactive computer programs. In essence, a variant
CAPP system attempts to create a work environment for the planner that utilizes the computer
to ―remember‖ (store and retrieve) similar process plans. Interactive programs are provided so
that any required editing can be performed expediently. Also,programs are provided to create
any documentation required.

Generative Approach

A generative CAPP system will automatically generate a process plan from engineering
specifications (graphical and textual) of the finished part. Many times when engineering
specifications are considered, only the graphical drawings come to mind; however, quite often
extensive textual information is also required, such as material type, special processing details,
and special inspection instructions. Considering the many details contained in some process
plans and the complexity of some parts, it is understandable that a truly universal generative
process planning system has not been developed. However, systems of this type have been
developed for special classes of parts with limited types of geometric features. The first step in
generating a process plan for a new part using a generative system is to input the engineering
specifications into the system. Ideally, these specifications would be read directly from a CAD
system. For this to occur, the CAPP system must have the ability to recognize the features of a
part, such as a hole, slot, gear tooth, and chamfer, as stored in raw
data form in the computer. Although this is being done in the laboratory for simple parts, it is
pragmatically beyond the state of the art. Consequently, the simpler approach of coding the
physical features of the part is used. The coding scheme utilized must define all geometric
features and associated details such as locations, tolerances, and sizes. Additionally, it must
describe the part in its rough state, because the system must be able to determine what material
must be removed to obtain a finished part. In a metal fabrication environment the initial form of
a part may vary considerably; for example, it may be a solid block of metal or a ―near-net-
shape‖ casting. The near- net-shape casting may require very little machining.
The second major component of a generative system is a set of programs that can
transform the coded data and accompanying textual information into a detailed process plan. In

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general, it may be impossible to develop such a program; however, we will consider some of the
things that a generative system must do.

Group technology (GT)

Group technology (GT) is a manufacturing philosophy in which similar parts are identified and
grouped together to take advantage of their similarities in manufacturing and design. In some
plants where GT has been implemented, the production equipment is arranged into machine
groups, or cells, in order to facilitate work flow and parts handling. In product design, there are
also advantages obtained by grouping parts into families. For the design of a new part, if an
effective design- retrieval system were available, a change in the existing design would be much
less time consuming than starting from scratch. This design-retrieval system is a manifestation
of the group technology principle applied to the design function. To implement such a system,
some form of parts classification and coding is required.
Parts classification and coding is concerned with identifying the similarities among parts and
relating these similarities to a coding system. Part similarities are of two types : design attributes
(such as geometric shape and size) and manufacturing attributes (the sequence of processing
steps required to make the part ).
Group technology and parts classification and coding are based on the concept of a part family.

PART FAMILIES

A part family is a collection of parts which are similar either because of geometric shape and
size or because similar processing steps are required in their manufacture. The parts within a
family are different, but their similarities are close enough to merit their identification as
members of the part family. The biggest single obstacle in changing over to group technology
from a traditional production shop is the problem of grouping parts into families. There are
three general methods for solving this problem.

1. Visual inspection
2. Production flow analysis (PFA)
3. Parts classification and coding system.

The visual inspection method is the least sophisticated and least expensive method. It involves
the classification of parts into families by looking at either the physical parts or photographs and
arranging them into similar groupings.

The second method, production flow analysis, is a method of identifying part families and
associated machine tool groupings by analyzing the route sheets for parts produced in a given
shop. It groups together the parts that have similar operation sequences and machine routings.
The disadvantage of PFA is that it accepts the validity of existing route sheets, with no
consideration given to whether these process plans are logical or consistent.

The third method, parts classification and coding, is the most time consuming and complicated
of the three methods. However it is the most frequently used method.

PARTS CLASSIFICATION AND CODING

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This method of grouping parts into families involves an examination of the individual design
and/ or manufacturing attributes of each part. The attributes of the part are uniquely identified
by means of a code number. This classification and coding may be carried out on the entire list
of active parts of the firm, or a sampling process may be used to establish the part families.
Many parts classification and coding system have been developed throughout the world, and
there are several commercially available packages. A classification and coding system should be
custom- engineered for a given company or industry.
Parts classification and coding systems divide themselves into one of three general categories :

1. System based on part design attributes.
2. System based on part manufacturing attributes.
3. System based on both design and manufacturing attributes.

Systems in the first category are useful for design retrieval and to promote design
standardization. Systems in the second category are used for computer aided process planning,
tool design, and other production related functions. The third category represents an attempt to
combine the functions and advantages of the other two systems into a single classification
scheme.

Part design attributes
Basic external shape        Major dimension
Basic internal shape        Minor dimension
Length/diameter ratio       Tolerances
Material type               Surface finish

Part manufacturing attributes
Major process             Operation sequence
Minor operations          Production time
Major dimensions          Batch size
Length/diameter ratio     Annual production
Surface finish            Fixtures needed
Machine tool              Cutting tools.

Coding system structure

A parts coding scheme consists of a sequence of symbols that identify the parts design and/ or
manufacturing attributes. The symbols in the code can be numeric, all alphabetic, or a
combination of both types but usually coding system use number digits only. There are three
basic code structures used in group technology applications.
1. Hierarchical structure
2. Chain type structure
3. Hybrid structure, a combination of the above two structures.

With the hierarchical structure, the interpretation of each succeeding symbol depends on the

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DEPARTMENT OF MECHANICAL ENGINEERING
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M 608 ADVANCED MACHINE TOOL LABORATORY

value of the preceding symbols. Other names commonly used for this structure are monocode
and and tree structure. The hierarchical code provides a relatively compact structure which
conveys much information about the part in a limited number of digits.

In the chain type structure, the interpretation of each symbol in the sequence is fixed and does
not depend on the value of the preceding digits. Another name commonly given to this structure
is polycode. The problem associated with polycodes is that they tend to be relatively long. The
use of a polycode allows for convenient identification of specific part attributes. This can be
helpful in recognizing parts with similar processing requirements.

Most of the commercial parts coding system used in industry are a combination of the two pure
structures. The hybrid structure is an attempt to achieve the best features of polycodes and
monocodes. Hybrid codes are typically constructed as a series of short polycodes. Within each
of these shorter chains, the digits are independent, but one or more symbols in the complete
code number are used to classify the part population into groups, as in the hierarchical structure.
This hybrid coding seems to best serve the needs of both design and production.

Three parts classification and coding systems

The following factors should be considered in selecting a parts coding and classification system
:

Objective : The prospective user should first define the objective for the system, whether it is to
be used for design retrieval or part-family manufacturing or both.

Scope and application : Related to the kind of information and range of products to be coded
and the requirements of the various departments of the company.

Costs and time : The company must consider the costs of installation, training and maintenance
for their parts classification and coding system.

Adaptability to other systems : Related to whether it can be readily integrated with other
existing company procedures, such as process planning, NC programming, and production
scheduling etc.

Management problems : It is important that all involved management personnel be informed
and supportive of the system.

The main three parts classification and coding system are:

1. Opitz system.
2. MICLASS system.
3. CODE system.

The opitz classification system

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This parts classification and coding system was developed by H. Opitz and it represents one of
the pioneering efforts in the group technology area and is perhaps the best known of the
classification and coding schemes.

The Opitz coding system uses the following digit sequence :

12345         6789         ABCD
The basic code consists of nine digits, which can be extended by adding four more digits. The
first nine digits are intended to convey both design and manufacturing data. The first five digits,
12345, are called the ―form code‖ and describe the primary design attributes of the part. The
next four digits, 6789, constitute the ―supplementary code‖. It indicates some of the attributes
that would be of use in manufacturing ( dimensions, work material, starting raw work piece,
shape and accuracy). The extra four digits, ABCD, are referred to as the ―secondary code‖ and
are intended to identify the production operation type and sequence. The secondary code can be
designed by the firm to serve its own particular needs.

The MICLASS System

MICLASS stands for Metal Institute Classification System and it was developed to help
automate and standardize a number of design, production, and management functions. These
include :
Standardization of Engineering drawings.
Retrieval of drawings according to classification number.
Standardization of process routings.
Automated process planning.
Selection of parts for processing on particular groups of machine tools.
Machine tool investment analysis.

The MICLASS classification number can range from 12 to 30 digits. The first twelve digits are
a universal code that can be applied to any part. Up to 18 additional digits can be used to code
data that are specific to the particular company or industry. For example, lot size, piece time,
cost data, and operation sequence might be included in the 18 supplementary digits.
The workpart attributes coded in the first 12 digits of the MICLASS number are as follows :

Ist digit                    Main shape
2nd and 3rd digits           Shape elements
4th digit                    Position of shape elements
5th and 6th digits           Main dimensions
7th digit                    Dimension ratio
8th digit                    Auxiliary dimension
9th and 10th digits          Tolerance codes
11th and 12th digits         Material codes

One of the unique features of MICLASS system is that parts can be coded using a computer
interactively.

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DEPARTMENT OF MECHANICAL ENGINEERING
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The CODE system

The CODE system is a parts classification and coding system developed and marketed by
Manufacturing Data systems, Inc. (MDSI), of Ann Arbor, Michigan. Its most universal
application is in design engineering for retrieval of part design data, but it also has applications
in manufacturing process planning, purchasing, tool design, and inventory control.
The CODE number has eight digits. For each digit there are 16 possible values ( zero through 9
and A through F ) which are used to describe the part‘s design and manufacturing
characteristics. The initial digit position indicates the basic geometry of the part and is called the
Major division of the CODE system. This digit would be used to specify whether the shape was
a cylinder, flat piece, block, or other. The interpretation of the remaining seven digits depends
on the value of the first digit, but these remaining digits form a chain-type structure. Hence the
CODE system possesses a hybrid structure.
The second and third digits provide additional information concerning the basic geometry and
principle manufacturing process for the part. Digits 4, 5, and 6 specify secondary manufacturing
processes such as threads, grooves, slots, and so forth. Digits 7 and 8 are used to indicate the
overall size of the part (ex: diameter and length for a turned part ) by classifying it into one of
16 size ranges for each of two dimensions.

GROUP TECHNOLOGY MACHINE CELLS

They are groups of machines arranged to produce similar part families. This cellular
arrangement of production equipment is designed to achieve an efficient work flow within the
cell. It also results in labor and machine specialization for the particular part families produced
by the cell. This presumably raises the productivity of the cell.

The composite part concept

Part families are defined by the fact that their members have similar design and manufacturing
attributes. The composite part concept takes this part family definition to its logical conclusion.
It conceives of a hypothetical part that represents all of the design and corresponding
manufacturing attributes possessed by the various individuals in the family. To produce one of
the members of the part family, operations are added and deleted corresponding to the attributes
of the particular part design.
A machine cell would be designed to provide all seven machining capabilities. The machines,
fixtures, and tools would be set up for efficient flow of work parts through the cell.

Design and Manufacturing Attributes of the composite part.

Number                 Design and Manufacturing Attributes
1. Turning operation for external cylindrical shape.
2. Facing operation for ends.
3. Turning operation to produce step.
4. External cylindrical grinding to achieve specified surface finish.
5. Drilling operation to create through – hole.
6. Counter bore.
7. Tapping operation to produce internal threads.

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DEPARTMENT OF MECHANICAL ENGINEERING
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In practice , the number of design and manufacturing attributes would be greater than seven, and
allowances would have to be made for variations in overall size and shape of parts in the part
family. Nevertheless, the composite part concept is useful for visualizing the machine cell
design problem.

Types of GT machine cells

The organization of machines into cells can follow one of three general patterns :

1. Single machine cell.
2. Group machine layout.
3. Flow line design.

The single machine approach can be used for workparts whose attributes allow them to be made
on basically one type of process, such as turning or milling.

The group machine layout is a cell design in which several machines are used together, with no
provision for conveyorized parts movement between the machines. The cell contains the
machines needed to produce a certain family of parts, and the machines are organized with the
proper fixtures, tools, and operators to efficiently produce the part family.

The flow line design is a group of machines connected by a conveyor system. Although this
design approaches the efficiency of an automated transfer line, the limitation of the flow line
layout is that all parts in the family must be processed through the machines in the same
sequence. Certain of the processing steps can be omitted, but the flow of work through the
system must be in one direction.

BENEFITS OF GROUP TECHNILOGY

If group technology is applied, a company will realize benefits in the following areas.
 Product design.
 Tooling and setups.
 Materials handling.
 Production and inventory control.
 Employee satisfaction
 Process planning procedures.

Product design benefits
In the area of product design, improvements and benefits are derived from the use of a parts
classification and coding system, together with a computerized design retrieval system. Use
of automated design-retrieval system helps to eliminate design duplication and proliferation
of new part designs. Other benefits of GT in design are that it improves cost estimating
procedures and helps to promote design standardization.

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Tooling and setups.
In tooling, an effort is made to design group jigs and fixtures that will accomodate every
member of a parts family. Work holding devices are designed to use special adapters which
convert the general fixture into one that can accept each part family member.
The machine tools in a GT cell do not require drastic changeovers in setup because of the
similarity in the workparts processed by them,.hence setup time is saved, and it becomes
more feasible to try to process parts in an order so as to achieve a bare minimum of setup
changeovers. It has been estimated that the use of group technology can result in a 69 %
reduction in set up time.

Materials handling
Another advantage in manufacturing is a reduction in the workpart move and waiting time.
The GT machine layouts lend themselves to efficient flow of materials through the shop.

Production and inventory control

Production scheduling is simplified with group technology. In effect, grouping of machines
into cells reduces the number of production centers that must be scheduled. Grouping of
parts into families reduces the complexity and size of the parts scheduling program. Also,
because of the reduced setups and more efficient materials handling with machine cells,
production lead times, work-in-process, and late deliveries can all be reduced. Estimates on
what can be expected are :

   70% reduction in production times.
   62% reduction in work-in-process inventories.
   82% reduction in overdue orders.

Employee satisfaction

The machine cell often allows parts to be processed from raw material to finished state by a
small group of workers. The workers are able to visualize their contributions to the firm
more clearly. This tends to cultivate an improved worker attitude and a higher level of job
satisfaction Another employee-related benefit of GT is that more attention tends to be given
to product quality. Workpart quality is more easily traced to a particular machine cell in
group technology. Consequently workers are more responsible for the quality of work they
accomplish.

Process planning procedures

The time and cost of the process planning function can be reduced through standardization
associated with group technology. A new part design is identified by its code number as
belonging to a certain parts family, for which the general process routing is known. The
logic of this procedure can be written into computer software to form a computer -
automated process planning system.

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DEPARTMENT OF MECHANICAL ENGINEERING
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Ex No.2: STUDY OF QUALITY CIRCLE CONCEPTS

OBJECTIVE:

To study about quality circle concept.

THEORY
TOTAL QUALITY MANAGEMENT

•   The American National Standards Institute (ANSI) and the American Society for
Quality (ASQ) define quality as:
―The totality of features and characteristics of a product or service that bears on its ability to

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DEPARTMENT OF MECHANICAL ENGINEERING
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satisfy given needs.‖

TQM is a comprehensive, organization-wide effort to improve the quality of products and
services, applicable to all organizations.

• How is customer satisfaction achieved?
Two dimensions: Product features and Freedom from deficiencies.
• Product features – Refers to quality of design.
Examples in manufacturing industry: Performance, Reliability, Durability, Ease of use,
Esthetics etc.
Examples in service industry: Accuracy, Timeliness, Friendliness and courtesy, Knowledge of
server etc.
• Freedom from deficiencies – Refers to quality of conformance.
Higher conformance means fewer complaints and increased customer satisfaction.
Reasons for quality becoming a cardinal priority for most organizations:
• Competition – Today‘s market demand high quality products at low cost. Having `high
quality‘ reputation is not enough! Internal cost of maintaining the reputation should be
less.
• Changing customer – The new customer is not only commanding priority based on
volume but is more demanding about the ―quality system.‖
• Changing product mix – The shift from low volume, high price to high volume, low
price have resulted in a need to reduce the internal cost of poor quality.
• Product complexity – As systems have become more complex, the reliability
requirements for suppliers of components have become more stringent.
• Higher levels of customer satisfaction – Higher customers expectations are getting
spawned by increasing competition.

Relatively simpler approaches to quality viz. product inspection for quality control and
incorporation of internal cost of poor quality into the selling price, might not work for today‘s
complex market environment.

Quality perspectives

Everyone defines Quality based on their own perspective of it. Typical responses about the
definition of quality would include:
1. Perfection
2. Consistency
3. Eliminating waste
4. Speed of delivery
5. Compliance with policies and procedures
6. Doing it right the first time
7. Delighting or pleasing customers
8. Total customer satisfaction and service

Judgmental perspective

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•   ―goodness of a product.‖
•   Shewhart‘s transcendental definition of quality – ―absolute and universally recognizable,
a mark of uncompromising standards and high achievement.‖
• Examples of products attributing to this image: Rolex watches, Lexus cars.
Product-based perspective
• ―function of a specific, measurable variable and that differences in quality reflect
differences in quantity of some product attributes.‖
• Example: Quality and price perceived relationship.

User-based perspective
• ―fitness for intended use.‖
• Individuals have different needs and wants, and hence different quality standards.
• Example – Nissan offering ‗dud‘ models in US markets under the brand name Datson
which the US customer didn‘t prefer.
Value-based perspective
• ―quality product is the one that is as useful as competing products and is sold at a lesser
price.‖
• US auto market – Incentives offered by the Big Three are perceived to be compensation
for lower quality.
Manufacturing-based perspective
• ―the desirable outcome of a engineering and manufacturing practice, or conformance to
specification.‖
• Engineering specifications are the key!
• Example: Coca-cola – ―quality is about manufacturing a product that people can depend
on every time they reach for it.‖

Evolution of TQM philosophies

• The Deming Philosophy
Definition of quality, ―A product or a service possesses quality if it helps somebody and enjoys
a good and sustainable market.‖

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Improve quality           Decrease cost                      Productivity improves
because of less
rework, fewer
mistakes.

Long-term                   Stay in                         Capture the market
strength                                                    and reduced cost.

The Deming philosophy

14 points for management:
1. Create and publish to all employees a statement of the aims and purposes of the
company. The management must demonstrate their commitment to this statement.
2. Learn the new philosophy.
3. Understand the purpose of inspection – to reduce the cost and improve the processes.
4. End the practice of awarding business on the basis of price tag alone.
5. Improve constantly and forever the system of production and service.
6. Institute training
8. Drive out fear. Create an environment of innovation.
9. Optimize the team efforts towards the aims and purposes of the company.
10. Eliminate exhortations for the workforce.
11. Eliminate numerical quotas for production.
12. Remove the barriers that rob pride of workmanship.
13. Encourage learning and self-improvement.
14. Take action to accomplish the transformation.

The Deming philosophy

• ―A System of Profound Knowledge‖
1. Appreciation for a system - A system is a set of functions or activities within an
organization that work together to achieve organizational goals. Management‘s job is to
optimize the system. (not parts of system, but the whole!). System requires co-operation.
2. Psychology – The designers and implementers of decisions are people. Hence
understanding their psychology is important.
3. Understanding process variation – A production process contains many sources of
variation. Reduction in variation improves quality. Two types of variations- common
causes and special causes. Focus on the special causes. Common causes can be reduced
only by change of technology.
4. Theory of knowledge – Management decisions should be driven by facts, data and

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Statistical Process Control (SPC)

Process management

•     Planning and administrating the activities necessary to achieve high quality in business
processes; and also identifying opportunities for improving quality and operational
performance – ultimately, customer satisfaction.
•     Process simplification reduces opportunities for errors and rework.
•     Processes are of two types – value-added processes and support processes.
•     Value-added processes – those essential for running the business and achieving and
maintaining competitive advantage. (Design process, Production/Delivery process)

•     Support processes – Those that are important to an organization‘s value-creation
processes, employees and daily operations.
•     Value creation processes are driven by external customer needs while support processes
are driven by internal needs.
•     To apply the techniques of process management, a process must be repeatable and
measurable.
•     Process owners are responsible for process performance and should have authority to
manage the process. Owners could range from high-level executive to workers who run
a cell.
•     Assigning owners ensures accountability.

Process improvement

•     Customer loyalty is driven by delivered value.

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•     Delivered value is created by business processes.

•     Sustained success in competitive markets require a business to continuously improve
delivered value.
•     To continuously improve value creation ability, a business must continuously improve
its value creation processes.

•     Continuous process improvement is an old management concept dating back to 1895.
However, those approaches were mainly productivity related.
•     More recently (1951) Toyota implemented Just-In-Time which relies on zero defects and
hence continuous improvement!

•     The Deming cycle: Originally developed by Walter Shewart, but renamed in 1950s
because Deming promoted it extensively.
•     Plan – Study the current system; identifying problems; testing theories of causes; and
developing solutions.
•     Do – Plan is implemented on a trial basis. Data collected and documented.
•     Study – Determine whether the trial plan is working correctly by evaluating the results.
•     Act – Improvements are standardized and final plan is implemented.

•     Variation of PDSA cycle: FADE – Focus, Analyze, Develop, Execute cycle!

Process improvement tools

Seven QC Tools

1. Flow charts
2. Check sheets
3. Histograms

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4.    Pareto diagrams
5.    Cause-and-effect diagrams
6.    Scatter diagrams
7.    Control charts

Flow charts

•     Process map identifies the sequence of activities or the flow in a process.
•     Objectively provides a picture of the steps needed to accomplish a task.
•     Helps all employees understand how they fit into the process and who are their suppliers
and customers.
•     Can also pinpoint places where quality-related measurements should be taken.
•     Also called process mapping and analysis.
•     Very successfully implemented in various organizations. e.g. Motorola reduced
manufacturing time for pagers using flow charts.

Check sheets
•  Special types of data collection forms in which the results may be interpreted on the
• Data sheets use simple columnar or tabular forms to record data. However, to generate
useful information from raw data, further processing generally is necessary.
• Additionally, including information such as specification limits makes the number of
nonconforming items easily observable and provides an immediate indication of the
quality of the process.

Pareto diagrams
• Based on the 85-15 Pareto distribution.
• Helpful in identifying the quality focus areas.
• Popularized by Juran.
• It is a histogram of the data from the largest frequency to the smallest.

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Cause-effect diagrams

•     Also called fishbone diagrams (because of their shape) or Ishikawa diagrams.
•     Helps in identifying root causes of the quality failure. (Helps in the diagnostic journey.)

Scatter diagrams

•     Graphical components of the regression analysis.
•     Often used to point out relationship between variables. Statistical correlation analysis

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used to interpret scatter diagrams.
Run charts and Control charts

•     Run chart: Measurement against progression of time.
•     Control chart: Add Upper Control Limit and Lower Control Limit to the run chart.

Quality circles

•     Teams of workers and supervisors that meet regularly to address work-related problems
involving quality and productivity.
•     Developed by Kaoru Ishikawa at University of Tokyo.
•     Became immediately popular in Japan as well as USA.
•     Lockheed Missiles and Space Division was the leader in implementing Quality circles in
USA in 1973 (after their visit to Japan to study the same).
•     Typically small day-to-day problems are given to quality circles. Since workers are most
familiar with the routine tasks, they are asked to identify, analyze and solve quality
problems in the routine processes.

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ISO 9000: 2000
•     Created by International Organization for Standardization (IOS) which was created in
1946 to standardize quality requirement within the European market.
•     IOS initially composed of representatives from 91 countries: probably most wide base
for quality standards.
•     Adopted a series of written quality standards in 1987 (first revised in 1994, and more
recently (and significantly) in 2000).
•     Prefix ―ISO‖ in the name refers to the scientific term ―iso‖ for equal. Thus, certified
organizations are assured to have quality equal to their peers.
•     Defines quality systems standards based on the premise that certain generic
characteristics of management principles can be standardized.
•     And that a well-designed, well-implemented and well managed quality system provides
confidence that outputs will meet customer expectations and requirements.
•     Standards are recognized by 100 countries including Japan and USA.
•     Intended to apply to all types of businesses. (Recently, B2B firm bestroute.com became
the first e-commerce company to get ISO certification.)

Created to meet five objectives:
1.    Achieve, maintain, and seek to continuously improve product quality in relation to the
requirements.
2.    Improve the quality of operations to continually meet customers‘ and stakeholders‘
needs.
3.    Provide confidence to internal management that quality requirements are being met.
4.    Provide confidence to the customers that quality requirements are being met.
5.    Provide confidence that quality system requirements are fulfilled.

• Consists of three documents
1. ISO 9000 – Fundamentals and vocabulary.

1. ISO 9001 – Requirements.
Organized in four sections: Management Responsibility; Resource Management; Product
Realization; and Measurement, Analysis and Improvement.

3. ISO 9004 – Guidelines for performance improvements

ISO 9000: 2000 Quality Management Principles

•     Principle 1: Customer Focus
•     Principle 3: Involvement of people
•     Principle 4: Process approach
•     Principle 5: Systems approach for management
•     Principle 6: Continual improvement
•     Principle 7: Factual approach to decision making
•     Principle 8: Mutually beneficial supplier relationships.

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ISO 9000: 2000 registration
• Originally intended to be a two-party process where the supplier is audited by its
customers, the ISO 9000 process became a third-party accreditation process.
• Independent laboratory or a certification agency conducts the audit.
• Recertification is required every three years.
• Individual sites – not entire company – must achieve registration individually.
• All costs are to be borne by the applicant.
• A registration audit may cost anywhere from \$10,000 to \$40,000.

Six Sigma

•     Business improvement approach that seeks to find and eliminate causes of defects and
errors in processes by focusing on outputs that are critical to customers.
•     The term Six Sigma is based on a statistical measure that equates 3.4 or fewer errors or
defects per million opportunities.
•     Motorola pioneered the concept of Six Sigma.
•     The late Bill Smith, a reliability engineer is credited with conceiving the idea of Six
Sigma.
•     GE (specifically CEO Jack Welch) extensively promoted it.

Core philosophy based on key concepts:
• Think in terms of key business processes and customer requirements with focus on
strategic objectives.
• Focus on corporate sponsors responsible for championing projects.
• Emphasize quantifiable measures such as defects per million opportunities (dpmo).
• Ensure appropriate metrics is identified to maintain accountability.
• Provide extensive training.
• Create highly qualified process improvement experts -―belts‖.
• Set stretch objectives for improvement.

Contrasts between traditional TQM and Six Sigma (SS) -
• TQM is based largely on worker empowerment and teams; SS is owned by business
• TQM is process based; SS projects are truly cross-functional.
• TQM training is generally limited to simple improvements tools and concepts; SS is
more rigorous with advanced statistical methods.
• TQM has little emphasis on financial accountability; SS requires verifiable return on
investment and focus on bottom line.

QS – 9000 : quality system standards

QS-9000 is a specially designed quality system model for automobile industries, which is
primarily based on the requirements of ISO-9000 standards. Therefore its objective is similar to
ISO- 9000 system, but means are different. Automobile industries claim that QS-9000 goes
beyond the scope of ISO-9000 by emphasizing and including the following :

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     Manufacturing capability assessment.
     Ability to demonstrate effectiveness in meeting the ‗intent of the standards‘ rather than
simply ‗do it as you documented it‘ approach of ISO-9000.
     Product Part Approval Process (PPAP), which requires those parts be approved prior to
shipment through PPAP or by explicit letter of approval by the buyer.

This implies that QS-9000 system emphasizes on the capability and reliability of the suppliers
through PRAP process in order to ensure ‗lowest possible level of defects‘ in the value added
final products, like an automobile. It is obvious that this standard is more for the maintenance
and improvement of quality in the entire supply- chain events of highly value added products
with high built in safety.

Like ISO 9000, QS-9000 system is also being revised with the changing context and experience.
Revision of QS-9000 of 1999, includes measurement of cost of poor quality to document
operational performance, incorporation of product safety into design and process control
procedures, and mistake-proofing methods in corrective and preventive action implementations.
These requirements are in addition to extensive requirements for documenting, work
instructions for operations, process monitoring and process capability for performance
compliance. Generally, QS-9000 covers all the requirements of ISO-9000 quality system plus
its own automobile specific requirements. Therefore, registration under QS-9000 system will
enable a company to achieve ISO-9000 registration also, but the reverse is not necessarily true.

In 1994, the three big automobile manufacturers – Ford, Chrysler and General motors-released
QS 9000, an interpretation and extension of ISO-9000 for automotive suppliers. QS-9000 is a
collaborative effort of these firms to standardize their individual quality requirements while
drawing upon the global ISO standards. This standardized quality system is aimed at reducing
the cost of doing business with suppliers and enhancing the competitive position of the auto-
makers and suppliers alike. QS-9000 applies to all internal and external suppliers of production
and service, parts and materials.
QS-9000 is based on ISO-9000 and includes all ISO requirements. It also includes additional
requirements such as continuous improvement, manufacturing capability, and production part
approval processes. QS-9000 not only states what must be done, but often how to do it. For
example: under Management responsibility, the QS-9000 standard requires companies to use a
formal, documented and comprehensive business plan ; to develop both short and long term
goals and plans based on the analysis of competitive products and benchmarking information;
and to revise and review the plan appropriately. The standards also require the methods to
determine the current and future customer expectations, an objective and valid process to collect
the information, and a process for determining customer satisfaction. The company must
document trends in quality and operational performance. The company must then compare their
trends with those of competitors to measure progress toward overall business objectives.

In addition, registration to ISO-9000 requires demonstration of effectiveness in meeting the
intent of standards, rather than simply the ―do it as you document it‖ philosophy.
For instance, under process control, ISO-9000 requires ―suitable maintenance of equipment to
ensure continuing process capability.‖ QS-9000 requires suppliers to identify key process
equipment, to provide appropriate resources for maintenance, and to develop an effective,
planned total preventive maintenance system. The system should include a procedure that

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describes the planned maintenance activities, scheduled maintenance, and predictive
maintenance methods.
Thus registration under QS-9000 standards will also achieve ISO-9000 registration, but ISO
certified companies must meet the additional QS-9000 requirements to achieve QS certification.

Statistical process control

Statistical process control is a method that uses statistical techniques, such as control charts, to
analyse a process,take appropriate action to gain and maintain statistical control and improve
process capability.

Control charts.
Control charts are specialized forms of run charts with statistically determined upper and lower
control limits.The purpose of control chart is to classify probable causes of process variation
into either common causes or special causes. The control limits help to determine if the process
has remained stable or if something has changed to make the process unstable at certain points.
Understanding, construction and interpretation of control charts require some clarification and
definition of a few statistical terms used in this connection. They are,

Mean : The mean or average is the sum total of all values counted divided by the number of
items counted.
Median : The median is the value halfway between the highest and the lowest values when all
data values are listed in ascending order or descending order. With an even number of data
points, the median is defined as the average of the two midpoint values.

Mode : The mode is the most frequently occurring value of the data set.

Normal Distribution : It is a symmetrical, bell shaped distribution of data set in which mean,
median, & mode are all the same.

Range : Range is the measure of the variability that exist in a data set . It is equal to the
difference between the highest value and the lowest value in the data set. It is denoted by R.

Standard Deviation : Standard deviation is a unit of measure to denote the spread of the process
output or a sampling statistics from the process i.e. the variability of a data set. It is denoted by
greek letter (σ ). Mathematically, a standard deviation is equal to the ‗square root of the
averaged squared differences between individual data values and the data set average‘.

σ      =    √(X1 –X)²+ ………+ (Xn –X)²
( n -1 )
Where n = no. of samples or data
X is set average or mean and X is individual value.

Standard deviation of a process can be calculated only if the process is stable.

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In a stable process, when data are plotted for frequency distribution, the distribution is generally
normal. It has been statistically established that in a normal distribution, most of the data points
lie within plus/minus three standard deviations from X-bar value. Thus, standard deviation
(sigma) can be taken as ‗Spread divided by six‘. It has also been established that for a normal
distribution :
68.26 % of data will be within 1 ‗sigma‘ from the mean
95.45 % of data will be within 2 ‗sigma‘ from the mean
99.73% of data will be within 3 ‗sigma‘ from the mean.
Therefore, if standard deviation is lower, all data values will fall closer to the process average.
Based on these observations, a stable process is controlled within +/-3 ‗sigma‘ and this concept
is widely used in control charts. ‗Sigma‘ used in control charts is referred to as sample standard
deviation, because control charts use sample data.
Control charts are most widely used statistical tools for the control of products or process
variability. Products manufactured under the same condition and to the same specification are
seldom identical and most certainly vary in some respect. Most important purpose of total
quality management is to improve the quality of process and products by eliminating variations.
Variations could be due to (a) Special causes (b) Common causes.
SPC, in combination with control charts, helps to distinguish between these causes of variation
and removal of the causes by systematic studies.
Steps in SPC practices involve :
1. Collection of data to a plan and plotting on a control chart.
2. Calculation of ‗control limits‘ and establishing whether the process is in a state of
statistical control or not.
3. Rendering the process stable, when needed, by first removing the ‗special causes‘.
4. Thereafter, reducing the common causes to the extent possible, so that output of the
process is centred around a ‗target value‘ of improvement.
5. Continuing to improve the ‗target value‘ by continuous improvement, which involves
continuous study and elimination of common causes.

Common causes influence all measurements in the same way, They produce random or natural
variations in the data pattern, when it is free from ‗special causes‘.
Common causes arise from many sources and do not reveal any unique pattern of variations.
Consequently, often they are difficult to identify and eliminate without commitment of
management for improvement. Examples of common causes are, lack of training and skill of
people, poor work environment, poor methods and unclear instructions, badly maintained
machine tools etc.
Special causes occur intermittently and get revealed as unusual patterns of variation on the
control chart. Examples of special causes are broken tools, power fluctuations, change of source
of vendor items etc. These causes can be eliminated without much trouble or higher
management intervention. Therefore, it is desirable to remove these causes first to render the
process stable before attempting to improve by minimizing common causes.

Control chart should indicate the process mean, and upper and lower control limits. These
three parameters have to be calculated for the set of data collected for the study. Control chart
shows how variable the process is and at what levels the process is performing. From the plot of
control chart, it can be known if any special cause is acting on the process and give indication
about the capability of the process. There are a number of control chart types, which are used

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for different data characteristics.
It should be noted that for variable data, control charts are to be used in pairs (ex: X-bar R-
chart) to get total information of the process. Often for improvement studies, large numbers of
data are used, and for convenience of treatment they are clubbed into ‗sub-groups‘ containing a
fixed number of data in each group. In such cases, ‗n‘ is taken as number of individuals in a
sub-group.
For quality improvement studies, common chart types are : X-bar – R chart, X-R chart. P chart
and u chart. Control charts indicate if the process is under control and any influence of special
causes. If there is any special cause, that can be easily removed by trained operating staff, and it
seldom needs the intervention of management. Presence of common causes, indicated by
random variations will require management actions for improvement by ‗process capability‘
study.

Process capability is a technique that is used to determine whether a process with its natural
variation is capable of meeting customer needs or specifications. It should be appreciated that a
process can be under control as per control chart and, yet, it may not meet the customer needs or
expectations. Process capability uses an objective measure, capability index, that compares
process specification limits with the process control limits.

SIX – SIGMA CONCEPTS

Six-sigma is a quality matrix that counts the number of defects per million opportunities
( DPMO ) at six levels. It is assumed that having natural tolerance equal to the design tolerance
would mean good quality. Higher the sigma level better is the quality with lower DPMO. A
sigma level of 3.5 would mean that a process has a chance for 22,700 DPMO. A perfect sigma
level of six would mean a DPMO of just 3. It signifies that it is possible to continually stretch
the capability of a process by systematically eliminating and changing the process deterrents
and environment.
Six-sigma practice is interwoven with many TQM principles, such as customer focus, data
based management and decision, improved design and manufacturing capability, and a
supportive work culture and employees. The efforts aim to drastically reduce defect levels to
only a few DPMO for strategic products and processes.

Six-sigma practice

General approach is to work in terms of reduction of variations and defects by following a four
phase approach.
1. Measure. Select critical quality characteristics, determine the frequency of defects, define
performance standards, validate measurement system, establish process capability and
evaluate current performance.
2. Analyse.Understand what, when, where and why of defects and causes by analyzing sources
of variation vis-à-vis target objectives. The process of analysis includes process mapping ,
identifying root causes, establishing cause and effect relationships.
3. Improve. Brainstorm and generate ideas, narrow the list of potential solutions and then
select the best solution , validate the solution ( use mathematical modeling if necessary ),
and develop implementation strategy.
4. Control. Maintain improvements by revalidating measurements, determining improved

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process capability and implementing statistical process control system to monitor
performance.

The technique was pioneered by Motorola and has been recognized as a strong business driver
due to its high potential to reduce the cost by drastically lowering COPQ ( cost of poor quality
). A company operating at a higher sigma level would be saving a tremendous amount of money
that otherwise be incurred in inspection, sorting, correction, cost of delay and customer
grievance.

Six-sigma practice involves measuring large number of process data, statistical analysis of those
data for identifying defects and their causes, determining their impact on cost, delivery delay
and customer satisfaction level, and finally taking effective measures to plug the source of
errors. In the ultimate analysis of the process, it is more of a business initiative than quality
initiative in a company.

Six-sigma and process capability.

Six-sigma is a statistical term and derived from parameters related to the process capability

Process capability (Cp) = Upper specification limit - Lower specification limit
6 ‗Standard deviation‘ (σ)

Assuming that the required Cp of the process for a given USL and LSL is 1.50 it can be
hypothetically worked out as per ‗six-sigma‘ level concept that :

σ X L = 1.50.

where L = Sigma level between 1 to 6.

Thus when L = 3.5 ,        σ = 1.50 / 3.50

And when L = 6,           σ = 1.50 / 6.0

Therefore for a given process, working for higher sigma level (L) would result in lower standard
deviation and higher process capability (Cp).

Therefore, concept of six-sigma level would physically mean that the dispersion of a process
output will become more centred around the process average or target value with increasing
sigma level, dispersion being closest with level of sigma reaching six.

Taguchi methods are statistical methods developed by Genichi Taguchi to improve the quality
of manufactured goods, and more recently also applied to biotechnology,[1] marketing and
statisticians, but others accept many of his concepts as being useful additions to the body of

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knowledge.

Taguchi's principal contributions to statistics are:

1. Taguchi loss function;
2. The philosophy of off-line quality control; and
3. Innovations in the design of experiments.

TAGUCHI METHOD

Dr. Taguchi of Nippon Telephones and Telegraph Company, Japan has developed a method
based on " ORTHOGONAL ARRAY " experiments which gives much reduced " variance " for
the experiment with " optimum settings " of control parameters. Thus the marriage of Design of
Experiments with optimization of control parameters to obtain BEST results is achieved in the
Taguchi Method. "Orthogonal Arrays" (OA) provide a set of well balanced (minimum)
experiments and Dr. Taguchi's Signal-to-Noise ratios (S/N), which are log functions of desired
output, serve as objective functions for optimization, help in data analysis and prediction of
optimum results.

Taguchi Method treats optimization problems in two categories,

[A] STATIC PROBLEMS :
Generally, a process to be optimized has several control factors which directly decide the target
or desired value of the output. The optimization then involves determining the best control
factor levels so that the output is at the the target value. Such a problem is called as a "STATIC
PROBLEM".
This is best explained using a P-Diagram which is shown below ("P" stands for Process or
Product). Noise is shown to be present in the process but should have no effect on the output!
This is the primary aim of the Taguchi experiments - to minimize variations in output even
though noise is present in the process. The process is then said to have become ROBUST.

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[B] DYNAMIC PROBLEMS :
If the product to be optimized has a signal input that directly decides the output, the
optimization involves determining the best control factor levels so that the "input signal /
output" ratio is closest to the desired relationship. Such a problem is called as a "DYNAMIC
PROBLEM".

This is best explained by a P-Diagram which is shown below. Again, the primary aim of the
Taguchi experiments - to minimize variations in output even though noise is present in the
process- is achieved by getting improved linearity in the input/output relationship.

8-STEPS IN TAGUCHI METHODOLOGY :

Taguchi method is a scientifically disciplined mechanism for evaluating and implementing
improvements in products, processes, materials, equipment, and facilities. These improvements
are aimed at improving the desired characteristics and simultaneously reducing the number of
defects by studying the key variables controlling the process and optimizing the procedures or
design to yield the best results.

The method is applicable over a wide range of engineering fields that include processes that
manufacture raw materials, sub systems, products for professional and consumer markets. In
fact, the method can be applied to any process be it engineering fabrication, computer-aided-
design, banking and service sectors etc. Taguchi method is useful for 'tuning' a given process for
'best' results.

Taguchi proposed a standard 8-step procedure for applying his method for optimizing any
process,

8-STEPS IN TAGUCHI METHODOLOGY:

Step-1: IDENTIFY THE MAIN FUNCTION, SIDE EFFECTS, AND FAILURE MODE

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Step-2: IDENTIFY THE NOISE FACTORS, TESTING CONDITIONS, AND QUALITY
CHARACTERISTICS

Step-3: IDENTIFY THE OBJECTIVE FUNCTION TO BE OPTIMIZED

Step-4: IDENTIFY THE CONTROL FACTORS AND THEIR LEVELS

Step-5: SELECT THE ORTHOGONAL ARRAY MATRIX EXPERIMENT

Step-6: CONDUCT THE MATRIX EXPERIMENT

Step-7: ANALYZE THE DATA, PREDICT THE OPTIMUM LEVELS AND
PERFORMANCE

Step-8: PERFORM THE VERIFICATION EXPERIMENT AND PLAN THE FUTURE
ACTION

SUMMARY :

Every experimenter develops a nominal process/product that has the desired functionality as
demanded by users. Beginning with these nominal processes, he wishes to optimize the
processes/products by varying the control factors at his disposal, such that the results are
reliable and repeatable (i.e. show less variations).

In Taguchi Method, the word "optimization" implies "determination of BEST levels of control
factors". In turn, the BEST levels of control factors are those that maximize the Signal-to-Noise
ratios. The Signal-to-Noise ratios are log functions of desired output characteristics. The
experiments, that are conducted to determine the BEST levels, are based on "Orthogonal
Arrays", are balanced with respect to all control factors and yet are minimum in number. This in
turn implies that the resources (materials and time) required for the experiments are also
minimum.

Taguchi method divides all problems into 2 categories - STATIC or DYNAMIC. While the
Dynamic problems have a SIGNAL factor, the Static problems do not have any signal factor. In
Static problems, the optimization is achieved by using 3 Signal-to-Noise ratios - smaller-the-
better, LARGER-THE-BETTER and nominal-the-best. In Dynamic problems, the optimization
is achieved by using 2 Signal-to-Noise ratios - Slope and Linearity.

Taguchi Method is a process/product optimization method that is based on 8-steps of planning,
conducting and evaluating results of matrix experiments to determine the best levels of control
factors. The primary goal is to keep the variance in the output very low even in the presence of
noise inputs. Thus, the processes/products are made ROBUST against all variations.

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Ex No.3: STUDY OF NUMERICAL CONTROL MACHINES
AND PROGRAMMABLE LOGIC CONTROLLERS

OBJECTIVE:

To study about numerical control machines and programmable logic controllers (PLC)

THEORY
uction.—The

Introduction.—The Electronic Industries Association (EIA) defines numerical control as "a
system in which actions are controlled by the direct insertion of numerical data at some point."
More specifically, numerical control, or NC as it will be called here, involves machines
controlled by electronic systems designed to accept numerical data and other instructions,
usually in a coded form. These instructions may come directly from some source such as a
punched tape, a floppy disk, directly from a computer, or from an operator.
The key to the success of numerical control lies in its flexibility. To machine a different part, it
is only necessary to "play" a different tape. NC machines are more productive than conventional
equipment and consequently produce parts at less cost even when the higher investment is
considered. NC machines also are more accurate and produce far less scrap than their
conventional counterparts. By 1985, over 110,000 NC machine tools were operating in the
United States. Over 80 per cent of the dollars being spent on the most common types of
machine tools, namely, drilling, milling, boring, and turning machines, are going into NC
equipment.
NC is a generic term for the whole field of numerical control and encompasses a complete field
of endeavor. Sometimes CNC, which stands for Computer Numerical Control and applies only
to the control system, is used erroneously as a replacement term for NC. Albeit a monumental
development, use of the term CNC should be confined to installations where the older hardware
control systems have been replaced.
Metal cutting is the most popular application, but NC is being applied successfully to other
equipment, including punch presses, EDM wire cutting machines, inspection machines, laser
and other cutting and torching machines, tube bending machines, and sheet metal cutting and
forming machines.
State of the CNC Technology Today.—Early numerical control machines were ordinary
machines retrofitted with controls and motors to drive tools and tables. The operations
performed were the same as the operations were on the machines replaced. Over the years, NC
machines began to combine additional operations such as automatically changing tools and
work pieces. The structure of the machines has been strengthened to provide more rigid
platforms. These changes have resulted in a class of machine that can outperform its
predecessors in both speed and accuracy. Typical capabilities of a modern machining center are
accuracy better than ±0.00035 inch; spindle speeds in the range up to 25,000 rpm or more, and
increasing; feed rates up to 400 inches per minute and increasing; tool change times hovering
between 2 and 4 seconds and decreasing. Specialized machines have been built that can achieve
accuracy better than one millionth (0.000001) of an inch.
Computer numerical control of machines has undergone a great deal of change in the last
decade, largely as a result of rapid increases in computer capability. Development of new and

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improved materials for tooling and bearings, improvements in tool geometry, and the added
structural stiffness of the new machines have made it possible to perform cutting operations at
speeds and feeds that were formerly impossible to attain. Numerical Control vs. Manual
Operations.—The initial cost of a CNC machine is generally much higher than a manual
machine of the same nominal capacity, and the higher initial cost leads to a higher overall cost
of the machine per hour of its useful life. However, the additional cost of a CNC machine has
to be considered against potential savings that the machine may make possible. Some of the
individual factors that make NC and CNC machining attractive are considered below.
Labor is usually one of the highest costs in the production of a part, but the labor rate paid to a
CNC machine operator may be lower than the rate paid to the operator of conventional
machines. This statement is particularly true when there is a shortage of operators with spe-
cialized skills necessary for setting up and operating a manual machine. However, it should not
be assumed that skilled CNC machine operators are not needed because most CNCs have
manual overrides that allow the operator to adjust feeds and speeds and to manually edit or
enter programs as necessary. Also, skilled setup personnel and operators are likely to promote
better production rates and higher efficiency in the shop. In addition, the labor rate for setting
up and operating a CNC machine can sometimes be divided between two or more machines,
further reducing the labor costs and cost per part produced.
The quantity and quality requirements for an order of parts often determines what manu-
facturing process will be used to produce them. CNC machines are probably most effective
when the jobs call for a small to medium number of components that require a wide range of
operations to be performed. For example, if a large number of parts are to be machined and the
allowable tolerances are large, then manual or automatic fixed-cycle machines may be the most
viable process. But, if a large quantity of high quality parts with strict tolerances are required,
then a CNC machine will probably be able to produce the parts for the lowest cost per piece
because of the speed and accuracy of CNC machines. Moreover, if the production run requires
designing and making a lot of specialized form tools, cams, fixtures, or jigs, then the
economics of CNC machining improves even more because much of the preproduction work is
not required by the nature of the CNC process.
CNC machines can be effective for producing one-of-a-kind jobs if the part is complicated and
requires a lot of different operations that, if done manually, would require specialized setups,
jigs, fixtures, etc. On the other hand, a single component requiring only one or two setups
might be more practical to produce on a manual machine, depending on the tolerances
required. When a job calls for a small to medium number of components that require a wide
range of operations, CNC is usually preferable. CNC machines are also especially well suited
for batch jobs where small numbers of components are produced from an existing part
program, as inventory is needed. Once the part program has been tested, a batch of the parts
can be run whenever necessary. Design changes can be incorporated by changing the part
program as required. The ability to process batches also has an additional benefit of eliminating
large inventories of finished components.
CNC machining can help reduce machine idle time. Surveys have indicated that when
machining on manual machines, the average time spent on material removal is only about 40
per cent of the time required to complete a part. On particularly complicated pieces, this ratio
can drop to as low as 10 per cent or even less. The balance of the time is spent on positioning
the tool or work, changing tools, and similar activities. On numerically controlled machines,
the metal removal time frequently has been found to be in excess of 70 per cent of the total
time spent on the part. CNC non machining time is lower because CNC machines perform

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quicker tool changes and tool or work positioning than manual machines. CNC part programs
require a skilled programmer and cost additional preproduction time, but specialized jigs and
fixtures that are frequently required with manual machines are not usually required with CNC
machines, thereby reducing setup time and cost considerably.
and longer tool life, as a result of better control over the feeds and speeds; improved quality
and consistently accurate parts, reduced scrap, and less rework; lower inspection costs after the
first part is produced and proven correct; reduced handling of parts because more operations
can be performed per setup; and faster response to design changes because most part changes
can be made by editing the CNC program.

Programmable Controller.—Frequently referred to as a PC or PLC (the latter term meaning Programmab
Logic Controller), a programmable controller is an electronic unit or small computer. PLCs are used to contr
machinery, equipment, and complete processes, and to assist CNC systems in the control of complex N
machine tools and flexible manufacturing modules and cells. In effect, PLCs are the technological replacemen
for electrical relay systems.

rogrammable

Fig-1
Power supply
Fig. 1. Programmable Controllers' Four Basic Elements As shown in Fig. 1, a PLC is composed of four bas
elements: the equipment for handling input and output (I/O) signals, the central processing unit (CPU), the pow
supply, and the memory. Generally, the CPU is a microprocessor and the brain of the PLC. Early PLCs us
hardwired special-purpose electronic logic circuits, but most PLCs now being offered are based o
microprocessors and have far more logic and control capabilities than was possible with hardwired systems. T
CPU scans the status of the input devices continuously, correlates these inputs with the control logic in t
memory, and produces the appropriate output responses needed to control the machine or equipment.
Input to a PLC is either discrete or continuous. Discrete inputs may come from push buttons, micro switche
limit switches, photocells, proximity switches or pressure switches, for instance. Continuous inputs may com
from sources such as thermocouples, potentiometers, or voltmeters. Outputs from a PLC normally are directed
actuating hardware such as solenoids, solenoid valves, and motor starters. The function of a PLC is to exami

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the status of an input or set of inputs and, based on this status, actuate or regulate an output or set of outputs.
Digital control logic and sensor input signals are stored in the memory as a series of binary numbers (zeros an
ones). Each memory location holds only one "bit" (either 0 or 1) of binary information; however, most of t
data in a PLC are used in groups of 8 bits, or bytes. A word is a group of bytes that is operated on at one time b
the PLC. The word size in modern PLCs ranges from 8 to 32 bits (1 to 4 bytes), depending on the design of t
PLC. In general, the larger the word size that a system is able to operate on (that is, to work on at one time), t
faster the system is going to perform. New systems are now beginning to appear that can operate on 64 bits
information at a time.
There are two basic categories of memory: volatile and nonvolatile. Volatile memory loses the stored informati
when the power is turned off, but nonvolatile memory retains its logic even when power is cut off. A backu
battery must be used if the information stored in volatile memory is to be retained. There are six commonly us
types of memory. Of these six, random-access memory (RAM) is the most common type because it is the easie
to program and edit. RAM is also the only one of the six common types that is volatile memory. The fi
nonvolatile memory types are: core memory, read-only memory (ROM), programmable read-only memo
(PROM), electronically alterable programmable read-only memory (EAPROM), and electronically erasab
programmable read-only memory (EEPROM). EEPROMs are becoming more popular due to their relative ea
of programming and their nonvolatile characteristic. ROM is often used as a generic term to refer to the gener
class of read-only memory types and to indicate that this type of memory is not usually reprogrammed.
More than 90 per cent of the microprocessor PLCs now in the field use RAM memory. RAM is primarily used
store data, which are collected or generated by a process, and to store programs that are likely to chan
frequently. For example, a part program for machining a workpiece on a CNC machining center is loaded in
and stored in RAM. When a different part is to be made, a different program can be loaded in its place. The no
volatile memory types are usually used to store programs and data that are not expected to be changed. Program
that directly control a specific piece of equipment and contain specific instructions that allow other program
(such as a part program stored in RAM) to access and operate the hardware are usually stored in nonvolat
memory or ROM. The benefit of ROM is that stored programs and data do not have to be reloaded into the mem
ory after the power has been turned off.
PLCs are used primarily with handling systems such as conveyors, automatic retrieval and storage system
robots, and automatic guided vehicles (AGV), such as are used in flexible manufacturing cells, modules, an
systems (see Flexible Manufacturing Systems (FMS), Flexible Manufacturing Cell, and Flexible Manufacturi
Module). PLCs are also to be found in applications as diverse as combustion chamber control, chemical proce
control, and printed-circuit-board manufacturing.

Type      No. of           General Applications          Math
I/Os                                        Capability

Mini        32   Replaces relays, timers, and              Yes
counters.
Micro      32-64 Replaces relays, timers, and              Yes
counters.
Small     64-128                                           Yes
Replaces relays, timers, and
counters. Used for materials
handling, and some process
control.

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Medium 128-512 Replaces relays, timers, and              Yes
counters. Used for materials
handling, process control, and data
collection.

Large      512+   Replaces relays, timers, and           Yes
counters. Master control for other
PLCs and cells and for generation
of reports. High-level network
capability

Types of PLCs may be divided into five groups consisting of micro, mini, small, medium, and
large according to the number of I/Os, functional capabilities, and memory capacity. The
smaller the number of I/Os and memory capacity, and the fewer the functions, the simpler the
PLC. Micro and mini PLCs are usually little more than replacements for relay systems, but
larger units may have the functional capabilities of a small computer and be able to handle
mathematical functions, generate reports, and maintain high-level communications.
The preceding guidelines have some gray areas because mini, micro, and small PLCs are now
available with large memory sizes and functional capacities normally reserved for medium and
large PLCs. The accompanying table compares the various types of PLCs and their applications.
Instructions that are input to a PLC are called programs. Four major programming languages
are used with PLCs, comprising ladder diagrams, Boolean mnemonics, functional blocks, and
English statements. Some PLC systems even support high-level programming languages such as
BASIC and PASCAL. Ladder diagrams and Boolean mnemonics are the basic control-level
languages. Functional blocks and English statements are considered high-level languages.
Ladder diagrams were used with electrical relay systems before these systems were replaced by
PLCs and are still the most popular programming method.

Fig. 2. One Rung on a Ladder Diagram

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A ladder diagram consists of symbols, or ladder logic elements, that represent relay contacts or
switches and other elements in the control system. One of the more basic symbols represents a
normally open switch and is described by the symbol 1 /. Another symbol is the normally closed
switch, described by the symbol When the normally open switch is activated, it will close, and
when the normally closed switch is activated, it will open. Fig. 2 shows one rung (line) on a
ladder diagram. Switch 1001 is normally open and switch 1002 is closed. A symbol for a coil
(0001) is shown at the right. If switch 1001 is actuated, it will close. If switch 1002 is not
activated, it will stay closed. With the two switches closed, current will flow through the line
and energize coil 0001. The coil will activate some mechanism such as an electric motor, a
robot, or an NC machine tool, for instance.
As an example, Fig. 3 shows a flexible manufacturing module (FMM), consisting of a turning
center (NC lathe), an infeed conveyor, an outfeed conveyor, a robot that moves workpieces
between the infeed conveyor, the turning center, and the outfeed conveyor, and a PLC. The
arrowed lines show the signals going to and coming from the PLC.

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Fig. 4 shows a ladder diagram for a PLC that would control the operations of the FMM by:
1)Activating the infeed conveyor to move the workpiece to a position where the robot can pick
it up
2)Activating the robot to pick up the workpiece and load it into the chuck on the NC lathe
3)Activating the robot to remove the finished workpiece and place it on the outfeed conveyor
4)Activating the outfeed conveyor to move the workpiece to the next operation

In Rung 2, switch 1002 (which has been changed in the program of the PLC from a normally
closed to a normally open switch) closes when it is activated as photocell 1 detects the
workpiece. The signal thus produced, together with the closing of the now normally open switch
1001, energizes the coil, causing the robot to pick up the workpiece from the infeed conveyor.
In Rung 3, switch 1004 on the lathe closes when processing of the part is completed and it is
ready to be removed by the robot. Photocell 2 checks to see if there is a space on the conveyor
to accept the completed part. If no part is seen by photocell 2, switch 1003 will remain closed,
and with switch 1004 closed, the coil will be energized, activating the robot to transfer the
completed part to the outfeed conveyor.
Rung 4 shows activation of the output conveyor when a part is to be transferred. Normally
open switch 1004 was closed when processing of the part was completed. Switch 1003 (which
also was changed from a normally closed to a normally open switch by the program) closes if
photocell 2 detects a workpiece. The circuit is then closed and the coil is energized, starting the
conveyor motor to move the workpiece clear to make way for the succeeding workpiece.
Closed-Loop System.—Also referred to as a servo or feedback system, a closed-loop system is
a control system that issues commands to the drive motors of an NC machine. The system then
compares the results of these commands as measured by the movement or location of the
machine component, such as the table or spindlehead. The feedback devices normally used for
measuring movement or location of the component are called resolvers, encoders, Inductosyns,
or optical scales. The resolver, which is a rotary analog mechanism, is the least expensive, and
has been the most popular since the first NC machines were developed. Resolvers are normally
connected to the lead-screws of NC machines. Linear measurement is derived from monitoring
the angle of rotation of the leadscrew and is quite accurate.
Encoders also are normally connected to the leadscrew of the NC machine, and measurements
are in digital form. Pulses, or a binary code in digital form, are generated by rotation of the
encoder, and represent turns or partial turns of the leadscrew. These pulses are well suited to the
digital NC system, and encoders have therefore become very popular with such systems.
Encoders generally are somewhat more expensive than resolvers.
The Inductosyn (a trade name of Farrand Controls, Inc.) also produces analog signals, but is
attached to the slide or fixed part of a machine to measure the position of the table, spindlehead,
or other component. The Inductosyn provides almost twice the measurement accuracy of the
resolver, but is considerably more expensive, depending on the length of travel to be measured.
Optical scales generally produce information in digital form and, like the Inductosyn, are
attached to the slide or fixed part of the machine. Optical scale measurements are more accurate
than either resolvers or encoders and, because of their digital nature, are well suited to the
digital computer in a CNC system. Like the Inductosyn, optical scales are more costly than
either resolvers or encoders.

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Open-Loop System.—A control system that issues commands to the drive motors of an NC
machine and has no means of assessing the results of these commands is known as an open-loop
system. In such a system, no provision is made for feedback of information concerning
movement of the slide(s), or rotation of the leadscrew(s). Stepping motors are popular as drives
for open-loop systems.
Adaptive Control.—Measuring performance of a process and then adjusting the process to
obtain optimum performance is called adaptive control. In the machine tool field, adaptive
control is a means of adjusting the feed and/or speed of the cutting tool, based on sensor
feedback information, to maintain optimum cutting conditions. A typical arrangement is seen in
Fig. 5. Adaptive control is used primarily for cutting higher-strength materialssuch as
titanium, although the concept is applicable to the cutting of any material. The costs of the
sensors and software have restricted wider use of the feature.

The sensors used for adaptive control are generally mounted on the machine drive shafts,
tools, or even built into the drive motor. Typically, sensors are used to provide information
such as the temperature at the tip of the cutting tool and the cutting force exerted by the tool.
The information measured by the sensors is used by the control system computer to analyze
the cutting process and adjust the feeds and speeds of the machine to maximize the material
removal rate or to optimize another process variable such as surface finish. For the computer
to effectively evaluate the process in real time (i.e., while cutting is in progress), details such
as maximum allowable tool temperature, maximum allowable cutting force, and information
about the drive system need to be integrated into the computer program monitoring the
cutting process.
Adaptive control can be used to detect worn, broken, or dull tooling. Ordinarily, the adaptive
control system monitors the cutting process to keep the process variables (cutting speed and
feed rate, for example) within the proper range. Because the force required to machine a
workpiece is lowest when the tool is new or recently resharpened, a steady increase in cutting
force during a machining operation, assuming that the feed remains the same, is an indication
that the tool is becoming dull (temperature may increase as well). Upon detecting cutting
forces that are greater than a predetermined maximum allowable force, the control system
causes the feed rate, the cutting speed, or both to be adjusted to maintain the cutting force
within allowable limits. If the cutting force cannot be maintained without causing the speed
and/or feed rate to be adjusted outside its allowable limits, the machine will be stopped,
indicating that the tool is too dull and must be resharpened or replaced.

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On some systems, the process monitoring equipment can interface directly with the machine
control system, as discussed above. On other systems, the adaptive control is implemented by
a separate monitoring system that is independent of the machine control system. These
systems include instrumentation to monitor the operations of the machine tool, but do not
have the capability to directly change operating parameters, such as feeds and speeds. In
addition, this type of control does not require any modification of the existing part programs
for control of the machine.
Flexible Manufacturing Systems (FMS).—A flexible manufacturing system (FMS) is a
computer-controlled machining arrangement that can perform a variety of continuous metal-
cutting operations on a range of components without manual intervention. The objective of such
a system is to produce components at the lowest possible cost, especially components of which
only small quantities are required. Flexibility, or the ability to switch from manufacture of one
type of component to another, or from one type of machining to another, without interrupting
production, is the prime requirement of such a system. In general, FMS are used for production
of numbers of similar parts between 200 and 2000, although larger quantities are not
uncommon. An FMS involves almost all the departments in a company, including engineering,
methods, tooling and part programming, planning and scheduling, purchasing, sales and
customer service, accounting, maintenance, and quality control. Initial costs of an FMS are
estimated as being borne (percentages in parentheses) by machine tools materials handling
systems tooling and fixtures pallets computer hardware computer software, wash stations,
automatic storage and retrieval systems, coolant and chip systems, spares, and others.
FMS are claimed to bring reductions in direct labor, production planning and control, and
inspection. Materials handling and shop supervision are reduced, and individual productivity is
raised. In the materials field, savings are made in tooling, scrap and rework, and floor space.
Inventory is reduced and many other costs are avoided. Intangible savings claimed to result
from FMS include reduced tooling changeover time, ability to produce complex parts, to
incorporate engineering changes more quickly and efficiently than with other approaches, and to
make special designs, so that a company can adapt quickly to changing market conditions.
Requirements for spare parts with good fit are easily met, and the lower costs combine with
higher quality to improve market share. FMS also are claimed to improve morale among
workers, leading to higher productivity, with less paper work and more orderly shop operations.
Better control of costs and improved cost data help to produce more accurate forecasts of sales
and manpower requirements. Response to surges in demand and more economical materials
ordering are other advantages claimed with FMS.
Completion of an FMS project is said to average 57 months, including 20 months from the
time of starting investigations to the placing of the purchase order. A further 13 months are
needed for delivery and a similar period for installation. Debugging and building of production
takes about another 11 months before production is running smoothly. FMS are expensive,
requiring large capital outlays and investments in management time, software, engineering, and
shop support Efficient operation of FMS also require constant workflow because gaps in the
production cycle are very costly.
Flexible Manufacturing Cell.—A flexible manufacturing cell usually consists of two or three
NC machines with some form of pallet-changing equipment or an industrial robot. Prismatic-
type parts, such as would be processed on a machining center, are usually handled on pallets.
Cylindrical parts, such as would be machined on an NC lathe, usually are handled with an
overhead type of robot The cell may be controlled by a computer, but is often run by

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programmable controllers. The systems can be operated without attendants, but the mixture of
parts usually must be less than with a flexible manufacturing system (FMS).
Flexible Manufacturing Module.—A flexible manufacturing module is defined as a single
machining center (or turning center) with some type of automatic materials handling equipment
such as multiple pallets for machining centers, or robots for manipulating cylindrical parts and
chucks for turning centers. The entire module is usually controlled by one or more
programmable logic controllers.
Axis Nomenclature.—To distinguish among the different motions, or axes, of a machine tool, a
system of letter addresses has been developed. A letter is assigned, for example, to the table of
or axis designations, are necessary for the electronic control system to assign movement
instructions to the proper machine element. The assignment of these letter addresses has been
standardized on a worldwide basis and is contained in three standards, all of which are in
agreement. These standards are EIA RS-267-B, issued by the Electronics Industries
Association; AIA NAS-938, issued by the Aerospace Industries Association; and ISO/R 841,
issued by the International Organization for Standardization.
The standards are based on a "right-hand rule," which describes the orientation of the motions
as well as whether the motions are positive or negative. If a right hand is laid palm up on the
table of a vertical milling machine, as shown in Fig. 1, for example, the thumb will point in the
positive Z-direction, the forefinger in the positive F-direction, and the erect middle finger in the
positive Z-direction, or up. The direction signs are based on the motion of the cutter relative to
the workpiece. The movement of the table shown in Fig. 2 is therefore positive, even though the
table is moving to the left, because the motion of the cutter relative to the workpiece is to the
right, or in the positive direction. The motions are considered from the part programmer's
viewpoint, which assumes that the cutter always moves around the part, regardless of whether
the cutter or the part moves. The right-hand rule also holds with a horizontal-spindle machine
and a vertical table, or angle plate, as shown in Fig. 3. Here, spindle movement back and away
from the angle plate, or work-piece, is a positive Z-motion, and movement toward the angle
plate is a negative Z-motion.
Rotary motions also are governed by a right-hand rule, but the fingers are joined and the thumb
is pointed in the positive direction of the axis. Fig. 4 shows the designations of the rotary
motions about the three linear axes, X, Y, and Z. Rotary motion about the X-axis is designated
as A; rotary motion about the F-axis is B; and rotary motion about the Z-axis is C. The fingers
point in the positive rotary directions. Movement of the rotary table around the F-axis shown in
Fig. 4 is a B motion and is common with horizontal machining centers. Here, the view is from
the spindle face looking toward the rotary table. Referring, again, to linear motions, if the
spindle is withdrawn axially from the work, the motion is a positive Z. A move toward the work
is a negative Z.
When a second linear motion is parallel to another linear motion, as with the horizontal boring
mill seen in Fig. 5, the horizontal motion of the spindle, or quill, is designated as Z and a
parallel motion of the angle plate is W. A movement parallel to the Z-axis is U and a movement
parallel to the F-axis is V. Corresponding motions are summarized as follows:

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Axis designations for a lathe are shown in Fig. 6. Movement of the cross-slide away from the
workpiece, or the centerline of the spindle, is noted as a plus Z. Movement toward the
workpiece is a minus X. The middle finger points in the positive Z-direction; therefore,
movement away from the headstock is positive and movement toward the headstock is negative.
Generally, there is no Y-movement.

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The machine shown in Fig. 6 is of conventional design, but most NC lathes look more like that
shown in Fig. 7. The same right-hand rule applies to this four-axis lathe, on which each turret
moves along its own two independent axes. Movement of the outside-diameter or upper turret,
up and away from the workpiece, or spindle centerline, is a positive Z-motion, and movement
toward the workpiece is a negative X-motion. The same rules apply to the £/-movement of the
inside-diameter, or boring, turret. Movement of the lower turret parallel to the Z-motion of the
outside-diameter turret is called the W-motion. A popular lathe configuration is to have both
turrets on one slide, giving a two-axis system rather than the four-axis system shown. Z-and Z-
therefore is a positive Z-motion.

Axis nomenclature for other machine configurations is shown in Fig. 9. The letters
with the prime notation (e.g., X', Y , Z', W , A', and B') mean that the motion shown is
positive, because the movement of the cutter with respect to the work is in a positive
direction. In these instances, the workpiece is moving rather than the cutter.

Total Indicator Reading (TIR).—Total indicator reading is used as a measure of the
range of machine tool error. TIR is particularly useful for describing the error in a
machine tool spindle, referred to as runout. As shown in Fig. 8, there are two types of
runout: axial and radial, which can be measured with a dial indicator. Axial runout
refers to the wobble of a spindle and is measured at the spindle face. Radial runout is
the range of movement of the spindle centerline and is measured on the side of the
spindle or quill.

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DEPARTMENT OF MECHANICAL ENGINEERING
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Fig.

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controls can select the required spindle speed and feed rate automatically by using a
materials look-up table; other systems request the appropriate feed and speed data. Tool
motions needed to machine a part are described by selecting a linear or circular motion
programming mode and entering endpoint and intersection coordinates of lines and
radius, diameter, tangent points, and directions of arcs and circles (with some controllers,
intersection and tangent points are calculated automatically). Machined elements such as
holes, slots, and bolt circles are entered by selecting the appropriate tool and describing
its action, or with "canned routines" built into the CNC to perform specific machining
operations. On some systems, if a feature is once described, it can be copied and/or
moved by: translation (copy and/or move), rotation about a point, mirror image (copy and
rotate about an axis), and scaling (copy and change size). On many systems, as each
command is entered, a graphic image of the part or operation gives a visual check that the
program is producing the intended results. When all the necessary data have been entered,
the program is constructed and can be run immediately or saved on tape, floppy disk, or
other storage media for later use.
Conversational programming gives complete control of machine operations to the shop
personnel, taking advantage of the experience and practical skills of the machine opera-
tor/programmer. Control systems that provide conversational programming usually
include many built-in routines (fixed or canned cycles) for commonly used machining
operations and may also have routines for specialized operations. Built-in routines speed
programming because one command may replace many lines of program code that would
take considerable time to write. Some built-in cycles allow complex machining
operations to be programmed simply by specifying the final component profile and the
starting stock size, handling such details as developing tool paths, depth of cut, number of
roughing passes, and cutter speed automatically. On turning machines, built-in cycles for
common. Although many CNC machines have a conversational programming mode, the
programming methods used and the features available are not standardized. Some control
systems cannot be programmed from the control panel while another program is running
(i.e., while a part is being machined), but those systems that can be thus programmed are
more productive because programming does not require the machine to be idle.
Conversational programming is especially beneficial In reducing programming time in
shops that do most of their part programming from the control panel of the machine.
Manual part programming describes the preparation of a part program by manually
writing the part program in word addressed format. In the past, this method implied pro-
gramming without using a computer to determine tool paths, speeds and feeds, or any of
the calculations normally required to describe the geometry of a part. Today, however,
computers are frequently used for writing and storing the program on disk, as well as for
calculations required to program the part. Manual part programming consists of writing
codes, in a format appropriate to the machine controller, that instruct the controller to per-
form a specific action. The most widely accepted form of coding the instructions for
numerically controlled machines uses the codes and formats suggested in the ANSI/EIA
RS-274-D-1980, standard. This type of programming is sometimes called G-code pro-
gramming, referring to a commonly used word address used in the RS-274-D standard.
Basic details of programming in this format, using the various codes available.
Computer-assisted part programming (CAPP) uses a computer to help in the preparation
of the detailed instructions for operating an NC machine. In the past, defining a curve or

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complicated surface profile required a series of complex calculations to describe the fea-
tures in intimate detail. However, with the introduction of the microprocessor as an inte-
gral part of the CNC machine, the process of defining many complex shapes has been
reduced to the simple task of calling up a canned cycle to calculate the path of the cutter.
Most new CNC systems have some graphic programming capability, and many use
graphic images of the part "drawn" on a computer screen. The part programmer moves a
cutter about the part to generate the part program or the detailed block format instructions
required by the control system. Machining instructions, such as the speed and feed rate,
are entered via the keyboard. Using the computer as an assistant is faster and far more
accurate than the manual part programming method.
Computer-assisted part programming methods generally can be characterized as either
language-based or graphics-based, the distinction between the two methods being prima-
rily in the manner by which the tool paths are developed. Some modern-language-based
programming systems, such as Compact II, use interactive alphanumeric input so that
programming errors are detected as soon as they are entered. Many of these programming
systems are completely integrated with computer graphics and display an image of the
part or operation as soon as an instruction is entered. The language-based programming
systems are usually based on, or are a variation of, the APT programming language,
which is discussed separately within this section (APT Programming).
The choice between computer-assisted part programming and manual part programming
depends on the complexity of the part (particularly its geometry) and how many parts
need to be programmed. The more complicated the part, the more benefit to be gained by
CAPP, and if many parts are to be programmed, even if they are simple ones, the benefits
of a computer-aided system are substantial. If the parts are not difficult to program but
involve muchrepetition, computer-assisted part programming may also be preferred. If
parts are to be programmed for several different control systems, a high-level part
programming language such as APT will make writing the part programs easier. Because
almost all machines have some deviations from standard practices, and few control
systems use exactly the same programming format, a higher-level language allows the
programmer to concentrate primarily on part geometry and machining considerations.
The postprocessors (see Postprocessors below) for the individual control systems
accommodate most of the variations in the programming required. The programmer only
needs to write the program; the postprocessor deals with the machine specifics.
Graphical programming involves building a two- or three-dimensional model of a part on
a computer screen by graphically defining the geometric shapes and surfaces of the part
using the facilities of a CAD program. In many cases, depending on features of the CAD
software package, the same computer drawing used in the design and drafting stage of a
project can also be used to generate the program to produce the part. The graphical
entities, such as holes, slots, and surfaces, are linked with additional information required
for the specific machining operations needed. Most of the cutter movements (path of the
cutter), such as those needed for the generation of pockets and lathe roughing cuts, are
handled automatically by the computer. The program may then sort the various
machining operations into an efficient sequence so that all operations that can be
performed with a particular tool are done together, if possible. The output of graphical
part programming is generally an alphanumeric part programming language output file, in
a format such as an APT or Compact II file.

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The part programming language file can be manually checked, and modified, as neces-
sary before being run, and to help detect errors, many graphics programming systems also
include some form of part verification software that simulates machining the part on the
computer screen. Nongraphic data, such as feed rates, spindle speeds and coolant on/off,
must be typed in by the part programmer or entered from a computer data base at the
appropriate points in the program, although some programs prompt for this information
when needed. When the part program language file is run or compiled, the result is a
center line data (CL data) file describing the part. With most computer-aided part
programming output files, the CL data file needs to be processed through a postprocessor
(see Postprocessors below) to tailor the final code produced to the actual machine being
used. Postprocessor output is in a form that can be sent directly to the control system, or
can be saved on tape or magnetic media and transferred to the machine tool when
necessary. The graphic image of the part and the alphanumeric output files are saved in
separate files so that either can be edited in the future if changes in the part become
necessary. Revised files must be run and processed again for the part modifications to be
included in the part program. Software for producing part programs is discussed further in
Postprocessors.—A postprocessor is computer software that contains a set of computer
instructions designed to tailor the cutter center line location data (CL data), developed by
a computerized part programming language, to meet the requirements of a particular
machine tool/system combination. Generally, when a machine tool is programmed in a
graphical programming environment or any high-level language such as APT, a file is
created that describes all movements required of a cutting tool to make the part. The file
thus created is run, or compiled, and the result is a list of coordinates (CL data) that
describes the successive positions of the cutter relative to the origin of the machine's
coordinate system. The output of the program must be customized to fit the input
requirements of the machine controller that will receive the instructions. Cutter location
data must be converted into a format recognized by the control system, such as G codes
and M codes, or into another language or proprietary format recognized by the controller.
Generally, some instructions are also added or changed by the programmer at this point.
The lack of standardization among machine tool control systems means that almost all
computerized part programming languages require a postprocessor to translate the com-
puter-generated language instructions into a form that the machine controller recognizes.
Postprocessors are software and are generally prepared for a fee by the machine tool
builder, the control system builder, a third party vendor, or by the user.
G-Code Programming
Programs written to operate numerical control (NC) machines with control systems that
comply with the ANSI/EIA RS-274-D-1980, Standard consist of a series of data blocks,
each of which is treated as a unit by the controller and contains enough information for a
complete command to be carried out by the machine. Each block is made up of one or
more words that indicate to the control system how its corresponding action is to be
performed. A word is an ordered set of characters, consisting of a letter plus some
numerical digits, that triggers a specific action of a machine tool. The first letter of the
word is called the letter address of the word, and is used to identify the word to the
control system. For example, X is the letter address of a dimension word that requires a
move in the direction of the X-axis, Y is the letter address of another dimension word;

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and F is the letter address of the feed rate. The assigned letter addresses and their
meanings, as listed in ANSI/EIA RS-274-D, are shown in Table 1.
Format Classification.—The format classification sheet completely describes the format
requirements of a control system and gives other important information required to pro-
gram a particular control including: the type of machine, the format classification short-
hand and format detail, a listing of specific letter address codes recognized by the system
(for example, G-codes: G01, G02, G17, etc.) and the range of values the available codes
may take (S range: 10 to 1800 rpm, for example), an explanation of any codes not specifi-
cally assigned by the Standard, and any other unique features of the system.
The format classification shorthand is a nine- or ten-digit code that gives the type of sys-
tem, the number of motion and other words available, the type and format of dimensional
data required by the system, the number of motion control channels, and the number of
numerically controlled axes of the system. The format detail very succinctly summarizes
details of the machine and control system. This NC shorthand gives the letter address
words and word lengths that can be used to make up a block. The format detail defines
the basic features of the control system and the type of machine tool to which it refers.
For example, the format detail.
Table 1. Letter Addresses Used in Numerical Control
Letter
A     Angular dimension about the X-axis. Measured in decimal parts Axis
of a degree                                                        nomenclature
B     Angular dimension about the 7-axis. Measured in decimal            Axis
parts of a degree                                                  nomenclature

C     Angular dimension about the Z-axis. Measured in decimal            Axis
parts of a degree Angular dimension about a special axis, or       nomenclature
third feed

D     function, or tool function for selection of tool compensation  Axis
nomenclature
E     Angular dimension about a special axis or second feed function Axis
nomenclature
F     Feed word (code)                                               Feed words
G     Preparatory word (code)                                        Preparatory
words
H     Un assigned
X-axis                                                         interpolation and
Axis                                                           interpolation and
axis                                                               interpolation and

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L     Unassigned
M     Miscellaneous or auxiliary function                                Miscellaneous
functions
N     Sequence number                                                    Sequence number
O     Sequence number for secondary head only                            Sequence number
P     Third rapid-traverse dimension or tertiary-motion                  Axis
dimension parallel to X                                            nomenclature

Q     Second rapid-traverse dimension or tertiary-motion dimension       Axis
parallel to Y                                                      nomenclature
First rap id-traverse dimension or tertiary-motion
R     dimension parallel to Z or radius for constant surface-speed       Axis
calculation                                                        nomenclature
S     Spindle-speed function                                             Spindle speed
T     Tool function                                                      Tool function
U     Secondary-motion dimension parallel to X                           Axis
nomenclature
V     Secondary-motion dimension parallel to Y                           Axis
nomenclature
w    Secondary-motion dimension parallel to Z                           Axis
nomenclature
X     Primary X-motion dimension                                         Axis
nomenclature
Y     Primary 7-motion dimension                                         Axis
nomenclature
z    Primary Z-motion dimension                                         Axis
nomenclature

N4G2X +         24Y + 24Z + 24B24I24J24F31T4M2

specifies that the NC machine is a machining center (has X-, Y-, and Z-axes) and a tool
changer with a four-digit tool selection code (T4); the three linear axes are programmed
with two digits before the decimal point and four after the decimal point (X + 24Y + 24Z
+ 24) and can be positive or negative; probably has a horizontal spindle and rotary table
(B24=rotary motion about the F-axis); has circular interpolation (I24J24);has a feed rate
range in which there are three digits before and one after the decimal point (F31); and can
handle a four-digit sequence number (N4), two-digit G-words (G2), and two-digit
miscellaneous words (M2). The sequence of letter addresses in the format detail is also
the sequence in which words with those addresses should appear when used in a block.
The information given in the format shorthand and format detail is especially useful
when programs written for one machine are to be used on different machines. Programs
that use the variable block data format described in RS-274-D can be used
interchangeably on systems that have the same format classification, but for complete
program compatibility between machines, other features of the machine and control
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system must also be compatible, such as the relationships of the axes and the availability
of features and control functions.
Control systems differ in the way that the numbers may be written. Most newer CNC
machines accept numbers written in a decimal-point format, however, some systems
require numbers to be in a fixed-length format that does not use an explicit decimal point.
In the latter case, the control system evaluates a number based on the number of digits it
has, including zeros. Zero suppression in a control system is an arrangement that allows
zeros before the first significant figure to be dropped (leading zero suppression) or allows
zeros after the last significant figure to be dropped (trailing zero suppression). An X-axis
movement of 05.3400, for example, could be expressed as 053400 if represented in the
full field format, 53400 (leading zero suppression), or 0534 (trailing zero suppression).
With decimal-point programming, the above number is expressed simply as 5.34. To
ensure program compatibility between machines, all leading and trailing zeros should be
included in numbers unless decimal-point programming is used.
Sequence Number (N-Word).—A block normally starts with a sequence number that
identifies the block within the part program. Most control systems use a four-digit
sequence number allowing step numbers up to N9999. The numbers are usually advanced
by fives or tens in order to leave spaces for additional blocks to be inserted later if
required. For example, the first block in a program would be N0000, the next block
N0005; the next N0010; and so on. The slash character, /, placed in a block, before the
sequence number, is called an optional stop and causes the block to be skipped over when
actuated by the operator. The block that is being worked on by the machine is often
displayed on a digital readout so that the operator may know the precise operation being
performed. Preparatory Word (G-Word).—A preparatory word (also referred to as a
preparatory function or G-code) consists of the letter address G and usually two digits.
The preparatory word is placed at the beginning of a block, normally following the
sequence number. Most newer CNC machines allow more than one G-code to be used in
a single block, although many of the older systems do not. To ensure compatability with
older machines and with the RS-274-D Standard, only one G-code per block should be
used.
The G-word indicates to the control system how to interpret the remainder of theblock.
For example, G01 refers to linear interpolation and indicates that the words following in
the block will move the cutter in a straight line. The G02 code indicates that the words
following in the block will move the cutter in a clockwise circular path. A G-word can
completely change the normal meaning of other words in a block. For example, X is
normally a dimension word that describes a distance or position in the X-direction.
However, if a block contains the G04 word, which is the code for a dwell, the X word
represents the time, in seconds, that the machine is to dwell.
The majority of G-codes are designated as modal, which means that once used, the code
remains in effect for succeeding blocks unless it is specifically changed or canceled.
Therefore, it is not necessary to include modal G-codes in succeeding blocks except to
change or cancel them. Unless a G-code is modal, it is only effective within its designated
block for the operation it defines. Table , G-Code Addresses, lists standardized G-code

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Code            Description           Code                Description
GOO       Rapid traverse, point to     G34          Thread cutting, increasing
G02       Circular interpolation —      G36-G39 G36 Permanently unassigned
G03       clockwise       movement      G37,G37.1,  Used       for      automatic
G04       (M,L)                        G37.2,G37.3  acceleration and deceleration
G05       Circular interpolation—      G37.4        when the blocks are short
counterclockwise                          (M,L)
movement (M,L)                             Used for tool gaging (M,L)
Dwell—a programmed
time     delay      (M,L)
Unassigned
G06        Parabolic interpolation     G38 G38.1       Used for probing to measure
G07       (M,L)                        G39, G39.1      the diameter and center of a
G08       Used for programming                         hole (M)
with cylindrical diameter                    Used with a probe to measure
values (L)                                   the parallelness of a part with
Programmed                                   respect to an axis (M)
acceleration (M,L). d                        Generates a nonprogrammed
Also        for      lathe                   block to improve cycle time
programming           with                   and corner cutting quality
cylindrical      diameter                    when used with cutter
values                                       compensation (M)
used with linear generated
block (L)
used used with circular
generated block (L)
Cancel cutter compensation/
offset (M)
Cutter compensation, left
(M)
G09       Programmed                    G39 G39.1
G10-G12   deceleration (M,L). d         G40
G13-G16   Used to stop the axis        G41
G13-G16   movement at a precise
location (M,L)
Unassigned. dSometimes
used for machine lock
and unlock devices
Axis selection (M,L)
Unassigned
G13       Used for computing lines     G42             Cutter compensation, right
G14,      and circle intersections     G43             (M) Cutter offset, inside

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G14.1   (M,L) Used for scaling                         corner (M,L)
(M,L)
G15-G16 Polar          coordinate     44        G45- Cutter offset, outside corner
G15,    programming (M)              G49     G50-G59 (M,L) Unassigned
G16.1   Cylindrical                  G50             Reserved for adaptive control
G16.2   interpolation—C       axis   G50.1           (M,L) Unassigned
G17-G19 (L)                                           Cancel mirror image (M,L)
G20      End face milling—C
axis (L)
X-Y,X-Z,        Y-Zplane
selection, respectively
(M,L) Unassigned
G22-    Unassigned                  G51.1              Program mirror image (M,L)
G32
G22-G23 Defines safety zones in      G52          G52 Unassigned
G22.1   which the machine axis       G53              Used to offset the axes with
G233.1  may not enter (M,L)          G53              respect to the coordinate zero
G24     Defines safety zones in      G54-G59          point (see G92) (M,L)
G27-G29 which the cutting tool                         Datum shift cancel
may not exit (M,L)                            Call for motion in the
Single-pass rough-facing                      machine coordinate system
cycle (L)                                     (M,L) Datum shifts (M,L)
Used for automatically
moving to and returning
from home position
(M,L)
G30     Return to an alternate        54-G59.3   G60- Allows for presetting of work
G31,    home position (M,L)          G62              coordinate systems (M,L)
G31.1,  External skip function,                       Unassigned
G31.2,  moves an axis on a
G31.3,  linear path until an
G31.4   external signal aborts the
G33     move (M,L)
G61     Modal equivalent of G09      G80      G81      Cancel fixed cycles
=       except that rapid moves      G82                Drill cycle, no dwell and
G62     are not taken to a           G83               rapid out (M,L)
=       complete stop before the     G84                Drill cycle, dwell and rapid
G63     next motion block is         G84.1             out (M,L)
■       executed (M,L)               G85                Deep hole peck drilling
G63 b= Automatic           corner    G86               cycle (M,L)
G64-G69 override, reduces the        G87 G88            Right-hand tapping cycle
G64     feed rate on an inside       G88.1             (M,L) Left-hand tapping
=       corner cut (M,L)             G88.2             cycle (M,L) Boring cycle, no
G65     Unassigned                   G88.3             dwell, feed out (M,L)
=       Tapping mode (M,L)            G88.4  G88.5      Boring cycle, spindle stop,

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G66         Unassigned                    G88.6          rapid out (M,L)
=           Cutting mode, usually          G89            Boring       cycle,     manual
G66.1 '    set by the system             G89.1          retraction (M,L)
G67         installer (M,L)               G89.2          Boring cycle, spindle stop,
G68         Calls for a parametric         G90           manual
G69         macro (M,L)                   G91        G92 retraction (M,L) Pocket
G70         Calls for a parametric         G93           milling (rectangular and
G71         macro.       Applies     to   G94             circular), roughing cycle
G72         motion blocks only            G95            (M)        Pocket        milling
G72 ' G72   (M,L)                          G96           (rectangular and
G73 b       Same as G66 but applies       G97            circular), finish cycle (M)
G73         to                                            Post milling, roughs out
G74         all blocks (M,L) Stop                        material around a specified
G74 G74    the modal parametric                         area (M)
=           macro (see G65, G66,                         Post milling, finish cuts
G74 G75     G66.1)                                       material
G75 G75     (M,L)                                         around       a    post     (M)
G76-G79     Rotates the coordinate                       Hemisphere              milling,
system (i.e., the axes)                      roughing
(M)                                          cycle (M)
Cancel axes rotation (M)                      Hemisphere             milling,
Inch programming (M,L)                       finishing cycle (M)
Metric       programming                      Boring cycle, dwell and feed
(M,L)              Circular                  out (M,L)
interpolation CW (three-                      Irregular pocket milling,
dimensional)           (M)                   roughing cycle (M)
Unassigned                                    Irregular pocket milling,
Used to perform the                          finishing cycle (M)
finish cut on a turned                       Absolute dimension input
part along the Z-axis                        (M,L)
after the roughing cuts                       Incremental dimension input
initiated under G73,                         (M,L)
G74, or G75 codes (L)                         Preload registers, used to
Unassigned                                   shift the coordinate axes
Deep hole peck drilling                     relative to the current tool
cycle (M); OD and ID                         position (M,L)
roughing cycle, running                       Inverse time feed rate
parallel to the Z-axis (L)                   (velocity/distance) (M,L)
Cancel       multiquadrant                    Feed rate in inches or
circular      interpolation                  millimeters per minute (ipm
(M,L) Move to home                           or mpm) (M,L)
position (M,L)                                Feed rate given directly in
Left-hand tapping cycle                      inches or millimeters per
(M)                                          revolution (ipr or mpr) (M,L)
Rough facing cycle (L)                        Maintains a constant surface
Multiquadrant circular                       speed, feet (meters) per
interpolation        (M,L)                   minute (L)
Unassigned                                    Spindle speed programmed

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Roughing routine for                          in rpm (M,L)
castings or forgings (L)
Unassigned
ab
G98-99            | Unassigned

a
Symbols following a description: (M) indicates that the code applies to a mill or
machining center; (L) indicates that the code applies to turning machines; (M,L) indicates
that the code applies to both milling and turning machines.
Codes that appear more than once in the table are codes that are in common use, but are
not defined by the Standard or are used in a manner that is different than that designated
by the Standard (e.g., see G61).
Most systems that support the RS-274-D Standard codes do not use all the codes avail-
able in the Standard. Unassigned G-words in the Standard are often used by builders of
machine tool control systems for a variety of special purposes, sometimes leading to con-
fusion as to the meanings of unassigned codes. Even more confusing, some builders of
systems and machine tools use the less popular standardized codes for other than the
meaning listed in the Standard. For these reasons, machine code written specifically for
one machine/controller will not necessarily work correctly on another machine controller
without modification.
Dimension words contain numerical data that indicate either a distance or a position. The
dimension units are selected by using G70 (inch programming) or G71 (metric program-
ming) code. G71 is canceled by a G70 command, by miscellaneous functions M02 (end
of program), or by M30 (end of data). The dimension words immediately follow the G-
word in a block and on multiaxis machines should be placed in the following order: X, Y,
Z, U, V, W, P, Q, R, A, B, C, D, and E.
Absolute programming (G90) is a method of defining the coordinate locations of points
to which the cutter (or workpiece) is to move based on the fixed machine zero point. In
Fig. 1, theX- Fcoordinates of PI areX= 1.0, Y= 0.5 and the coordinates of P2 areX = 2.0,
Y= 1.1. To indicate the movement of the cutter from one point to another when using the
absolute coordinate system, only the coordinates of the destination point P2 are needed.
Incremental programming (G91) is a method of identifying the coordinates of a particu-
lar location in terms of the distance of the new location from the current location. In the
example shown in Fig. 2, a move from PI to P2 is written as X + 1.0, Y + 0.6. If there is
no movement along the Z-axis, Z is zero and normally is not noted. An X - Y incremental
move from P2 to P3 in Fig. 2 is written as X + 1.0, Y - 0.7.

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Most CNC systems offer both absolute and incremental part programming. The
choice is handled by G-code G90 for absolute programming and G91 for incremental
programming. G90 and G91 are both modal, so they remain in effect until canceled.
The G92 word is used to preload the registers in the control system with desired values.
A common example is the loading of the axis-position registers in the control system for
a lathe. Fig. 3 shows a typical home position of the tool tip with respect to the zero point
on the machine. The tool tip here is registered as being 15.0000 inches in the Z-direction
and 4.5000 inches in the X-direction from machine zero. No movement of the tool is
required. Although it will vary with different control system manufacturers, the block to
accomplish the registration shown in Fig. 3 will be approximately:
N0050G92X4.5Z15.0
MiscellaneousFunctions (M-Words).—Miscellaneous functions, or M-codes, also
referred to as auxiliary functions, constitute on-off type commands. M functions are used
to control actions such as starting and stopping of motors, turning coolant on and off,
changing tools, and clamping and unclamping parts. M functions are made up of the letter
M followed by a two-digit code. Table lists the standardized M-codes, however, the func-
tions available will vary from one control system to another. Most systems provide fewer
M functions than the complete list and may use some of the unassigned codes to provide
additional functions that are not covered by the Standard. If an M-code is used in a block,
it follows the T-word and is normally the last word in the block.
Table 3. Miscellaneous Function Words
Code                                       Description
MOO                    Automatically stops the machine. The operator
must push a button to continue with the remainder
of the program.
M01                    An optional stop acted upon only when the
operator has previously signaled for this command
by pushing a button. The machine will
automatically stop when the control system senses
the M01 code.
M02                    This end-of-pro gram code stops the machine when
all commands in the block are completed. May
include rewinding of tape.
M03                    Start spindle rotation in a clockwise direction—
looking out from the spindle face.
M04                    Start spindle rotation in a counterclockwise
direction—looking out from the spindle face.
M05                    Stop the spindle in a normal and efficient manner.
M06                    Command to change a tool (or tools) manually or
automatically. Does not cover tool selection, as is
possible with the T-words.
M07 to M08                 M07 (coolant 2) and M08 (coolant 1) are codes to
turn on coolant. M07 may con-trol flood coolant
and M08 mist coolant.
M09                    Shuts off the coolant.
MIOtoMll                  M10 applies to automatic clamping of the machine
slides, workpiece, fixture spindle, etc. Mil is an
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unclamping code.
M12                    An inhibiting code used to synchronize multiple
sets of axes, such as a four-axis lathe having two
M13                    Starts CWspindle motion and coolant on in the
same command.
M14                    Starts CCWspindle motion and coolant on in the
same command.
M15toM16                  Rapid traverse of feed motion in either the +(M15)
or —(Ml6) direction.
M17 toM18                  Unassigned.
M19                    Oriented spindle stop. Causes the spindle to stop at
a predetermined angular position.
M20 to M29                 Permanently unassigned.
Code                   Description
M30                    An end-of-tape code similar to M02, but M30 will
also rewind the tape; also may switch
automatically to a second tape reader.
M31                    A command known as interlock bypass for
temporarily circumventing a normally provided
interlock.
M32 to M35                 Unassigned.
M36 to M39                 Permanently unassigned.
M40 to M46                 Used to signal gear changes if required at the
machine; otherwise, unassigned.
M47                    Continues program execution from the start of the
program unless inhibited by an interlock signal.
M48 to M49                 M49 deactivates a manual spindle or feed override
and returns the parameter to the programmed
value; M48 cancels M49.
M50 to M57                 Unassigned.
M58 to M59                 Holds the rpm constant at the value in use when
M59 is initiated; M58 cancels M59.
M60 to M89                 Unassigned.
M90 to M99                 Reserved for use by the machine user.
Feed Function (F-Word).—F-word stands for feed-rate word or feed rate. The meaning
of the feed word depends on the system of units in use and the feed mode. For example,
F15 could indicate a feed rate of 0.15 inch (or millimeter) per revolution or 15 inches (or
millimeters) per minute, depending on whether G70 or G71 is used to indicate inch or
metric programming and whether G94 or G95 is used to specify feed rate expressed as
inches (or mm) per minute or revolution. The G94 word is used to indicate inches/minute
(ipm) or millimeters/minute (mmpm) and G95 is used for inches/revolution (ipr) or
millimeters/revolution (mmpr). The default system of units is selected by G70 (inch
programming) or G71 (metric programming) prior to using the feed function. The feed
function is modal, so it stays in effect until it is changed by setting a new feed rate. In a
block, the feed function is placed immediately following the dimension word of the axis

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to which it applies or immediately following the last dimension word to which it applies
if it is used for more than one axis.

In turning operations, when G95 is used to set a constant feed rate per revolution, the
spindle speed is varied to compensate for the changing diameter of the work — the
spindle speed increases as the working diameter decreases. To prevent the spindle speed
from increasing beyond a maximum value, the S-word, see Spindle Function (S-Word), is
used to specify the maximum allowable spindle speed before issuing the G95 command.
If the spindle speed is changed after the G95 is used, the feed rate is also changed
accordingly. If G94 is used to set a constant feed per unit of time (inches or millimeters
per minute), changes in the spindle speed do not affect the feed rate.
Feed rates expressed in inches or millimeters per revolution can be converted to feed
rates in inches or millimeters per minute by multiplying the feed rate by the spindle speed
in revolutions per minute: feed/minute = feed/revolution X spindle speed in rpm. Feed
rates for milling cutters are sometimes given in inches or millimeters per tooth. To
convert feed per tooth to feed per revolution, multiply the feed rate per tooth by the
number of cutter teeth: feed/revolution = feed/tooth X number of teeth.
For certain types of cuts, some systems require an in verse- time feed command that is
the reciprocal of the time in minutes required to complete the block of instructions. The
feed command is indicated by a G93 code followed by an F-word value found by
dividing the feed rate, in inches (millimeters) or degrees per minute, by the distance
moved in the block: feed command = feed rate/distance = (distance/time)/distance =
1/time.
Feed-rate override refers to a control, usually a rotary dial on the control system panel,
that allows the programmer or operator to override the programmed feed rate. Feed-rate
override does not change the program; permanent changes can only be made by
modifying the program. The range of override typically extends from 0 to 150 per cent of
the programmed feed rate on CNC machines; older hardwired systems are more
restrictive and most cannot be set to exceed 100 per cent of the preset rate.
Spindle Function (S-Word).—An S-word specifies the speed of rotation of the spindle.
The spindle function is programmed by the address S followed by the number of digits
specified in the format detail (usually a four-digit number). Two G-codes control the
selection of spindle speed input: G96 selects a constant cutting speed in surface feet per
minute (sfm) or meters per minute (mpm) and G97 selects a constant spindle speed in
revolutions per minute (rpm).

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In turning, a constant spindle speed (G97) is applied for threading cycles and for
machining parts in which the diameter remains constant. Feed rate can be programmed
with either G94 (inches or millimeters per minute) or G95 (inches or millimeters per
revolution) because each will result in a constant cutting speed to feed relationship.
G96 is used to select a constant cutting speed (i.e., a constant surface speed) for facing
and other cutting operations in which the diameter of the workpiece changes. The spindle
speed is set to an initial value specified by the S-word and then automatically adjusted as
the diameter changes so that a constant surface speed is maintained. The control system
adjusts spindle speed automatically, as the working diameter of the cutting tool changes,
decreasing spindle speed as the working diameter increasesor increasing spindle speed as
the working diameter decreases. When G96 is used for a constant cutting speed, G95 in a
succeeding block maintains a constant feed rate per revolution.
Speeds given in surface feet or meters per minute can be converted to speeds in revolu-
tions per minute (rpm) by the formulas:

where d is the diameter, in inches or millimeters, of the part on a lathe or of the cutter on
a milling machine; and7E is equal to 3.14159.
Tool Function (T-Word).—The T-word calls out the tool that is to be selected on a
machining center or lathe having an automatic tool changer or indexing turret. On
machines without a tool changer, this word causes the machine to stop and request a tool
change. This word also specifies the proper turret face on a lathe. The word usually is
accompanied by several numbers, as in TO 101, where the first pair of numbers refers to
the tool number (and carrier or turret if more than one) and the second pair of numbers
refers to the tool offset number. Therefore, TO 101 refers to tool 1, offset 1.
Information about the tools and the tool setups is input to the CNC system in the form of
a tool data table. Details of specific tools are transferred from the table to the part
program via the T-word. The tool nose radius of a lathe tool, for example, is recorded in
the tool data table so that the necessary tool path calculations can be made by the CNC
system. The miscellaneous code M06 can also be used to signal a tool change, either
manually or automatically.
Compensation for variations in the tool nose radius, particularly on turning machines,
allows the programmer to program the part geometry from the drawing and have the tool
follow the correct path in spite of variations in the tool nose shape. Typical of the data
required, as shown in Fig. 4, are the nose radius of the cutter, the X and Z distances from
the gage point to some fixed reference point on the turret, and the orientation of the cutter
(tool tip orientation code), as shown in Fig. 5. Details of nose radius compensation for
numerical control is given in a separate section (Indexable Insert Holders for NC).
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Tool tip orientation codes

Tool offset, also called cutter offset, is the amount of cutter adjustment in a direction par-
allel to the axis of a tool. Tool offset allows the programmer to accommodate the varying
dimensions of different tooling by assuming (for the sake of the programming) that all the
tools are identical. The actual size of the tool is totally ignored by the programmer who
programs the movement of the tools to exactly follow the profile of the workpiece shape.
Once tool geometry is loaded into the tool data table and the cutter compensation controls
of the machine activated, the machine automatically compensates for the size of the tools
in the programmed movements of the slide. In gage length programming, the tool length
and tool radius or diameter are included in the program calculations. Compensation is
then used only to account for minor variations in the setup dimensions and tool size.

0.0065

in the X and Z axes
Fig. 6.
Customarily, the tool offset is used in the beginning of a program to initialize each indi-
vidual tool. Tool offset also allows the machinist to correct for conditions, such as tool
wear, that would cause the location of the cutting edge to be different from the pro-
grammed location. For example, owing to wear, the tool tip in Fig. 6 is positioned a dis-
tance of 0.0065 inch from the location required for the work to be done. To compensate
for this wear, the operator (or part programmer), by means of the CNC control panel,
adjusts the tool tip with reference to the X- and Z-axes, moving the tool closer to the work
by 0.0065 inch throughout its traverse. The tool offset number causes the position of the
cutter to be displaced by the value assigned to that offset number.

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Fig. 7. (A)                             (B)

Changes to the programmed positions of cutting tool tip(s) can be made by tool length
offset programs included in the control system. A dial or other means is generally
provided on milling, drilling, and boring machines, and machining centers, allowing the
operator or part programmer to override the programmed axial, or Z-axis, position. This
feature is particularly helpful when setting the lengths of tools in their holders or setting a
tool in a turret, as shown in Fig. 7, because an exact setting is not necessary. The tool can
be set to an approximate length and the discrepancy eliminated by the control system.
The amount of offset may be determined by noting the amount by which the cutter is
moved manually to a fixed point on the fixture or on the part, from the programmed Z-
axis location. For example, in Fig. 7, the programmed Z-axis motion results in the cutter
being moved to position A, whereas the required location for the tool is at B. Rather than
resetting the tool or changing the part program, the tool length offset amount of 0.0500
inch is keyed into the control system. The 0.0500-inch amount is measured by moving the
cutter tip manually to position B and reading the distance moved on the readout panel.
Thereafter, every time that cutter is brought into the machining position, the programmed
Z-axis location will be overridden by 0.0500 inch.
Manual adjustment of the cutter center path to correct for any variance between nominal
and actual cutter radius is called cutter compensation. The net effect is to move the path
of the center of the cutter closer to, or away from, the edge of the workpiece, as shown in
Fig. 8. The compensation may also be handled via a tool data table.
When cutter compensation is used, it is necessary to include in the program a G41 code
if the cutter is to be to the left of the part and a G42 code if to the right of the part, as
shown in Fig. 8. A G40 code cancels cutter compensation. Cutter compensation with
earlier hardwire systems was expensive, very limited, and usually held to ±0.0999 inch.
The range for cutter compensation with CNC control systems can go as high as
±999.9999 inches, although adjustments of this magnitude are unlikely to be required.

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Minutes (and seconds) are expressed as
decimal parts of a degree.

2

Linear Interpolation.—The ability of the control system to guide the workpiece along
a straight-line path at an angle to the slide movements is called linear interpolation. Move
merits of the slides are controlled through simultaneous monitoring of pulses by
the control system. For example, if monitoring of the pulses for the X-axis of a milling
machine is at the same rate as for the F-axis, the cutting tool will move at a 45-degree
angle relative to the X-axis. However, if the pulses are monitored at twice the rate for the
X-axis as for the Y-axis, the angle that the line of travel will make with the X-axis will be
26.57 degrees (tangent of 26.57 degrees = ]Q, as shown in Fig. 9. The data required are
the distances traveled in theX- and F-directions, and from these data, the control system
will generate the straight line automatically. This monitoring concept also holds for linear
motions along three axes. The required G-code for linear interpolation blocks is G01. The
code is modal, which means that it will hold for succeeding blocks until it is changed.
Circular Interpolation.—A simplified means of programming circular arcs in one
plane, using one block of data, is called circular interpolation. This procedure eliminates
the need to break the arc into straight-line segments. Circular interpolation is usually
handled in one plane, or two dimensions, although three-dimensional circular
interpolation is described in the Standards. The plane to be used is selected by a G or
preparatory code. In Fig. 10, G17 is used if the circle is to be formed in the X-Y plane,

Fig. 10.                               Fig. 11.

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G18 if in the X-Z plane, and G19 if in the Y-Z plane. Often the control system is preset
for the circular interpolation feature to operate in only one plane (e.g., theX-Fplane for
milling machines or machining centers or the X-Z plane for lathes), and for these
machines, the G-codes are not necessary.
A circular arc may be described in several ways. Originally, the RS-274 Standard speci-
fied that, with incremental programming, the block should contain:
1)A G-code describing the direction of the arc, G02 for clockwise (CW), and G03 for
counterclockwise (CCW).
2)Directions for the component movements around the arc parallel to the axes. In the
example shown in Fig. 11, the directions areX = +1.1 inches and Y= +1.0 inch. The signs
are determined by the direction in which the arc is being generated. Here, bothX and Fare
positive.
3)The I dimension, which is parallel to the X-axis with a value of 1.3 inches, and the J
dimension, which is parallel to the F-axis with a value of 0.3 inch. These values, which
locate point A with reference to the center of the arc, are called offset dimensions. The
block for this work would appear as follows:
N0025 G02 X011000 Y0100001013000 J003000 (The sequence number, N0025, is
arbitrary.) The block would also contain the plane selection (i.e., G17, G18, or G19),
ifthis selection is not preset in the system. Most of the newer control systems allow
duplicate words in the same block, but most of the older systems do not. In these older
systems, it is necessary to insert the plane selection code in a separate and prior block, for
example, N0020 G17.
Another stipulation in the Standard is that the arc is limited to one quadrant. Therefore,
four blocks would be required to complete a circle. Four blocks would also be required to
complete the arc shown in Fig. 12, which extends into all four quadrants.
When utilizing absolute programming, the coordinates of the end point are described.
Again from Fig. 11, the block, expressed in absolute coordinates, appears as:
N0055 G02 X01800 Y0190001013000 J003000 where the arc is continued from a
previous block; the starting point for the arc in this block would be the end point of the
previous block.

+Y

-X

-Y
Fig. 12.                                     Fig. 13.
The Standard still contains the format discussed, but simpler alternatives have been
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gramming in one block, by inclusion of a G75 word. In the absolute-dimension mode
(G90), the coordinates of the arc center are specified. In the incremental-dimension mode
(G91), the signed (plus or minus) incremental distances from the beginning point of the
arc to the arc center are given. Most system builders have introduced some variations on
this format. One system builder utilizes the center and the end point of the arc when in an
absolute mode, and might describe the block for going from A to B in Fig. 13 as: N0065
G75 G02 X2.5 Y0.712.2 J1.6
The I and the J words are used to describe the coordinates of the arc center. Decimal-
point programming is also used here. A block for the same motion when programmed
incrementally might appear as:
N0075 G75 G02 XI. 1 Y - 1.610.7 J0.7
This approach is more in conformance with the RS-274-D Standard in that the X and Y
values describe the displacement between the starting and ending points (points A and B),
and the I and J indicate the offsets of the starting point from the center. Another and even
more convenient way of formulating a circular motion block is to note the coordinates of
the ending point and the radius of the arc. Using absolute programming, the block for the
motion in Fig. 13 might appear as:
N0085 G75 G02 X2.5 Y0.7 R10.0
The starting point is derived from the previous motion block. Multiquadrant circular
interpolation is canceled by a G74 code.
Helical and Parabolic Interpolation.—Helical interpolation is used primarily for mill-
ing large threads and lubrication grooves, as shown in Fig. 14. Generally, helical interpo-

N0080X.8            Cutter is moved to the right 0.8 inch.

N0090G00Z.25        Cutter is moved axially out of pocket at rapid traverse rate. Last
M93                 block of subroutine is signaled by word M93

N0100X.75Y.5         Cutter is moved to bottom left-hand corner of second pocket at
rapid traverse rate.

N0110M94      Word M94 calls for repetition of the subroutine that starts at
N0030         sequence number N0030 and ends at sequence number N0090
N0120G00X.2Y- After the second pocket is cut by repetition of sequence numbers
I.3           N0030 through N0090, the cutter is moved to start the third pocket.

N0130M94            Repetition of subroutine is called for by word M94 and the third
N0030               pocket is cut.

lation involves motion in all three axes (X, Y, Z) and is accomplished by using circular

Parametric Expressions and Macros.—Parametric programming is a method whereby
a variable or replaceable parameter representing a value is placed in the machining code
instead of using the actual value. In this manner, a section of code can be used several or
many times with different numerical values, thereby simplifying the programming and

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reducing the size of the program. For example, if the values of X and Y in lines N0040 to
N0080 of the previous example are replaced as follows:
N0040X#1
N0050 Y#2
N0060X#3
N0070 Y#4
then the subroutine starting at line N0030 is a parametric subroutine. That is, the
numbers following the # signs are the variables or parameters that will be replaced with
actual values when the program is run. In this example, the effect of the program changes
is to allow the same group of code to be used for milling pockets of different sizes. If on
the other hand, lines N0010, N0100, and N0120 of the original example were changed in
a similar manner, the effect would be to move the starting location of each of the slots to
the location specified by the replaceable parameters.
Before the program is run, the values that are to be assigned to each of the parameters or
variables are entered as a list at the start of the part program in this manner:
#1 = .8
#2 = .2 #3 = .8 #4 = .2
All that is required to repeat the same milling process again, but this time creating a
different size pocket, is to change the values assigned to each of the parameters # 1, #2,
#3, and #4 as necessary. Techniques for using parametric programming are not
standardized and are not recognized by all control systems. For this reason, consult the
programming manual of the particular system for specific details.
As with a parametric subroutine, macro describes a type of program that can be recalled
to allow insertion of finite values for letter variables. The difference between a macro and
a parametric subroutine is minor. The term macro normally applies to a source program
that is used with computer-assisted part programming; the parametric subroutine is a fea-
ture of the CNC system and can be input directly into that system.
Conditional Expressions.—It is often useful for a program to make a choice between
two or more options, depending on whether or not a certain condition exists. A program
can contain one or more blocks of code that are not needed every time the program is run,
but are needed some of the time. For example, refer to the previous program for milling
three slots. An occasion arises that requires that the first and third slots be milled, but not
the second one. If the program contained the following block of code, the machine could
be easily instructed to skip the milling of the second slot:
N0095 IF [#5 EQ 0] GO TO N0120
In this block, #5 is the name of a variable; EQ is a conditional expression meaning
equals; and GO TO is a branch statement meaning resume execution of the program at
the following line number. The block causes steps NO 100 and N0110 of the program to
be skipped if the value of #5 (a dummy variable) is set equal to zero. If the value assigned
to #5 is any number other than zero, the expression (#5 EQ 0) is not true and the
remaining instructions in block N0095 are not executed. Program execution continues
with the next step, N0100, and the second pocket is milled. For the second pocket to be
milled, parameter #5 is initialized at the beginning of the program with a statement such
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as #5 = 1 or #5 = 2. Initializing #5 = 0 guarantees that the pocket is not machined. On
control systems that automatically initialize all variables to zero whenever the system is
reset or a program is loaded, the second slot will not be machined unless the #5 is
assigned a nonzero value each time the program is run.

Other conditional expressions are: NE = not equal to; GT = greater than; LT = less than;
GE = greater than or equal to; and LE = less than or equal to. As with parametric expres-
sions, conditional expressions may not be featured on all machines and techniques and
implementation will vary. Therefore, consult the control system programming manual for
the specific command syntax.
Fixed (Canned) Cycles.—Fixed (canned) cycles comprise sets of instructions providing
for a preset sequence of events initiated by a single command or a block of data. Fixed
cycles generally are offered by the builder of the control system or machine tool as part of
the software package that accompanies the CNC system. Limited numbers of canned
cycles began to appear on hardwire control systems shortly before their demise. The
canned cycles offered generally consist of the standard G-codes covering drilling, boring,
and tapping operations, plus options that have been developed by the system builder such
as thread cutting and turning cycles. Some standard canned cycles included in RS-274-D
are shown herewith. A block of data that might be used to generate the cycle functions is
also shown above each illustration. Although the G-codes for the functions are
standardized, the other words in the block and the block format are not, and different
control system builders have different arrangements. The blocks shown are reasonable
examples of fixed cycles and do not represent those of any particular system builder.

The G81 block for a simple drilling cycle is:
N _ G81 X Y _ C __ D__ F __ EOB
N _ X _ Y _ EOB

This G81 drilling cycle will move the drill poi down to C at a rapid traverse rate; the
drill point will next be fed from C to D at the programmed feed rate, then returned to C at
the rapid traverse rate. If the cycle is to be repeated at a subsequent point, such as point E

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in the illustration, it is necessary Only to give the required X and Y coordinates. This
repetition capability is typical of canned cycles.
The G82 block for a spotfacing or drilling cycle with a dwell is:
N _ G82 X Y __ C __ D __ T __ F __EOB

This G82 code produces a cycle that is very similar to the cycle of the G81 code except
for the dwell period at point D. The dwell period allows the tool to smooth out the bottom
of the counterbore or spotface. The time for the dwell, in seconds, is noted as a T-word.
The G83 block for a peck-drilling cyle is:
N _ G83 X Y __ C __ D __ K __ F __ EOB

In the G83 peck-drilling cycle, the drill is moved from point A to point B and then
to point C at the rapid traverse rate; the drill is then fed the incremental distance K,
followed by rapid return to C. Down feed again at the rapid traverse rate through the
distance K is next, after which the drill is fed another distance K. The drill is thenrapid
traversed back to C, followed by rapid traverse for a distance of K + K; down feed to D
follows before the drill is rapid traversed back to C, to end the cycle.
The G84 block for a tapping cycle is:
_G84 X Y __ C __ D __ F_EOB

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_                                                 _

The G85 block for a boring cycle with tool retraction at the feed rate is:
N _ G85 X Y __ C __ D __ F __ EOB

In the G85 boring cycle, the tool is moved from point A to point B and then to point C at
the rapid traverse rate. The tool is next fed to point D and then, while still rotating, is
moved back to point C at the same feed rate.
The G86 block for a boring cycle with rapid traverse retraction is:
N _ G86 X Y __ C __ D __ F __ EOB

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The G86 boring cycle is similar to the G85 cycle except that the tool is withdrawn at the
rapid traverse rate.
The G87 block for a boring cycle with manual withdrawal of the tool is:
N _ G87 X Y __ C __ D __ F __ EOB

In the G87 canned boring cycle, the cutting tool is moved from A to B and then to C at
the rapid traverse rate. The tool is then fed to D. The cycle is identical to the other boring
cycles except that the tool is withdrawn manually.
The G88 block for a boring cycle with dwell and manual withdrawal is:
N _ G88 X Y __ C __ D __ T __ F __EOB

In the G88 dwell cycle, the tool is moved from A to B to C at the rapid traverse rate and
then fed at the prescribed feed rate to D. The tool dwells at D, then stops rotating and is
withdrawn manually.
The G89 block for a boring cycle with dwell and withdrawal at the feed rate is:
N _ G89 X Y __ C __ D __ T __ F __EOB

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Turning Cycles.—Canned turning cycles are available from most system builders and
are designed to allow the programmer to describe a complete turning operation in one or
a few blocks. There is no standard for this type of operation, so a wide variety of
programs have developed. Fig. 16 shows a hypothetical sequence in which the cutter is
moved from the start point to depth for the first pass. If incremental programming is in
effect, this distance is specified as Dl. The depths of the other cuts will also be
programmed as D2, D3, and so on. The length of the cut will be set by the W-word, and
will remain the same with each pass. The preparatory word that calls for the roughing
cycle is Gil. The roughing feed rate is 0.03 ipr (inch per revolution), and the finishing
feed rate (last pass) is 0.005 ipr. The block appears as follows:
N0054 Gil W = 3.1 Dl = .4 D2 = .3 D3 = .3 D4 = . 1 Fl = .03 F2 = .005
Thread Cutting.—Most NC lathes can produce a variety of thread types including con-
groove) perpendicular to the spindle axis, and threads containing a combination of the
so that the feed rate is made consistent with, and dependent upon, the selected speed
(rpm) of the spindle.
The thread lead is generally noted by either an I- or a K-word. The I-word is used if the
thread is parallel to the X-axis and the K-word if the thread is parallel to the Z-axis, the

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latter being by far the most common. The G-word for a constant-lead thread is G33, for
G35. Taper threads are obtained by noting the X- and Z-coordinates of the beginning and
end points of the thread if the G90 code is in effect (absolute programming), or the
incremental movement from the beginning point to the end point of the thread if the G91
code (incremental programming) is in effect.
N0001 G91                    Incremental programming)

N0002 GOO X-. 1000             (Rapid traverse to depth)
N0003
G33 Z-1.0000 K.0625          (Produce a thread with a constant lead of 0.625 inch)

1000                          Withdraw at rapid traverse)
N0005Z1.0000                  (Move back to start point)

Fig. 17.                                       Fig. 18.
Multiple threads are specified by a code in the block that spaces the start of the threads
equally around the cylinder being threaded. For example, if a triple thread is to be cut, the
threads will start 120 degrees apart. Typical single-block thread cutting utilizing a plunge
cut is illustrated in Fig. 17 and shows two passes. The passes are identical except for the
distance of the plunge cut. Builders of control systems and machine tools use different
code words for threading, but those shown below can be considered typical. For clarity,
both zeros and decimal points are shown.
The only changes in the second pass are the depth of the plunge cut and the withdrawal.
The blocks will appear as follows:
N0006X-.1050
N0007 G33 Z - 1.0000 K.0625
N0008 GOO X. 1050
N0009Z 1.000
Compound thread cutting, rather than straight plunge thread cutting, is possible also, and
is usually used on harder materials. As illustrated in Fig. 18, the starting point for the
thread is moved laterally in the -Z direction by an amount equal to the depth of the cut
times the tangent of an angle that is slightly less than 30 degrees. The program for the
second pass of the example shown in Fig. 18 is as follows:
N0006 X-.1050 Z-.0028
N0007 G33 Z - 1.0000 K.0625
N0008 GOO X. 1050

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N0009Z 1.0000
Fixed (canned), one-block cycles also have been developed for CNC systems to produce
the passes needed to complete a thread. These cycles may be offered by the builder of the
control system or machine tool as standard or optional features. Subroutines also can gen-
erally be prepared by the user to accomplish the same purpose (see Subroutine). A one-
block fixed threading cycle might look something like:
N0048 G98 X - .2000 Z - 1.0000 D.0050 F.0010 where G98 =
preparatory code for the threading cycle
X-.2000 = total distance from the starting point to the bottom of the thread Z-
1.0000 = length of the thread D.0050 = depths of successive cuts F.0010 =
depth(s) of the finish cut(s)
APT Programming
APT.—APT stands for Automatically Programmed Tool and is one of many computer
languages designed for use with NC machine tools. The selection of a computer-assisted
part-programming language depends on the type and complexity of the parts being
machined more than on any other factor. Although some of the other languages may be
easier to use, APT has been chosen to be covered in this book because it is a
nonproprietary language in the public domain, has the broadest range of capability, and is
one of the most advanced and universally accepted NC programming languages available.
APT (or a variation thereof) is also one of the languages that is output by many computer
programs that produce CNC part programs directly from drawings produced with CAD
systems.
APT is suitable for use in programming part geometry from simple to exceptionally
complex shapes. APT was originally designed and used on mainframe computers,
however, it is now available, in many forms, on mini- and microcomputers as well. APT
has also been adopted as ANSI Standard X3.37and by the International Organization for
Standardization (ISO) as a standardized language for NC programming. APT is a very
dynamic program and is continually being updated. APT is being used as a processor for
part-programming graphic systems, some of which have the capability of producing an
APT program from a graphic screen display or CAD drawing and of producing a graphic
display on the CAD system from an APT program.
APT is a high-level programming language. One difference between APT and the
ANSI/EIA RS-274-D (G-codes) programming format discussed in the last section is that
APT uses English like words and expressions to describe the motion of the tool or work-
piece. APT has the capability of programming the machining of parts in up to five axes,
and also allows computations and variables to be included in the programming statements
so that a whole family of similar parts can be programmed easily. This section describes
the general capabilities of the APT language and includes a ready reference guide to the
basic geometry and motion statements of APT, which is suitable for use in programming
the machining of the majority of cubic type parts involving two-dimensional movements.
Some of the three-dimensional geometry capability of APT and a description of its five-
dimensional capability are also included.

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Section 0 Controls              the
information flow

PARTNO              Section 1         Section 2 Heart      Section 3          Section 4
XXXX                Converts           of APT system.      Handles            Converts to the
MACHIN/XXX          English-like       Performs            redundant          block data and
X CUTTER/ .25       part program       geometry calcu-     operations         format
FROM/PI             into computer      lations. Output     and axis           required by the
(( )) )) ((        language. Also     is center-line      shifts.            machine
FINI                checks for syn-    path of cutter or                      tool/system
tax errors in      cutter location                        combination.
the part           (CLC),                                 Referred to as
program.           described as                           a
coordinate                             postprocessor.
points.

Tape output or
direct to machine
control system
via DNC

As shown above, the APT system can be thought of comprising the input program, the
five sections 0 through IV, and the output program. The input program shown on the left
progresses through the first four sections and all four are controlled by the fifth, section 0.
Section IV, the postprocessor, is the software package that is added to sections II and III
to customize the output and produce the necessary program format (including the G-
words, M-words, etc.) so that the coded instructions will be recognizable by the control
system. The postprocessor is software that is separate from the main body of the APT
program, but for purposes of discussion, it may be easier to consider it as a unit within the
APT program.

APT Computational Statements.—Algebraic and trigonometric functions and compu-
tations can be performed with the APT system as follows:

Arithmetic   APT Form        Arithmetic      APT Form  Arithmetic              APT Form
Form                         Form                      Form
25x25        25*25             252           25**2     cos 0                   COSF(0)
25 / 25      25/25             25n           25**n     tan0                   TANF(0)
25+ 25       25 + 25           Root 25      SQRTF(25) arctan 5000             ATANF(.5)
25-25        25-25              sin 0       SINF(0)

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Computations may be used in the APT system in two ways. One way is to let a factor
equal the computation and then substitute the factor in a statement; the other is to put the
computation directly into the statement. The following is a series of APT statements illus-
trating the first approach.
PI = POINT/0,0,1
T = (25*2/3 + (3**2-l))
P2= POINT/0,0
The second way would be as follows;
PI = POINT/0,0,1
P2 = POINT/(25*2/3 + (3**2 - 1)),0,0
Note: The parentheses have been used as they would be in an algebraic formula so that
the calculations will be carried out in proper sequence. The operations within the inner
parentheses would be carried out first. It is important for the total number of left-hand
parentheses to equal the total number of right-hand parentheses; otherwise, the program
will fail.
APT Geometry Statements—Before movements around the geometry of a part can be
described, the geometry must be defined. For example, in the statement GOTO/PI, the
computer must know where PI is located before the statement can be effective. PI there-
fore must be described in a geometry statement, prior to its use in the motion statement
GOTO/PI. The simplest and most direct geometry statement for a point is PI = POINT/X
ordinate, Y ordinate, Z ordinate
If the Z ordinate is zero and the point lies on the X—Y plane, the Z location need not be
noted. There are other ways of defining the position of a point, such as at the intersection
of two lines or where a line is tangent to a circular arc. These alternatives are described
below, together with ways to define lines and circles. Referring to the preceding
statement, PI is known as a symbol. Any combination of letters and numbers may be used
as a symbol providing the total does not exceed six characters and at least one of them is
a letter. MOUSE2 would be an acceptable symbol, as would CAT3 or FRISBE. However,
it is sensible to use symbols that help define the geometry. For example, C1 or CIR3
would be good symbols for a circle. A good symbol for a vertical line would be VL5.
Next, and after the equal sign, the particular geometry is noted. Here, it is a POINT. This
word is a vocabulary word and must be spelled exactly as prescribed. Throughout, the
designers of APT have tried to use words that are as close to English as possible. A slash
follows the vocabulary word and is followed by a specific description of the particular
geometry, such as the coordinates of the point PI. A usable statement for PI might appear
as PI = POINT/1,5,4. The 1 would be the X ordinate; the 5, the F ordinate; and the 4, the
Z ordinate.
Lines as calculated by the computer are infinitely long, and circles consist of 360
degrees. As the cutter is moved about the geometry under control of the motion
statements, the lengths of the lines and the amounts of the arcs are "cut" to their proper
size. (Some of the geometry statements shown in the accompanying illustrations for
defining POINTS, LINES, CIRCLES, TABULATED CYLINDERS, CYLINDERS,
CONES, and SPHERES, in the APT language, may not be included in some two-

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Points

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Circles

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DS is used as the symbol for the Drive Surface; PS as the symbol for the Part Surface;
and CS as the symbol for the Check Surface. The surfaces must be denoted in this
sequence. The drive surface is the surface that the cutter will move along after coming in
contact with the three surfaces. The two statements applicable to the two-surface start-up
(Fig. 4b) are:

FROM/PI GO/TO,DS,TO,PS

The one-surface start-up (Fig. 4c) is:

FROM/PI GO/TO,DS
Plane
s

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Tabulated Cylinder

A tabulated cylinder is the line that is formed when an irregular cylinder intersects a
plane. The plane intersected in the figure at the left is the X-Y plane.
A section of the line can be defined by a series of points on the line, as seen at the right.
This line is called a TABCYL. The line must pass through all the points, therefore, it is
best not to use too many. The statement to the computer would read:
TAB I = TABCYL/NOZ, SPLINE, Pi, p2, p3, p4, p5, p6
or
TAB 1 = TABCYL/NOZ, SPLINE, X., Y., x2, y2, x3, y3, x4, y4, x5, y5, x6, y6
(where X and Y are the coordinates of the points)
3-D Geometry

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G0RGT/L2, PAST, L3

Note that, in all three motion statements, the slash mark (/) lies between the GO and the
TO. When the cutter is moving to a point rather than to surfaces, such as in a start-up, the
statement is GOTO/ rather than GO/TO. A two-surface start-up, Fig. 3, when completed,
might appear as shown in Fig. 5, which includes the motion statements needed. The
motion statements, as they would appear in a part program, are shown at the left, below:
FROM/PI                         FROM/PI
GO/TO,Ll ,TO,PS                 GOTO/P2
GORGT/Ll,TO,L2                  GOTO/P3
GORGT/L2,PAST,L3                GOTO/P4
GORGT/L3,TO,L4                  GOTO/P5
GOLFT/L4,TANTO,C 1              GOTO/P6
GOFWD/C1 ,TANTO,L5 GOTO/P7
GOFWD/L5,PAST,Ll GOTO/P2
GOTO statements can move the cutter throughout the range of the machine, as shown in
Fig. 6. APT statements for such movements are shown at the right in the preceding exam-
ple. The cutter may also be moved incrementally, as shown in Fig. 7. Here, the cutter is to
move 2 inches in the + X direction, 1 inch in the + Y direction, and 1.5 inches in the + Z
direction. The incremental move statement (indicated by DLTA) is:
GODLTA/2,1,1.5
The first position after the slash is the X movement; the second the Y movement, and the
third, the Z movement.
Five-Axis Machining: Machining on five axes is achieved by causing the APT program
to generate automatically a unit vector that is normal to the surface being machined, as
shown in Fig. 8. The vector would be described by its X, Y, and Zcomponents. These
components, along with theZ, Y, and Z coordinate positions of the tool tip, are fed into
the postprocessor, which determines the locations and angles for the machine tool head
and/or table.

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APT Postprocessor Statements.—Statements that refer to the operation of the machine
rather than to the geometry of the part or the motion of the cutter about the part are called
postprocessor statements. APT postprocessor statements have been standardized interna-
tionally. Some common statements and an explanation of their meaning follow:
MACHIN/ Specifies the postprocessor that is to be used. Every postprocessor has an
identity code, and this code must follow the slash mark (/). For example:
MACHIN/LATH,82
FEDRATE/Denotes the feed rate. If in inches per minute (ipm), only the number

need be shown. If in inches per revolution (ipr), IPR must be shown, for example: FED-
RAT/.005JPR
RAPID Means rapid traverse and applies only to the statement that immediately follows
it

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SPINDL/'Refers to spindle speed. If in revolutions per minute (rpm), only the number
need be shown. If in surface feet per minute (sfm), the letters SFM need to be shown, for
example: SPINDL/ 100SFM
COOLNT/Means cutting fluid and can be subdivided into: COOLNT/ON,
COOLNT/MIST, COOLNT/FLOOD, COOLNT/OFF
TURRET/Used to call for a selected tool or turret position

Fig. 9. Symbols for Geometrical Elements CYCLE/ Specifies a cycle operation such as a
drilling     or   boring     cycle.  An     example    of    a    drilling   cycle     is:
CYCLE/DRILL,RAPTO,.45,FEDTO,0,IPR,.004. The next statement might be GOTO/PI
and the drill will then move to PI and perform the cycle operation. The cycle will repeat
until the CYCLE/OFF statement is read END Stops the machine but does not turn off the
control system
APT Example Program.—A dimensioned drawing of a part and a drawing with the sym-
bols for the geometry elements are shown in Fig. 9. A complete APT program for this
part, starting with the statement PARTNO 47F36542 and ending with FINI, is shown at
the left below.

(1)  PARTNO                                    (1)  PARTNO
(2)  CUTTER/. 25                               (2)  CUTTER/. 25
(3)  FEDRAT/5                                  (3)  FEDRAT/5
(4)  SP = POINT/-.5, -.5, .75                  (4)  SP = POINT/-.5, -.5, .75
(5)  PI = POINT/0, 0, 1                        (5)  PI = POINT/0, 0, 1
(6)  LI = LINE/PI, ATANGL, 0                   (6)  LI = LINE/PI, ATANGL, 0
(7)  CI =CIRCLE/(1.700+ 1.250), .250,          (7)  CI = CIRCLE/(1.700 + 1.250),
.250                                           .250, .250
(8) C2 = CIRCLE/1.700, 1.950, .5               (8) C2 = CIRCLE/1.700, 1.950, .5
(9) L2 = LINE/RIGHT, TANTO, CI,                (9) L2 = LINE/RIGHT, TANTO, CI,
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RIGHT, TANTO, C2                                     RIGHT, TANTO, C2
(10) L3 = LINE/PI, LEFT, TANTO, C2                  (10) L3 = LINE/PI, LEFT, TANTO,
C2
(11) FROM/SP                                      (11) FROM/SP
(12) GO/TO, LI                                    (12) FRO -.500                    -.5000
.7500 M
(13) GORGT/L1, TANTO, CI                          (13) GO/TO/, LI
(14) GOFWD/C1, TANTO, L2                          (14) GT       -.5000              -.1250
.0000
(15) GOFWD/L2, TANTO, C2                          (15) GORGT/L1, TANTO, CI
(16) GOFWD/C2, TANTO, L3                          (16) GT 2.9500             -.1250
.0000
(17) GOFWD/L3,PAST,Ll                             (17) GOFWD/C1, TANTO, L2
(18) GOTO/SP                                      (18) CIR 2.9500 .2500
.3750 CCLW
(19) FINI                                         (19)       3.2763       .4348
.0000
(20) GOFWD/L2, TANTO, C2
(21) GT 2.2439             2.2580
.0000
(22) GOFWD/C2, TANTO, L3
(23) CIR 1.700         1.9500
.6250 CCLW
(24)       1.1584      2.2619
.0000
(25) GOFWD/L3, PAST, LI
(26) GT -.2162            -.1250
.0000
(27) GOTO/SP
(28) GT -.5000            -.5000
.7500
(29) FINI
The numbers at the left of the statements are for reference purposes only, and are not
part of the program. The cutter is set initially at a point represented by the symbol SP,
having coordinates X = -0.5, Y= -0.5, Z = 0.75, and moves to LI (extended) with a one-
surface start-up so that the bottom of the cutter rests on the X-Fplane. The cutter then
moves counterclockwise around the part, past LI (extended), and returns to SP. The
coordinates of PI areX = 0,F=0, andZ=l.
Referring to the numbers at the left of the program:
(1)PARTNO must begin every program. Any identification can follow.
(2)The diameter of the cutter is specified. Here it is 0.25 inch.
(3) The feed rate is given as 5 inches per minute, which is contained in a postprocessor
statement.
(4)-(10) Geometry statements.
(11)—(IS) Motion statements.
(19) All APT programs end with FINI.

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Lines (1) through (10) repeat the geometry statements from the original program. The
motion statements are also repeated, and below each motion statement are shown the X,
Y, and Zcoordinates of the end points of the center-line (CL) movements for the cutter.
Two lines of data follow those for the circu-lar movements. For example, Line (18),
which follows Line (17), GOFWD/Cl,TANTO,L2, describes the X coordinate of the
center of the arc, 2.9500, the Y coordinate of the center of the arc, 0.2500, and the radius
of the arc required to be traversed by the cutter.
This radius is that of the arc shown on the part print, plus the radius of the cutter (0.2500
+ 0.1250 = 0.3750). Line (18) also shows that the cutter is traveling in a counterclockwise
(CCLW) motion. A circular motion is described in Lines (22), (23), and (24). Finally, the
cutter is directed to return to the starting point, SP, and this command is noted in Line
(27). The X, Y, and Zcoordinates of SP are shown in Line (28).

APT for Turning.—In its basic form, APT is not a good program for turning. Although
APT is probably the most suitable program for three-, four-, and five-axis machining, it is
awkward for the simple two-axis geometry required for lathe operations. To overcome
this problem, preprocessors have been developed especially for lathe part programming.
The statements in the lathe program are automatically converted to basic APT statements
in the computer and processed by the regular APT processor. An example of a lathe
program, based on the APT processor and made available by the McDonnell Douglas
Automation Co., is shown below. The numbers in parentheses are not part of the
program, but are used only for reference. Fig. 10 shows the general set-up for the part,
and Fig. 11 shows an enlarged view of the part profile with dimensions expressed along
what would be the X-and F-axes on the part print.

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(1) PARTNO LATHE EXAMPLE
(2) MACHIN/MODEL LATHE
(3)Tl = TOOL/FACE, 1, XOFF, -1, YOFF, -6, RADIUS, .031
(4) BLANK 1 = SHAPE/FACE, 3.5, TURN, 2
(5)PARTI = SHAPE/FACE, 3.5, TAPER, 3.5, .5, ATANGL,-45, TURN, 1,\$
FILLET, .25 FACE, 1.5 TURN, 2
(6)           FROM/(20-l),(15-6)
(7)           LATHE/ROUGH, BLANK 1, PARTI, STEP, .1, STOCK, .05,\$ SFM,300,
IPR,.01,T1
(8)           LATHE/FINISH, PARTI, SFM, 400, IPR, .005, Tl
(9)           END
(10)          FINI
Line (3) describes the tool. Here, the tool is located on face 1 of the turret and its tip is -1
inch "off (offset) in the X direction and -6 inches "off in the Fdirection, when considering
X-Y rather than X—Z axes. The cutting tool tip radius is also noted in this statement.
Line (4) describes the dimensions of the rough material, or blank. Lines parallel to the X-
axis are noted as FACE lines, and lines parallel to the Z-axis are noted as TURN lines.
The FACE line (LN1) is located 3.5 inches along the Z-axis and parallel to the X-axis.
The TURN line (LN2) is located 2 inches above the Z-axis and parallel to it. Note that in
Figs. 10 and 11, the X-axis is shown in a vertical position and the Z-axis in a horizontal
position. Line (5) describes the shape of the finished part. The term FILLET is used in
this statement to describe a circle that is tangent to the line described by TURN, 1 and the
line that is described by FACE, 1.5. The \$ sign means that the statement is continued on
the next line. These geometry elements must be contiguous and must be described in
sequence. Line (6) specifies the position of the tool tip at the start of the operation,
relative to the point of origin. Line (7) describes the roughing operation and notes that the
material to be roughed out lies between BLANK1 and PARTI; that the STEP, or depth of
roughing cuts, is to be 0.1 inch; that 0.05 inch is to be left for the finish cut; that the speed
is to be 300 sfm and the feed rate is to be 0.01 ipr; and that the tool to be used is
identified by the symbol Tl. Line (8) describes the finish cut, which is to be along the
contour described by PART 1.
Indexable Insert Holders for NC.—Indexable insert holders for numerical control lathes
are usually made to more precise standards than ordinary holders. Where applicable,
reference should be made to American National Standard B212.3-1986, Precision
Holders for Indexable Inserts. This standard covers the dimensional specifications, styles,
and designations of precision holders for indexable inserts, which are defined as tool
holders that locate the gage insert (a combination of shim and insert thicknesses) from the
back or front and end surfaces to a specified dimension with a ± 0.003 inch (± 0.08 mm)
tolerance. In NC programming, the programmed path is that followed by the center of the
tool tip, which is the center of the point, or nose radius, of the insert. The surfaces
produced are the result of the path of the nose and the major cutting edge, so it is
necessary to compensate for the nose or point radius and the lead angle when writing the
program. Table, from B212.3, gives the compensating dimensions for different holder
styles. The reference point is determined by the intersection of extensions from the major
and minor cutting edges, which would be the location of the point of a sharp pointed tool.
The distances from this point to the nose radius are LI and D\;L2 and D2 are the distances
from the sharp point to the center of the nose radius. Threading tools have sharp corners

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and do not require a radius compensation. Other dimensions of importance in
programming threading tools are also given in Table 2; the data were developed by
Kennametal, Inc.

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L-l and D-l over sharp point to nose radius; and L-2 and D-2 over sharp point to
center of nose radius. The D-1 dimension for the B, E, D, M, P, S, T, and V style tools
are over the sharp point of insert to a sharp point at the intersection of a line on the
lead angle on the cutting edge of the insert and the C dimension. The L-1 dimensions
on K style tools are over the sharp point of insert to sharp point intersection of lead
angle and F dimensions.
All dimensions are in inches.
Insert
Size             T          R           U           Y           X           Z
5
2             4Wide      .040        .075        .040        .024        .140
3
3            /16Wide     .046        .098        .054        .031        .183
:
4             4Wide      .053        .128        .054        .049        .239

3
5              /8Wide    .099        .190

The C and F characters are tool holder dimensions other than the shank size. In all
instances, the C dimension is parallel to the length of the shank and the F dimension is
parallel to the side dimension; actual dimensions must be obtained from the
manufacturer. For all K style holders, the C dimension is the distance from the end of
the shank to the tangent point of the nose radius and the end cutting edge of the insert.
For all other holders, the C dimension is from the end of the shank to a tangent to the
nose radius of the insert. The F dimension on all B, D, E, M, P, and V style holders is
measured from the back side of the shank to the tangent point of the nose radius and
the side cutting edge of the insert. For all A, F, G, J, K, and L style holders, the F
dimension is the distance from the back side of the shank to the tangent of the nose
V-Flange Tool Shanks and Retention Knobs.—Dimensions of standard tool shanks and
corresponding spindle noses are suitable for spindles used in milling and associated
machines. Corresponding equipment for higher-precision numerically controlled
machines, using retention knobs instead of drawbars, is usually made to the
ANSI/ASME B5.50-1985 standard.

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A          B        C    D     E       F  G      H       /       K
Tolerance   ±0.005 ±0.01 Min. +       UNC ±0.01 ±0.00 +0.00 +0.000
0          0.015 - 2B   0     2     0     - -0.015
0.000                    0.015
Size Gage
Dia.
30 1.250        1.875 0.188    1.00 0.516 0.500- 1.531 1.812 0.735             0.640
13
40 1.750     2.687   0.188 1.12 0.641 0.625- 2.219 2.500 0.985              0.890
11
45 2.250     3.250   0.188 1.50 0.766 0.750- 2.969 3.250 1.235              1.140
10
50 2.750     4.000   0.250 1.75 1.031 1.000- 3.594 3.875 1.485              1.390
8
60 4.250     6.375   0.312 2.25 1.281 1.250- 5.219 5.500 2.235              2.140
7
A          L           M       N     P       R       S        T            Z
Tolerance   ±0.001   ±0.005 +0.000 Min.     ±0.002 ±0.010 Min.              +0.000
-0.015                        Flat             -0.005
Size      Gage
Dia.
30 1.250     0.645 1.250      0.030    1.38     2.176    0.590     0.650    1.250
40 1.750     0.645 1.750      0.060    1.38     2.863    0.720     0.860    1.750

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45 2.250        0.770 2.250      0.090      1.38      3.613   0.850     1.090    2.250
50 2.750        1.020 2.750      0.090      1.38      4.238   1.125     1.380    2.750
60 4.250        1.020 4.250      0.120      1.500     5.683   1.375     2.04     4.250
0.200

Notes: Taper tolerance to be 0.001 in. in 12in. applied in direction that increases rate of
taper. Geometric dimensions symbols are to ANSI Y14.5M-1982. Dimensions are in
inches. Deburr all sharp edges. Unspecified fillets and radii to be 0.03 + 0.010/?, or 0.03
± 0.010 x 45 degrees. Data for size 60 are not part of Standard. For all sizes, the values
for dimensions U (tol. ± 0.005) are 0.579: for F(tol. + 0.010), 0.440; for W(tol. ±0.002),
0.625; for X (tol. ±0.005), 0.151; and for Y(tol. ±0.002), 0.750.

Size/            A            B             C                D         E              F
Totals       UNC 2A        ±0.005        ±0.005          ±0.040     ±0.005        ±0.005
30          0.500-13      0.520         0.385           1.10       0.460         0.320
40          0.625-11      0.740         0.490           1.50       0.640         0.440
45          0.750-10      0.940         0.605           1.80       0.820         0.580
50          1.000-8       1.140         0.820           2.30       1.000         0.700
60          1.250-7       1.460         1.045           3.20       1.500         1.080

G               H          /            K           L       M             R
Size/       ±0.010      ±0.010     ±0.010                   +0.000 - ±0.040       +0.010 -
Totals                                                      0.010                 0.005
30          0.04        0.10       0.187         0.65 0.64 0.53      0.19         0.094
40          0.06        0.12       0.281         0.94 0.92 0.75      0.22         0.094

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45         0.08       0.16        0.375      1.20 1.18 1.00          0.22       0.094

50         0.10       0.20        0.468      1.44 1.42 1.25          0.25       0.125
60         0.14       0.30        0.500      2.14 2.06 1.50          0.31       0.125

Notes: Dimensions are in inches. Material: low-carbon steel. Heat treatment: carburize
and harden to 0.016 to 0.028 in. effective case depth. Hardness of noted surfaces to be
Rockwell 56-60; core hardness Rockwell C35-45. Hole / shall not be carburized.
Surfaces C and R to be free from tool marks. Deburr all sharp edges. Geometric
dimension symbols are to ANSI Y14.5M-1982. Data for size 60 are not part of
Standard.

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Ex No.4: STUDY OF TOLERANCE CHARTING
TECHNIQUES
OBJECTIVE:

To study about tolerance charting techniques.

THEORY
ALLOWANCES AND TOLERANCES FOR FITS
Limits and Fits.—Fits between cylindrical parts, i.e., cylindrical fits, govern the proper
assembly and performance of many mechanisms. Clearance fits permit relative freedom
of motion between a shaft and a hole—axially, radially, or both. Interference fits secure a
certain amount of tightness between parts, whether these are meant to remain
permanently assembled or to be taken apart from time to time. Or again, two parts may be
required to fit together snugly—without apparent tightness or looseness. The designer's
problem is to specify these different types of fits in such a way that the shop can produce
them. Establishing the specifications requires the adoption of two manufacturing limits
for the hole and two for the shaft, and, hence, the adoption of a manufacturing tolerance
on each part.
In selecting and specifying limits and fits for various applications, it is essential in the
interests of interchangeable manufacturing that 1) standard definitions of terms relating to
limits and fits be used; 2) preferred basic sizes be selected wherever possible to reduce
material and tooling costs; 3) limits be based upon a series of preferred tolerances and
allowances; and 4) a uniform system of applying tolerances (preferably unilateral) be
used. These principles have been incorporated in both the American and British standards
for limits and fits. Information about these standards is given beginning on page 627.
Basic Dimensions.—The basic size of a screw thread or machine part is the theoretical or
nominal standard size from which variations are made. For example, a shaft may have a
basic diameter of 2 inches, but a maximum variation of minus 0.010 inch may be permit-
ted. The minimum hole should be of basic size wherever the use of standard tools repre-
sents the greatest economy. The maximum shaft should be of basic size wherever the use
of standard purchased material, without further machining, represents the greatest econ-
omy, even though special tools are required to machine the mating part.
Tolerances.—Tolerance is the amount of variation permitted on dimensions or surfaces
of machine parts. The tolerance is equal to the difference between the maximum and
minimum limits of any specified dimension. For example, if the maximum limit for the
diameter of a shaft is 2.000 inches and its minimum limit 1.990 inches, the tolerance for
this diameter is 0.010 inch. The extent of these tolerances is established by determining
the maximum and minimum clearances required on operating surfaces. As applied to the
fitting of machine parts, the word tolerance means the amount that duplicate parts are
allowed to vary in size in connection with manufacturing operations, owing to
unavoidable imperfections of workmanship. Tolerance may also be defined as the amount
that duplicate parts are permitted to vary in size to secure sufficient accuracy without

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unnecessary refinement. The terms ―tolerance‖ and ―allowance‖ are often used
interchangeably, but, according to common usage, allowance is a difference in
dimensions prescribed to secure various classes of fits between different parts.
Unilateral and Bilateral Tolerances.—The term ―unilateral tolerance‖ means that the
total tolerance, as related to a basic dimension, is in one direction only. For example, if
the basic dimension were 1 inch and the tolerance were expressed as 1.000 - 0.002, or as
1.000 + 0.002, these would be unilateral tolerances because the total tolerance in each is
in one direction. On the contrary, if the tolerance were divided, so as to be partly plus and
partly minus, it would be classed as ―bilateral.‖

Thus,
+0.001 1.000
-0.001 is an example of bilateral tolerance, because the total
tolerance of 0.002 is given in two directions—plus and minus.

1)When unilateral tolerances are used, one of the three
following methods should be used to Specify, limiting
dimensions only as Diameter of hole: 2.250, 2.252
Diameter of shaft: 2.249, 2.247
2)One limiting size may be specified with its tolerances as
Diameter of hole: 2.250 + 0.002, -0.000

Diameter of shaft: 2.249 + 0.000, -0.002

3)     The nominal size may be specified for both parts, with a notation showing
both allow
ance and tolerance, as

Diameter of hole: 214 + 0.002, -0.000 Diameter of
shaft: 214 - 0.001, -0.003
Bilateral tolerances should be specified as such, usually with plus and minus tolerances

Application of Tolerances.—According to common practice, tolerances are
applied in such a way as to show the permissible amount of dimensional variation in the
direction that is less dangerous. When a variation in either direction is equally dangerous,
a bilateral tolerance should be given. When a variation in one direction is more dangerous
than a variation in another, a unilateral tolerance should be given in the less dangerous
direction.
For nonmating surfaces, or atmospheric fits, the tolerances may be bilateral, or unilat-
eral, depending entirely upon the nature of the variations that develop in manufacture. On
mating surfaces, with few exceptions, the tolerances should be unilateral.
Where tolerances are required on the distances between holes, usually they should be
bilateral, as variation in either direction is normally equally dangerous. The variation in
the distance between shafts carrying gears, however, should always be unilateral and

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plus; otherwise, the gears might run too tight. A slight increase in the backlash between
gears is seldom of much importance.
One exception to the use of unilateral tolerances on mating surfaces occurs when tapers
are involved; either bilateral or unilateral tolerances may then prove advisable, depending
upon conditions. These tolerances should be determined in the same manner as the toler-
ances on the distances between holes. When a variation either in or out of the position of
the mating taper surfaces is equally dangerous, the tolerances should be bilateral. When a
variation in one direction is of less danger than a variation in the opposite direction, the
tolerance should be unilateral and in the less dangerous direction.
Locating Tolerance Dimensions.—Only one dimension in the same straight line can be
controlled within fixed limits. That dimension is the distance between the cutting surface
of the tool and the locating or registering surface of the part being machined. Therefore, it
is incorrect to locate any point or surface with tolerances from more than one point in the
same straight line.
Every part of a mechanism must be located in each plane. Every operating part must be
located with proper operating allowances. After such requirements of location are met, all
other surfaces should have liberal clearances. Dimensions should be given between those
points or surfaces that it is essential to hold in a specific relation to each other. This
restriction applies particularly to those surfaces in each plane that control the location of
other component parts. Many dimensions are relatively unimportant in this respect. It is
good practice to establish a common locating point in each plane and give, as far as
possible, all such dimensions from these common locating points. The locating points on
the drawing, the locatingor registering points used for machining the surfaces and the
locating points for measuring should all be identical.
The initial dimensions placed on component drawings should be the exact dimensions
that would be used if it were possible to work without tolerances. Tolerances should be
given in that direction in which variations will cause the least harm or danger. When a
variation in either direction is equally dangerous, the tolerances should be of equal
amount in both directions, or bilateral. The initial clearance, or allowance, between
operating parts should be as small as the operation of the mechanism will permit. The
maximum clearance should be as great as the proper functioning of the mechanism will
permit.
Direction of Tolerances on Gages.—The extreme sizes for all plain limit gages shall not
exceed the extreme limits of the part to be gaged. All variations in the gages, whatever
their cause or purpose, shall bring these gages within these extreme limits.
The data for gage tolerances on page 656 cover gages to inspect workpieces held to
tolerances in the American National Standard ANSI B4.4M-1981.
Allowance for Forced Fits.—The allowance per inch of diameter usually ranges from
0.001 inch to 0.0025 inch, 0.0015 being a fair average. Ordinarily the allowance per inch
decreases as the diameter increases; thus the total allowance for a diameter of 2 inches
might be 0.004 inch, whereas for a diameter of 8 inches the total allowance might not be
over 0.009 or 0.010 inch. The parts to be assembled by forced fits are usually made cylin-
drical, although sometimes they are slightly tapered. The advantages of the taper form are
that the possibility of abrasion of the fitted surfaces is reduced; that less pressure is
required in assembling; and that the parts are more readily separated when renewal is
required. On the other hand, the taper fit is less reliable, because if it loosens, the entire fit

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is free with but little axial movement. Some lubricant, such as white lead and lard oil
mixed to the consistency of paint, should be applied to the pin and bore before
assembling, to reduce the tendency toward abrasion.
Pressure for Forced Fits.—The pressure required for assembling cylindrical parts depends
not only upon the allowance for the fit, but also upon the area of the fitted surfaces, the
pressure increasing in proportion to the distance that the inner member is forced in. The
approximate ultimate pressure in tons can be determined by the use of the following for-
mula in conjunction with the accompanying table of "Pressure Factors." Assuming that A
= area of surface in contact in "fit"; a = total allowance in inches; P = ultimate pressure
required, in tons; F = pressure factor based upon assumption that the diameter of the hub
is twice the diameter of the bore, that the shaft is of machine steel, and that the hub is of
cast iron:
P=AxaxF
2

Pressure Factors
Diameter Pressure Diam Pressu Diame Press Diam Pressu Diame                               Pressure
,                 eter,   re ter,      ure eter,      re ter,
Inches    Factor Inches Factor Inches Factor Inches Factor Inches                          Factor

1     500         3k2        132           6    75         9    48.7        14      30.5

395        33/4        123        614     72       91'2   46.0     141/2      29.4

325           4        115         61'2   69        10    43.5        15      28.3

13/4     276        41/4        108        63/4    66      101/2   41.3      151'2     27.4

2     240         41'2       101           7    64        11    39.3        16      26.5

21/4    212        43/4        96         71/4    61              37.5      161/2     25.6

21'2    189           5        91          71'2   59        12    35.9        17      24.8

23/4     171        51/4        86         73/4    57      121/2   34.4      171'2     24.1

3     156         51'2       82            8    55        13    33.0        18      23.4

3^4     143        53/4        78          81'2   52      131/2   31.7

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Allowance for Given Pressure.—By transposing the preceding formula, the approxi-
2P
mate allowance for a required ultimate tonnage can be determined. Thus, a =           . The
AF
average ultimate pressure in tons commonly used ranges from 7 to 10 times the diameter
in inches.
Expansion Fits.—In assembling certain classes of work requiring a very tight fit, the
inner member is contracted by sub-zero cooling to permit insertion into the outer member
and a tight fit is obtained as the temperature rises and the inner part expands. To obtain
the sub-zero temperature, solid carbon dioxide or "dry ice" has been used but its
temperature of about 109 degrees F. below zero will not contract some parts sufficiently
to permit insertion in holes or recesses. Greater contraction may be obtained by using
high purity liquid nitrogen which has a temperature of about 320 degrees F. below zero.
During a temperature reduction from 75 degrees F. to -321 degrees F., the shrinkage per
inch of diameter varies from about 0.002 to 0.003 inch for steel; 0.0042 inch for
aluminum alloys; 0.0046 inch for magnesium alloys; 0.0033 inch for copper alloys;
0.0023 inch for monel metal; and 0.0017 inch for cast iron (not alloyed). The cooling
equipment may vary from an insulated bucket to a special automatic unit, depending upon
the kind and quantity of work. One type of unit is so arranged that parts are precooled by
vapors from the liquid nitrogen before immersion. With another type, cooling is entirely
by the vapor method.
Shrinkage Fits.—General practice seems to favor a smaller allowance for shrinkage fits
than for forced fits, although in many shops the allowances are practically the same for
each, and for some classes of work, shrinkage allowances exceed those for forced fits.
The shrinkage allowance also varies to a great extent with the form and construction of
the part that has to be shrunk into place. The thickness or amount of metal around the
hole is the most important factor. The way in which the metal is distributed also has an
influence on the results. Shrinkage allowances for locomotive driving wheel tires adopted
by the American Railway Master Mechanics Association are as follows:
Center diameter, inches 38 44 50 56 62 66
Allowances, inches       0.040 0.047 0.053 0.060 0.066 0.070
Whether parts are to be assembled by forced or shrinkage fits depends upon conditions.
For example, to press a tire over its wheel center, without heating, would ordinarily be a
rather awkward and difficult job. On the other hand, pins, etc., are easily and quickly
forced into place with a hydraulic press and there is the additional advantage of knowing
the exact pressure required in assembling, whereas there is more or less uncertainty con-
nected with a shrinkage fit, unless the stresses are calculated. Tests to determine the
difference in the quality of shrinkage and forced fits showed that the resistance of a
shrinkage fit to slippage for an axial pull was 3.66 times greater than that of a forced fit,
and in rotation or torsion, 3.2 times greater. In each comparative test, the dimensions and
allowances were the same.
Allowances for Shrinkage Fits.—The most important point to consider when calculating
shrinkage fits is the stress in the hub at the bore, which depends chiefly upon the
shrinkage allowance. If the allowance is excessive, the elastic limit of the material will be
exceeded and permanent set will occur, or, in extreme conditions, the ultimate strength of

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the metal will be exceeded and the hub will burst. The intensity of the grip of the fit and
the resistance to slippage depends mainly upon the thickness of the hub; the greater the
thickness, the stronger the grip, and vice versa. Assuming the modulus of elasticity for
steel to be 30,000,000, and for cast iron, 15,000,000, the shrinkage allowance per inch of
nominal diameter can be determined by the following formula, in which A = allowance
per inch of diameter; T = true tangential tensile stress at inner surface of outer member; C
= factor taken from one of the accompanying tables, Factors for Calculating Shrinkage Fit
Allowances.

For a cast-iron hub and steel shaft:
A =7/(2+C)
30,000,000                                            (1)

When both hub and shaft are of steel:

A=    T (1 + C)
30,000,000                                               (2)

If the shaft is solid, the factor C is taken from Table 1; if it is hollow and the hub is of steel,
factor C is taken from Table 2; if it is hollow and the hub is of cast iron, the factor is taken
from Table 3.
Ta e 1 . Fa o                       o a lcula i g hh i kka e i                            l lo a ance
T a b lb l e .1 F a c tcot r sr sf of r rC C lac u l a t itn n gS S r irn n a g g eFF ti t AAllo w w n c e s s

Ratio of          Steel Hub           Cast-iron               Ratio of          Steel Hub           Cast-iron
D2                                            Hub             D2                                            Hub
Diameters D                                                   Diameters D~
1.5            0.227                 0.234                    2.8            0.410                 0.432
1.6            0.255                 0.263                    3.0            0.421                 0.444
1.8            0.299                 0.311                    3.2            0.430                 0.455
2.0            0.333                 0.348                    3.4            0.438                 0.463
2.2            0.359                 0.377                    3.6            0.444                 0.471
2.4            0.380                 0.399                    3.8            0.450                 0.477
2.6            0.397                 0.417                    4.0            0.455                 0.482

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Example 1: A steel crank web 15 inches outside diameter is to be shrunk on a 10-
inch solid steel shaft. Required the allowance per inch of shaft diameter to
produce a maximum tensile stress in the crank of 25,000 pounds per square inch,
assuming the stresses in the crank to be equivalent to those in a ring of the
diameter given.
The ratio of the external to the internal diameters equals 15 ■+ 10 = 1.5; T =
25,000 pounds; from Table 1, C = 0.227. Substituting in Formula (2):
25,000 x ( 1 + 0.227)
A = —- ------- --------- = 0.001 inch
30,000,000

The ratio of the external to the internal diameters equals 15 ■+ 10 = 1.5; T = 25,000
pounds; from Table 1, C = 0.227. Substituting in Formula (2):
Example 2: Find the allowance per inch of diameter for a 10-inch shaft having a 5-inch
axial through hole, other conditions being the same as in Example 1.
The ratio of external to internal diameters of the hub equals 15 ■+ 10 = 1.5, as before,
and the ratio of external to internal diameters of the shaft equals 10 ■+ 5 = 2. From Table
2, we find that factor C = 0.455; T = 25,000 pounds. Substituting these values in Formula
(2):
A=25,000(1 + 0.455)/ 3000000 = 0.0012 inch
The allowance is increased, as compared with Example 1, because the hollow shaft is
more compressible.

Table 2. Factors for Calculating Shrinkage Fit Allowances
D                D                                 D           D
- 1-    C        - 2-     *>!             C        - 2-        - 1-        C
D       D                D        D                        D             D
1       0                 1        0                        1            0

2.0     0.468             2.0           0.798                   2.0       0.926
1.5     2.5     0.368    2.4      2.5           0.628     3.4           2.5       0.728
3.0     0.322             3.0           0.549                   3.0       0.637

3.5     0.296             3.5           0.506                   3.5       0.587
2.0     0.527             2.0           0.834                   2.0       0.941
2.5     0.414             2.5           0.656                   2.5       0.740
1.6     3.0     0.362    2.6      3.0           0.574     3.6           3.0       0.647

3.5     0.333             3.5           0.528                   3.5       0.596
2.0     0.621             2.0           0.864                   2.0       0.953

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2.5     0.488             2.5           0.679                   2.5      0.749
1.8   3.0     0.427    2.8      3.0           0.594     3.8           3.0      0.656

3.5     0.393             3.5           0.547                   3.5      0.603
2.0     0.696             2.0           0.888                   2.0      0.964
2.0   2.5     0.547    3.0      2.5           0.698     4.0           2.5      0.758

3.0     0.479             3.0           0.611                   3.0      0.663
3.5     0.441             3.5           0.562                   3.5      0.610
2.0     0.753             2.0           0.909
2.5     0.592             2.5           0.715
2.2   3.0     0.518    3.2      3.0           0.625

3.5     0.477               3.5            0.576
Values of factor C for hollow steel shafts and cast-iron
hubs.
Notation as in Table
1.
Table 3. Factors for Calculating Shrinkage Fit Allowances
D                      D                                 D          D
- 2-           C       - 2-      *>!             C       - 2-       - 1-       C
D
1 D0                 D
1       D
0                      D
1          D
0

2.0     0.455             2.0           0.760                   2.0      0.876
1.5   2.5     0.357    2.4      2.5           0.597     3.4           2.5      0.689
3.0     0.313             3.0           0.523                   3.0      0.602

3.5     0.288             3.5           0.481                   3.5      0.555
2.0     0.509             2.0           0.793                   2.0      0.888
1.6   2.5     0.400    2.6      2.5           0.624     3.6           2.5      0.698
3.0     0.350             3.0           0.546                   3.0      0.611

3.5     0.322             3.5           0.502                   3.5      0.562
2.0     0.599             2.0           0.820                   2.0      0.900
1.8   2.5     0.471    2.8      2.5           0.645     3.8           2.5      0.707
3.0     0.412             3.0           0.564                   3.0      0.619

3.5     0.379             3.5           0.519                   3.5      0.570
2.0     0.667             2.0           0.842                   2.0      0.909
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2.0   2.5     0.524         3.0   2.5            0.662     4.0           2.5       0.715
3.0     0.459               3.0            0.580                   3.0       0.625

3.5     0.422               3.5            0.533                   3.5       0.576
2.0     0.718               2.0            0.860
2.2   2.5     0.565         3.2   2.5            0.676
3.0     0.494               3.0            0.591

3.5     0.455              3.5            0.544
Values of factor C for hollow steel shafts of external and internal diameters D1 and D0,
respectively, and steel hubs of nominal external diameter D2.

Example 3: If the crank web in Example 1 is of cast iron and 4000 pounds per square
inch is the maximum tensile stress in the hub, what is the allowance per inch of diameter?
D2/D1= 1.5      T   = 4000
In Table 1, we find that C = 0.234. Substituting in Formula (1), for cast-iron hubs, A =
0.0003 inch, which, owing to the lower tensile strength of cast iron, is end out one-third
the shrinkage allowance in Example 1, although the stress is two-thirds of the elastic
limit.
Temperatures for Shrinkage Fits.—The temperature to which the outer member in a
shrinkage fit should be heated for clearance in assembling the parts depends on the total
expansion required and on the coefficient a of linear expansion of the metal (i.e., the
increase in length of any section of the metal in any direction for an increase in
temperature of 1 degree F). The total expansion in diameter that is required consists of the
total allowance for shrinkage and an added amount for clearance. The value of the
coefficient a is, for nickel-steel, 0.000007; for steel in general, 0.0000065; for cast iron,
0.0000062. As an example, take an outer member of steel to be expanded 0.005 inch per
inch of internal diameter, 0.001 being the shrinkage allowance and the remainder for
clearance. Then
A x to = 0.005
0.005
t = ------ - = 769 degrees F
0.0000065
The value t is the number of degrees F that the temperature of the member must be
raised above that of the room temperature.
ANSI Standard Limits and Fits (ANSI B4.1-1967 (R1994)).—This American National
Standard for Preferred Limits and Fits for Cylindrical Parts presents definitions of terms
applying to fits between plain (non threaded) cylindrical parts and makes recommenda-
tions on preferred sizes, allowances, tolerances, and fits for use wherever they are
applicable. This standard is in accord with the recommendations of American-British-

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Canadian (ABC) conferences up to a diameter of 20 inches. Experimental work is being
carried on with the objective of reaching agreement in the range above 20 inches. The
recommendations in the standard are presented for guidance and for use where they might
serve to improve and simplify products, practices, and facilities. They should have
application for a wide range of products.
As revised in 1967, and reaffirmed in 1979, the definitions in ANSI B4.1 have been
expanded and some of the limits in certain classes have been changed.
Factors Affecting Selection of Fits.—Many factors, such as length of engagement, bear-
ing load, speed, lubrication, temperature, humidity, and materials must be taken into con-
sideration in the selection of fits for a particular application, and modifications in the
ANSI recommendations may be required to satisfy extreme conditions. Subsequent
adjustments may also be found desirable as a result of experience in a particular
application to suit critical functional requirements or to permit optimum manufacturing
economy. Definitions.—The following terms are defined in this standard:
Nominal Size: The nominal size is the designation used for the purpose of general iden-
tification.
Dimension: A dimension is a geometrical characteristic such as diameter, length, angle,
or center distance.
Size: Size is a designation of magnitude. When a value is assigned to a dimension, it is
referred to as the size of that dimension. (It is recognized that the words "dimension" and
"size" are both used at times to convey the meaning of magnitude.)
Allowance: An allowance is a prescribed difference between the maximum material
limits of mating parts. (See definition of Fit). It is a minimum clearance (positive allow-
ance) or maximum interference (negative allowance) between such parts.
Tolerance: A tolerance is the total permissible variation of a size. The tolerance is the
difference between the limits of size.
Basic Size: The basic size is that size from which the limits of size are derived by the
application of allowances and tolerances.
Design Size: The design size is the basic size with allowance applied, from which the
limits of size are derived by the application of tolerances. Where there is no allowance,
the design size is the same as the basic size.
Actual Size: An actual size is a measured size.
Limits of Size: The limits of size are the applicable maximum and minimum sizes.
Maximum Material Limit: A maximum material limit is that limit of size that provides
the maximum amount of material for the part. Normally it is the maximum limit of size of
an external dimension or the minimum limit of size of an internal dimension.*
Minimum Material Limit: A minimum material limit is that limit of size that provides
the minimum amount of material for the part. Normally it is the minimum limit of size of
an external dimension or the maximum limit of size of an internal dimension.*
Tolerance Limit: A tolerance limit is the variation, positive or negative, by which a size
is permitted to depart from the design size.
Unilateral Tolerance: A unilateral tolerance is a tolerance in which variation is permitted
in only one direction from the design size.
Bilateral Tolerance: A bilateral tolerance is a tolerance in which variation is permitted in
both directions from the design size.
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Unilateral Tolerance System: A design plan that uses only unilateral tolerances is known
as a Unilateral Tolerance System.
Bilateral Tolerance System: A design plan that uses only bilateral tolerances is known as
a Bilateral Tolerance System.
Fit: Fit is the general term used to signify the range of tightness that may result from the
application of a specific combination of allowances and tolerances in the design of
mating parts.
Actual Fit: The actual fit between two mating parts is the relation existing between them
with respect to the amount of clearance or interference that is present when they are
assembled. (Fits are of three general types: clearance, transition, and interference.)
Clearance Fit: A clearance fit is one having limits of size so specified that a clearance
always results when mating parts are assembled.
Interference Fit: An interference fit is one having limits of size so specified that an inter-
ference always results when mating parts are assembled.
Transition Fit: A transition fit is one having limits of size so specified that either a clear-
ance or an interference may result when mating parts are assembled.
Basic Hole System: A basic hole system is a system of fits in which the design size of
the hole is the basic size and the allowance, if any, is applied to the shaft.
Basic Shaft System: A basic shaft system is a system of fits in which the design size of
the shaft is the basic size and the allowance, if any, is applied to the hole.
*
An example of exceptions: an exterior corner radius where the maximum radius is the
minimum material limit and the minimum radius is the maximum material limit.

Preferred Basic Sizes.—In specifying fits, the basic size of mating parts may be chosen
from the decimal series or the fractional series in the following table.
Decimal                        Fractional
0.01 2.0 8                0.015              2 14 2 . 2 5 0 0                    9.5000
0      0      .           625
5
0
0.01 2.2 9                0.031              2 12 2 . 5 0 0 0              10   10.0000
2      0      .           25
0
0
0.01 2.4 9 1              0.062             2 3-4 2 . 7 5 0 0            1 0 12 10.5000
6      0      . 16        5
5
0
3
0.02 2.6 1                0.093                 3 3.0000                   11   11.0000
0      0    0. 4          75
0
0
0.02 2.8 1                0.125              3 14 3 . 2 5 0 0                   11.5000
5      0    0.            0
5
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0
0.03 3.0 1             0.156              3 1/2    3.5000           12     1 .0000
2    0   1.            25
0
0
0.04 3.2 1      4      0.187              3 3/4    3.7500        1 2 12    1 .5000
0    0   1.            5
5
0
0.05 3.4 1             0.250                 4     4.0000           13     13.0000
0   2.            0
0
0
0.06 3.6 1      4      0.312              4 1/4    4.2500        1 3 12    13.5000
0   2.            5
5
0
0.08 3.8 1     '       0.375              4 1/2    4.5000           14     14.0000
0   3.    %       0
0
0
0.10 4.0 1     %       0.437               4 3/4   4.7500        1 4 12    14.5000
0   3.            5
5
0
0.12 4.2 1      \      0.500                 5     5.0000           15     15.0000
0   4.            0
0
0
0.16 4.4 1      4      0.562              5 1/4    5.2500        1 5 12    15.5000
0   4.            5
5
0
0.20 4.6 1     %       0.625              5 1/2    5.5000           16     16.0000
0   5.            0
0
0
0.24 4.8 1     %       0.687              5 3/4    5.7500        1 6 12    16.5000
0   5.            5
5
0
3
0.30 5.0 1             0.750                 6     6.0000           17     17.0000
0   6.    /4      0
0
0
7
0.40 5.2 1             0.875              6 1/2    6.5000        1 7 12    17.5000
0   6.    /8      0

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5
0
0.50 5.4   1    1       1.000                 7    7.0000            18     18.0000
0     7.           0
0
0
0.60 5.6   1     1      1.250              7 1/2   7.5000         1 8 12    18.5000
1
0     7.    4      0
5
0
0.80 5.8   1            1.500                 8    8.0000            19     19.0000
0     8.           0
0
0
1.00 6.0   1    13/     1.750              8 1/2   8.5000         1 9 12    19.5000
0     8.    4      0
5
0
1.20 6.5   1    2       2.000                 9    9.0000             0       0.0000
0     9.           0
0
0
1.40 7.0   1
0     9.
5
0
1.60 7.5   2
0     0.
0
0
1.80 8.0
0
All dimensions
are in inches.
Preferred Series of Tolerances and Allowances (In thousandths           nch)
of an
0.1     1        10 100 0.3                 3                                     30
1.2      12 125                   3.5                                     35
0.15 1.4         14      0.4                4                                     40
1.6      16 160                   4.5                                     45
1.8      18      0.5                5                                     50
0.2     2        20 200 0.6                 6                                     60
2.2      22      0.7                7                                     70
0.25 2.5         25 250 0.8                 8                                     80
2.8      28      0.9                9

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Standard Tolerances.—The series of standard tolerances shown in Table 1 are so
arranged that for any one grade they represent approximately similar production difficul-
ties throughout the range of sizes. This table provides a suitable range from which appro-
priate tolerances for holes and shafts can be selected and enables standard gages to be
used. The tolerances shown in Table 1 have been used in the succeeding tables for
different classes of fits.

Si
ze

Inches           4       5     6       7     8      9      10        11       12 13
Over          To    Tolerances in thousandths of an incha
0         0.12 0.12    0.15 0.25     0.4   0.6    1.0    1.6       2.5        4         6
0.12         0.24 0.15    0.20 0.3      0.5   0.7    1.2    1.8       3.0        5         7
0.24         0.40 0.15    0.25 0.4      0.6   0.9    1.4    2.2       3.5        6         9
0.40         0.71 0.2     0.3   0.4     0.7   1.0    1.6    2.8       4.0        7        10
0.71         1.19 0.25    0.4   0.5     0.8   1.2    2.0    3.5       5.0        8        12
1.19         1.97 0.3     0.4   0.6     1.0   1.6    2.5    4.0       6         10        16
1.97         3.15 0.3     0.5   0.7     1.2   1.8    3.0    4.5       7         12        18
3.15         4.73 0.4     0.6   0.9     1.4   2.2    3.5    5         9         14        22
4.73         7.09 0.5     0.7   1.0     1.6   2.5    4.0    6         10        16        25
7.09         9.85 0.6     0.8   1.2     1.8   2.8    4.5    7         12        18        28
9.85        12.41 0.6     0.9   1.2     2.0   3.0    5.0    8         12        20        30
12.41         15.75 0.7     1.0   1.4     2.2   3.5    6      9         14        22        35
15.75         19.69 0.8     1.0   1.6     2.5   4      6      10        16        25        40
19.69         30.09 0.9     1.2   2.0     3     5      8      12        20        30        50
30.09         41.49 1.0     1.6   2.5     4     6      10     16        25        40        60
41.49         56.19 1.2     2.0   3       5     8      12     20        30        50        80
56.19         76.39 1.6     2.5   4       6     10     16     25        40        60    100
76.39 100.9         2.0     3     5       8     12     20     30        50        80    125
100.9 131.9         2.5     4     6       10    16     25     40        60       100    160
131.9 171.9         3       5     8       12    20     30     50        80       125    200
171.9 200          4       6     10      16    25     40     60        100      160    250

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Table 2. Relation of Machining Processes to Tolerance Grades

ANSI Standard Fits.—Tables 3 through 9 inclusive show a series of standard
types and classes of fits on a unilateral hole basis, such that the fit produced by mating
parts in any one class will produce approximately similar performance throughout the
range of sizes. These tables prescribe the fit for any given size, or type of fit; they also
prescribe the standard limits for the mating parts that will produce the fit. The fits listed
in these tables contain all those that appear in the approved American-British-Canadian
proposal.
Selection of Fits: In selecting limits of size for any application, the type of fit is deter-
mined first, based on the use or service required from the equipment being designed; then
the limits of size of the mating parts are established, to insure that the desired fit will be
produced.
Theoretically, an infinite number of fits could be chosen, but the number of standard fits
shown in the accompanying tables should cover most applications.
Designation of Standard Fits: Standard fits are designated by means of the following
symbols which, facilitate reference to classes of fit for educational purposes. The symbols
are not intended to be shown on manufacturing drawings; instead, sizes should be speci-
fied on drawings. The letter symbols used are as follows:
RC=Running or Sliding Clearance Fit LC = Locational Clearance Fit LT = Transition
Clearance or Interference Fit LN= Locational Interference Fit FN= Force or Shrink Fit
These letter symbols are used in conjunction with numbers representing the class of fit;
thus FN 4 represents a Class 4, force fit.
Each of these symbols (two letters and a number) represents a complete fit for which the
minimum and maximum clearance or interference and the limits of size for the mating
parts are given directly in the tables.

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Description of Fits.—The classes of fits are arranged in three general groups: running and
sliding fits, locational fits, and force fits.
Running and Sliding Fits (RC): Running and sliding fits, for which limits of clearance
are given in Table 2, are intended to provide a similar running performance, with suitable
lubrication allowance, throughout the range of sizes. The clearances for the first two
classes, used chiefly as slide fits, increase more slowly with the diameter than for the
other classes, so that accurate location is maintained even at the expense of free relative
motion.
These fits may be described as follows:
RC 1 Close sliding fits are intended for the accurate location of parts that must assemble
without perceptible play.
RC 2 Sliding fits are intended for accurate location, but with greater maximum clearance
than class RC 1. Parts made to this fit move and turn easily but are not intended to run
freely, and in the larger sizes may seize with small temperature changes.
RC 3 Precision running fits are about the closest fits that can be expected to run freely,
and are intended for precision work at slow speeds and light journal pressures, but are not
suitable where appreciable temperature differences are likely to be encountered.
RC 4 Close running fits are intended chiefly for running fits on accurate machinery with
moderate surface speeds and journal pressures, where accurate location and minimum
play are desired.
RC 5 and RC 6 Medium running fits are intended for higher running speeds, or heavy
journal pressures, or both.
RC 7 Free running fits are intended for use where accuracy is not essential, or where
large temperature variations are likely to be encountered, or under both these conditions.
RC 8 and RC 9 Loose running fits are intended for use where wide commercial
tolerances may be necessary, together with an allowance, on the external member.
Locational Fits (LC, LT, and LN): Locational fits are fits intended to determine only the
location of the mating parts; they may provide rigid or accurate location, as with interfer-
ence fits, or provide some freedom of location, as with clearance fits. Accordingly, they
are divided into three groups: clearance fits (LC), transition fits (LT), and interference fits
(LN).
These are described as follows:
LC Locational clearance fits are intended for parts which are normally stationary, but
that can be freely assembled or disassembled. They range from snug fits for parts
requiring accuracy of location, through the medium clearance fits for parts such as
spigots, to the looser fastener fits where freedom of assembly is of prime importance.
LT Locational transition fits are a compromise between clearance and interference fits,
for applications where accuracy of location is important, but either a small amount of
clearance or interference is permissible.
LN Locational interference fits are used where accuracy of location is of prime impor-
tance, and for parts requiring rigidity and alignment with no special requirements for bore
pressure. Such fits are not intended for parts designed to transmit frictional loads from
one part to another by virtue of the tightness of fit. These conditions are covered by force
fits.

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Force Fits: (FN): Force or shrink fits constitute a special type of interference fit, nor-
mally characterized by maintenance of constant bore pressures throughout the range of
sizes. The interference therefore varies almost directly with diameter, and the difference
between its minimum and maximum value is small, to maintain the resulting pressures
within reasonable limits.
These fits are described as follows:
FN 1 Light drive fits are those requiring light assembly pressures, and produce more or
less permanent assemblies. They are suitable for thin sections or long fits, or in cast-iron
external members.
FN 2 Medium drive fits are suitable for ordinary steel parts, or for shrink fits on light
sections. They are about the tightest fits that can be used with high-grade cast-iron
external members.
FN 3 Heavy drive fits are suitable for heavier steel parts or for shrink fits in medium
sections.
FN 4 and FN 5 Force fits are suitable for parts that can be highly stressed, or for shrink
fits where the heavy pressing forces required are impractical.
Graphical Representation of Limits and Fits.—A visual comparison of the hole and shaft
tolerances and the clearances or interferences provided by the various types and classes of
fits can be obtained from the diagrams on page 633. These diagrams have been drawn to
scale for a nominal diameter of 1 inch.
Use of Standard Fit Tables.—Example 1: A Class RC 1 fit is to be used in assembling a
mating hole and shaft of 2-inch nominal diameter. This class of fit was selected because
the application required accurate location of the parts with no perceptible play (see
Description of Fits, RC 1 close sliding fits). From the data in Table 2, establish the limts
of size and clearance of the hole and shaft.
Maximum hole = 2 + 0.005 = 2.00005; minimum hole = 2 inches
Maximum shaft = 2 - 0.0004 = 1.9996; minimum shaft = 2 - 0.0007 = 1.9993 inches
Minimum clearance = 0.0004; maximum clearance = 0.0012 inch

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Class RC 1      Class RC 2       Class RC 3        Class RC 4
Standar        Standard        Standard          Standard
d
Nomial      Tolerance        Tolerance        Tolerance        Tolerance
Limits            Limits          Limits            Limits
Size Clea Hole Shaf         Hol Shaf        Hole Shaft       Hole Shaft
Range, r-           t          e    t
Inches ance H5 g4      Clear H6 g5 Clear H7          f6 Clear H8       f7
a
ancea           ancea            ancea

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Over                               Values shown below are in thousandths of an inch
To
0 - 0.12 0.1   +0.2 -0.1     0.1 +0.2 -0.1 0.3      +0.4     -0.3   0.3 +0.6     -0.3
5
0.45    0   -       0.55 0 -0.3 0.95          0     -0.55   1.3    0     -0.7
0.25
0.12 - 0.15 +0.2 -         0.15 +0.3   -     0.4   +0.5     -0.4   0.4 +0.7     -0.4
0.24            0.15                0.15
0.5  0 -0.3        0.65 0      -    1.12     0      -0.7   1.6    0     -0.9
0.35
0.24 - 0.2 +0.25 -0.2       0.2 +0.4 -0.2    0.5   +0.6     -0.5   0.5 +0.9     -0.5
0.40 0.6    0     -       0.85 0      -     1.5    0       -0.9   2.0 0        -1.1
0.35                0.45
0.40 - 0.25 +0.3 -         0.25 +0.4 -       0.6   +0.7     -0.6   0.6 +1.0     -0.6
0.71            0.25                0.25
0.75 0      -       0.95 0      -     1.7     0      -1.0   2.3    0     -1.3
0.45                0.55
0.71 - 0.3 +0.4 -0.3        0.3 +0.5 -0.3    0.8   +0.8     -0.8   0.8 +1.2     -0.8
1.19 0.95 0       -        1.2  0 -0.7      2.1    0       -1.3   2.8 0        -1.6
0.55
1.19 - 0.4 +0.4 -0.4       0.4 +0.6 -0.4     1.0   +1.0     -1.0   1.0 +1.6     -1.0
1.97 1.1    0 -0.7        1.4  0 -0.8       2.6            -1.6   3.6 0        -2.0

1.97 - 0.4    +0.5 -0.4    0.4 +0.7 -0.4     1.2   + 1.2    -1.2   1.2 +1.8     -1.2
3.15 1.2      0 -0.7      1.6  0 -0.9       3.1            -1.9   4.2 0        -2.4

3.15 - 0.5    +0.6 -0.5    0.5 +0.9 -0.5     1.4   +1.4     -1.4   1.4 +2.2     -1.4
4.73 1.5      0 -0.9      2.0  0 -1.1       3.7            -2.3   5.0 0        -2.8

4.73 - 0.6    +0.7 -0.6    0.6 +1.0 -0.6     1.6   +1.6     -1.6   1.6 +2.5     -1.6
7.09 1.8      0 -1.1      2.3  0 -1.3       4.2            -2.6   5.7 0        -3.2

7.09 - 0.6    +0.8 -0.6    0.6 +1.2 -0.6     2.0   +1.8     -2.0   2.0 +2.8     -2.0
9.85 2.0      0 -1.2      2.6  0 -1.4       5.0    0       -3.2   6.6 0        -3.8

9.85 - 0.8    +0.9 -0.8    0.8 +1.2 -0.8     2.5   +2.0     -2.5   2.5 +3.0     -2.5
12.41 2.3      0 -1.4      2.9  0 -1.7       5.7    0       -3.7   7.5 0        -4.5

12.41 - 1.0    +1.0 -1.0    1.0 +1.4 -1.0     3.0   +2.2     -3.0   3.0 +3.5     -3.0
15.75 2.7      0 -1.7      3.4  0 -2.0       6.6    0       -4.4   8.7 0        -5.2

15.75 - 1.2    +1.0 -1.2    1.2 +1.6 -1.2     4.0   +2.5     -4.0 4.0 +4.0       -4.0
19.69 3.0      0 -2.0      3.8  0 -2.2       8.1    0       -5.6 10.5 0         -6.5

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Class RC 1       Class RC 2         Class RC 3           Class RC 4
Standar         Standard          Standard             Standard
d
Nomin         Tolerance         Tolerance         Tolerance             Tolerance
al       Limits             Limits            Limits               Limits
Size Clea Hole Shaf            Hol Shaf         Hole Shaft           Hole Shaft
Range, r-             t           e     t
Inches ance H5 g4         Clear H6 g5 Clear H7            f6 Clear H8           f7
a                  a                a                    a
ance             ance                ance
Over                              Values shown below are in thousandths of an inch
To
0 - 0.1 +0.2 -0.1 0.1 +0.25 -0.1 0.3 +0.4            -0.3 0.3 +0.6 -0.3
0.12
0.45 0       -  0.55    0    -0.3 0.95    0    -0.55     1.3 0        -0.7
0.25

0.12 - 0.15 +0.2 -    0.15 +0.3 -    0.4               +0.5   -0.4   0.4 +0.7   -0.4
0.24            0.15           0.15
0.5  0 -0.3 0.65    0     - 1.12                0     -0.7   1.6   0    -0.9
0.35

0.24 - 0.2 +0.25 -0.2 0.2 +0.4 -0.2 0.5                +0.6   -0.5   0.5 +0.9   -0.5
0.40
0.6   0     -  0.85 0     -  1.5                 0     -0.9   2.0   0    -1.1
0.35          0.45

0.40 - 0.25 +0.3 -    0.25 +0.4 -    0.6               +0.7   -0.6   0.6 +1.0   -0.6
0.71            0.25           0.25
0.75 0      -  0.95  0     -  1.7                0     -1.0   2.3   0    -1.3
0.45           0.55

0.71 - 0.3 +0.4 -0.3      0.3   +0.5 -0.3        0.8   +0.8   -0.8   0.8 +1.2   -0.8
1.19
0.95 0     -       1.2     0       -0.7   2.1    0     -1.3   2.8   0    -1.6
0.55

1.19 - 0.4   +0.4 -0.4    0.4   +0.6 -0.4        1.0   +1.0   -1.0   1.0 +1.6   -1.0
1.97
1.1     0   -0.7   1.4     0       -0.8   2.6          -1.6   3.6   0    -2.0

162
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1.97 - 0.4   +0.5 -0.4    0.4   +0.7 -0.4        1.2   + 1.2   -1.2   1.2 +1.8   -1.2
3.15
1.2     0   -0.7   1.6     0       -0.9   3.1           -1.9   4.2   0    -2.4

3.15 - 0.5   +0.6 -0.5    0.5   +0.9 -0.5        1.4   +1.4    -1.4   1.4 +2.2   -1.4
4.73
1.5     0   -0.9   2.0     0       -1.1   3.7           -2.3   5.0   0    -2.8

4.73 - 0.6   +0.7 -0.6    0.6   +1.0 -0.6        1.6   +1.6    -1.6   1.6 +2.5   -1.6
7.09
1.8     0   -1.1   2.3     0       -1.3   4.2           -2.6   5.7   0    -3.2

7.09 - 0.6   +0.8 -0.6    0.6   +1.2 -0.6        2.0   +1.8    -2.0   2.0 +2.8   -2.0
9.85
2.0     0   -1.2   2.6     0       -1.4   5.0    0      -3.2   6.6   0    -3.8

9.85 - 0.8   +0.9 -0.8    0.8   +1.2 -0.8        2.5   +2.0    -2.5   2.5 +3.0   -2.5
12.41
2.3     0   -1.4   2.9     0       -1.7   5.7    0      -3.7   7.5   0    -4.5

12.41 - 1.0   +1.0 -1.0    1.0   +1.4 -1.0        3.0   +2.2    -3.0   3.0 +3.5   -3.0
15.75
2.7     0   -1.7   3.4     0       -2.0   6.6    0      -4.4   8.7   0    -5.2

15.75 - 1.2   +1.0 -1.2    1.2   +1.6 -1.2        4.0   +2.5    -4.0   4.0 +4.0   -4.0
19.69
3.0     0   -2.0   3.8     0       -2.2   8.1    0      -5.6 10.5    0    -6.5

Nomin     Class LT    Class LT    Class LT    Class LT    Class LT    Class LT
al Size   1           2           3           4           5           6
Range, Fit Std.    Fit Std.    Fit Std.    Fit Std.    Fit Std.    Fit Std.
163
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M 608 ADVANCED MACHINE TOOL LABORATORY

a              a              a
Inches         Tolera        Tolera          Tolera a Tolera a Tolera a Tolera
Over           nce           nce             nce        nce          nce         nce
To             Limits        Limits          Limits     Limits       Limits      Limits
Ho Sh         Ho Sh           Ho Sh      Ho Sh        Ho Sh       Ho Sh
le aft        le aft          le aft     le aft       le aft      le aft
H7 js6        H8 js7          H7 k6      H8 k7        H7 n6       H7 n7
Values shown below are in thousandths of an
inch
0-       -     +0. +0. -     +0. +0.                            - +0. +0. - +0. +0.
0.12     0.1   4 0 12 0.2    60 2-                              0.5 4 0 5 0.6 4 0 65
2         - +0.         0.2                            +0.      +0. 5       +0.
+0.       0.1 8                                        15       25 +0.      25
52        2                                                         15
-     +0. +0. -     +0. +0.                            - +0. +0. - +0. +0.
0.1   5 0 15 0.2    7 0 25                             0.6 5 0 6 0.8 5 0 8
0.12 -
5         - 5           -                              +0.      +0. +0.     +0.
0.24
+0.       0.1 +0.       0.2                            2        3 2         3
65        5 95          5
0.24 -   -     +0. +0. -     +0. +0. -       +0. +0. -     +0. +0. -     +0. +0. -      +0. +1.
0.40     0.2   6 0 2 - 0.3   9 0 3 - 0.5     6 0 5 0.7     9 0 7 0.8     6 0 8 1.0      60 0
+0.       0.2 +1.       0.3 +0.         +0. +0.       +0. +0.       +0. +0.        +0.
8             2             5           1 8           1 2           4 2            4
0.40 -   -     +0. +0. -     +1. +0. -       +0. +0. -     +1. +0. -     +0. +0. -1.2   +0. +1.
0.71     0.2   7 0 2 - 0.3   0 35 0.5        7 0 5 0.8     0 8 0.9       7 0 9 +0.      70 2
+0.       0.2 5     0 - +0.             +0. +0.   0 +0. +0.         +0. 2          +0.
9             +1.       0.3 6           1 9           1 2           5              5
35        5
-     +0. +0. -     +1. +0. -       +0. +0. - +1. +0. -1.1 +0. +1.1 -1.4 +0. +1.
0.2   8 0 25 0.4    2 4 - 0.6       8 0 6 0.9 2 9 +0. 8 0 +0. +0. 8 0 4
0.71 -
5         - +1.     0 0.4 +0.           +0. +1.1 0 +0. 2       6 2           +0.
1.19
+1.       0.2 6             7           1          1                         6
05        5
1.19 -   -     +1. +0. -     +1. +0. -   +1. +0. -1.1      +1. +1.1 -1.3 +1. +1.   -1.7 +1. +1.
1.97     0.3   0 3 - 0.5     6 5 - 0.7   0 7 +1.           6 +0. +0. 0 3           +0. 0 7
+1.       0.3 +2.   0 0.5 +0.       +0. 5         0 1 3             +0.   3        +0.
3             1             9       1                               7              7
1.97 -   -     +1. +0. -     +1. +0. -   +1. +0. -1.3      +1. +1. -1.5 +1. +1.    - +1. +2.
3.15     0.3   2 3 - 0.6     8 6 - 0.8   2 8 +1.           8 3 +0. 2 5             2.0 2 0
+1.       0.3 +2.   0 0.6 +1.1      +0. 7         0 +0. 4           +0.   +0.      +0.
5             4                     1                 1             8     4        8
3.15 -   -     +1. +0. -     +2. +0. - +1. +1. -1.5        +2. +1. - +1. +1.       - +1. +2.
4.73     0.4   4 4 - 0.7     2 0 7 - 1.0 4 0 +2.           2 0 5 1.9 4 9           2.4 4 4
+1.       0.4 +2.       0.7 +1.     +0. 1             +0. +0.       +1.   +0.      +1.
8             9             3       1                 1 4           0     4        0

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M 608 ADVANCED MACHINE TOOL LABORATORY

4.73 -      -     +1. +0. -      +2. +0. -1.1 +1. +1.1 -1.7 +2. +1.   -     +1. +2. -       +1. +2.
7.09        0.5   6 5 - 0.8      5 0 8 - +1. 6 +0. +2. 5 0 7          2.2   6 2 2.8         6 8
+2.       0.5 +3.        0.8 5        1 4           +0.   +0.       +1. +0.         +1.
1             3                                     1     4         2 4             2
7.09 -      -     0 +0. -        +2. +0. -1.4 0 +1. - +2. +2.         -     0 +2. -         0 +3.
9.85        0.6       6 - 0.9    8 0 9 - +1.      4 2.0 8 0 0         2.6       6 3.2           2
+2.       0.6 +3.        0.9 6        +0. +2.       +0.   +0.       +1. +0.         +1.
4             7                       2 6           2     4         4 4             4
-     +2. +0. -      +3. +1. -1.4 +2. +1. - +3. +2.       -     +2. +2. -       +2. +3.
9.85 -      0.6   0 0 6 - 1.0    0 0 0 - +1. 0 0 4 2.2 0 0 2          2.6   0 0 6 3.4       00 4
12.41       +2.       6.6 +4.        1.0 8        +0. +2.       +0.   +0.       +1. +0.         +1.
6             0                       2 8           2     6         4 6             4
12.41 -     -     +2. +0. -      +3. +1. - +2. +1. - +3. +2.          -     +2. +3. -       +2. +3.
15.75       0.7   2 0 7 - 1.0    5 0 0 - 1.6 2 0 6 2.4 5 0 4          3.0   2 0 0 3.8       20 8
+2.       0.7 +4.        1.0 +2.      +0. +3.       +0.   +0.       +1. +0.         +1.
9             5              0        2 3           2     6         6 6             6
15.75 -     -     +2. +0. -1.2   +4. +1.      +2. +1. - +4. +2.       -     +2. +3. -       +2. +4.
19.69       0.8   5 0 8 - +5.    0 0 2 - +2. 5 0 8 2.7 0 0 7          3.4   5 0 4 4.3       50 3
+3.       0.8 2          1.2 3        +0. +3.       +0.   +0.       +1. +0.         +1.
3                                     2 8           2     7         8 7             8

Class FN 1            Class FN        Class FN          Class FN            Class FN
2               3                 4                   5
Standar           Standard        Standard          Standard            Standard
d
Inter- Toleranc          Toleranc       Toleranc           Toleranc           Tolerance
ference e                 e              e                  e
Nom               Limits     In     Limits     In Limits          In Limits         In   Limits
inal                         ter               ter                ter               ter
-                 -                  -                 -
Size             Ho         fe     Hol Sh fe Hol Sh              fe Hol Sh         fe    Hol Sh
Range             le        ren     e    aft ren e       aft     ren e      aft    ren    e    aft
,                              -                 -                  -                 -
Inche            H6 Sh ce          H7     s6 ce H7        t6    ce H7       u6    ce    H8    x7
s                      aft a                    a                a                 a

Over                                   Values shown below are in thousandths of an inch
To
4.73- 1.2       +1. +2. 1. +1.6 +4. 3. +1.6 +6. 5. +1.6 +8. 7. +2.5 +1
5.52                0   99          5 4        0 4          0 5      1.6
2.9     +2. 4. 0    +3. 6.      +5. 8.      +7. 1 0     +1
2 5         5 0        0 0          0 1.6    0.0

165
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M 608 ADVANCED MACHINE TOOL LABORATORY

5.52-     1.5 +1. +3. 2. +1.6 +5. 3. +1.6 +6. 5. +1.6 +8. 9. +2.5 +1
6.30             0   2 4         0 4        0 4          0 5      3.6
3.2     +2. 5.      +4. 6.      +5. 8.      +7. 1 0     +1
5 0         0 0        0 0          0 3.6    2.0

6.30-     1.8 +1. +3. 2. +1.6 +5. 4. +1.6 +7. 6. +1.6 +9. 9. +2.5 +1
7.09             0   5 9         5 4        0 4          0 5      3.6
3.5     +2. 5.      +4. 7.      +6. 9.      +8. 1 0     +1
8 5         5 0        0 0          0 3.6    2.0

7.09-     1.8 +1. +3. 3. +1.8 +6. 5. +1.8 +8. 7. +1.8 +1 1 +2.8 +1
7.88             2   8 2         2 2        2 2        0.2 1.2  5.8
3.8     +3. 6.      +5. 8.      +7. 1       +9. 1 0   +1
0 2         0 2        0 0.2        0 5.8  4.0

7.88-     2.3 +1. +4. 3. +1.8 +6. 5. +1.8 +8. 8. +1.8 +1 1 +2.8 +
8.86             2   3 2         2 2        2 2        1.2 3.2  17.8
4.3     +3. 6.      +5. 8.      +7. 1       +1 1 0    +1
5 2         0 2        0 1.2      0.0 7.8  6.0

8.86-     2.3 +1. +4. 4. +1.8 +7. 6. +1.8 +9. 1 +1.8 +1 1 +2.8 +1
9.85             2   3 2         2 2        2 0.2     3.2 3.2  7.8
4.3     +3. 7. 0    +6. 9. 0    +8. 1 0    +1 1 0    +1
5 2         0 2        0 3.2     2.0 7.8  6.0

9.85-     2.8 +1. +4. 4. +2.0 +7. 7. +2.0    + 1 +2.0 +1 1 +3.0 +2
11.03            2   9 0         2 0       10.2 0.0    3.2 5.0  0.0
4.9     +4. 7. 0    +6. 1 0      +9. 1 0    +1 2 0    +1
0 2         0 0.2        0 3.2    2.0 0.0  8.0

11.03      2.8 +1. +4. 5. +2.0 +8. 7. +2.0 +1 1 +2.0 +1 1 +3.0 +2
-                2   9 0         2 0       0.2 2.0   5.2 7.0  2.0
12.41
4.9       +4. 8. 0        +7. 1 0         +9. 1 0         +1 2 0         +2
0 2             0 0.2          0 5.2          4.0 2.0       0.0

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12.41    3.1 +1. +5. 5. +2.2 +9. 7. +2.2 +1 1 +2.2 +1 1 +3.5 +2
-                4   5 8         4 8       1.4 3.8   7.4 8.5  4.2
13.98
5.5        +4. 9. 0        +8. 1 0          +1 1 0          +1 2 0          +2
5 4             0 1.4          0.0 7.4         6.0 4.2        2.0

13.98     3.6 +1. +6. 5. +2.2 +9. 9. +2.2 +1 1 +2.2 +1 2 +3.5 +2
-                4   1 8         4 8       3.4 5.8   9.4 1.5  7.2
15.75
6.1        +5. 9. 0        +8. 1 0          +1 1 0          +1 2 0          +2
0 4             0 3.4          2.0 9.4         8.0 7.2        5.0

15.75     4.4 +1. +7. 6. +2.5 +1 + +2.5 +1 1 +2.5 +2 2 +4.0 +3
-                6   0 5       0.6 9.5   3.6 7.5   1.6 4.0  0.5
17.72
7.0        +6. 1 0         +9. 1 0          +1 2 0          +2 3 0          +2
0 0.6           0 3.6          2.0 1.6         0.0 0.5        8.0

17.72    4.4 +1. +7. 7. +2.5 +1 1 +2.5 +1 1 +2.5 +2 2 +4.0 +3
-                6   0 5       1.6 1.5   5.6 9.5   3.6 6.0  2.5
19.69
7.0 0      +6. 1 0          +1 1 0          +1 2 0          +2 3 0          +3
0 1.6          0.0 5.6         4.0 3.6         2.0 2.5        0.0

Modified Standard Fits.—Fits having the same limits of clearance or
interference as those shown in Tables 3 to 7 may sometimes have to be produced by using
holes or shafts having limits of size other than those shown in these tables. These
modifications may be accomplished by using either a Bilateral Hole (System B) or a
Basic Shaft System (Symbol S). Both methods will result in nonstandard holes and shafts.
Bilateral Hole Fits: (Symbol B): The common situation is where holes are produced with
fixed tools such as drills or reamers; to provide a longer wear life for such tools, a
bilateral tolerance is desired.
The symbols used for these fits are identical with those used for standard fits except that
they are followed by the letter B. Thus, LC 4B is a clearance locational fit, Class 4,
except that it is produced with a bilateral hole.
The limits of clearance or interference are identical with those shown in Tables 3 to 7 for
the corresponding fits.
The hole tolerance, however, is changed so that the plus limit is that for one grade finer
than the value shown in the tables and the minus limit equals the amount by which the
plus limit was lowered. The shaft limits are both lowered by the same amount as the
lower limit of size of the hole. The finer grade of tolerance required to make these
modifications may be obtained from Table 1. For example, an LC 4B fit for a 6-inch

167
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M 608 ADVANCED MACHINE TOOL LABORATORY

diameter hole would have tolerance limits of + 4.0, - 2.0 ( + 0.0040 inch, - 0.0020 inch);
the shaft would have tolerance limits of - 2.0, - 6.0 ( - 0.0020 inch, - 0.0060 inch).
Basic Shaft Fits: (Symbol S): For these fits, the maximum size of the shaft is basic. The
limits of clearance or interference are identical with those shown in Tables 3 to 7 for the
corresponding fits and the symbols used for these fits are identical with those used for
standard fits except that they are followed by the letter S. Thus, LC 4S is a clearance
locational fit, Class 4, except that it is produced on a basic shaft basis.
The limits for hole and shaft as given in Tables 3 to 7 are increased for clearance fits
(decreased for transition or interference fits) by the value of the upper shaft limit; that is,
by the amount required to change the maximum shaft to the basic size.
American National Standard Preferred Metric Limits and Fits.—This standard ANSI
B4.2-1978 (R1994) describes the ISO system of metric limits and fits for mating parts as
approved for general engineering usage in the United States.
It establishes: 1) the designation symbols used to define dimensional limits on drawings,
material stock, related tools, gages, etc.; 2) the preferred basic sizes (first and second
choices); 3) the preferred tolerance zones (first, second, and third choices); 4) the pre-
ferred limits and fits for sizes (first choice only) up to and including 500 millimeters; and
5) the definitions of related terms.
The general terms "hole" and "shaft" can also be taken to refer to the space containing or
contained by two parallel faces of any part, such as the width of a slot, or the thickness of
a key.
Definitions.—The most important terms relating to limits and fits are shown in Fig. 1 and
are defined as follows:
Basic Size: The size to which limits of deviation are assigned. The basic size is the same
for both members of a fit. For example, it is designated by the numbers 40 in 40H7.
Deviation: The algebraic difference between a size and the corresponding basic size.
Upper Deviation: The algebraic difference between the maximum limit of size and the
corresponding basic size.
Lower Deviation: The algebraic difference between the minimum limit of size and the
corresponding basic size.
Fundamental Deviation: That one of the two deviations closest to the basic size. For
example, it is designated by the letter H in 40H7.
Tolerance: The difference between the maximum and minimum size limits on a part.

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M 608 ADVANCED MACHINE TOOL LABORATORY

Tolerance Zone: A zone representing the tolerance and its position in relation to the
basic size.
Tolerance Zone: A zone representing the tolerance and its position in relation to the
basic size.

International Tolerance Grade: (IT): A group of tolerances that vary depending on
the basic size, but that provide the same relative level of accuracy within a given grade.
For example, it is designated by the number 7 in 40H7 or as IT7.
Hole Basis: The system of fits where the minimum hole size is basic. The fundamental
deviation for a hole basis system is H.
Shaft Basis: The system of fits where the maximum shaft size is basic. The fundamental
deviation for a shaft basis system is h.
Clearance Fit: The relationship between assembled parts when clearance occurs under
all tolerance conditions.
Interference Fit: The relationship between assembled parts when interference occurs
under all tolerance conditions.
Transition Fit: The relationship between assembled parts when either a clearance or an
interference fit can result, depending on the tolerance conditions of the mating parts.

169
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M 608 ADVANCED MACHINE TOOL LABORATORY

Tolerances Designation.—An "International Tolerance grade" establishes the magnitude
of the tolerance zone or the amount of part size variation allowed for external and internal
dimensions alike (see Fig. 1). Tolerances are expressed in grade numbers that are
consistent with International Tolerance grades identified by the prefix IT, such as IT6,
IT11, etc. A smaller grade number provides a smaller tolerance zone.
A fundamental deviation establishes the position of the tolerance zone with respect to
the basic size (see Fig. 1). Fundamental deviations are expressed by tolerance position
letters.
Capital letters are used for internal dimensions and lowercase or small letters for external
dimensions.
Symbols.—By combining the IT grade number and the tolerance position letter, the toler-
ance symbol is established that identifies the actual maximum and minimum limits of the
part. The toleranced size is thus defined by the basic size of the part followed by a symbol
composed of a letter and a number, such as 40H7, 40f7, etc.
A fit is indicated by the basic size common to both components, followed by a symbol
corresponding to each component, the internal part symbol preceding the external part
symbol, such as 40H8/f7.
Some methods of designating tolerances on drawings are:
A)40H8
B) 40H8 (40.039
40.000)
C) (40.039 40H8
40.000)
Table 10. American National Standard Preferred Metric Sizes

Basic Size,  Basic Size,                Basic Size,                   Basic Size,
mm           mm                        mm                            mm
1st    2nd   1st    2nd             1st           2nd             1st            2nd
Choic Choice Choice Choice          Choice       Choice           Choice         Choice
e
1             6                     40                           250
1.1            7                            45                               280
1.2            8                     50                           300
1.4            9                            55                               350
1.6           10                     60                           400
1.8           11                            70                               450
2            12                     80                           500
2.2           14                            90                               550
2.5           16                     100                          600
2.8           18                            110                              700
3            20                     120                          800
3.5           22                            140                              900
4            25                     160                          1000
4.5           28                            180
5            30                     200
5.5           35                            220

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M 608 ADVANCED MACHINE TOOL LABORATORY

metal products. Table 10 gives preferred metric diameters from 1 to 320
millimeters for round metal products. Wherever possible, sizes should be selected
from the Preferred Series shown in the table. A Second Preference series is also
shown. A Third Preference Series not shown in the table is: 1.3, 2.1, 2.4, 2.6, 3.2, 3.8,
4.2, 4.8, 7.5, 8.5, 9.5, 36, 85, and 95.
Most of the Preferred Series of sizes are derived from the American National
Standard "10 series" of preferred numbers (see American National Standard for
Preferred Numbers on page 19). Most of the Second Preference Series are derived
from the "20 series" of preferred numbers. Third Preference sizes are generally from
the "40 series" of preferred numbers.
For preferred metric diameters less than 1 millimeter, preferred across flat metric
sizes of square and hexagon metal products, preferred across flat metric sizes of
rectangular metal products, and preferred metric lengths of metal products, reference
should be made to the Standard.
Preferred Fits.—First-choice tolerance zones are used to establish preferred fits in
the Standard for Preferred Metric Limits and Fits, ANSI B4.2, as shown in Figs. 2 and
3. A complete listing of first-, second-, and third

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M 608 ADVANCED MACHINE TOOL LABORATORY

Hole basis fits have a fundamental deviation of H on the hole, and shaft basis fits
have a fundamental deviation of h on the shaft and are shown in Fig. 2 for hole basis
and Fig. 3 for shaft basis fits. A description of both types of fits, that have the same
relative fit condition,
is given in Table 11. Normally, the hole basis system is preferred; however, when a com-
mon shaft mates with several holes, the shaft basis system should be used.
The hole basis and shaft basis fits shown in Table 11 are combined with the first-choice
sizes shown in Table 10 to form Tables 12, 13, 14, and 15, where specific limits as well
as the resultant fits are tabulated.
If the required size is not tabulated in Tables 12 through 15 then the preferred fit can be
calculated from numerical values given in an appendix of ANSI B4.2-1978 (R1984). It is
anticipated that other fit conditions may be necessary to meet special requirements, and a
preferred fit can be loosened or tightened simply by selecting a standard tolerance zone as
given in the Standard. Information on how to calculate limit dimensions, clearances, and
interferences, for nonpreferred fits and sizes can also be found in an appendix of this
Standard.

172
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

ISO
SYMBOL
Hole Shaft                        DESCRIPTION
Basis Basis
H11/c11 C11/h11 Loose running fit for wide commercial tolerances
or allowances on external members.
Clear

H9/d9 D9/h9 Free running fit not for use where accuracy is            More
ance
Fits

essential, but good for large temperature              Clearance
variations, high running speeds, or heavy journal
pressures.
H8/f7   F8/h7 Close Running fit for running on accurate
machines and for accurate moderate speeds and
journal pressures.
H7/g6 G7/h6 Sliding fit not intended to run freely, but to move
H7/h6 H7/h6 and turn freely and locate accurately.
Locational clearance fit provides snug fit for
locating stationary parts; but can be freely
assembled and disassembled.
Trans

H7/k6 K7/h6 Locational transition fit for accurate location, a
ition
Fits

compromise between clearance and interferance.
H7/n6 N7/h6 Locational transition fit for more accurate location
where greater interferance is permissible.
a
H7/p6   P7/h6 Locational interference fit for parts requiring         More
Interferenc

rigidity and alignment with prime accuracy of          Interferance
e Fits

location but without special bore pressure
requirements.
H7/s6   S7/h6 Medium drive fit for ordinary steel parts or shrink
fits on light sections, the tightest fit usable with
cast iron.
H7/u6 U7/h6 Force fit suitable for parts which can be highly
stressed or for shrink fits where the heavy
pressing forces required are impractical.

173
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Loose         Free         Close               Sliding      Locational
Running       Running      Running                          Clearance
Basic           Ho Sha        H Sha         Ho Sha           Hol Sh           Hol Sh
le ft         ole ft        le ft            e   aft          e    aft
Size            H1 C1 Fit     H d9      Fit H8 f7     Fit    H7 g6        Fit H7 h6 Fit
1    1        9
1      Max    1.06 0.9 0.    1. 0.9 0. 1. 0.99 0.           1.0    0.9    0.    1.0    1.0    0.
0    40 180   025 80    070 014 4     030    10     98     018   10     00     016
Min     1.0 0.8 0.    1. 0.9 0. 1. 0.98 0.           1.0    0.9    0.    1.0    0.9    0.
00 80 060     000 95    020 000 4     006    00     92     002   00     94     000
1.2 Max        1.2 1.1 0.    1. 1.1 0. 1. 1.19 0.           1.2    1.1    0.    1.2    1.2    0.
60 40 180     225 80    070 214 4     030    10     98     018   10     00     016
Min     1.2 1.0 0.    1. 1.1 0. 1. 1.18 0.           1.2    1.1    0.    1.2    1.1    0.
00 80 060     200 55    020 200 4     006    00     92     002   00     94     000
1.6 Max        1.6 1.5 0.    1. 1.5 0. 1. 1.59 0.           1.6    1.5    0.    1.6    1.6    0.
60 40 180     625 80    070 614 4     030    10     98     018   10     00     016
Min     1.6 1.4 0.    1. 1.5 0. 1. 1.58 0.           1.6    1.5    0.    1.6    1.5    0.
00 80 060     600 55    020 600 4     006    00     92     002   00     94     000
2      Max     2.0 1.9 0.    2. 1.9 0. 2. 1.99 0.           2.0    1.9    0.    2.0    2.0    0.
60 40 180     025 80    070 014 4     030    10     98     018   10     00     016
Min     2.0 1.8 0.    2. 1.9 0. 2. 1.98 0.           2.0    1.9    0.    2.0    1.9    0.
00 80 060     000 55    020 000 4     006    00     92     002   00     94     000
2.5 Max        2.5 2.4 0.    2. 2.4 0. 2. 2.49 0.           2.5    2.4    0.    2.5    2.5    0.
60 40 180     525 80    070 514 4     030    10     98     018   10     00     016
Min     2.5 2.3 0.    2. 2.4 0. 2. 2.48 0.           2.5    2.4    0.    2.5    2.4    0.
00 80 060     500 55    020 500 4     006    00     92     002   00     94     000
3      Max     3.0 2.9 0.    3. 2.9 0. 3. 2.99 0.           3.0    2.9    0.    3.0    3.0    0.
60 40 180     025 80    070 014 4     030    10     98     018   10     00     016
Min     3.0 2.8 0.    3. 2.9 0. 3. 2.98 0.           3.0    2.9    0.    3.0    2.9    0.
00 80 060     000 55    020 000 4     006    00     92     002   00     94     000
4       Ma     4.0 3.9 0.    4. 3.9 0. 4. 3.99 0.           4.0    3.9    0.    4.0    4.0    0.
x      75 30 220     030 70    090 018 0     040    12     96     024   12     00     020
Min    4.0 3.8 0.    4. 3.9 0. 4. 3.97 0.           4.0    3.9    0.    4.0    3.9    0.
00 55 070     000 40    030 000 8     010    00     88     004   00     92     000
5      Max     5.0 4.9 0.    5. 4.9 0. 5. 4.99 0.           5.0    4.9    0.    5.0    5.0    0.
75 30 220     030 70    090 018 0     040    12     96     024   12     00     020
Min     5.0 4.8 0.    5. 4.9 0. 5. 4.97 0.           5.0    4.9    0.    5.0    4.9    0.
00 55 070     000 40    030 000 8     010    00     88     004   00     92     000
6      Max     6.0 5.9 0.    6. 5.9 0. 6. 5.99 0.           6.0    5.9    0.    6.0    6.0    0.
75 30 220     030 70    090 018 0     040    12     96     024   12     00     020
Min     6.0 5.8 0.    6. 5.9 0. 6. 5.97 0.           6.0    5.9    0.    6.0    5.9    0.
00 55 070     000 40    030 000 8     010    00     88     004   00     92     000
8      Max     8.0 7.9 0.    8. 7.9 0. 8. 7.98 0.           8.0    7.9    0.    8.0    8.0    0.
90 20 260     036 60    112 022 7     050    15     95     029   15     00     024
Min     8.0 7.8 0.    8. 7.9 0. 8. 7.97 0.           8.0    7.9    0.    8.0    7.9    0.
00 30 080     000 24    040 000 2     013    00     86     005   00     91     000

174
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

10    Max     10. 9.9 0. 10 9.9         0. 10 9.98     0. 10. 9.9 0. 10. 10. 0.
090 20 260 .03 60         112 .02 7      050 015 95 029 015 000 024
6                 2
Min    10. 9.8 0. 10 9.9         0. 10 9.97     0. 10. 9.9 0. 10. 9.9 0.
000 30 080 .00 24         040 .00 2      013 000 86 005 000 91 000
0                 0
12    Max     12. 11. 0. 12 11.         0. 12 11.9     0. 12. 11. 0. 12. 12. 0.
110 905 315 .04 956       136 .02 84     061 018 994 035 018 000 029
3                 7
Min    12. 11. 0. 12 11.         0. 12 11.9     0. 12. 11. 0. 12. 11. 0.
000 795 095 .00 907       050 .00 66     016 000 983 006 000 989 000
0                 0
16    Max     16. 15. 0. 16 15.         0. 16 15.9     0. 16. 15. 0. 16. 16. 0.
110 905 315 .04 950       136 .02 84     061 018 994 035 018 000 029
3                 7
Min    16. 15. 0. 16 15.         0. 16 15.9     0. 16. 15. 0. 16. 15. 0.
000 795 095 .00 907       050 .00 66     016 000 983 006 000 989 000
0                 0
20    Max     20. 19. 0. 20 19.         0. 20 19.9     0. 20. 19. 0. 20. 20. 0.
130 890 370 .05 935       169 .03 80     074 021 993 041 021 000 034
2                 3
Min    20. 19. 0. 20 19.         0. 20 19.9     0. 20. 19. 0. 20. 19. 0.
000 760 110 .00 883       065 .00 59     020 000 980 007 000 987 000
0                 0
25    Max     25. 24. 0. 25 24.         0. 25 24.9     0. 25. 24. 0. 25. 25. 0.
130 890 370 .05 935       169 .03 80     074 021 993 041 021 000 034
2                 3
Min    25. 24. 0. 25 24.         0. 25 24.9     0. 25. 24. 0. 25. 24. 0.
000 760 110 .00 883       065 .00 59     020 000 980 007 000 987 000
0                 0

175
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Loose                 Free             Close            Sliding     Locational
Running               Running          Running                      Clearance
Basic       Hole    Sha          Ho Sha           Ho Sha           Hol Sh        Hol Sh
ft           le ft            le ft            e    aft      e    aft
Sizea       H11     C1     Fi    H9 d9      Fi    H8 f7      Fi    H7 g6     Fit H7 h6 Fit
1      tb               tb                tb                  b         b

30       M 30.130 29.     0.    30. 29.9 0.      30. 29.9 0.      30. 29. 0. 30. 30. 0.
a          890    37    052 35     16    033 80     07    021 993 041 021 000 034
x                  0                9                4
M 30.000 29.     0.    30. 29.8 0.      30. 29.9 0.      30. 29. 0. 30. 29. 0.
i          760    11    000 83     06    000 59     02    000 980 007 000 987 000
n                  0                5                0
40       M 40.160 39.     0.    40. 39.9 0.      40. 39.9 0.      40. 39. 0. 40. 40. 0.
a          880    44    062 20     20    039 75     08    025 991 050 025 000 041
x                  0                4                9
M 40.000 39.     0.    40. 39.8 0.      40. 39.9 0.      40. 39. 0. 40. 39. 0.
i          720    12    000 58     08    000 50     02    000 975 009 000 984 000
n                  0                0                5
50       M 50.160 49.     0.    50. 49.9 0.      50. 49.9 0.      50. 49. 0. 50. 50. 0.
a          870    45    062 20     20    039 75     08    025 991 050 025 000 041
x                  0                4                9
M 50.000 49.     0.    50. 49.8 0.      50. 49.9 0.      50. 49. 0. 50. 49. 0.
i          710    13    000 58     08    000 50     02    000 975 009 000 984 000
n                  0                0                5
60       M 60.190 59.     0.    60. 59.9 0.      60. 59.9 0.      60. 59. 0. 60. 60. 0.
a          860    52    074 00     24    046 70     10    030 990 059 030 000 049
x                  0                8                6
M 60.000 59.     0.    60. 59.8 0.      60. 59.9 0.      60. 59. 0. 60. 59. 0.
i          670    14    000 26     10    000 40     03    000 971 010 000 981 000
n                  0                0                0
80       M 80.190 79.     0.    80. 79.9 0.      80. 79.9 0.      80. 79. 0. 80. 80. 0.
a          850    53    074 00     24    046 70     10    030 990 059 030 000 049
x                  0                8                6
M 80.000 79.     0.    80. 79.8 0.      80. 79.9 0.      80. 79. 0. 80. 79. 0.
i          660    15    000 26     10    000 40     03    000 971 010 000 981 000
n                  0                0                0
100       M 100.22 99.     0.    10 99.8 0.       10 99.9 0.       100 99. 0. 100 10 0.
a 0        830    61    0.08 80    29    0.05 64    12    .035 988 069 .035 0.00 057
x                  0    7           4    4           5                      0
M 100.00 99.     0.    10 99.7 0.       10 99.9 0.       100 99. 0. 100 99. 0.
i 0        610    17    0.00 93    12    0.00 29    03    .000 966 012 .000 978 000
n                  0    0           0    0           6
120       M 120.22 119     0.    12 119. 0.       12 119. 0.       120 11     0. 120 12 0.
a 0        .820   62    0.08 880 29      0.05 964 12      .035 9.98 069 .035 0.00 057
x                  0    7           4    4           5         8             0
M120.00 119      0.    12 119. 0.       12 119. 0.       120 11     0. 120 11 0.

176
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

i 0         .600 18   0.00   793     12    0.00   929     03    .000 9.96   012 .000 9.97   000
n                 0   0               0    0               6         6               8
160     M 160.25    159 0.    16     159.    0.    16     159.    0.    160 15       0. 160 16      0.
a 0         .790 71   0.10   855     34    0.06   957     14    .040 9.98   079 .040 0.00   065
x                 0   0               5    3               6         6               0
M 160.00    159 0.    16     159.    0.    16     159.    0.    160 15       0. 160 15      0.
i 0         .540 21   0.00   755     14    0.00   917     04    .000 9.96   014 .000 9.97   000
n                 0   0               5    0               3         1               5
200     M 200.29    199 0.    20     199.    0.    20     199.    0.    200 19       0. 200 20      0.
a 0         .760 82   0.11   830     40    0.07   950     16    .046 9.98   090 .046 0.00   075
x                 0   5               0    2               8         5               0
M 200.00    199 0.    20     199.    0.    20     199.    0.    200 19       0. 200 19      0.
i 0         .470 24   0.00   715     17    0.00   904     05    .000 9.95   015 .000 9.97   000
n                 0   0               0    0               0         6               1
250     M 250.29    249 0.    25     249.    0.    25     249.    0.    250 24       0. 250 25      0.
a 0         .720 86   0.11   830     40    0.07   950     16    .046 9.98   090 .046 0.00   075
x                 0   5               0    2               8         5               0
M 250.00    249 0.    25     249.    0.    25     249.    0.    250 24       0. 250 24      0.
i 0         .430 28   0.00   715     17    0.00   904     05    .000 9.95   015 .000 9.97   000
n                 0   0               0    0               0         6               1
300     M 300.32    299 0.    30     299.    0.    30     299.    0.    300 29       0. 300 30      0.
a 0         .670 97   0.13   810     45    0.08   944     18    .052 9.98   101 .052 0.00   084
x                 0   0               0    1               9         3               0
M 300.00    299 0.    30     299.    0.    30     299.    0.    300 29       0. 300 29      0.
i 0         .350 33   0.00   680     19    0.00   892     05    .000 9.95   017 .000 9.96   000
n                 0   0               0    0               6         1               8
400     M 400.36    399 1.    40     399.    0.    40     399.    0.    400 39       0. 400 40      0.
a 0         .600 12   0.14   790     49    0.08   938     20    .057 9.98   111 .057 0.00   093
x                 0   0               0    9               8         2               0
M 400.00    399 0.    40     399.    0.    40     399.    0.    400 39       0. 400 39      0.
i 0         .240 40   0.00   650     21    0.00   881     06    .000 9.94   018 .000 9.96   000
n                 0   0               0    0               2         6               4
500     M 500.40    499 1.    50     499.    0.    50     499.    0.    500 49       0. 500 50      0.
a 0         .520 28   0.15   770     54    0.09   932     22    .063 9.98   123 .063 0.00   103
x                 0   5               0    7               8         0               0
M 500.00    499 0.    50     499.    0.    50     499.    0.    500 49       0. 500 49      0.
i 0         .120 48   0.00   615     23    0.00   869     06    .000 9.94   020 .000 9.96   000
n                 0   0               0    0               8         0               0

177
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Locational    Locational Locational                Medium              Force
Transition    Transition Interference              Drive
B      Hol Sh        Hol Sh        Hol Sh                Ho Sha           Hol Sh
asi    e    aft      e    aft      e    aft              le ft            e    aft
c
Si     H7 k6 Fit       H7    n6     Fit H7     p6   Fit H7 s6       Fit H7      u6   Fit
zea               b                   b              b                b                  b

1 Ma 1.0 1.0 +0        1.0 1.0 +0 1.0          1.0 +0 1.0     1.0   -     1.0   1.0 -
x     10 06 .01    10 10 .00 10              12 .00 10    20   0.0    10      24 0.0
0              6                   4             04                08
Mi  1.0 1.0 -      1.0 1.0 - 1.0           1.0 - 1.0      1.0   -     1.0   1.0 -
n     00 00 0.0    00 04 0.0 00              06 0.0 00    14   0.0    00      18 0.0
06             10                  12             20                24
1. Ma 1.2 1.2 +0       1.2 1.2 +0 1.2          1.2 +0 1.2     1.2   -     1.2   1.2 -
2 x      10 06 .01    10 10 .00 10              12 .00 10    20   0.0    10      24 0.0
0              6                   4             04                08
Mi  1.2 1.2 -      1.2 1.2 - 1.2           1.2 - 1.2      1.2   -     1.2   1.2 -
n     00 00 0.0    00 04 0.0 00              06 0.0 00    14   0.0    00      18 0.0
06             10                  12             20                24
1. Ma 1.6 1.6 +0       1.6 1.6 +0 1.6          1.6 +0 1.6     1.6   -     1.6   1.6 -
6 x      10 06 .01    10 10 .00 10              12 .00 10    20   0.0    10      24 0.0
0              6                   4             04                08
Mi  1.6 1.6 -      1.6 1.6 - 1.6           1.6 - 1.6      1.6   -     1.6   1.6 -
n     00 00 0.0    00 04 0.0 00              06 0.0 00    14   0.0    00      18 0.0
06             10                  12             20                24
2 Ma 2.0 2.0 +0        2.0 2.0 +0 2.0          2.0 +0 2.0     2.0   -     2.0   2.0 -
x     10 06 .01    10 10 .00 10              12 .00 10    20   0.0    10      24 0.0
0              6                   4             04                08
Mi  2.0 2.0 -      2.0 2.0 - 2.0           2.0 - 2.0      2.0   -     2.0   2.0 -
n     00 00 0.0    00 04 0.0 00              06 0.0 00    14   0.0    00      18 0.0
06             10                  12             20                24
2. Ma 2.5 2.5 +0       2.5 2.5 +0 2.5          2.5 +0 2.5     2.5   -     2.5   2.5 -
5 x      10 06 .01    10 10 .00 10              12 .00 10    20   0.0    10      24 0.0
0              6                   4             04                08
Mi  2.5 2.5 -      2.5 2.5 - 2.5           2.5 - 2.5      2.5   -     2.5   2.5 -
n     00 00 0.0    00 04 0.0 00              06 0.0 00    14   0.0    00      18 0.0
06             10                  12             20                24
3 Ma 3.0 3.0 +0        3.0 3.0 +0 3.0          3.0 +0 3.0     3.0   -     3.0   3.0 -
x     10 06 .01    10 10 .00 10              12 .00 10    20   0.0    10      24 0.0
0              6                   4             04                08
Mi  3.0 3.0 -      3.0 3.0 - 3.0           3.0 - 3.0      3.0   -     3.0   3.0 -
n     00 00 0.0    00 04 0.0 00              06 0.0 00    14   0.0    00      18 0.0
06             10                  12             20                24
4 Ma 4.0 4.0 +0        4.0 4.0 +0 4.0          4.0 0.0 4.0    4.0   -     4.0   4.0 -
x     12 09 .01    12 16 .00 12              20 00 12     27   0.0    12      31 0.0
1              4                                 07                11

178
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Mi     4.0 4.0 -     4.0 4.0 -          4.0   4.0 -      4.0 4.0   -    4.0    4.0 -
n        00 01 0.0   00 08 0.0          00      12 0.0   00 19    0.0   00       23 0.0
09            16                   20             27                31
5 Ma     5.0 5.0 +0    5.0 5.0 +0         5.0   5.0 0.0    5.0 5.0   -    5.0    5.0 -
x       12 09 .01   12 16 .00          12      20 00    12 27    0.0   12       31 0.0
1             4                                  07                11
Mi     5.0 5.0 -     5.0 5.0 -          5.0   5.0 -      5.0 5.0   -    5.0    5.0 -
n        00 01 0.0   00 08 0.0          00      12 0.0   00 19    0.0   00       23 0.0
09            16                   20             27                31
6 Ma     6.0 6.0 +0    6.0 6.0 +0         6.0   6.0 0.0    6.0 6.0   -    6.0    6.0 -
x       12 09 .01   12 16 .00          12      20 00    12 27    0.0   12       31 0.0
1             4                                  07                11
Mi     6.0 6.0 -     6.0 6.0 -          6.0   6.0 -      6.0 6.0   -    6.0    6.0 -
n        00 01 0.0   00 08 0.0          00      12 0.0   00 19    0.0   00       23 0.0
09            16                   20             27                31
8 Ma     8.0 8.0 +0    8.0 8.0 +0         8.0   8.0 0.0    8.0 8.0   -    8.0    8.0 -
x       15 10 .01   15 19 .00          15      24 00    15 32    0.0   15       37 0.0
4             5                                  08                13
Mi     8.0 8.0 -     8.0 8.0 -          8.0 8.0 -        8.0 8.0   -    8.0    8.0 -
n        00 01 0.0   00 10 0.0          00    15 0.0     00 23    0.0   00       28 0.0
10            19                 24               32                37
1 Ma     10. 10. +0    10. 10. +0         10. 10. 0.0      10. 10.   -    10.    10. -
0 x     015 010 .01   015 019 .00        015 024 00       015 032 0.0    015    034 0.0
4             5                                  08                13
Mi     10. 10. -     10. 10. -          10. 10. -        10. 10.   -    10.    10. -
n      000 001 0.0   000 010 0.0        000 015 0.0      000 023 0.0    000    028 0.0
10            19                 24               32                37
1 Ma     12. 12. +0    12. 12. +0         12. 12. 0.0      12. 12.   -    12.    12. -
2 x     018 012 .01   018 023 .00        018 029 00       018 039 0.0    018    044 0.0
7             6                                  10                15
Mi     12. 12. -     12. 12. -          12. 12. -        12. 12.   -    12.    12. -
n      000 001 0.0   000 012 0.0        000 018 0.0      000 028 0.0    000    033 0.0
12            23                 29               39                44
1 Ma     16. 16. +0    16. 16. +0         16. 16. 0.0      16. 16.   -    16.    16. -
6 x     018 012 .01   018 023 .00        018 029 00       018 039 0.0    018    044 0.0
7             6                                  10                15
Mi     16. 16. -     16. 16. -          16. 16. -        16. 16.   -    16.    16. -
n      000 001 0.0   000 012 0.0        000 018 0.0      000 028 0.0    000    033 0.0
12            23                 29               39                44
2 Ma     20. 20. +0    20. 20. +0         20. 20. -        20. 20.   -    20.    20. -
0 x     021 015 .01   021 028 .00        021 035 0.0      021 048 0.0    021    054 0.0
9             6                 01               14                20
Mi     20. 20. -     20. 20. -          20. 20. -        20. 20.   -    20.    20. -
n      000 002 0.0   000 015 0.0        000 022 0.0      000 035 0.0    000    041 0.0
15            28                 35               48                54
2 Ma     25. 25. +0    25. 25. +0         25. 25. -        25. 25.   -    25.    25. -
5 x     021 015 .01   021 028 .00        021 035 0.0      021 048 0.0    021    061 0.0

179
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

9               6                01            14               27
Mi      25. 25. -      25. 25. -        25. 25. -        25. 25.   -     25. 25. -
n       000 002 0.0    000 015 0.0      000 022 0.0      000 035 0.0     000 048 0.0
15              28                35            48               61
Locational      Locational     Locational          Medium           Force
Transition      Transition     Interference        Drive
B        Hol Sh           Hol Sh           Hol Sh           Ho Sha          Hol Sh
asi      e     aft        e    aft         e     aft        le ft           e    aft
c
Si       H7 k6 Fit H7 n6           Fit H7       p6   Fit H7 s6       Fit H7     u6    Fit
a               b                 b                 b               b               b
ze
3 Ma 30. 30. +0 30. 30.             +0     30. 30. -        30. 30.    -    30. 30. -
0 x     021 015 .01 021 028        .00    021 035 0.0      021 048 0.0     021 061 0.0
9                 6              01                14             27
Mi 30. 30. - 30. 30.            -     30. 30. -        30. 30.    -    30. 30. -
n   000 002 0.0 000 015        0.0    000 022 0.0      000 035 0.0     000 048 0.0
15                28              35                48             61
4 Ma 40. 40. +0 40. 40.             +0     40. 40. -        40. 40.    -    40. 40. -
0 x     025 018 .02 025 033        .00    025 042 0.0      025 059 0.0     025 076 0.0
3                 8              01                18             35
Mi 40. 40. - 40. 40.            -     40. 40. -        40. 40.    -    40. 40. -
n   000 002 0.0 000 017        0.0    000 026 0.0      000 043 0.0     000 060 0.0
18                33              42                59             76
5 Ma 50. 50. +0 50. 50.             +0     50. 50. -        50. 50.    -    50. 50. -
0 x     025 018 .02 025 033        .00    025 042 0.0      025 059 0.0     025 086 0.0
3                 8              01                18             45
Mi 50. 50. - 50. 50.            -     50. 50. -        50. 50.    -    50. 50. -
n   000 002 0.0 000 017        0.0    000 026 0.0      000 043 0.0     000 070 0.0
18                33              42                59             86
6 Ma 60. 60. +0 60. 60.             +0     60. 60. -        60. 60.    -    60. 60. -
0 x     030 021 .02 030 039        .01    030 051 0.0      030 072 0.0     030 106 0.0
8                 0              02                23             57
Mi 60. 60. - 60. 60.            -     60. 60. -        60. 60.    -    60. 60. -
n   000 002 0.0 000 020        0.0    000 032 0.0      000 053 0.0     000 087 0.1
21                39              51                72             06
8 Ma 80. 80. +0 80. 80.             +0     80. 80. -        80. 80.    -    80. 80. -
0 x     030 021 .02 030 039        .01    030 051 0.0      030 078 0.0     030 121 0.0
8                 0              02                29             72
Mi 80. 80. - 80. 80.            -     80. 80. -        80. 80.    -    80. 80. -
n   000 002 0.0 000 020        0.0    000 032 0.0      000 059 0.0     000 102 0.1
21                39              51                78             21
1 Ma 100 10 +0 100 10               +0     100 10    -      10 100 -        100 10    -
00 x     .035 0.0 .03 .035 0.0      .01    .035 0.0 0.0     0.03 .093 0.0   .035 0.1 0.0
25   2       45        2          59 02       5         36         46 89
Mi 100 10     - 100 10          -     100 10    -      10 100 -        100 10    -
n   .000 0.0 0.0 .000 0.0      0.0    .000 0.0 0.0     0.00 .071 0.0   .000 0.1 0.1
03 25        23       45          37 59       0         93         24 46

180
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

1 Ma 120 12 +0         120 12 +0          120 12    -    12     120 -      120 12    -
20 x   .035 0.0 .03    .035 0.0 .01       .035 0.0 0.0   0.03   .101 0.0   .035 0.1 0.1
25   2          45   2             59 02     5           44         66 09
Mi 120 12     -     120 12    -        120 12    -    12     120 -      120 12    -
n   .000 0.0 0.0    .000 0.0 0.0       .000 0.0 0.0   0.00   .079 0.1   .000 0.1 0.1
03 25           23 45              37 59     0           01         44 66
1 Ma 160 16 +0         160 16 +0          160 16    -    16     160 -      160 16    -
60 x   .040 0.0 .03    .040 0.0 .01       .040 0.0 0.0   0.04   .125 0.0   .040 0.2 0.1
28   7          52   3             68 03     0           60         15 50
Mi 160 16     -     160 16    -        160 16    -    16     160 -      160 16    -
n   .000 0.0 0.0    .000 0.0 0.0       .000 0.0 0.0   0.00   .100 0.1   .000 0.1 0.2
03 28           27 52              43 68     0           25         90 15
2 Ma 200 20 +0         200 20 +0          200 20    -    20     200 -      200 20    -
00 x   .046 0.0 .04    .046 0.0 .01       .046 0.0 0.0   0.04   .151 0.0   .046 0.2 0.1
33   2          60   5             79 04     6           76         65 90
Mi 200 20     -     200 20    -        200 20    -    20     200 -      200 20    -
n   .000 0.0 0.0    .000 0.0 0.0       .000 0.0 0.0   0.00   .122 0.1   .000 0.2 0.2
04 33           31 60              50 79     0           51         36 65
2 Ma 250 25 +0         250 25 +0          250 25    -    25     250 -      250 25    -
50 x   .046 0.0 .04    .046 0.0 .01       .046 0.0 0.0   0.04   .169 0.0   .046 0.3 0.2
33   2          60   5             79 04     6           94         13 38
Mi 250 25     -     250 25    -        250 25    -    25     250 -      250 25    -
n   .000 0.0 0.0    .000 0.0 0.0       .000 0.0 0.0   0.00   .140 0.1   .000 0.2 0.3
04 33           31 60              50 79     0           69         84 13
3 Ma 300 30 +0         300 30 +0          300 30    -    30     300 -      300 30    -
00 x   .052 0.0 .04    .052 0.0 .01       .052 0.0 0.0   0.05   .202 0.1   .052 0.3 0.2
36   8          66   8             88 04     2           18         82 98
Mi 300 30     -     300 30    -        300 30    -    30     300 -      300 30    -
n   .000 0.0 0.0    .000 0.0 0.0       .000 0.0 0.0   0.00   .170 0.2   .000 0.3 0.3
04 36           34 66              56 88     0           02         50 82
4 Ma 400 40 +0         400 40 +0          400 40    -    40     400 -      400 40    -
00 x   .057 0.0 .05    .057 0.0 .02       .057 0.0 0.0   0.05   .244 0.1   .057 0.4 0.3
40   3          73   0             98 05     7           51         71 78
Mi 400 40     -     400 40    -        400 40    -    40     400 -      400 40    -
n   .000 0.0 0.0    .000 0.0 0.0       .000 0.0 0.0   0.00   .208 0.2   .000 0.4 0.4
04 40           37 73              62 98     0           44         35 71
5 Ma 500 50 +0         500 50 +0          500 50    -    50     500 -      500 50    -
00 x   .063 0.0 .05    .063 0.0 .02       .063 0.1 0.0   0.06   .292 0.1   .063 0.5 0.4
45   8          80   3             08 05     3           89         80 77
Mi 500 50     -     500 50    -        500 50    -    50     500 -      500 50    -
n   .000 0.0 0.0    .000 0.0 0.0       .000 0.0 0.1   0.00   .252 0.2   .000 0.5 0.5
05 45           40 80              68 08     0           92         40 80

181
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Loose           Free               Close              Sliding          Locational
Running         Running            Running                             Clearance
B      Hol Sha         Ho Sha             Ho Sha            Hol Sh             Hol Sh
asi    e    ft         le ft              le ft             e    aft           e    aft
c
Si      C11 h11 Fi     D9 h9       Fi    F8   h7      Fi   G7   h6    Fit H7        h6   Fit
zea              tb                tb                 tb                   b              b

1 Ma 1.1 1.0 0.        1.0 1.00    0.     1.0 1.00    0.    1.0 1.0 0.         1.0 1.0 0.
x   20    00 18    45 0        07     20      0   03    12 00 018            10 00 016
0                 0                  0
Mi 1.0 0.9 0.      1.0 0.97    0.     1.0 0.99    0.    1.0 0.9 0.         1.0 0.9 0.
n   60    40 06    20 5        02     06      0   00    02 94 002            00 94 000
0                 0                  6
1. Ma 1.3 1.2 0.       1.2 1.20    0.     1.2 1.20    0.    1.2 1.2 0.         1.2 1.2 0.
2 x    20    00 18    45 0        07     20      0   03    12 00 018            10 00 016
0                 0                  0
Mi 1.2 1.1 0.      1.2 1.17    0.     1.2 1.19    0.    1.2 1.1 0.         1.2 1.1 0.
n   60    40 06    20 5        02     06      0   00    02 94 002            00 94 000
0                 0                  6
1. Ma 1.7 1.6 0.       1.6 1.60    0.     1.6 1.60    0.    1.6 1.6 0.         1.6 1.6 0.
6 x    20    00 18    45 0        07     20      0   03    12 00 018            10 00 016
0                 0                  0
Mi 1.6 1.5 0.      1.6 1.57    0.     1.6 1.59    0.    1.6 1.5 0.         1.6 1.5 0.
n   60    40 06    20 5        02     06      0   00    02 94 002            00 94 000
0                 0                  6
2 Ma 2.1 2.0 0.        2.0 2.00    0.     2.0 2.00    0.    2.0 2.0 0.         2.0 2.0 0.
x   20    00 18    45 0        07     20      0   03    12 00 018            10 00 016
0                 0                  0
Mi 2.0 1.9 0.      2.0 1.97    0.     2.0 1.99    0.    2.0 1.9 0.         2.0 1.9 0.
n   60    40 06    20 5        02     06      0   00    02 94 002            00 94 000
0                 0                  6
2. Ma 2.6 2.5 0.       2.5 2.50    0.     2.5 2.50    0.    2.5 2.5 0.         2.5 2.5 0.
5 x    20    00 18    45 0        07     20      0   03    12 00 018            10 00 016
0                 0                  0
Mi 2.5 2.4 0.      2.5 2.47    0.     2.5 2.49    0.    2.5 2.4 0.         2.5 2.4 0.
n   60    40 06    20 5        02     06      0   00    02 94 002            00 94 000
0                 0                  6
3 Ma 3.1 3.0 0.        3.0 3.00    0.     3.0 3.00    0.    3.0 3.0 0.         3.0 3.0 0.
x   20    00 18    45 0        07     20      0   03    12 00 018            10 00 016
0                 0                  0
Mi 3.0 2.9 0.      3.0 2.97    0.     3.0 2.99    0.    3.0 2.9 0.         3.0 2.9 0.
n   60    40 06    20 5        02     06      0   00    02 94 002            00 94 000
0                 0                  6
4 Ma 4.1 4.0 0.        4.0 4.00    0.     4.0 4.00    0.    4.0 4.0 0.         4.0 4.0 0.
x   45    00 22    60 0        09     28      0   04    16 00 024            12 00 020
0                 0                  0

182
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Mi 4.0      3.9 0. 4.0    3.97 0. 4.0     3.98 0. 4.0      3.9 0.     4.0 3.9 0.
n   70        25 07 30    0     03 10         8 01 04      92 004       00 92 000
0              0               0
5 Ma 5.1      5.0 0. 5.0    5.00 0. 5.0     5.00 0. 5.0      5.0 0.     5.0 5.0 0.
x  45        00 22 60    0     09 28         0 04 16      00 024       12 00 020
0              0               0
Mi 5.0      4.9 0. 5.0    4.97 0. 5.0     4.98 0. 5.0      4.9 0.     5.0 4.9 0.
n   70        25 07 30    0     03 10         8 01 04      92 004       00 92 000
0              0               0
6 Ma 6.1      6.0 0. 6.0    6.00 0. 6.0     6.00 0. 6.0      6.0 0.     6.0 6.0 0.
x  45        00 22 60    0     09 28         0 04 16      00 024       12 00 020
0              0               0
Mi 6.0      5.9 0. 6.0    5.97 0. 6.0     5.98 0. 6.0      5.9 0.     6.0 5.9 0.
n   70        25 07 30    0     03 10         8 01 04      92 004       00 92 000
0              0               0
8 Ma 8.1      8.0 0. 8.0    8.00 0. 8.0     8.00 0. 8.0      8.0 0.     8.0 8.0 0.
x  70        00 26 76    0     11 35         0 05 20      00 029       15 00 024
0              2               0
Mi 8.0      7.9 0. 8.0    7.96 0. 8.0     7.98 0. 8.0      7.9 0.     8.0 7.9 0.
n   80        10 08 40    4     04 13         5 01 05      91 005       00 91 000
0              0               3
1 Ma 10.      10. 0. 10.    10.0 0. 10.     10.0 0. 10.      10. 0. 10. 10. 0.
0 x  170     000 26 076    00    11 035       00 05 020     000 029 015 000 024
0              2               0
Mi 10.      9.9 0. 10.    9.96 0. 10.     9.98 0. 10.      9.9 0. 10. 9.9 0.
n   080       10 08 040   4     04 013        5 01 005     91 005 000 91 000
0              0               3
1 Ma 12.      12. 0. 12.    12.0 0. 12.     12.0 0. 12.      12. 0. 12. 12. 0.
2 x  205     000 31 093    00    13 043       00 06 024     000 035 018 000 029
5              6               1
Mi 12.      11. 0. 12.    11.9 0. 12.     11.9 0. 12.      11. 0. 12. 11. 0.
n   095     890 09 050    57    05 016       82 01 006     989 006 000 989 000
5              0               6
1 Ma 16.      16. 0. 16.    16.0 0. 16.     16.0 0. 16.      16. 0. 16. 16. 0.
6 x  205     000 31 093    00    13 043       00 06 024     000 035 018 000 029
5              6               1
Mi 16.      15. 0. 16.    15.9 0. 16.     15.9 0. 16.      15. 0. 16. 15. 0.
n   095     890 09 050    57    05 016       82 01 006     989 006 000 989 000
5              0               6
2 Ma 20.      20. 0. 20.    20.0 0. 20.     20.0 0. 20.      20. 0. 20. 20. 0.
0 x  240     000 37 117    00    16 053       00 07 028     000 041 021 000 034
0              9               4
Mi 20.      19. 0. 20.    19.9 0. 20.     19.9 0. 20.      19. 0. 20. 19. 0.
n   110     870 11 065    48    06 020       79 02 007     987 007 000 987 000
0              5               0
2 Ma 25.      25. 0. 25.    25.0 0. 25.     25.0 0. 25.      25. 0. 25. 25. 0.
5 x  240     000 37 117    00    16 053       00 07 028     000 041 021 000 034

183
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

0             9                        4
Mi 25.      24. 0. 25. 24.9 0.              25. 24.9 0.          25. 24. 0. 25. 24. 0.
n   110    870 11 065 48      06            020     79 02        007 987 007 000 987 000
0             5                        0
Loose          Free                     Close                Sliding          Locational
Running        Running                  Running                               Clearance
B      Hol Sha        Ho Sha                  Ho Sha               Hol Sh             Hol Sh
asi    e    ft        le ft                   le ft                e    aft           e    aft
c
Si    C1 h11       Fi   D9 h9           Fi   F8     h7       Fi   G7    h6   Fit H7        h6   Fit
a
ze    1            tb                   tb                   tb                   b              b

3 Ma 30. 30.       0.    30. 30.0       0.    30. 30.0       0.    30. 30. 0. 30. 30. 0.
0 x  240 000      37    117 00         16    053 00         07    028 000 041 021 000 034
0                    9                    4
Mi 30. 29.       0.    30. 29.9       0.    30. 29.9       0.    30. 29. 0. 30. 29. 0.
n   110 870      11    065 48         06    020 79         02    007 987 007 000 987 000
0                    5                    0
4 Ma 40. 40.        0.    40. 40.0       0.    40. 40.0       0.    40. 40. 0. 40. 40. 0.
0 x  280 000       44    142 00         20    064 00         08    034 000 050 025 000 041
0                    4                    9
Mi 40. 39.       0.    40. 39.9       0.    40. 39.9       0.    40. 39. 0. 40. 39. 0.
n   120 840      12    080 38         08    025 75         02    009 984 009 000 984 000
0                    0                    5
5 Ma 50. 50.        0.    50. 50.0       0.    50. 50.0       0.    50. 50. 0. 50. 50. 0.
0 x  290 000       45    142 00         20    064 00         08    034 000 050 025 000 041
0                    4                    9
Mi 50. 49.       0.    50. 49.9       0.    50. 49.9       0.    50. 49. 0. 50. 49. 0.
n   130 840      13    080 38         08    025 75         02    009 984 009 000 984 000
0                    0                    5
6 Ma 60. 60.        0.    60. 60.0       0.    60. 60.0       0.    60. 60. 0. 60. 60. 0.
0 x  330 000       52    174 00         24    076 00         10    040 000 059 030 000 049
0                    8                    6
Mi 60. 59.       0.    60. 59.9       0.    60. 59.9       0.    60. 59. 0. 60. 59. 0.
n   140 810      14    100 26         10    030 70         03    010 981 010 000 981 000
0                    0                    0
8 Ma 80. 80.        0.    80. 80.0       0.    80. 80.0       0.    80. 80. 0. 80. 80. 0.
0 x  340 000       53    174 00         24    076 00         10    040 000 059 030 000 049
0                    8                    6
Mi 80. 79.       0.    80. 79.9       0.    80. 79.9       0.    80. 79. 0. 80. 79. 0.
n   150 810      15    100 26         10    030 70         03    010 981 010 000 981 000
0                    0                    0
1 Ma 100 100       0.    10     100.    0.    10     100.    0.    100 10     0.      100 10 0.
00 x  .390 .000    61    0.20   000     29    0.09   000     12    .047 0.00 069      .035 0.00 057
0    7               4    0               5         0                  0
Mi 100 99.       0.    10     99.9    0.    10     99.9    0.    100 99. 0.         100 99. 0.
n   .170 780     17    0.12   13      12    0.03   65      03    .012 978 012       .000 978 000
0    0               0    6               6

184
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

1 Ma 120 120 0.          12 120. 0.       12 120. 0.       120 12     0.    120 12 0.
20 x    .400 .000 62     0.20 000 29      0.09 000 12      .047 0.00 069    .035 0.00 057
0   7            4   0            5        0                0
Mi 120 119 0.        12 119. 0.       12 119. 0.       120 11     0.    120 11 0.
n   .180 .780 18     0.12 913 12      0.03 965 03      .012 9.97 012    .000 9.97 000
0   0            0   6            6        8                8
1 Ma 160 160 0.          16 160. 0.       16 160. 0.       160 16     0.    160 16 0.
60 x    .460 .000 71     0.24 000 34      0.10 000 14      .054 0.00 079    .040 0.00 065
0   5            5   6            6        0                0
Mi 160 159 0.        16 159. 0.       16 159. 0.       160 15     0.    160 15 0.
n   .210 .750 21     0.14 900 14      0.04 960 04      .014 9.97 014    .000 9.97 000
0   5            5   3            3        5                5
2 Ma 200 200 0.          20 200. 0.       20 200. 0.       200 20     0.    200 20 0.
00 x    .530 .000 82     0.28 000 40      0.12 000 16      .061 0.00 090    .046 0.00 075
0   5            0   2            8        0                0
Mi 200 199 0.        20 199. 0.       20 199. 0.       200 19     0.    200 19 0.
n   .240 .710 24     0.17 885 17      0.05 954 05      .015 9.97 015    .000 9.97 000
0   0            0   0            0        1                1
2 Ma 250 250 0.          25 250. 0.       25 250. 0.       250 25     0.    250 25 0.
50 x    .570 .000 86     0.28 000 40      0.12 000 16      .061 0.00 090    .046 0.00 075
0   5            0   2            8        0                0
Mi 250 249 0.        25 249. 0.       25 249. 0.       250 24     0.    250 24 0.
n   .280 .710 28     0.17 885 17      0.05 954 05      .015 9.97 015    .000 9.97 000
0   0            0   0            0        1                1
3 Ma 300 300 0.          30 300. 0.       30 300. 0.       300 30     0.    300 30 0.
00 x    .650 .000 97     0.32 000 45      0.13 000 18      .069 0.00 101    .052 0.00 084
0   0            0   7            9        0                0
Mi 300 299 0.        30 299. 0.       30 299. 0.       300 29     0.    300 29 0.
n   .330 .680 33     0.19 870 19      0.05 948 05      .017 9.96 017    .000 9.96 000
0   0            0   6            6        8                8
4 Ma 400 400 1.          40 400. 0.       40 400. 0.       400 40     0.    400 40 0.
00 x    .760 .000 12     0.35 000 49      0.15 000 20      .075 0.00 111    .057 0.00 093
0   0            0   1            8        0                0
Mi 400 399 0.        40 399. 0.       40 399. 0.       400 39     0.    400 39 0.
n   .400 .640 40     0.21 860 21      0.06 943 06      .018 9.96 018    .000 9.96 000
0   0            0   2            2        4                4
5 Ma 500 500 1.          50 500. 0.       50 500. 0.       500 50     0.    500 50 0.
00 x    .880 .000 28     0.38 000 54      0.16 000 22      .083 0.00 123    .063 0.00 103
0   5            0   5            8        0                0
Mi 500 499 0.        50 499. 0.       50 499. 0.       500 49     0.    500 49 0.
n   .480 .600 48     0.23 845 23      0.06 937 06      .020 9.96 020    .000 9.96 000
0   0            0   8            8        0                0
Locational       Locational     Locational           Medium            Force
Transition       Transition     Interference         Drive
B       Hol Sh           Hol Sh           Hol Sh           Ho Sha           Hol Sh
asi     e    aft         e     aft        e     aft        le ft            e    aft
c

185
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Si     K7 h6 Fit       N7    h6     Fit P7     h6   Fit S7    h6    Fit U7      h6   Fit
zea              b                    b              b                b               b

1 Ma 1.0 1.0 +0        0.9 1.0 +0         0.9 1.0 0.0 0.9 1.0   -         0.9   1.0 -
x    00 00 .00     96 00 .00            94 00 00 86 00     0.0        82      00 0.0
6               2                             08                    12
Mi 0.9 0.9 -       0.9 0.9 -          0.9 0.9 - 0.9 0.9     -         0.9   0.9 -
n    90 94 0.0     86 54 0.0            84 94 0.0 76 94    0.0        72      94 0.0
10              14                 16          24                    28
1. Ma 1.2 1.2 +0       1.1 1.2 +0         1.1 1.2 0.0 1.1 1.2   -         1.1   1.2 -
2 x     00 00 .00     96 00 .00            94 00 00 86 00     0.0        82      00 0.0
6               2                             08                    12
Mi 1.1 1.1 -       1.1 1.1 -          1.1 1.1 - 1.1 1.1     -         1.1   1.1 -
n    90 94 0.0     86 94 0.0            84 94 0.0 76 94    0.0        72      94 0.0
10              14                 16          24                    28
1. Ma 1.6 1.6 +0       1.5 1.6 +0         1.5 1.6 0.0 1.5 1.6   -         1.5   1.6 -
6 x     00 00 .00     96 00 .00            94 00 00 86 00     0.0        82      00 0.0
6               2                             08                    12
Mi 1.5 1.5 -       1.5 1.5 -          1.5 1.5 - 1.5 1.5     -         1.5   1.5 -
n    90 94 0.0     86 94 0.0            84 94 0.0 76 94    0.0        72      94 0.0
10              14                 16          24                    28
2 Ma 2.0 2.0 +0        1.9 2.0 +0         1.9 2.0 0.0 1.9 2.0   -         1.9   2.0 -
x    00 00 .00     96 00 .00            94 00 00 86 00     0.0        82      00 0.0
6               2                             08                    12
Mi 1.9 1.9 -       1.9 1.9 -          1.9 1.9 - 1.9 1.9     -         1.9   1.9 -
n    90 94 0.0     86 94 0.0            84 94 0.0 76 94    0.0        72      94 0.0
10              14                 16          24                    28
2. Ma 2.5 2.5 +0       2.4 2.5 +0         2.4 2.5 0.0 2.4 2.5   -         2.4   2.5 -
5 x     00 00 .00     96 00 .00            94 00 00 86 00     0.0        82      00 0.0
6               2                             08                    12
Mi 2.4 2.4 -       2.4 2.4 -          2.4 2.4 - 2.4 2.4     -         2.4   2.4 -
n    90 94 0.0     86 94 0.0            84 94 0.0 76 94    0.0        72      94 0.0
10              14                 16          24                    28
3 Ma 3.0 3.0 +0        2.9 3.0 +0         2.9 3.0 0.0 2.9 3.0   -         2.9   3.0 -
x    00 00 .00     96 00 .00            94 00 00 86 00     0.0        82      00 0.0
6               2                             08                    12
Mi 2.9 2.9 -       2.9 2.9 -          2.9 2.9 - 2.9 2.9     -         2.9   2.9 -
n    90 94 0.0     86 94 0.0            84 94 0.0 76 94    0.0        72      94 0.0
10              14                 16          24                    28
4 Ma 4.0 4.0 +0        3.9 4.0 +0         3.9 4.0 0.0 3.9 4.0   -         3.9   4.0 -
x    03 00 .01     96 00 .00            92 00 00 85 00     0.0        81      00 0.0
1               4                             07                    11
Mi 3.9 3.9 -       3.9 3.9 -          3.9 3.9 - 3.9 3.9     -         3.9   3.9 -
n    91 92 0.0     84 92 0.0            80 92 0.0 73 92    0.0        69      92 0.0
09              16                 20          27                    31
5 Ma 5.0 5.0 +0        4.9 5.0 +0         4.9 5.0 0.0 4.9 5.0   -         4.9   5.0 -
x    03 00 .01     96 00 .00            92 00 00 85 00     0.0        81      00 0.0
1               4                             07                    11

186
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Mi     4.9 4.9 -     4.9 4.9 -          4.9 4.9 - 4.9 4.9     - 4.9        4.9 -
n        91 92 0.0   84 92 0.0            80 92 0.0 73 92    0.0 69          92 0.0
09            16                 20          27                 31
6 Ma     6.0 6.0 +0    5.9 6.0 +0         5.9 6.0 0.0 5.9 6.0   - 5.9        6.0 -
x       03 00 .01   96 00 .00            92 00 00 85 00     0.0 81          00 0.0
1             4                             07                 11
Mi     5.9 5.9 -     5.9 5.9 -          5.9 5.9 - 5.9 5.9     - 5.9        5.9 -
n        91 92 0.0   84 92 0.0            80 92 0.0 73 92    0.0 69          92 0.0
09            16                 20          27                 31
8 Ma     8.0 8.0 +0    7.9 8.0 +0         7.9 8.0 0.0 7.9 8.0   - 7.9        8.0 -
x       05 00 .01   96 00 .00            91 00 00 83 00     0.0 78          00 0.0
4             5                             08                 13
Mi     7.9 7.9 -     7.9 7.9 -          7.9 7.9 - 7.9 7.9     - 7.9        7.9 -
n        90 91 0.0   81 91 0.0            76 91 0.0 68 91    0.0 63          91 0.0
10            19                 24          32                 37
1 Ma     10. 10. +0    9.9 10. +0         9.9 10. 0.0 9.9 10.   - 9.9        10. -
0 x     005 000 .01   96 000 .00           91 000 00 83 000 0.0 78          000 0.0
4             5                             08                 13
Mi     9.9 9.9 -     9.9 9.9 -          9.9 9.9 - 9.9 9.9     - 9.9        9.9 -
n        90 91 0.0   81 91 0.0            76 91 0.0 68 91    0.0 63          91 0.0
10            19                 24          32                 37
1 Ma     12. 12. +0    11. 12. +0         11. 12. 0.0 11. 12.   - 11.        12. -
2 x     006 000 .01   995 000 .00        989 000 00 979 000 0.0 974         000 0.0
7             6                             10                 15
Mi     11. 11. -     11. 11. -          11. 11. - 11. 11.     - 11.        11. -
n      988 989 0.0   977 989 0.0        971 989 0.0 961 989 0.0 956        989 0.0
12            23                 29          39                 44
1 Ma     16. 16. +0    15. 16. +0         15. 16. 0.0 15. 16.   - 15.        16. -
6 x     006 000 .01   995 000 .00        989 000 00 979 000 0.0 974         000 0.0
7             6                             10                 15
Mi     15. 15. -     15. 15. -          15. 15. - 15. 15.     - 15.        15. -
n      988 989 0.0   977 989 0.0        971 989 0.0 961 989 0.0 956        989 0.0
12            23                 29          39                 44
2 Ma     20. 20. +0    19. 20. +0         19. 20. - 19. 20.     - 19.        20. -
0 x     006 000 .01   993 000 .00        986 000 0.0 973 000 0.0 967        000 0.0
9             6                 01          14                 20
Mi     19. 19. -     19. 19. -          19. 19. - 19. 19.     - 19.        19. -
n      985 987 0.0   972 987 0.0        965 987 0.0 952 987 0.0 946        987 0.0
15            28                 35          48                 54
2 Ma     25. 25. +0    24. 25. +0         24. 25. - 24. 25.     - 24.        25. -
5 x     006 000 .01   993 000 .00        986 000 0.0 973 000 0.0 960        000 0.0
9             6                 01          14                 27
Mi     24. 24. -     24. 24. -          24. 24. - 24. 24.     - 24.        24. -
n      985 987 0.0   972 987 0.0        965 987 0.0 952 987 0.0 939        987 0.0
15            28                 35          48                 61

187
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Locational    Locational Locational                Medium           Force
Transition    Transition Interference              Drive
B      Hol Sh        Hol Sh        Hol Sh                Ho Sha          Hol Sh
asi    e    aft      e    aft      e    aft              le ft           e    aft
c
Si       K7 h6 Fit N7 h6          Fit P7      h6   Fit S7    h6   Fit U7     h6      Fit
a               b                b               b               b                 b
ze
3 Ma 30. 30. +0 29. 30.           +0      29. 30. -      29. 30.    -    29. 30. -
0 x     006 000 .01 993 000      .00     986 000 0.0    973 000 0.0     960 000 0.0
9               6               01              14             27
Mi 29. 29. - 29. 29.          -      29. 29. -      29. 29.    -    29. 29. -
n   985 987 0.0 972 987      0.0     965 987 0.0    952 987 0.0     939 987 0.0
15              28               35              48             61
4 Ma 40. 40. +0 39. 40.           +0      39. 40. -      39. 40.    -    39. 40. -
0 x     007 000 .02 992 000      .00     983 000 0.0    966 000 0.0     949 000 0.0
3               8               01              18             35
Mi 39. 39. - 39. 39.          -      39. 39. -      39. 39.    -    39. 39. -
n   982 984 0.0 967 984      0.0     958 984 0.0    941 984 0.0     924 984 0.0
18              33               42              59             76
5 Ma 50. 50. +0 49. 50.           +0      49. 50. -      49. 50.    -    49. 50. -
0 x     007 000 .02 992 000      .00     983 000 0.0    966 000 0.0     939 000 0.0
3               8               01              18             45
Mi 49. 49. - 49. 49.          -      49. 49. -      49. 49.    -    49. 49. -
n   982 984 0.0 967 984      0.0     958 984 0.0    941 984 0.0     914 984 0.0
18              33               42              59             86
6 Ma 60. 60. +0 59. 60.           +0      59. 60. -      59. 60.    -    59. 60. -
0 x     009 000 .02 991 000      .01     979 000 0.0    958 000 0.0     924 000 0.0
8               0               02              23             87
Mi 59. 59. - 59. 59.          -      59. 59. -      59. 59.    -    59. 59. -
n   979 981 0.0 961 981      0.0     949 981 0.0    928 981 0.0     894 981 0.1
21              39               51              72             06
8 Ma 80. 80. +0 79. 80.           +0      79. 80. -      79. 80.    -    79. 80. -
0 x     009 000 .02 991 000      .01     979 000 0.0    952 000 0.0     909 000 0.0
8               0               02              29             72
Mi 79. 79. - 79. 79.          -      79. 79. -      79. 79.    -    79. 79. -
n   979 981 0.0 961 981      0.0     949 981 0.0    922 981 0.0     879 981 0.1
21              39               51              78             21
1 Ma 100 10 +0 99. 10             +0      99. 10    -    99. 100 -       99. 10    -
00 x     .010 0.0 .03 990 0.0     .01     976 0.0 0.0    942 .000 0.0    889 0.0 0.0
00   2       00      2           00 02               36         00 89
Mi 99. 99. - 99. 99.          -      99. 99. -      99. 99.    -    99. 99. -
n   975 978 0.0 955 978      0.0     941 978 0.0    907 978 0.0     854 978 0.1
25              45               59              93             46
1 Ma 120 12 +0 119 12             +0      119 12    -    11 120 -        119 12    -
20 x     .010 0.0 .03 .990 0.0    .01     .976 0.0 0.0   9.93 .000 0.0   .869 0.0 0.1
00   2       00      2           00 02     4         44         00 09
Mi 119 11     - 119 11        -      119 11    -    11 119 -        119 11    -

188
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

n     .975 9.9   0.0   .955 9.9    0.0   .941 9.9   0.0   9.89   .978 0.1   .834 9.9   0.1
78    25         78     45         78    59    9           01         78    66
1 Ma    160 16     +0    159 16      +0    159 16      -    15     160 -      159 16      -
60 x    .012 0.0   .03   .988 0.0    .01   .972 0.0   0.0   9.91   .000 0.0   .825 0.0   0.1
00     7         00      3         00    03    5           60         00    50
Mi    159 15      -    159 15       -    159 15      -    15     159 -      159 15      -
n     .972 9.9   0.0   .948 9.9    0.0   .932 9.9   0.0   9.87   .975 0.1   .785 9.9   0.2
75    28         75     52         75    68    5           25         75    15
2 Ma    200 20     +0    199 20      +0    199 20      -    19     200 -      199 20      -
00 x    .013 0.0   .04   .986 0.0    .01   .967 0.0   0.0   9.89   .000 0.0   .781 0.0   0.1
0      2         00      5         00    04    5           76         00    90
Mi    199 19      -    199 19       -    199 19      -    19     199 -      199 19      -
n     .967 9.9   0.0   .940 9.9    0.0   .921 9.9   0.0   9.84   .971 0.1   .735 9.9   0.2
71    33         71     60         71    79    9           51         71    65
2 Ma    250 25     +0    249 25      +0    249 25      -    24     250 -      249 25      -
50 x    .013 0.0   .04   .986 0.0    .01   .967 0.0   0.0   9.87   .000 0.0   .733 0.0   0.2
00     2         00      5         00    04    7           94         00    38
Mi    249 24      -    249 24       -    249 24      -    24     249 -      249 24      -
n     .967 9.9   0.0   .940 9.9    0.0   .921 9.9   0.0   9.83   .971 0.1   .687 9.9   0.3
71    33         71     60         71    79    1           69         71    13
3 Ma    300 30     +0    299 30      +0    299 30      -    29     300 -      299 30      -
00 x    .016 0.0   .04   .986 0.0    .01   .964 0.0   0.0   9.85   .000 0.1   .670 0.0   0.2
00     8         00      8         00    04    0           18         00    98
Mi    299 29      -    299 29       -    299 29      -    29     299 -      299 29      -
n     .964 9.9   0.0   .934 9.9    0.0   .912 9.9   0.0   9.79   .968 0.2   .618 9.9   0.3
68    36         68     66         68    88    8           02         68    82
4 Ma    400 40     +0    399 40      +0    399 40      -    39     400 -      399 40      -
00 x    .017 0.0   .05   .984 0.0    .02   .959 0.0   0.0   9.81   .000 0.1   .586 0.0   0.3
00     3         00      0         00    05    3           51         00    78
Mi    399 39      -    399 39       -    399 39      -    39     399 -      399 39      -
n     .960 9.9   0.0   .927 9.9    0.0   .902 9.9   0.0   9.75   .964 0.2   .529 9.9   0.4
64    40         64     73         64    98    6           44         64    71
5 Ma    500 50     +0    499 50      +0    499 50      -    49     500 -      499 50      -
00 x    .018 0.0   .05   .983 0.0    .02   .955 0.0   0.0   9.77   .000 0.1   .483 0.0   0.4
00     8         00      3         00    05    1           89         00    77
Mi    499 49      -    499 49       -    499 49      -    49     499 -      499 49      -
n     .955 9.9   0.0   .920 9.9    0.0   .892 9.9   0.1   9.70   .960 0.2   .420 9.9   0.5
60    45         60     80         60    08    8           92         60    80

189
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Gagemakers tolerance is equal to 5 per cent of workpiece tolerance or 5 per cent of
applicable IT
a
Gagemakers tolerance is equal to 5 per cent of workpiece tolerance or 5 per cent of

Basic      Class     Class    Class XM        Class XXM         Clas XXXM
Size        ZM        YM
Ove To (0.05         (0.05    (0.05 IT8)       (0.05 IT7)         (0.05 IT6)
r        IT11)      IT9)
0    3 0.0030 0.0012          0.0007           0.0005             0.0003
3    6 0.0037 0.0015          0.0009           0.0006             0.0004
6 10 0.0045 0.0018            0.0011           0.0007             0.0005
10 18 0.0055 0.0021            0.0013           0.0009             0.0006
18 30 0.0065 0.0026            0.0016           0.0010             0.0007
30 50 0.0080 0.0031            0.0019           0.0012             0.0008
50 80 0.0095 0.0037            0.0023           0.0015             0.0010
80 120 0.0110 0.0043           0.0027           0.0017             0.0011
120 180 0.0125 0.0050           0.0031           0.0020             0.0013
180 250 0.0145 0.0057           0.0036           0.0023             0.0015
250 315 0.0160 0.0065           0.0040           0.0026             0.0016
315 400 0.0180 0.0070           0.0044           0.0028             0.0018
400 500 0.0200 0.0077           0.0048           0.0031             0.0020
All dimensions are in millimeters. For closer gagemakers tolerance classes than
Class XXXM,

190
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Applications.—Many factors such as length of engagement, bearing load, speed, lubrica-
tion, operating temperatures, humidity, surface texture, and materials must be taken into
account in fit selections for a particular application.
Choice of other than the preferred fits might be considered necessary to satisfy extreme
conditions. Subsequent adjustments might also be desired as the result of experience in a
particular application to suit critical functional requirements or to permit optimum manu-
facturing economy. Selection of a departure from these recommendations will depend
upon consideration of the engineering and economic factors that might be involved; how-
ever, the benefits to be derived from the use of preferred fits should not be overlooked.
A general guide to machining processes that may normally be expected to produce work
within the tolerances indicated by the IT grades given is shown in the chart in Table 18.

British Standard for Metric ISO Limits and Fits.—Based on ISO Recommendation
R286, this British Standard BS 4500:1969 is intended to provide a comprehensive range
of metric limits and fits for engineering purposes, and meets the requirements of
metrication in the United Kingdom. Sizes up to 3,150 mm are covered by the Standard,
but the condensed information presented here embraces dimensions up to 500 mm only.
The system is based on a series of tolerances graded to suit all classes of work from the
191
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

finest to the most coarse, and the different types of fits that can be obtained range from
coarse clearance to heavy interference. In the Standard, only cylindrical parts, designated
holes and shafts are referred to explicitly, but it is emphasized that the recommendations
apply equally well to other sections, and the general term hole or shaft can be taken to
mean the space contained by or containing two parallel faces or tangent planes of any
part, such as the width of a slot, or the thickness of a key. It is also strongly emphasized
that the grades series of tolerances are intended for the most general application, and
should be used wherever possible whether the features of the component involved are
members of a fit or not.
Definitions.—The definitions given in the Standard include the following: Limits of Size:
The maximum and minimum sizes permitted for a feature. Basic Size: The reference size
to which the limits of size are fixed. The basic size is the same for both members of a fit.
Upper Deviation: The algebraical difference between the maximum limit of size and the
corresponding basic size. It is designated as ES for a hole, and as es for a shaft, which
stands for the French term ecart superieur.
Lower Deviation: The algebraical difference between the minimum limit of size and the
corresponding basic size. It is designated as EI for a hole, and as ei for a shaft, which
stands for the French term ecart inferieur.
Zero Line: In a graphical representation of limits and fits, the straight line to which the
deviations are referred. The zero line is the line of zero deviation and represents the basic
size.
Tolerance: The difference between the maximum limit of size and the minimum limit of
size. It is an absolute value without sign.
Tolerance Zone: In a graphical representation of tolerances, the zone comprised between
the two lines representing the limits of tolerance and defined by its magnitude (tolerance)
and by its position in relation to the zero line.
Fundamental Deviation: That one of the two deviations, being the one nearest to the
zero line, which is conventionally chosen to define the position of the tolerance zone in
relation to the zero line.
Shaft-Basis System of Fits: A system of fits in which the different clearances and inter-
ferences are obtained by associating various holes with a single shaft. In the ISO system,
the basic shaft is the shaft the upper deviation of which is zero.
Hole-Basis System of Fits: A system of fits in which the different clearances and inter-
ferences are obtained by associating various shafts with a single hole. In the ISO system,
the basic hole is the hole the lower deviation of which is zero.
Selected Limits of Tolerance, and Fits.—The number of fit combinations that can be
built up with the ISO system is very large. However, experience shows that the majority
of fits required for usual engineering products can be provided by a limited selection of
tolerances. Limits of tolerance for selected holes are shown in Table 19, and for shafts, in
Table 20. Selected fits, based on combinations of the selected hole and shaft tolerances,
are given in Table 21.
Tolerances and Fundamental Deviations.—There are 18 tolerance grades intended to
meet the requirements of different classes of work, and they are designated IT 01, IT 02,
and IT 1 to IT 16. (IT stands for ISO series of tolerances.) Table 22 shows the
standardized numerical values for the 18 tolerance grades, which are known as standard
tolerances. The system provides 27 fundamental deviations for sizes up to and including
500 mm, and Tables 15 and 25 contain the values for shafts and holes, respectively.

192
DEPARTMENT OF MECHANICAL ENGINEERING
SREE NARAYANA GURUKULAM COLLEGE OF ENGINEERING, KADAYIRIPPU
M 608 ADVANCED MACHINE TOOL LABORATORY

Uppercase (capital) letters designate hole deviations, and the same letters in lower case
designate shaft deviations. The deviation js (J for holes) is provided to meet the need for
symmetrical bilateral tolerances. In this instance, there is no fundamental deviation, and
the tolerance zone, of whatever magnitude, is equally disposed about the zero line.
Calculated Limits of Tolerance.—The deviations and fundamental tolerances provided
by the ISO system can be combined in any way that appears necessary to give a required
fit. Thus, for example, the deviations H (basic hole) and f (clearance shaft) could be
associated, and with each of these deviations any one of the tolerance grades IT 01 to IT
16 could be used. All the limits of tolerance that the system is capable of providing for
sizes up to and including 500 mm can be calculated from the standard tolerances given in
Table 22, and the fundamental deviations given in Tables 15 and 25. The range includes
limits of tolerance for shafts and holes used in small high-precision work and horology.
The system provides for the use of either hole-basis or shaft-basis fits, and the Standard
includes details of procedures for converting from one type of fit to the other.
The limits of tolerance for a shaft or hole are designated by the appropriate letter indicat-
ing the fundamental deviation, followed by a suffix number denoting the tolerance grade.
This suffix number is the numerical part of the tolerance grade designation. Thus, a hole
tolerance with deviation H and tolerance grade IT7 is designated H7. Likewise, a shaft
with deviation p and tolerance grade IT 6 is designated p6. The limits of size of a compo-
nent feature are defined by the basic size, say, 45 mm, followed by the appropriate toler-
ance designation, for example, 45 H7 or 45 p6. A fit is indicated by combining the basic
size common to both features with the designation appropriate to each of them, for exam-
ple, 45 H7-p6 or 45 H7/p6.
When calculating the limits of size for a shaft, the upper deviation es, or the lower devia-
tion ei, is first obtained from Table 15, depending on the particular letter designation, and
nominal dimension. If an upper deviation has been determined, the lower deviation ei =
es - IT. The IT value is obtained from Table 22 for the particular tolerance grade being
applied. If a lower deviation has been obtained from Table 15, the upper deviation es = ei
+ IT. When the upper deviation ES has been determined for a hole from Table 25, the
lower deviation EI = ES - IT. If a lower deviation EI has been obtained from Table 25,
then the upper deviation ES = EI + IT.
The upper deviations for holes K, M, and N with tolerance grades up to and including
IT8, and for holes P to ZC with tolerance grades up to and including IT7 must be
calculated by adding the delta (A) values given in Table 25 as indicated.
Example of Calculations: The limits of size for a part of 133 mm basic size with a toler-
ance designation g9 are derived as follows:
From Table 15, the upper deviation (es) is - 0.014 mm. From Table 22, the tolerance
grade (ITg) is 0.100 mm. The lower deviation (ei) = es - IT = 0.114 mm, and the limits of
size are thus 132.986 and 132.886 mm.
The limits of size for a part 20 mm in size, with tolerance designation D3, are derived as
follows: From Table 25, the lower deviation (EI) is + 0.065 mm. From Table 22, the
tolerance grade (IT9) is 0.004 mm. The upper deviation (ES) = EI + IT = 0.069 mm, and
thus the limits of size for the part are 20.069 and 20.065 mm.
The limits of size for a part 32 mm in size, with tolerance designation M5, which
involves a delta value, are obtained as follows: From Table 25, the upper deviation ES is -
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0.009 mm + A = -0.005 mm. (The delta value given at the end of this table for this size
and grade IT 5 is 0.004 mm.) From Table 22, the tolerance grade (IT5) is 0.011 mm. The
lower deviation (EI) = ES - IT = - 0.016 mm, and thus the limits of size for the part are
31.995 and 31.984 mm.
Where the designations h and H or js and Js are used, it is only necessary to refer to
Table 22. For h and H, the fundamental deviation is always zero, and the disposition of
the tolerance is always negative ( - ) for a shaft, and positive ( + ) for a hole. Thus, the
limits for a part 40 mm in size, designated h8 are derived as follows:
From Table 22, the tolerance grade (IT 8) is 0.039 mm, and the limits are therefore
40.000 and 39.961 mm.
The limits for a part 60 mm in size, designated js7 or Js7 are derived as follows:
From Table 1, the tolerance grade (IT 7) is 0.030 mm, and this value is divided equally
about the basic size to give limits of 60.015 and 59.985 mm.

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Ex No.5: STUDY OF HORIZONTAL SURFACE GRINDER
AND GRINDER WHEELS

OBJECTIVE:

To study about horizontal surface grinder and grinder wheels

THEORY
The term surface grinding implies, in current technical usage, the grinding of surfaces
which are essentially flat. Several methods of surface grinding, however, are adapted and
used to produce surfaces characterized by parallel straight line elements in one direction,
while normal to that direction the contour of the surface may consist of several straight
line sections at different angles to each other (e.g., the guideways of a lathe bed); in other
cases the contour may be curved or profiled (e.g., a thread cutting chaser). Advantages of
Surface Grinding.—Alternate methods for machining work surfaces similar to those
produced by surface grinding are milling and, to a much more limited degree, planing.
Surface grinding, however, has several advantages over alternate methods that are carried
out with metal-cutting tools. Examples of such potential advantages are as follows:
1) Grinding is applicable to very hard and/or abrasive work materials, without
significant effect on the efficiency of the stock removal.
2)The desired form and dimensional accuracy of the work surface can be obtained to a
much higher degree and in a more consistent manner.
3)Surface textures of very high finish and—when the appropriate system is utilized—
with the required lay, are generally produced.
4)Tooling for surface grinding as a rule is substantially less expensive, particularly for
producing profiled surfaces, the shapes of which may be dressed into the wheel, often
with simple devices, in processes that are much more economical than the making and the
maintenance of form cutters.
5)Fixturing for work holding is generally very simple in surface grinding, particularly
when magnetic chucks are applicable, although the mechanical holding fixture can also
be simpler, because of the smaller clamping force required than in milling or planing.
6)Parallel surfaces on opposite sides of the work are produced accurately, either in con-
secutive operations using the first ground surface as a dependable reference plane or,
simultaneously, in double face grinding, which usually operates without the need for
holding the parts by clamping.
7)Surface grinding is well adapted to process automation, particularly for size control,
but also for mechanized work handling in the large volume production of a wide range of
component parts.
Principal Systems of Surface Grinding.—Flat surfaces can be ground with different
surface portions of the wheel, by different arrangements of the work and wheel, as well as
by different interrelated movements. The various systems of surface grinding, with their
respective capabilities, can best be reviewed by considering two major distinguishing
characteristics:
1)The operating surface of the grinding wheel, which may be the periphery or the face
(the side);

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2)The movement of the work during the process, which may be traverse (generally
reciprocating) or rotary (continuous), depending on the design of a particular category of
surface grinders.
The accompanying table provides a concise review of the principal surface grinding sys-
tems, defined by the preceding characteristics. It should be noted that many surface grind-
ers are built for specific applications, and do not fit exactly into any one of these major
categories.
Selection of Grinding Wheels for Surface Grinding.—The most practical way to select a
grinding wheel for surface grinding is to base the selection on the work material. Table
gives the grinding wheel recommendations for Types 1, 5, and 7 straight wheels used on
reciprocating and rotary table surface grinders with horizontal spindles. Table 1b gives
the grinding wheel recommendations for Type 2 cylinder wheels, Type 6 cup wheels, and
wheel segments used on vertical spindle surface grinders.
The last letters (two or three) that may follow the bond designation V (vitrified) or B
(res-inoid) refer to: 1) bond modification, "BE" being especially suitable for surface
grinding; 2) special structure, "P" type being distinctively porous; and 3) for segments
made of 23A type abrasives, the term 12VSM implies porous structure, and the letter "P"
is not needed.
Table 1a. Grinding Wheel Recommendations for Surface Grinding— Using Straight
Wheel Types 1, 5, and 7

Horizontal-spindle, reciprocating-table surface grinders
Material       Wheels less than 16 inches in          Wheels 16 inches in diameter
diameter                               and over

Cast iron      37C36-K8V or 23A46-I8VBE                23A36-I8VBE
Nonferrous     37C36-K8V                               37C36-K8V
metal

Soft steel     23A46-J8VBE                             23A36-J8VBE

Straight Wheel Types 1, 5, and 7
Horizontal-spindle, reciprocating-table surface grinders
Material     Wheels less than 16 inches in          Wheels 16 inches in diameter
diameter                               and over
Hardened     32A46-H8VBE or 32A60-F12VBEP 32A36-H8VBE or 32A36-
steel—                                                F12VBEP
contact
Hardened     32A46-I8VBE                              32A36-J8VBE
steel—
narrow
contact or
interrupted
cut

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General-     23A46-H8VBE                          23A36-I8VBE
purpose
wheel
Cemented     Diamond wheelsa                      Diamond wheelsa
carbides
General diamond wheel recommendations are listed in Table 5 on page 1168.

Horizontal-spindle, rotary-table surface grinders
Material                        Wheels of any diameter
Cast iron                          37C36-K8V or 23A46-I8VBE
Nonferrous metals                  37C36-K8V
Soft steel                         23A46-J8VBE
Hardened steel—                    32A46-J8VBE
narrow contact or
interrupted cut
General-purpose wheel              23A46-I8VBE
Cemented carbides—roughing         Diamond wheelsa
Courtesy of Norton Company
Table 1b. Grinding Wheel Recommendations for Surface Grinding—Using Type 2
Cylinder Wheels, Type 6 Cup Wheels, and Wheel Segments

Material        Type 2          Type 6            Wheel
Cylinder Wheels   Cup Wheels        Segments
High tensile      37C24-HKV       37C24-HVK         37C24-HVK
cast iron and
nonferrous
metals
Soft steel,       23A24-I8VBE or 23A24-I8VBE        23A24-I8VSM or
malleable cast   23A30-                            23A30-H12VSM
iron, steel      G12VBEP
castings,
boiler plate
Hardened          32A46-G8VBE     32A46-G8VBE       32A36-G8VBE or 32A46-
contact          32A36-          E12VBEP
E12VBEP
Hardened          32A46-H8VBE     32A60-H8VBE       32A46-G8VBE or 32A60-
steel—narrow                                       G12VBEP
contact or
interrupt cut
General-       23A30-H8VBE                          23A30-H8VSM or 23A30-
purpose use    or                                   G12VSM
23A30-
E12VBEP

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The wheel markings in the tables are those used by the Norton Co., complementing the
basic standard markings with Norton symbols. The complementary symbols used in these
tables, that is, those preceding the letter designating A (aluminum oxide) or C (silicon
carbide), indicate the special type of basic abrasive that has the friability best suited for
particular work materials. Those preceding A (aluminum oxide) are
57—a versatile abrasive suitable for grinding steel in either a hard or soft state.
38—the most friable abrasive.
32—the abrasive suited for tool steel grinding.
23 —an abrasive with intermediate grinding action, and
19—the abrasive produced for less heat-sensitive steels.
Those preceding C (silicon carbide) are
37—a general application abrasive, and
39—an abrasive for grinding hard cemented carbide.

Systems of Surface Grinding — Diagrams

Reciprocating — Periphery of Wheel

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Principal Systems of Surface Grinding—Principles of Operation

Effective Grinding Surface—Periphery of Wheel Movement of Work—Reciprocating
Work is mounted on the horizontal machine table that is traversed in a reciprocating
movement at a speed generally selected from a steplessly variable range. The transverse
movement, called cross feed of the table or of the wheel slide, operates at the end of the
reciprocating stroke and assures the gradual exposure of the entire work surface, which
commonly exceeds the width of the wheel. The depth of the cut is controlled by the
downfeed of the wheel, applied in increments at the reversal of the transverse movement.
Effective Grinding Surface—Periphery of Wheel Movement of Work—
Rotary
Work is mounted, usually on the full-diameter magnetic chuck of the circular machine
table that rotates at a preset constant or automatically varying speed, the latter main-
taining an approximately equal peripheral speed of the work surface area being ground.
The wheelhead, installed on a cross slide, traverses over the table along a radial path,
moving in alternating directions, toward and away from the center of the table. Infeed is
by vertical movement of the saddle along the guideways of the vertical column, at the end
Effective Grinding Surface—Face (Side) of Wheel Movement of Work—Reciprocating
Operation is similar to the reciprocating table-type peripheral surface grinder, but
grinding is with the face, usually with the rim of a cup-shaped wheel, or a segmental
wheel for large machines. Capable of covering a much wider area of the work surface

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than the peripheral grinder, thus frequently no need for cross feed. Provides efficient
stock removal, but is less adaptable than the reciprocating table-type peripheral grinder.
Effective Grinding Surface—Face (Side) of Wheel Movement of Work—Rotary
The grinding wheel, usually of segmental type, is set in a position to cover either an
annular area near the periphery of the table or, more commonly, to reach beyond the table
center. A large circular magnetic chuck generally covers the entire table surface and
facilitates the mounting of workpieces, even of fixtures, when needed. The uninterrupted
passage of the work in contact with the large wheel face permits a very high rate of stock
removal and the machine, with single or double wheelhead, can be adapted also to
automatic operation with continuous part feed by mechanized work handling.
Effective Grinding Surface—Face (Side) of Wheel Movement of Work—Traverse
Along Straight or Arcuate Path
Operates with practically the entire face of the wheel, which is designated as an abrasive
disc (hence "disc grinding") because of its narrow width in relation to the large diameter.
Built either for one or, more frequently, for two discs operating with opposed faces for
the simultaneous grinding of both sides of the workpiece. The parts pass between the
operating faces of the wheel (a) pushed-in and retracted by the drawer like movement of a
feed slide; (b) in an arcuate movement carried in the nests of a rotating feed wheel; (c)
nearly diagonally advancing along a rail. Very well adapted to fully mechanized work
handling.
Process Data for Surface Grinding.—In surface grinding, similarly to other metal-cut-
ting processes, the speed and feed rates that are applied must be adjusted to the
operational conditions as well as to the objectives of the process. Grinding differs,
however, from other types of metal cutting methods in regard to the cutting speed of the
tool; the peripheral speed of the grinding wheel is maintained within a narrow range,
generally 5500 to 6500 surface feet per minute. Speed ranges different from the common
one are used in particular processes which require special wheels and equipment.

Table 2. Basic Process Data for Peripheral Surface Grinding on
Reciprocating Table Surface Grinders
Work         Hardness Material        Wheel Tabl Downfeed, in. Crossfeed
Material                Condition      Speed, e       per pass   per pass,
fpm      Spee              fraction of
d,                 wheel
fpm                width
Rou Finish
gh
Plain        52     Rc Annealed,      5500    50 to 0.00 0.0005      14
carbon steel max.       Cold drawn    to      100 3        max.
6500
52 to       Carburized   5500    50 to 0.00 0.0005                 '-10
65 Rc      and/or       to 6500 100 3       max.
quenched and
tempered

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Alloy steels 52 Rc                     5500    50 to 0.00 0.001
Annealed or
max.                     to 6500 100 3       max.
quenched and
tempered
52 to 65 Carburized            5500    50 to 0.00 0.0005
Rc        and/or               to 6500 100 3       max.
quenched and
tempered
Tool steels 150     to Annealed    5500               50 to 0.00 0.0005         15
275 Bhn               to                 100 2       max.
6500
56 to 65 Quenched     5500               50 to    0.00    0.0005   >4
Rc       and tempered to 6500             100     2       max.
1
Nitriding    200   to Normalized, 5500                50 to    0.00    0.001    4
steels       350 Bhn annealed      to 6500            100      3       max.
60 to 65 Nitrided     5500               50 to    0.00    0.0005
Rc                    to 6500             100     3       max.
1
Cast steels 52 Rc     Normalized, 5500                50 to    0.00    0.001    4
max.    annealed     to                 100      3       max.
6500
Over        Carburized        5500    50 to 0.00 0.0005
52 Rc      and/or            to 6500 100 3       max.
quenched and
tempered
1
Gray irons    52 Rc       As       cast,    5000    50 to 0.00 0.001            3
max.       annealed,         to 6500 100 3       max.
and/or
quenched and
tempered
1
Ductile       52 Rc       As       cast,    5500    50 to 0.00 0.001            5
irons          max.       annealed    or    to 6500 100 3       max.
quenched and
tempered
1
Stainless     135 to      Annealed or       5500      50 to 0.00 0.0005         4
steels,        235 Bhn    cold drawn        to        100 2       max.
martensitic                                  6500
1
Over            Quenched          5500      50 to    0.00 0.0005      8
275 Bhn        and tempered      to 6500    100     1     max.
1
Aluminum 30 to 150        As cast, cold     5500      50 to    0.00 0.001       3
alloys    Bhn             drawn       or    to        100      3     max.
treated            6500
In establishing the proper process values for grinding, of prime consideration are the
work material, its condition, and the type of operation (roughing or finishing). Table 2
gives basic process data for peripheral surface grinding on reciprocating table surface

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grinders. For different work materials and hardness ranges data are given regarding table
speeds, downfeed (infeed) rates and cross feed, the latter as a function of the wheel width.
Common Faults and Possible Causes in Surface Grinding.—Approaching the ideal
performance with regard to both the quality of the ground surface and the efficiency of
surface grinding, requires the monitoring of the process and the correction of conditions
adverse to the attainment of that goal.

Table 3. Common Faults and Possible Causes in Surface Grinding
WORK       METALL           SURFA         WHEEL        WORK
DIMENSIO URGICAL            CE          CONDITIO RETAIN
N          DEFECTS          QUALIT N                 MENT
Y
CAUSES                              F

Wheel glazing
Burnishing of

Work sliding
A

Scratches on

Rapid wheel
Poor finish
Burning or

Not firmly
U
Work not

Poor size

Feed lines
Work not

on chuck
checking
L    holding

parallel

Chatter

surface

Wheel

seated
marks
T
work

wear
flat

S
Heat         X XX                                                           X
treat       X X
WORK CONDITION

stresses    X
Work
too thin
Work
warped
Abrupt
section
changes
Grit too    X         X     X      XX        XX X             XX X X
fine Grit                   X                                X   X
too                                         X                    X
coarse                                      X
GRINDING WHEEL

too hard
too soft
Wheel
not
balanced
Dense
structure
Improper    X  X       X    X     X              X X X                 X    XX X
coolant     XX X      X                         X    X                 X
COOLANT
TOOLING

Insuffici      X                                 X   X
ent                                             X
AND

coolant
Dirty

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coolant
Diamond
loose or
chipped
Diamond
dull
No or
poor
magnetic
force
Chuck
surface
worn or
burred
MACHI

Chuck       X   X
SETUP
AND

not
NE

aligned
Vibratio                                  X
ns in
machine
Plane of    X   X
moveme
nt out of
parallel
Too low     X  X    X    X     X     X       X X X         X X              X
work        XX X                              X                             X
speed       X  X
Too light
feed Too
heavy
cut
Chuck
retained
swarf
Chuck
OPERATIONAL

CONDITIONS

improper
Insuffici
ent
blocking
of parts
Wheel
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runs off
the work
Wheel
dressing
too fine
Wheel
edge not
chamfere
d Loose
dirt
under
guard
Defective, or just not entirely satisfactory surface grinding
may have any one or more of several causes. Exploring and
determining the cause for eliminating its harmful effects is
facilitated by knowing the possible sources of the experienced
undesirable performance. Table 3, associating the common
faults with their possible causes, is intended to aid in
determining the actual cause, the correction of which should
restore the desired performance level.
While the table lists the more common faults in surface
grinding, and points out their fre quent causes, other t ypes of
improper performance and/or other causes, in addition to those
indicated, are not excluded.

GRINDING FEEDS AND SPEEDS
It is recommend a small range of depths and work speeds at constant wheel speed,
including small variations in wheel and work material composition. Wheel life or
grinding stiffness are seldom considered.
Grinding parameter recommendations typically range as follows:
• Wheel speeds are usually recommended in the 1200 to 1800 m/min (4000 to 6000 fpm)
range, or in rare cases up to 3600 m/min (12000 fpm)
• Work speeds are in the range 20 to 40 m/min (70 to 140 fpm); and, depths of cut of
0.01 to 0.025 mm (0.0004 to 0.001 inch) for roughing, and around 0.005 mm (.0002 in.)
for finish grinding.
• Grit sizes for roughing are around 46 to 60 for easy-to-grind materials, and for diffi-
cult-to-grind materials higher such as 80 grit. In finishing, a smaller grit size (higher grit
number) is recommended. Internal grinding grit sizes for small holes are approximately
100 to 320.
• Specific metal removal rate, SMRR, represents the rate of material removal per unit of
wheel contact width and are commonly recommended from 200 to 500 mm3/mm
width/min (0.3 to 0.75 in3/inch width/min).
• Grinding stiffness is a major variable in determining wheel-life and spark-out time. A
typical value of system stiffness in outside-diameter grinding, for 10:1 length/diameter
ratio, is approximately KST = 30-50 N/|J,m. System stiffness KST is calculated from the
stiffness of the part, Kw and the machine and fixtures, Km. Machine values can be

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obtained from manufacturers, or can be measured using simple equipment along with the
part stiffness.
Generally a lower wheel hardness (soft wheel) is recommended when the system
stiffness is poor or when a better finish is desired Basic Rules
The wheel speed V and equivalent chip thickness ECT = SMRR + V + 1000 are the pri-
mary parameters that determine wheel-life, forces and surface finish in grinding. The fol-
lowing general rules and recommendations, using ECT, are based on extensive laboratory
and industry tests both in Europe and USA. The relationships and shapes of curves
pertaining to grinding tool-life, grinding time, and cost are similar to those of any metal
cutting operation such as turning, milling and drilling.
In turning and milling, the ECT theory says that if the product of feed times depth of cut
is constant, the tool-life is constant no matter how the depth of cut or feed is varied, pro-
vided that the cutting speed and cutting edge length are maintained constant.
In grinding, wheel-life T remains constant for constant cutting speed V, regardless of
how depth of cut ar or work speed Vw are selected as long as the specific metal removal
rate SMMR = Vw X ar is held constant (neglecting the influence of grinding contact
width).
ECT is much smaller in grinding than in milling, ranging from about 0.0001 to 0.001
mm (0.000004 to 0.00004 inch). See the section MACHINING ECONOMETRICS
starting on page 1056 for a detailed explanation of the role of ECT in conventional
machining. Wheel life T and Grinding Ratio.—A commonly used measure of relative
wheel-life in grinding is the grinding ratio that is used to compare grindability when
varying grinding wheel composition and work material properties under otherwise
constant cutting conditions.
The grinding ratio is defined as the slope of the wear curve versus metal removal rate:
grinding ratio = MRR + W*, where MRR is the metal removal rate, and W* is the
volume wheel wear at which the wheel has to be dressed. The grinding ratio is not a
measure of wheel-life, but a relationship between grinding ratio and wheel-life T can be
obtained from the formula grinding ratio = SMRR X T— W*, where SMRR (specific
metal removal rate) is determined from MRR = SMRR X T or from ECT = SMRR — V
— 1000.
Thus, grinding ratio = 1000 X ECT X V X T— W*, and T = grinding ratio X W* —
(1000 X ECT X V), provided that the wheel wear criterion W* is valid for all data
combinations.
Example 1: If W* in one test is found to be 500 mm3 for ECT = 0.00033 mm and V =
3600 m/min, and grinding ratio = 10, then wheel-life will vary with measured grinding
ratios, wheel speed, and ECT as follows: T =500 X grinding ratio — (V X ECT) = 4.2
minutes.
In the remainder of this section the grinding ratio will not used, and wheel-life is
expressed in terms of ECT or SMRR and wheel speed V.
ECT in Grinding.—In turning and milling, ECT is defined as the volume of chips
removed per unit cutting edge length per revolution of the work or cutter. In milling
specifically, ECT is defined as the ratio of (number of teeth z X feed per tooth fz X radial
depth of cut ar X and axial depth of cut and (cutting edge length CEL divided by %D),
where D is the cutter diameter, thus, the formula grinding ratio = SMRR X T— W*,

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where SMRR (specific metal removal rate) is determined from MRR = SMRR X T or
from ECT = SMRR — V — 1000.
Thus, grinding ratio = 1000 X ECT X V X T— W*, and T = grinding ratio X W* —
(1000 X ECT X V), provided that the wheel wear criterion W* is valid for all data
combinations.
Example 1: If W* in one test is found to be 500 mm3 for ECT = 0.00033 mm and V =
3600 m/min, and grinding ratio = 10, then wheel-life will vary with measured grinding
ratios, wheel speed, and ECT as follows: T =500 X grinding ratio — (V X ECT) = 4.2
minutes.
In the remainder of this section the grinding ratio will not used, and wheel-life is
expressed in terms of ECT or SMRR and wheel speed V.
ECT in Grinding.—In turning and milling, ECT is defined as the volume of chips
removed per unit cutting edge length per revolution of the work or cutter. In milling
specifically, ECT is defined as the ratio of (number of teeth z X feed per tooth f X radial
depth of cut ^ X and axial depth of cut and (cutting edge length CEL divided by %D),
where D is the cutter diameter, thus,

Dz a a
fz r a
ECT =----------
CEL

In grinding, the same definition of ECT applies if we replace the number of teeth with
the average number of grits along the wheel periphery, and replace the feed per tooth by
the average feed per grit. This definition is not very practical, however, and ECT is better
defined by the ratio of the specific metal removal rate SMMR, and the wheel speed V.
Thus, ECT = 1000 X SMRR — V. Keeping ECT constant when varying SMRR requires
that the wheel speed must be changed proportionally.
In milling and turning ECT can also be redefined in terms of SMRR divided by the work
and the cutter speeds, respectively, because SMRR is proportional to the feed rate FR.
Work Speed and Depth of Cut Selection: Work speed Vw is determined by dividing
SMMR by the depth of cut ar, or by using the graph in Fig. 1.

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F i g . 1 . W o r k s p e e d Vw v s . d e p t h o f c u t ar Referring to Fig. 1, for depths
of cuts of 0.01 and 0.0025 mm, a specific metal removal rate SMMR = 1000 mm3/mm
width/min is achieved at work speeds of 100 and 400 m/min, respectively, and for
SMMR =100 mm3/mm width/min at work speeds of 10 and 40 m/min, respectively.
Unfortunately, the common use of low values of work speed (20 to 40 m/min) in finish-
ing cause thermal surface damage, disastrous in critical parts such as aircraft components.
As the grains slide across the work they generate surface heat and fatigue-type loading
may cause residual tensile stresses and severe surface cracks. Proper finish grinding
conditions are obtained by increasing the work speed 5 to 10 times higher than the above
recommendations indicate. These higher work speeds will create compressive stresses
that are not detrimental to the surface. The by-product of higher work speeds is much
higher SMRR values and thereby much shorter grinding times. Compressive stresses are
also obtained by reducing the depth of cut ar
Wheel Life Relationships and Optimum Grinding Data.—Figs. 2a, 2b, and 2c show, in
three planes, the 3-dimensional variation of wheel-life T with wheel speed V and ECT
when grinding a hardened tool steel. Fig. 2a depicts wheel-life versus wheel speed (the
T— V plane) with constant ECT appearing as approximately straight lines when plotted in
log-log coordinates.
In grinding, the wheel-life variation follows curves similar to those obtained for conven-
tional metal cutting processes, including a bend-off of the Taylor lines (T—V graph)
towards shorter life and lower cutting speeds when a certain maximum life is achieved for
each value of ECT. In the two other planes (T—ECT, and V—ECT), it is usually find
smooth curves in which the maximum values of wheel-life are defined by points along a
curve called the H—curve.

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Fig. 2a. Taylor lines: T vs. V, ECT plotted for grinding M4 tool steel, hardness Rc 64
Example 2:
The variation of SMRR = V X ECT X 1000 and wheel-life at various wheel speeds can
be obtained from Fig. 2a. Using sample values of ECT = 33 X 10-5 mm and V = 1300 and
1900 m/min, SMRR = 1300 X 33 X 10-5 X 1000= 429, and 1900 X 33 X 10-5 X 1000 =
627 mm3/mm width/min, respectively; the corresponding wheel lives are read off as
approximately 70 and 30 minutes, respectively.

Fig. 2b depicts wheel-life T versus ECT with constant wheel speed V shown as
curves plotted in log-log coordinates, similar to those for the other cutting operations.

Example 3: Fig. 2b shows that maximum values of wheel-life occur along the H-curve.
For the 3 speeds 1800, 2700, and 3600 m/min, maximum wheel lives are approximately

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70, 14 and 4 minutes, respectively, at ECT around 17 X 10-5 through 20 X 10-5 mm along
the H/-curve. Left and right of the /-curve wheel-life is shorter.
Fig. 2c depicts wheel speed V versus ECT with wheel-life T parameter shown as curves
in log-log coordinates, similar to those for the other cutting operations, with the
characteristic H- and G-curves.

Fig. 2c. V vs. ECT, T plotted

Optimum grinding data for roughing occur along the G-curve, which is determined from
the V-ECT graph by drawing 45-degree lines tangent to the T-curves, as shown in Fig. 2c,
and drawing a line (the G-curve) through the points of tangency on the respective T-
curves, thus the location and direction of the G-curve is determined. Globally optimum
data correspond to the T-curve for which wheel-life is calculated using the corresponding
equivalent tooling-cost time, Tv, calculated from T v = T rpl + 60 X C E + H r , minutes,
where T rpl is the time required to replace wheel, CE = cost per wheel dressing = wheel
cost + cost per dressing, and /R is the hourly rate.
Minimum cost conditions occur along the G-curve; if optimum life To was determined
at either 10 or 30 minutes then Vo = 1500 and 1100 m/min, respectively, and ECT is
around 65 - 70 X 10-5 mm in both cases. The corresponding optimum values of SMRR
are 1000 X 1500 X 67 X 10-5 = 1000 and 1000 X 1100 X 67 X 10-5 = 740
mm3/min/mm wheel contact width (1.5 to 1.1in3/in/min).
Using Fig. 1 we find optimum work speeds for depths of cut ar = 0.01 and 0.005 mm to
be Vw = 100 and 75 m/min, and 200 and 150 m/min (330 and 250 fpm, and 660 and 500
fpm) respectively for 10- and 30-minute wheel-life.
These high work speeds are possible using proper dressing conditions, high system stiff-
ness, good grinding fluid quality and wheel composition.
Fig. 3 shows the variation of specific metal removal rate with wheel speed for several
materials and a range of ECTs at 10- and 30-minutes wheel-life. ECT decreases when
moving to the left and down along each curve. The two curves for unhardened 1020 steel

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have the largest values of SMRR, and represent the most productive grinding conditions,
while the heat resistant alloy Inconel yields the least productive grinding conditions. Each
branch attains a maximum SMRR along the G-curve (compare with the same curve in the
V-ECT graph, Fig. 2c) and a maximum speed region along the //-curve. When the
SMRR-values are lower than the //-curve the ECT values for each branch decrease
towards the bottom of the graph, then the speed for constant wheel-life must be reduced
due to the fact that the ECT values are to the left of their respective /-curves in V-ECT
graphs.

Parts of Horizontal Surface Grinding

Base:

The base has a column at the back for supporting the wheel head. The base also contains
the drive mechanisms.

Table:

The table is fitted to the saddle on carefully machined ways. It reciprocates along ways
to provide the longitudinal feed. T-slots are provided in the table surface for clamping the
work pieces directly on the table or for clamping grinding fixtures or a magnetic chuck.
On some machines the table can be moved in or out from the vertical column which
supports the wheel head. This movement is called cross feed.

The wheel head is mounted on the column secured to the base. It has ways for vertical
slide which can be raised or lowered with the grinding wheel only manually by rotating a
hand wheel to accommodate work pieces of different heights and to set for wheel for
depth of cut. Horizontal, crosswise movement of the wheel slide with the wheel actuated
by hand or by hydraulic drive, accomplishes the cross feed of the wheel. The grinding
wheel rotates at constant speed; it is powered by a special in built motor.

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Ex No.6:               STUDY OF SHAPING MACHINE

OBJECTIVE:

THEORY

Flat surfaces can be machined by means of shaping machines. The chips are cut off in
strips from the work piece by the straight main stroke. The machine is suitable for
machining work pieces up to 800 mm length. Shaping machine are cheaper than millers,
will remove more quickly but are not capable of such a wide range of work.

Principle Parts
j. Base or Body
This is a heavy hollow casting supporting the main parts. The ram-operating
mechanism and often the motor drive is contained within casting.

This is fixed to the front vertical face of the body. It can be raised and lowered by
hand and locked in position.

l. Table
The table is of machined cast iron, slotted on top , bottom and sides for the bolting
on of work. It is sometimes made to swivel and can be traversed sideways by hand or
power feed.

m. Ram
The base casting has sideways machined on its top face to take the ram which moves
horizontally across it.

The head can be moved vertically and is usually arranged so that it can swivel as
well. Vertical movement of the head is usually by hand.

o. Tool box or Clapper box
This is fixed to the head and can be swivelled and locked at an angle to alter the
position of the tool in relation to the work. the box carries the cutting tool and swivels
on a pin for relief and lift on the back stroke.

p. Front support or table steady
This supports the table during cutting operations.

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q. Driving mechanism
The crank is slotted and rotates on the pivot. it is connected to the bull wheel or
crank gear by means of the crank pin. The link connects the crank to the ram. the
length of stoke of the ram is decided by the position of the crank pin in the slot of the
bull wheel. the further it is from the centre the longer the stroke. this same mechanism
ensures that the idle return stroke is quicker than the forward cutting stroke.

r. Table feed mechanism
The feed is arranged so that the table is moved a set amount after each stroke. The
driving disk is slotted and attached to it is the connecting rod, the latter being
adjustable for position in the disk slot. The connecting rod is linked to a fulcrum
through a rocker arm in such a way that rotation of the disk causes the rocker arm to
reciprocate. The reversible pole is fixed to the top end of the rocker arm, its lower end
engaging with a sprocket on the feed screw. Clockwise and anticlockwise movement
of the sprocket is possible by rotating the Paul through 180 degree neutral position is
provided. The amount of feed is governed by position of pin in the slot of the driving
disc.

Shaping tools
In most cases, shaping tools are made of high- speed steel. Very often, tips are made
of cemented carbide. The shape of cutting edge depends on the work to be executed.
Only in exceptional cases, these tools differ from turning tools.

Rough Cutting tools
These are supposes to cut off as much materials as possible within short time.

Finishing tools
These must provide smooth surfaces on the work pieces.

The cutting speed during shaping
The distance which is covered by the shaping tool in meters per minute during the
working stroke is called cutting speed.(va) The speed during the non-cutting speed is
called return speed(vr).

Cutting speed (va) = Length of stroke(in m)
Time for working stroke (in min)
= L m/min
Ta

Return stroke(vr)      = Length of stroke (in m)
Time for non cutting speed (in min)
= L m/min
Tr
While shaping on a machine with rocker arm driver, the cutting speed is not uniform. At
the starting point of the stroke, the cutting speed equals to zero. It increases to the
maximum value in the middle of the cutting stroke and decreases to zero at the end of the
stroke. The same applies for the highest speed during the return stroke.

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STUDY OF HORIZONTAL SURFACE GRINDING MACHINE

Surface grinding is the method of grinding designed to carry out the removal of metal
from a part or parts less expensively and with greater precision than could be achieved by
machining processes with cutting tools of steel, or by hand or machine filling.

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Horizontal-spindle surface grinder: These machines use in circumference of straight
grinding wheels, and are able to deal with a wide range of work needing super finish and
extremely fine limits of accuracy. They yield a greater output and take off metal faster
than similar machines using cup shaped, segmental or annular wheels. If a rotating table
is used, finished comprising concentric circles can be obtained and is often popular.

Main Parts
Base:
The base has a column at the back for supporting the wheel head. The base also
contains the drive mechanisms.

Table:
The table is fitted to the saddle on carefully machined ways. It reciprocates along
ways to provide the longitudinal feed. T-slots are provided in the table surface for
clamping the work pieces directly on the table or for clamping grinding fixtures or a
magnetic chuck. On some machines the table can be moved in or out from the vertical
column which supports the wheel head. This movement is called cross feed.

The wheel head is mounted on the column secured to the base. It has ways for vertical
slide which can be raised or lowered with the grinding wheel only manually by
rotating a hand wheel to accommodate work pieces of different heights and to set for
wheel for depth of cut. Horizontal, crosswise movement of the wheel slide with the
wheel actuated by hand or by hydraulic drive, accomplishes the cross feed of the
wheel. The grinding wheel rotates at constant speed; it is powered by a special in built
motor.

Grinding wheel

A grinding wheel is a multi tooth cutter made up of many hard particles known as
abrasive which have been crushed to leave sharp edges which do cutting. The abrasive
grains are mixed with a suitable bond, which acts as a matrix or holder when the wheel is
in use.
The performance of a grinding wheel is usually evaluated in term of the grinding ratio,
which is defined as

G = (Volume of material required) / (volume of wheel wear)

Characteristics Of The Grinding Wheel

Wheel parameters that influence the grinding performance are
1. Abrasive material: An abrasive is a substance is used for grinding and polishing
operations.Abrasive may classified as:
(a) Natural
(i)sand stone (ii)emery (iii) corundum (iv) diamonds

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(b) Artificial
(i)silicon carbide (ii) aluminum oxide

2. Abrasive size: choice of the grain size depends upon the properties of the work
material, surface finish, desired rate of metal removal etc..Coarse grain(grit size 10-
24) give faster metal removal and fine grits(grit size70-80) are used for fining
operations. For soft and ductile material coarse grain is preferred while for brittile
material finer grains are preferred.

3. Bond: To ensure an effective and continuous action, it is imperative that the grains of
abrasive materialshould be held firmly together to form a series of cutting edges. The
material used for holding them is known as bond.
(i)    Vitrified bond (ii)silicate bond (iii) shellac bond (iv) resinoid bond (v) rubber
bond

4. Grade: Grinding wheel grade refers to the strength with which the bond holds the
grains together. Wheel with hardness rating A to I are classified as soft, J to P as
medium, Q to Z as hard.

5. Structure: Structurre of a grinding wheel refers the relationship between the volume
of the abrasive material, volume of bond and the volume of voids present in the
grinding wheel.

Standard Marking System

The Indian standard marking system for grinding wheels shall consists of six symbols
denoted in following succession.
1. Abrasive type: A for Alumina, S for Silicon carbide etc..
2. Grain size: mesh number
3. Grade: Letters A for very soft, and Z for very hard.
4. Structure: 15 for very dense structure.
5. Bond type: V- vitrified, R-rubber etc..
6. Manufactures owned private mark

For example, W     A    46   K 5     V    17

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