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BITSPilaniPilani Campus
VINAYAK KALLURI
BITSPilaniPilani Campus
BITS Pilani, Pilani Campus
Introduction
Mechanical Drive : a mechanism which is intended to transmit
mechanical power over a certain distance, usually in terms of speed
and torque
Mechanical Drives are classified into two groups according to their
principle of operation
Mechanical drives that transmit power by means of engagement ,
e.g., gear drives and chain drives.
Mechanical drives that transmit power by means of friction , e.g.,
belt drives and rope drives.
The selection of proper mechanical drive for a given application
depends upon number of factors like centre distance, velocity ratio,
shifting arrangement, maintenance considerations and cost.
BITS Pilani, Pilani Campus
Gear Drives
Toothed wheels, which transmit power and motion
from one shaft to another by means of successive
engagement of teeth.
Most suitable drive, if the centre distance is small
The efficiency of gear drives is very high compared
to other mechanical drives ( up to 99 %)
Changing a velocity ratio over a wide range is
possible, with the help of special provision called
gear box.
BITS Pilani, Pilani Campus
Gear Drives
In any pair of gears, the smaller one is called pinion
and the larger one is called gear immaterial of
which is driving the other
When pinion is the driver, it results in step down
drive in which the output speed decreases and the
torque increases
when the gear is the driver, it results in step up
drive in which the output speed increases and the
torque decreases.
BITS Pilani, Pilani Campus
Classification
Gears are arranged between two shafts , which are
1. Parallel
2.Intersecting
3.Non parallel & Non intersecting
BITS Pilani, Pilani Campus
Used to transmit motion
between two parallel shafts
Teeth parallel to the axis of
rotation
It has the largest
applications and easy to
manufacture
Spur Gear
Spur Gear
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Helical Gear
Also used for parallel shafts, like spur gears
Teeth inclined to the axis of rotation.
The inclined tooth develops thrust loads
Quiet in operation
Teeth engage gradually reducing shocks
BITS Pilani, Pilani Campus
Herringbone Gears
Two helical gears with opposing helical angles side-by-side
Axial thrust gets cancelled
BITS Pilani, Pilani Campus
Bevel Gear
Teeth formed on conical surfaces and straight teeth tapering towards
an apex
Used for transmitting motion between intersecting shafts
Simple and most commonly used gear in bevel gear family
BITS Pilani, Pilani Campus
Spiral Bevel GearA bevel gear with a helical angle of spiral teeth.
More complex to manufacture, but offers a higher
strength and lower noise
Zerol Bevel GearA spiral bevel with zero degree of spiral angle
tooth advance
It has the characteristics of both the straight and
spiral bevel gears
Miter Gear
For one to one ratio
Used to change the direction
Bevel Gear
BITS Pilani, Pilani Campus
Hypoid Gear
Crossed Helical Gear
Two helical gears of opposite helix angle will
mesh if their axes are crossed
Strength is very less due to point contact
Also called as screw gears
Similar to spiral bevel gears, but have non
intersecting axis
Blanks of hypoid gears are hyperboloids of
revolution. Hence the name.
BITS Pilani, Pilani Campus
Worms and worm gears
oUsed for large speed reductions (more than 3) between two
perpendicular and non-intersecting shafts
o Driver called worm resembles a screw.
BITS Pilani, Pilani Campus
GEARS
WormCrossed
helical
BevelHelicalSpur
Intersecting ShaftNon Parallel &
Non Intersecting Shaft
Hypoid
Parallel shaft
Double
(Herringbone)Single
Bevel Spiral BevelZerol Bevel Miter
Classification Summary
BITS Pilani, Pilani Campus
Classification: A special cases
Rack and pinion
Comprises a pair of gears which convert rotational motion
into linear motion.
circular pinion engages teeth on a linear "gear( the rack)
Rotational motion applied to the pinion will cause the
rack to move to the side, up to the limit of its travel.
BITS Pilani, Pilani Campus
Classification: A special cases
INTERNAL GEAR
Used to transmitting motion between two parallel shafts
Annular wheels are having teeth on the inner periphery
The meshing pinion and annular gear are running in thesame direction
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For Different GEARS
Gear Geometry Nomenclature
Gear Force Analysis
Gear tooth Bending strength
Gear tooth Surface fatigue
Design of Gear Drive
BITS Pilani, Pilani Campus
NOMENCLATURE
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IMPORTANT PARAMETERS OF GEARS
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Conjugate Action
Cam A and follower B in
contact. When the
contacting surfaces are
involutes profiles, the
ensuing conjugate action
produces a constant angular-
velocity ratio.
BITS Pilani, Pilani Campus
Law of Gearing
BITS Pilani, Pilani Campus
Law of Gearing
Because of similar triangles
V1cos = V2cos
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Law of Gearing
When two gears are in mesh, their pitch circles roll on
one another without slipping.
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Constructing an involute profile
A0-starting point
A1B1=A1A0A2B2=A2A0 and so on
Divide the base circle into
a number of equal parts,
and construct radial lines
OA0, OA1, OA2, etc.
Beginning at A1, construct
perpendiculars A1B1, A2B2,
A3B3, etc.
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Involute curve
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Involute curve
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Gear involute action
To transmit motion at a constant angular-velocity ratio, the pitch point
must remain fixed; that is, all the lines of action for every instantaneous
point of contact must pass through the same point P.
BITS Pilani, Pilani Campus
Gear layout circles
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Pressure line or line of action and pressure angle
the radius of the base circle, rb = r cos
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A template for drawing gear teeth.
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Tooth action in involute profiles
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Line of action
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Tooth Systems
Standard and Commonly Used Tooth Systems for Spur Gears
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Tooth Systems
Tooth Sizes in General Uses
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Contact Ratio
Arc of action
BITS Pilani, Pilani Campus
BITS Pilani, Pilani Campus
Problem:
A spur gear set has a module of 4 mm and a velocity ratio of 2.8. the
pinion has 20 teeth. Find the number of teeth on the driven gear, the
pitch diameters, and theoretical center-to-center distance. If a
contact length is 20 mm and pressure angle is 250, then find the
contact ratio.
Ans:
P= m = 12.56 mm
mc = Lab/ p cos = 20/ 12.56 x cos 250 = 1.75
BITS Pilani, Pilani Campus
Interference in gears, why it occurs?
1) Due to the presence of non-
involute portion on the tooth
below the base circle
2) Interference is present if C &
D, the points of tangency of
line of action to the base
circles, lie inside the initial and
final points of contact (equal to
the points of intersection of the
line of action with the
addendum circles).
BITS Pilani, Pilani Campus
The consequence of interference is cutting away of material
resulting in weakening of the gears against fatigue.
When gear teeth are produced by a generation process,
interference is automatically eliminated because the cutting tool
removes the interfering portion of the flank. This effect is called
as undercutting.
But gear generation is not a solution to interference problem
because the gear would anyway have been weakened in strength.
The solution lies in controlling the minimum number of teeth
on the pinion and the pressure angle.
Rober Lipp (Machine Design, Vol. 54, 1982) carried out a
detailed study on the control of the interference in gears.
Interference in gears
BITS Pilani, Pilani Campus
Avoiding Interference in Gears (Robert Liipp study)
For a 20 pressure
angle, with k = 1, NP=13
i.e. 13 teeth on pinion
and gear are
interference-free.
BITS Pilani, Pilani Campus
Interference can also be avoided (or reduced) by using a larger pressure angle.
This results in a smaller base circle, so that more of the tooth profile becomes involute.
Thus the demand for smaller pinions with fewer teeth will require the pressure angle of 25 degrees
The pressure angle can not be arbitrarily large because a larger pressure results in
higher bearing loads
Lower the torque capacity and
Decreased contact ratio
L1ab
Interference in Gears
BITS Pilani, Pilani Campus
Problem: 138
For a spur gear-set with = 20, while avoiding
interference, find:
(a) The smallest pinion tooth count that will run
with itself
(b) The smallest pinion tooth count at a ratio mG =
2.5, and the largest gear tooth count possible with
this pinion
(c) The smallest pinion that will run with a rack
BITS Pilani, Pilani Campus
BITS Pilani, Pilani Campus
Parallel Helical Gears
Parallel helical gears are used to transmit motion between parallel
shafts. The helix angle is the same on each gear, but one gear must
have a right-hand helix and the other a left-hand helix.
The initial contact of spur-gear teeth is a line extending all the way
across the face of the tooth. The initial contact of helical-gear teeth
is a point that extends into a line as the teeth come into more
engagement.
BITS Pilani, Pilani Campus
Parallel Helical Gears
In spur gears the line of contact is parallel to the axis of rotation; in
helical gears the line is diagonal across the face of the tooth.
It is this gradual engagement of the teeth and the smooth transfer of
load from one tooth to another that gives helical gears the ability to
transmit heavy loads at high speeds.
Helical gears subject the shaft bearings to both radial and thrust
loads. To avoid thrust, a double helical gear (herringbone) is
equivalent to two helical gears of opposite hand, mounted side by
side on the same shaft.
When two or more single helical gears are mounted on the same
shaft, the hand of the gears should be selected so as to produce the
minimum thrust load.
BITS Pilani, Pilani Campus
Parallel Helical Gears
BITS Pilani, Pilani Campus
Standard Tooth Proportions for Helical Gears
[1 mn]
[1.25 mn]
BITS Pilani, Pilani Campus
A parallel helical gearset consists of a 19-tooth pinion
driving a 57-tooth gear. The pinion has a left-hand helix
angle of 30, a normal pressure angle of 20, and a normal
module of 2.5 mm. Find:
(a) The normal, transverse, and axial circular pitches
(b) The transverse diametral pitch and the transverse
pressure angle
(c) The addendum, dedendum, and pitch diameter of each
gear
Problem
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Solution
BITS Pilani, Pilani Campus
Interference in helical gears
The smallest pinion that
run with a rack is
Largest gear with a specified pinion is
Gear ratio mG = NG/NP = m, the smallest pinion tooth count is
The smallest tooth number NP of a helical-spur pinion that will
run without interference with a gear with the same number of
teeth is
BITS Pilani, Pilani Campus
Problem: 139
For a helical gear-set with = 20 and = 30
while avoiding interference, find:
(a) The smallest pinion tooth count that will run
with itself
(b) The smallest pinion tooth count at a ratio mG =
2.5, and the largest gear tooth count possible with
this pinion
(c) The smallest pinion that will run with a rack
BITS Pilani, Pilani Campus