Gears transmit power and motion between two shafts. There are different types of gears classified based on the orientation of shafts and teeth. Gear geometry includes parameters like pitch circle, pressure angle, addendum and dedendum. Strength of gear teeth depends on factors like load, tooth dimensions and material properties. Dynamic loads account for inaccuracies and are higher than steady loads. Design considers factors like load calculation, permissible stresses, and load distribution to ensure safe and reliable operation of gear drives.

1. Design of Gear Drives

2. Presentation Outline
 Introduction
 Types of Gears and their Applications
 Gear Geometry
2

3. Introduction
 Gears are defined as toothed wheels or
multi-lobed cams, which transmit power and
motion from one shaft to another by means
of successive engagement of teeth.
3

4. Features of Gear Drives
 Gear Drives have the following advantages:
 It transmits exact velocity ratio
 Large power can be transmitted
 It may be used for small centre distances of
shafts
 High efficiency
 Reliable operation and service
 Compact layout
4

5. Features of Gear Drives contd..
 Gear Drives have the following disadvantages:
 Relatively higher manufacturing cost
 Higher maintenance cost
 Cause noise and vibration when it is subjected to
wear and tear
 Requires suitable lubricants and reliable method /
mechanism of applying it for its proper operation
5

6. Classification of Gears
 The gear wheels may be classified based on
the following criteria
1. According to the orientation of axes of the
shafts
2. According to the peripheral velocity of the
gears
3. According to the type of gearing
4. According to the orientation of teeth on the
gear surface
6

7. 1. According to the orientation of
axes of the shafts
 The axes of two shafts between which the
motion is to be transmitted may be
categorized as
a. Parallel
b. Intersecting
c. Non-intersecting and non-parallel
7

8. 1. According to the orientation of axes
of the shafts contd..
a. Parallel - Spur gears and helical gears (single
and double) fall under this category.
8
Spur Gears Helical Gears

9. 1. According to the orientation of axes
of the shafts contd..
b. Intersecting – Two non-parallel or intersecting,
but co-planar shafts can be connected by
bevel gears.
9
Straight Bevel Gears Helical Bevel Gears

10. 1. According to the orientation of axes
of the shafts contd..
c. Non-Intersecting and non-parallel – These
gears are called skew bevel gears or hypoid
bevel gears
10
Hypoid Bevel Gears

11. 2. According to the peripheral
velocity of the gears
 In this case gears may be classified as
a. Low velocity – Peripheral velocity < 3 ms-1
b. Medium velocity – Peripheral velocity will be
3 –15 ms-1
c. High velocity – Peripheral velocity > 15 ms-1
11

12. 3. According to the type of gearing
 The gears may be classified as
a. External gearing – The gears of the two
shafts mesh externally with each other
b. Internal gearing - The gears of the two
shafts mesh internally with each other. The
larger of the two wheels is called Annular
wheel and smaller wheel is called Pinion.
c. Rack and pinion – The gear of a shaft
meshes externally and internally with the
gears in a straight line. The straight line gear
is called Rack and the gear wheel is called
the Pinion. 12

13. 3. According to the type of gearing
contd..
13
External Gearing Internal Gearing Rack & Pinion

14. 4. According to the orientation of
teeth on the gear surface
 In this case gears may be classified as
a. Straight – Spur gears
b. Inclined – Helical gears
c. Curved – Spiral gears
14

15. Gear Geometry
 Gears have their own geometry.
15

16. Gear Geometry contd..
1. Pitch Circle: An imaginary circle which by pure
rolling action, would give the same motion as the
actual gear.
2. Pitch Circle Diameter: The diameter of the pitch
circle. The size of the gear is usually specified by
the pitch circle diameter.
3. Pitch Point: Common point of contact between two
pitch circles.
4. Pressure Angle or Angle of Obliquity (Ф): The angle
between the common normal to two gear teeth at
the point of contact and the common tangent at the
pitch point. (Generally 14.50 and 200) 16

17. Gear Geometry contd..
5. Addendum: Radial distance of a tooth from the pitch
circle to the top of the tooth.
6. Dedendum: Radial distance of a tooth from the pitch
circle to the bottom of the tooth.
7. Addendum Circle: The circle drawn through the top
of the teeth and is concentric with the pitch circle.
8. Dedendum Circle: The circle drawn through the
bottom of the teeth. Also called Root Circle.
9. Circular Pitch (Pc): The distance measured on the
circumference of the pitch circle from a point of one
tooth to the corresponding point on the next tooth.
17

18. Gear Geometry contd..
9. Circular Pitch (Pc) contd..
Mathematically, Circular Pitch
where
D – Diameter of the Pitch Circle (mm)
Z – Number of teeth on the gear wheel
 It can be shown that the two gears will mesh together
correctly, if the two wheels have the same circular pitch.
 If D1 and D2 are the pitch circle diameters of the two
meshing gears with teeth Z1 and Z2 respectively, then
for them to mesh correctly,
18
Z
D
Pc


2
2
1
1
Z
D
Z
D
Pc



 or
2
1
2
1
Z
Z
D
D


19. Gear Geometry contd..
10. Module (m): It is the ratio between the pitch
circle diameter in millimeters to the number of
teeth.
Module
m can take values 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6,
8, 10, 12, 16, 20, ………..
If Dp and Dg are the pitch circle diameters of the
meshing pinion and gear, having teeth Zp and Zg
respectively, then
19
Z
D
m 
p
p mZ
D  and g
g mZ
D 

20. Gear Geometry contd..
 The centre-to-centre distance (α) between the
pinion and gear is given by
11. Clearance: This is the amount by which the
dedendum of a given gear exceeds the
addendum of its mating tooth.
20
   
g
p
g
p mZ
mZ
D
D 



2
1
2
1

 
2
g
p Z
Z
m 



21. Gear Geometry contd..
12. Total Depth: Radial distance between the
addendum and the dedendum circle of a gear.
It is equal to the sum of the addendum and
dedendum.
13. Working Depth: Radial distance from the
addendum circle to the clearance circle. It is
equal to the sum of the addendum of the two
meshing gears.
14. Tooth Thickness: Width of the tooth measured
along the pitch circle.
15. Tooth Space: Width of space between the two
adjacent teeth measured along the pitch circle.21

22. Gear Geometry contd..
16. Top Land: Surface of the top of the tooth.
17. Flank of the tooth: Surface of the tooth below
the pitch surface.
18. Profile: Curve formed by the face and flank of
the tooth.
19. Fillet Radius: The radius that connects the root
circle to the profile of the tooth.
20. Path of Contact: The path traced by the point
of contact of two teeth from the beginning to
the end of engagement.
22

23. Velocity Ratio (i)
 This is the ratio of angular velocity of the driving
gear (pinion) to the angular velocity of the driven
gear.
 This is also the ratio of number of teeth between
gear and pinion.
where
np – Speed of pinion (rpm)
ng – Speed of gear (rpm)
23
p
g
g
p
Z
Z
n
n
i 


24. Standard Systems of Gear Teeth
 All standard systems prescribe involute
profile for gear teeth. There are three
standard systems for the shape of gear
teeth:
 14.50 full depth involute system
 200 full depth involute system
 200 stub involute system
24

25. Standard Systems of Gear Teeth
contd..
25
Parameter 14.50 full depth
system
200 full depth
system
200 stub
system
Pressure Angle 14.50 200 200
Module m m m
Addendum m m 0.8m
Dedendum 1.157m 1.25m m
Clearance 0.157m 0.25m 0.2m
Working Depth 2m 2m 1.6m
Total Depth 2.157m 2.25m 1.8m
Tooth Thickness 1.5708m 1.5708m 1.5708m

26. Causes of Gear Failure
 The different modes of failure of gears are
as follows:
 Bending failure: Breakage of gear teeth
 Pitting: Surface fatigue failure due to
formation of pits
 Scoring: Due to generation of excessive heat
 Abrasive wear: Damage of gear surface due
to foreign particles
 Corrosive wear: Due to corrosion of gear
surfaces 26

27. Design Considerations for Gear
Drives
 The following requirements must be met in
the design of a gear drive
 Gear tooth should have sufficient strength
against failure under static or dynamic
loading
 Gear teeth should have high wear resistance
 Economical usage of space and material
 Proper alignment of gears and minimum
deflection of shafts
 Efficient lubrication of gears 27

28. Strength of Gear Teeth
 This is determined from the Lewis Equation
and provides satisfactory results.
 Consider each tooth as a cantilever beam
loaded by a normal load (WN)
 It is resolved into two components, a
tangential component (WT) and a radial
component (WR) acting perpendicular and
parallel to the centreline of the tooth
respectively as shown below.
28

29. Strength of Gear Teeth contd..
 The tangential component (WT) introduces a
bending stress which tends to break the tooth.
 The radial component (WR) introduces a
compressive stress of relatively small magnitude.29

30. Strength of Gear Teeth contd..
 Hence the bending stress is used as the basis for
design calculations.
 It can be shown that the section BC is the section
of maximum stress or the critical section.
 Maximum Bending Stress at section BC is given
by
30
I
My
w 


31. Strength of Gear Teeth contd..
where
M – Maximum bending moment at critical section
BC given by WT X h (Nmm)
WT – Tangential load on the tooth (N)
h – Length of the tooth (mm)
y – Half the thickness of the tooth (t) at BC = t/2
(mm)
I – Moment of inertia about the centreline of the
tooth bt3/12 (mm4)
b – Width of gear face (mm)
31

32. Strength of Gear Teeth contd..
 By substituting the values
32
2
3
6
12
2
1
)
(
bt
h
W
bt
t
h
W
T
T
w 


h
bt
W w
T
6
2


 In this expression, t and h are variables depending
upon the size of the tooth and its profile.

33. Strength of Gear Teeth contd..
 Let t = xpc and h = kpc ; where x and k are constants
 Substituting x2/6k = y ; where y is a constant
 The quantity y is known as Lewis form factor and
WT is called the beam strength of the tooth.
33
k
x
bp
kp
p
x
b
W c
w
c
c
w
T
6
6
2
2
2

 

my
b
y
bp
W w
c
w
T 

 


34. Strength of Gear Teeth contd..
 Value of y is independent of the size of the tooth
and depends only on the number of teeth and the
system of gear teeth.
 The value of y in terms of the number of teeth may
be expressed as:
 for 14.50 full depth
involute system
 for 200 full depth
involute system
 for 200 stub system
34
T
y
684
.
0
124
.
0 

T
y
912
.
0
154
.
0 

T
y
841
.
0
175
.
0 


35. Permissible Working Stress for
Gear Teeth
 The permissible working stress (σw) depends
upon the material for which an allowable static
stress (σo) is specified.
 According to the Barth formula, the permissible
working stress
where
σo – Allowable static stress (N/m2)
Cv – Velocity factor 35
v
o
w C

 

36. Permissible Working Stress for
Gear Teeth contd..
Velocity factor (Cv) are expressed as follows:
 for ordinary cut gears operating at
velocities up to 12.5 m/s.
 for precisely cut gears operating at
velocities up to 12.5 m/s.
 for very precisely cut gears operating
at velocities up to 20 m/s.
36
v
Cv


3
3
v
Cv


5
.
4
5
.
4
v
Cv


6
6

37. Permissible Working Stress for
Gear Teeth contd..
 for high precision gears
operating at velocities up to
20 m/s.
 for non-metallic gears
 In the above expressions v is the pitch line velocity
in m/s.
37
v
Cv


75
.
0
75
.
0
25
.
0
1
75
.
0









v
Cv

38. Design Tangential Tooth Load
 It can be expressed that
where
WT – Permissible tangential tooth load (N)
P – Power transmitted (W)
v – Pitch line velocity (m/s)
CS – Service factor
38
S
T C
v
P
W 

39. Design Tangential Tooth Load
contd..
 The table below shows service factor values for
different types of loads.
39

40. Dynamic Tooth Load
 The dynamic loads are generated due to
the following reasons:
 Inaccuracies of tooth spacing
 Irregularities in tooth profiles
 Deflections of teeth under loads
 A closer approximation to the actual
conditions may be made by the use of
equations generated through extensive
tests. 40

41. Dynamic Tooth Load contd..
 It can be expressed that
where
WD – Total dynamic load (N)
WT – Steady load due to transmitted torque
(N)
WI – Incremental load due to dynamic action
(N)
 The incremental load (WI) depends upon the pitch
line velocity, face width, material of gears, accuracy
of cut and tangential load. 41
I
T
D W
W
W 


42. Dynamic Tooth Load contd..
 For average conditions, the dynamic load is
determined with the Buckingham equation:
where
WD – Total dynamic load (N)
WT – Steady transmitted load (N)
v – Pitch line velocity (m/s)
b – Face width of gears (mm)
C – Dynamic factor (N/mm) 42
T
T
T
I
T
D
W
C
b
v
W
C
b
v
W
W
W
W







.
21
)
.
(
21

43. Dynamic Tooth Load contd..
 Value of C may be determined by:
where
K – 0.107, for 14.50 full depth involute system
– 0.111, for 200 full depth involute system
– 0.115, for 200 stub system
EP – Young’s modulus for the pinion material (N/mm2)
EG – Young’s modulus for the gear material (N/mm2)
e – Tooth error in action (mm) 43
G
P E
E
e
K
C
1
1
.



44. Static Tooth Load
 Static tooth load (Endurance strength) is
obtained by Lewis formula by substituting elastic
limit stress (σe) in place of permissible working
stress (σw) as shown below:
 For safety against tooth breakage, static tooth
load (WS) should be greater than the dynamic
load (WD).
44
my
b
y
bp
W e
c
e
S 

 


45. Wear Tooth Load
 The maximum load that gear teeth can carry,
without premature wear depends upon the radii
of curvature of the tooth profiles and on the
elasticity and surface fatigue limits of the
materials. The limiting load for satisfactory wear
of gear teeth, is given by:
where
WW – Limiting load for wear (N)
DP – Pitch circle diameter of pinion (mm)
b – Face width of pinion (mm)
45
bQK
D
W P
W 

46. Wear Tooth Load contd..
where
Q – Ratio factor
for external gears
for internal gears
V.R – Velocity Ratio = TG/TP
K – Load-stress factor (N/mm2)
46
P
G
G
T
T
T
R
V
R
V
Q




2
1
.
.
2
P
G
G
T
T
T
R
V
R
V
Q




2
1
.
.
2

47. Wear Tooth Load contd..
Load Stress Factor
where
σes – Surface endurance limit (N/mm2)
Ф – Pressure angle
EP – Young’s modulus for the pinion material
(N/mm2)
EG – Young’s modulus for the gear material
(N/mm2) 47








G
P
es
E
E
Sin
K
1
1
4
.
1
2

