# Introduction to Gear Trains by fnz82095

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```									Introduction to
Gear Trains
Zhengjian XU
29th OCT 2008
Introduction to gear trains
Gear Types
pinion
Spur gear: gear with radial teeth parallel to its axis

Rack

Rack & Pinion a        toothed wheel (pinion) engages a notched bar (rack)
to convert rotary motion into linear motion

Bevel Gear       Either of a pair of toothed wheels whose working
surfaces are inclined to nonparallel axes.
Introduction to gear trains
Gear Types
Helical gear: a gear that has the teeth cut at an angle to the center line of the
gear. This kind of gear is useful because there is no chance of intermittent tooth-to-
tooth operation because there are at least two teeth engaged at any time. It can
operate quieter than spur gear.

Worm gear: A worm is used to reduce speed. For
each complete turn of the worm
shaft the gear shaft advances only
one tooth of the gear.
Unlike ordinary gears, the motion is
not reversible, a worm can drive a
gear to reduce speed but a gear
cannot drive a worm to increase it.

Harmonic gear: The harmonic gear allows high
reduction ratios with concentric shafts and with very
low backlash and vibration. It is based on a very simple
construction utilising metals elasto-mechanical property
Introduction to gear trains
Gear Types
Herringbone gear:
The two helix angle come together in the center of the gear face to form a 'V‘.

Differential gear: A vehicle's wheels rotate at different speeds,
especially when turning corners. The differential is designed to drive a pair
of wheels with equal force, while allowing them to rotate at different speeds

Input torque is applied to the ring gear (blue), which turns the      If the left side gear (red) encounters resistance, the
entire carrier (blue), providing torque to both side gears (red and   planet gear (green) rotates about the left side gear,
yellow), which in turn may drive the left and right wheels. If the    in turn applying extra rotation to the right side gear
resistance at both wheels is equal, the planet gear (green) does      (yellow).
not rotate, and both wheels turn at the same rate.
Introduction to gear trains
Kinematics of Gears
Fundamental law of gearing: Angular velocity Ratio is constant
throughout the mesh.
Introduction to gear trains
Gear tooth nomenclature

Pitch circle: A circle the radius of which is
equal to the distance from the gear axis to
the pitch point. .
Addendum circle: A circle bounding the
ends of the teeth, in a right section of the
gear.
Root (or dedendum) circle: The circle
bounding the spaces between
the teeth, in a right section of the gear.
the pitch circle and the addendum circle.
the pitch circle and the root circle.
Clearance: The difference between the
dedendum of one gear and the addendum
of the mating gear.
Gear tooth nomenclature
Face of a tooth: That part of the
tooth surface lying outside the pitch
surface.
Flank of a tooth: The part of the
tooth surface lying inside the pitch
surface.
Circular thickness (also called the
tooth thickness) : The thickness of
the tooth measured on the pitch
circle. It is the length of an arc and
not the length of a straight line.
Fillet : The small radius that
connects the profile of a tooth to the
root circle.
Introduction to gear trains
Gear tooth nomenclature

Figure shows two teeth of a gear with the
standard nomenclature defined.

Since
Tooth contact nomenclature
Point of contact: any point at which two tooth
profiles touch each other.

Path of action: the locus of successive
contact points between a pair of gear teeth,
during the phase of engagement.

Line of action: The line of action is the
path of action for involute gears. It is the
straight line passing through the pitch point
and tangent to both base circles.
Tooth contact nomenclature
Line of contact: a line or curve along which
two tooth surfaces are tangent to each other   Line of contact

Surface of action: the imaginary surface in
which contact occurs between two engaging
tooth surfaces.

Plane of action: the surface of action for
involute, parallel axis gears with either
spur or helical teeth. It is tangent to the
base cylinders.
Introduction to gear trains
Gear tooth nomenclature
Generation of the Involute
Curve
This involute curve is the
path traced by a point on a
line as the line rolls without
slipping on the
circumference of a circle. It
may also be defined as a
path traced by the end of a
string which is originally
wrapped on a circle when
the string is unwrapped from
the circle. The circle from
which the involute is derived
is called the base circle.
Introduction to gear trains
Gear tooth nomenclature

The pressure angle is the angle between the line of
action and the common tangent. (has been standardized
14.50 200 250)
Introduction to gear trains
Gear tooth nomenclature
Minimum number of Teeth
Introduction to gear trains

Simple gear train
From the fundamental law of gearing

The sign “-” is necessary to take into account the change in direction
of rotation.

The sign “+” is also to take into account the change in direction of
rotation for internal gear.
Introduction to gear trains
Planar gear trains
Example: Find the output angular velocity for the planetary gear
train shown when the input angular velocity W4= 50 rad/sec
conterclokwise.
Solution:
The velocity of point A

Also the velocity of A can be expressed

Then we get
Introduction to gear trains
Planar gear trains
Letting r2=Pc*n2, r3=Pc*n3

Using the tooth relationship to replace the

Substituting back into the other equation
Introduction to gear trains
Find the speed reductions possible for the transmission
The power is transmitted through gears
0-4-5-6-10-12 for this instant status.
From the fundamental law of gearings
We get:

If the gear 3-4 slides to the left (disengaging gear
4-5) and gear 1-2 to the left (engaging 1-9) then
the power is transmitted through 0-1-9-6-10-12.

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