# Linear Measurements

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```					Chapter (2) : Linear Measurements                                        Dr Jehad Yamin

Linear Measurements
1. Introduction :

When man first sought a unit of length, he adopted parts of his body, mainly his
hands, arms and feet. For example, ancient Egyptians used the “Cubit” for their
measurements. It is equal to the distance between the tip of the forefinger to the
elbow.
Today, the entire industrial world has adapted the “International Meter” as a standard
for linear measurement. It was defined in 1960 officially as being 1650763.73
wavelengths of the orange-red radiation given off by electrically excited Krypton 86
gas under vacuum. Accordingly, the English Inches has been officially defined as
2.54 cm, thus, the inch is 41929.399 wavelengths of the orange-red radiation given
off by electrically excited Krypton 86 gas under vacuum.

Classification :

There are several ways of classification of linear measurement instruments. One
such classification is:

(1) Line Measurement (i.e. measuring distance between two lines) &
(2) End Measurement (i.e. measuring distance between two faces or ends).

Another method is based on the resolution as follows:

(1) Low Resolution (e.g. scale alone or in conjunction with other devices like
calipers)
(2) Medium Resolution (e.g. micrometer, vernier instruments)
(3) High Resolution, and,
(4) Super Resolution. (e.g. interferometers)

2.1 Low Resolution Line Measurement Instruments

These are devices that incorporate graduation spacing representing known
distances.

Accuracy is affected by:
(4) Instrument design,
(5) Geometric deficiencies, and,
(6) Workman’s experience.

Observational errors are mainly due to: (1) Parallax and (2) Misalignment.
Sensitivity of these instruments depend on the instrument’s basic design (i.e. least
count).
Chapter (2) : Linear Measurements                                        Dr Jehad Yamin

2.1.1 Steel Rule

Type: This is a low-resolution line-measuring instrument.

Operating principle: comparing an unknown length to a previously calibrated
one.

Construction: It consists of a strip of hardened steel having line graduations
etched or engraved at intervals of fraction of standard unit of length. These
graduations may not be uniform all throughout its length. This allows for multiple use
for particular range as per accuracy required.

How to use: As shown in figure below.
Chapter (2) : Linear Measurements                                        Dr Jehad Yamin

Basic desirable qualities:
(1) Clearly engraved lines, (2) Minimum thickness, (3) Good quality spring steel, (4)
Graduations on both sides, (5) Low coefficient of thermal expansion.

Degree of accuracy affected by:
(1) Quality of rule, (2) Skill of user in estimation the parts of mm.

Reliability of measurement when using scale for direct measurement depends on
the proper positioning of the scale in relation to workplace.

Graduate rule accessories: For good reliability, several accessories are available
to help improve accuracy of positioning. These include: Hooks (This is used for (1)
Good alignment of the “zero” point of the scale with border line of an object surface,
(2) Keep the rule in position normal to the edge of the surface), Clamping shafts,
decimal rules (these are short rules used for measurement of lengths below 1/64” it
has least count of 0.01”), Foot rests, square head and center finders (used to allow
for location of centerline on the face of round objects), Parallel clamps (used for
proper alignment of rule with axis of cylinder).

2.1.2. Calipers
These are accessories to scales and help measuring directly those parts that cannot
be measured directly by the scale.

Construction & Use: They consist of two legs hinged at the top with the
ends of the legs span the parts to be inspected.

Classification: Calipers may be broadly classified as :
1. Spring Type calipers (where the spring tension holds the legs of the calipers
Chapter (2) : Linear Measurements                                        Dr Jehad Yamin

2. Firm-Joint calipers (where the friction created at the junction of the legs
tension holds the legs of the calipers firmly. They can also be further classified
as : Inside, Outside, Transferable, and Hermophrodite calipers.

2.1.3. Firm Joint Calipers

Operating principle: They are devices for comparing measurements against
known dimensions.

Construction: The legs are made from carbon & alloy steel containing not more
than 0.05% Sulphur, and 0.05% Phosphorous with working ends suitably hardened
and tempered to hardness of 400-500 HV and faces up to 650 + 50 HV. They are
joined together by a rivet. They have rectangular cross section.

Qualities: They should be free from cracks, seams, dirt, flaws and must have
smooth bright finish.

Nominal Size is the distance between the center of the rolling end and the
extreme working end of a leg.

Caliper’s Capacity is the maximum dimension that can be measured by the
caliper. It should not be lesser than the nominal size.

The accuracy depends on the sense and feel of the operator. Therefore, caliper
should be held gently and square to the work with slight gauging pressure applied.

2.1.4. Spring Calipers
One end of the adjusting screw is hinged to one leg and a steel ball is positively
fixed to the free end of the adjusting screw for the purpose of retaining the adjusting
nut.
Chapter (2) : Linear Measurements                                       Dr Jehad Yamin

2.1.4. Outside Calipers
Used to measure the outside dimensions.

2.1.5 Inside Calipers
Used to measure the inside dimensions and to transfer reading to a scale with
hooks.

2.1.6 : Dial Calipers:
Provide typical direct reading capability of 0.02mm.

Self reading: transfer calipers, Hermophrodite calipers, surface plates, V-blocks,
combination set.

2.2. Precision (medium resolution) linear measurement
Since modern production is more concerned with interchangeability of products,
great precision dimensional control became a must. This necessitates the use of
more precise measuring instruments.

2.2.1. Characteristics of precise measuring instruments

(1)   High degree of sensitivity,
(2)   High degree of accuracy,
(3)   Minimum inertia in moving parts, and
(4)   Freedom from variance.

In order to achieve the above characteristics, the following principles must be
observed :
Principle of alignment, Principle of kinematics, Principle of measuring contacts,
Selection of measuring instrument, and Inspection must guarantee that this same
measurement technique will yield comparable results if repeated.

2.2.2. The Vernier Instruments

Operating principle: when two scales or divisions slightly different in sizes are
used, the difference between them can be utilized to enhance the accuracy of
measurement.
Chapter (2) : Linear Measurements                                         Dr Jehad Yamin

Construction: Explain with reference to figure below.

(1) The last numbered division on the main scale to the left of the “Zero” of vernier
scale is noted. If the scale is graduated in cm, then multiply by 10 mm, as this is
the official engineering dimensional unit.
(2) Note how many graduations are showing between this numbered division and
the “Zero” of the vernier scale. If the scale is graduated in Cm, then multiply this
number with 1 mm.
(3) Find the line on the vernier scale, which coincides with a line on the main scale.
Multiply this number with the least count of the vernier scale.
Chapter (2) : Linear Measurements                                        Dr Jehad Yamin

Design of the vernier scale :

A relation can be derived between the size of the size of divisions on the main scale
and the size of divisions on the vernire scale.

Let, Cm = size of divisions on main scale (mm)
Cv= size of divisions on vernier scale (mm)
N = number of the total divisions on vernier scale.
Now, when the zeros on the two scales coincide, we have

(n-1) * Cm = n * Cv
Hence, the size of the division on the vernier scale “Cv” is found as :
[(n-1)/n] * Cm = Cv
And the accuracy of the scale is found by subtracting the size of the vernier scale
from that f the main scale.
Hence;
Accuracy = Cm – Cv
= Cm /n

Example on how to read the vernier scale :
Let us take the first example as shown in the fisgure below :

Hence;
Cv = [24/25] * 0.5
= 0.48mm
Accuracy = 0.5/25
= 0.02mm
This represents the accuracy to which the reading can be taken.

The dimension on the vernier caliper is taken as follows :
Step (1) : Calculate the accuracy of the vernier caliper.
Step (2) :Take the value on the main scale against the zero division of the vernier
scale.
Step (3) : Count the number of the division on the vernier scale that totally coincides
with anyone on the main scale.

Total reading = main scale reading of step (2) + Accuracy * number of division of
step (3).
Chapter (2) : Linear Measurements                                         Dr Jehad Yamin

For figure (a) above :
Accuracy = 0.5/25 = 0.02mm
Main scale reading opposite to zero division of VS = 22mm
Division number 16 totally coincides with one division on M.S.
Total reading = 22 + 0.02 * 16 = 22.32mm

Graduation characteristics: they should be clearly engraved so that they are
clearly visible.

Sources of Errors with Vernier Caliper :
Caliper not properly set to zero, Manipulation of the vernier scale reading, Wear in
measuring tips, non-perpendicular plane between bar and jaws, or between jaws
and workpiece.

Care to be taken in using the Vernier Scale :
(1) Not to be treated as a wrench or hammer since they are not rugged,
(2) Should not be dropped or tossed aside rather, handled with care,
(3) Should be cleaned from dirt.

Precautions :
(1) Use the fixed jaw as the reference jaw,
(2) Do not play with the sliding jaw on the scale in order not to lose accuracy,
(3) Regularly check the tips of the jaws for possible wear.

Other types of vernier scales are :
Vernier Height Scale; Vernier Depth Scale; Master Dial Indicator V.C. :

2.2.3. The Micrometer

Operating principle: a circular movement of a threaded spindle produces an axial
movement. The distance moved by the spindle (axial or linear movement) per
revolution (circular movement of the thimble) depends on the pitch of the threaded
spindle.
Chapter (2) : Linear Measurements                                        Dr Jehad Yamin

Advantages of micrometer over V.C. :
Easier and clearer readability, Lesser observational errors due to parallax, Portable,
Easy to handle, Easy operation, Reasonable cost.

Construction & Operation: Explain with reference to figure below.
Chapter (2) : Linear Measurements                                         Dr Jehad Yamin

The micrometer is used as follows :
1) Check the zero reading, (2) Place the part to be measured in between the
measuring faces, (3) Advance the spindle by rotating the ratchet until it begins to slip
and a sound of click is heard. This indicates that there is no further ovement of the
spindle, finally (4) Take the reading as explained below.

(1) The last numbered division showing above the index line to the left of the
thimble is noted (this is usually in mm).
(2) Note if there is any half-mm line showing below the index line between the last
numbered division and the thimble and add 0.5mm to the first reading..
(3) Add the number of lines on the thimble that coincides with the index lie.

Accuracy * number of divisions on
the thimble scale that coincides with
horizontal line on barrel

From figure above :
Accuracy = 0.5/50 = 0.01mm
Division number 47 (zero line is not counted) matches.
Total reading = 11.5 + 0.01 * 47 = 11.97mm.

The measurement to a third degree of decimal can be made with micrometer by
employing vernier scale alongwith the thimble and barrel divisions. This vernier scale
is employed on the barrel or sleeve as shown below. This system is called Vernier
Micrometer.
Chapter (2) : Linear Measurements                                         Dr Jehad Yamin

Accuracy of sleeve * number of divisions on
the thimble scale that is just below that on the
horizontal line on barrel +
Accuracy of vernier * number of divisions on
the vernier scale that coincides with
horizontal line on thimble
0.01 * 16 (on sleeve) +
0.001 * 6 (on vernier scale)
= 10.666mm

Lack of flatness of anvil, Inaccurate setting to “Zero” reading before use, Lack of
parallelism between anvil and spindle or anvil and workpiece.

Cleaning of micrometer : Clean after every time of use, should never be dunked in
solvent or kerosene as a whole, should always remain free from oil, dust, grit or dirt.

Precautions :
(1) Apply workpiece gently between spindle and anvil,
(2) Use proper size for proper dimensions,
(3) Follow proper method of handling,
(4) Regularly inspect parts and make sure that spindle moves freely.

Accuracy with micrometer measurements depends on :
(1) Degree of calibration of spindle movement.
(2) Linearity of spindle movement.

Other types of micrometers are :
Inside Micrometer : pp. 145; Depth Gauge Micrometer : pp. 149; Threaded Gauge
Micrometer : pp. 150; Outside Gauge Micrometer : Digital Micrometer : pp. 154

2.2.4. The Slip Gauges (Gauge Blocks)

Basic Principle: End type linear measurement device.

Construction & Operation: Explain with reference to figures below.
Chapter (2) : Linear Measurements                                             Dr Jehad Yamin

Classification : based on their guaranteed accuracy, they are classified as :
AA Master        Slip Gauge. Has accuracy of + 2 microns per meter.
A Reference Slip Gauge. Has accuracy of + 4 microns per meter.
B Working Slip Gauge. Has accuracy of + 8 microns per meter.

Grades of slip gauges : based on their guaranteed accuracy, they are classified as
:
OO Grade.                 Used as a standard in the standard room only.
Calibration Grade.        Has actual size for calibration.
1 Grade.                  For more precise work such as with sine bars.

Sets of gauge blocks :They are available in different sets for different units Metric
and English:

Metric (56 pieces)             Metric (103 pieces)         English (81 pieces)
9 Pieces 1.001-1.009            49 pieces     1.01-1.49   9 pieces 0.1001-0.1009”
++0.001 mm                      ++0.01mm                  ++0.0001”
9 Pieces       1.01-1.09        49 pieces     0.50-24.5   49 pieces 0.1010-0.1490”
++0.010 mm                      ++0.5 mm                  ++0.001”
9 Pieces          1.0-1.9       4 pieces 25, 50, 75,      19 pieces 0.0500-0.9500”
++0.100 mm                      1000 mm                   ++0.050”
25     Pieces       1-25        1 piece 1.005mm           4   pieces 1.0,2.0,3.0,4.0”
++1.000 mm                                                ++1.0”
3     Pieces       25-75
++ 25 mm
1 Piece 1.0005
Chapter (2) : Linear Measurements                                       Dr Jehad Yamin

Protecting Gauge Blocks: Another two gauges are added which are made extra
wear resistant to reduce wear during inspection. They are called “Protector Gauge
Blocks”. Usually have dimensions of 1mm, 1.5mm, 2mm or 2.5mm. They are
marked with letter “P” on its measuring faces.

Selecting and building up of blocks: To build up the blocks to the required length
(1) Note down the required dimension,
(2) Deduct from it the size of two protecting blocks,
(3) Add blocks that eliminates the least digit of the number,
(4) Continue till you reach zero.

Accuracy is affected by :
(1) Dimensional instability of material,
(2) Wear during operation or use,
(3) Damage during storage and handling,
(4) Change in parallelism.

To reduce errors and improve accuracy :
(1) Repeated and periodical inspection and calibration,
(2) Select the least number of gauge blocks for a given or required size (this helps
reducing accumulative errors).

Calibration : because of the repeated use of gauges, the may develop wear or
damage of certain type. Repeated and regular inspection is needed to care for any
error that may arise. There are several methods of calibration. One such method is
by the use of interferometers (read by yourself).

Example: List the slips to be wrung together to produce an overall dimension of
92.357mm using two protective gauge blocks of 2.5mm size.
Chapter (2) : Linear Measurements                                       Dr Jehad Yamin
Answer:        (1) Original size                             = 92.357
(2) Deduct two protective slip gauges         = 05.000
Remainder             = 87.357
(3) Add block to eliminate least digit        = 01.007
Remainder             = 86.350
(4) Repeat step No. (3)                       = 01.050
Remainder             = 85.300
(5) Repeat step No. (3)                       = 01.300
Remainder             = 84.000
(6) Reduce to nearest big number              = 09.000
Remainder             = 75.000
(7) Add one block of 75.000mm                 = 75.000
Remainder             = 00.000

How to wring Blocks together

When wringing blocks together, take care not to damage them. The correct
sequence of movement to wring blocks together, illustrated as follows :

1. Clean the blocks with a clean, soft cloth.
2. Wipe each of the contacting surfaces on the clean palm of the hand or on the
wrist. This procedure removes any dust particles left by the cloth and also
applies a light film of oil.
3. Place the end of one block over the end of another block as shown in Figure.
4. While applying pressure on the two blocks, slide one block over the other.

NOTE: If the blocks do not adhere to each other, it is generally because the blocks
have not been thoroughly cleaned.

Care of Gage Blocks
1. Gage blocks should always be protected from dust and dirt by being kept in a
closed case when not in use.
Chapter (2) : Linear Measurements                                       Dr Jehad Yamin
2. Gages should not be handled unnecessarily since they absorb heat from the
hand. Should this occur, the gage blocks must be permitted to return to room
temperature before use.
3. Fingering of lapped surfaces should be avoided to prevent tarnishing and rusting.
4. Care should be taken not to drop gage blocks or scratch their lapped surfaces.
5. Immediately after use, each block should be cleaned, oiled, and replaced in the
storage case.
6. Before gage blocks are wrung together, their faces must be free from oil and dust.
7. Gage blocks should never be left wrung together for any length of time. The slight
moisture between the blocks can cause rusting, which will permanently damage
the blocks.

Effect of Temperature

While the effect of temperature on ordinary measuring instruments is negligible,
changes in temperature are important when precision gage blocks are handled.
Gage blocks have been calibrated at 68°F (20°C), but human body temperature is
about 98°F (37°C). A 1°F (0.5°C) rise in temperature will cause a 4-in. (100-mm)
stack of gage blocks to expand approximately 0.000025 in. (0.0006 mm); therefore,
these blocks should be handled as little as possible.

The following suggestions are offered to eliminate as much temperature-change
error as possible :
1. Handle gage blocks only when they must be moved.
2. Hold them by hand for as little time as possible.
3. Hold them between the tips of the fingers so that the area of contact is small,
or use insulated tweezers.
4. Have the work and gage blocks at the same temperature.
5. If a temperature-controlled room is not available, both the work and gage
blocks may be placed in kerosene until both are at the same temperature.
6. Where extreme accuracy is necessary, use insulating gloves and tweezers to
prevent temperature change during handling.

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