1. Part III Design of Power Transmission Systems

6. Chapter 10 Design of Gears
Key Terms:
spur gears
helical gears
bevel gears
pinion
gear
driving gear
driven gear
tangential force
radial force
axial force
normal force
module
face width

7. 10.1 Introduction Advantages and Disadvantages of Gears Advantages:
high efficiency, High reliability, Constant transmission ratio, compactness, etc.
Disadvantages:
Cost much, can not be used in the case of large center distance, etc.

8. 2. Types of Gears 1)Classification by working condition
encased gearing
open gearing
semi-open gearing 2) Classification by the case hardness of gear tooth
soft tooth surface (case hardness  350HBS)
hard tooth surface (case hardness > 350HBS)

9. 10.2 Gear failures and Design Criteria
1) breakage

10. 2) pitting

12. 3) gluing

14. 4) abrasive wear

15. 5) ridging

16. 2. Design Criteria 1)Cased gear: Contact Strength Bending Strength
2)Opened gear:

17. 3. Gear Materials (Table 10.1)
1）forged steel
carbon steel
alloy steel
quench、 temper、 (Q&T)、 normalize
casehardening
carburizing
nitriding
Heat-treating

18. 2) Cast Steel
3) Cast Iron
gray cast iron
nodular iron
4) Non-metal

19. 10.8 Gear Blank Design
1) Gear shafts (e < 2mt)

20. 2) Gears with solid hub (da<200mm)

21. 3) Gears with thinned web (da>200~500mm)

22. 4) Spoked gears (da > 400~1000mm)

23. Styles
Gear shaft
Solid hub

24. Styles
spoke
Gear shaft

25. Styles
Thinned web

26. 10.9 Efficiency and Lubrication in Gear Sets
mesh efficiency,
stirring efficiency,
bearing efficiency

27. 2. Lubrication
1) bath lubrication (v<12m/s)

29. 2) splash lubrication
3) atomized lubrication (v> 12m/s)

30. 10.4 Design of Spur Gears

31. Nomenclature of Spur Gear

32. 1. Forces on Spur Gear Teeth
Normal Force Fn
Radial Force Fr
Tangential Force Ft
Pinion
Gear
Direction:

33. Magnitude: T1——nominal torque d1——reference diameter of pinion
——pressure angle

34. Example 1
Mating 2-module, 200 gears are shown. Gear 1 is driving at 960 rpm and transmitting 25 kW. Gear 2 is driving a conveyor.Draw the radial and tangential forces on gears. Compute their magnitude.
Solutions

35. 2. Calculated Load Where Ftc—— calculated load F —— nominal load
K—— load factor

36. K=KAKVKK Where KA—— application factor KV——dynamic factor
K——load partition factor
K——load distribution factor \

37. KA KA is an application factor
considers that the load variation, vibration, shock, speed changes which may result in peak loads greater than nominal loads.
Table 10.2

38. KV
Kv is a dynamic factor which accounts for the higher actual load caused by the deformation of gear teeth, the base pitch error, profile error, backlash, etc.
for spur gears: Kv=1.05~1.4
for helical gears: Kv=1.02~1.2

40. Modified Tooth Face
base pitch
pb1>pb2

41. K
K is a load partition factor which reflects the non-uniformity of tooth loading among two or more teeth due to manufacture error and teeth deformation.
for spur gears: K=1~1.2
for helical gears: K=1~1.4

42. K
K is a load distribution factor which reflects the non-uniformity of tooth loading over the face width of the teeth, arising from gear and mounting inaccuracy, elastic deformation of shafts and bearings, etc.
for soft surface: K=1~1.2
for hard surface: K=1.1~1.35

43. Fig.10.9 Uneven distribution load on gear teeth

44. Crowning gear teeth

45. 3.Contact Fatigue Strength of Spur Gear Teeth
Design Criterion:
H[H]
Where
H——contact stress
[H]——allowable contact stress

46. Contact Stress Fn: normal force L: contact length of cylinders
1, 2: Poisson’s ratio
E1，E2：elastic modulus
1, 2: radius of curvature

47. let Z——coefficient of contact ratio ZE——elastic coefficient 弹
table 10.3

48. Mating Teeth

49. let
ZH——zone factor
for standard spur gear ZH=2.5

50. Contact Strength
Check Formula:
Design Formula:
d——face width factor

51. Notes If H1> H3 then gear 3 is stronger than gear 1
• reference diameter or center distance is related to contact strength
• Where [H]=min{[H1], [H2]}

52. 4.Bending Fatigue Strength of Spur Gear Teeth
Design Criterion:
F[F]
Where
F——bending stress
[F]——allowable bending stress

53. Gear teeth Analyzed as a cantilever beam

54. YFa——tooth form factor, table 10

55. Ysa——stress concentration factor , table 10.4
Y——coefficient of contact ration

56. Bending Strength
Check Formula:
Design Formula:

57. Notes If F1> F3 then gear 3 is stronger than gear 1
module m is related to bending strength
Where

58. Example 2
A spur gear set, its parameters are shown below by table. Try to compare which gear is easier to pitting, which one is easier to breakage?
gear m z b
YFa
YSa
[F]
[H] 1 3 17 60
2.97
1.52
390
500 2 45 50
2.35
1.68
370
470

59. 5.Allowable Stresses and Design Parameters
Allowable Contact Stress:
Hlim——endurance limit for contact strength
KHN——life factor for contact strength
SH——factor of safety for contact strength

60. (2) Allowable Bending Stress:
Flim——endurance limit for bending strength
KFN——life factor for bending strength
SF——factor of safety for bending strength
YST——stress correction factor ， YST=2.0

61. (3) Endurance limits Hlim, Flim
Fig and Fig.10.15
(4) Life factors KHN, KFN
Fig and Fig.10.17
N=60njLh
N——expected number of load cycles
n ——rotational speed of the gear
j——number of load application
Lh——design life

62. (5) Factor of safety SH, SF
Table 10.5
(6) Design parameters
1)Pressure angle 

63. 2) Number of teeth z, module m
for encased gears : z1=20~40;
for open gears: z1=17~20;
z2=uz1;
m: table 10.6
3) Face width factor
table 10.7
b2=b, b1=b+(5~10)mm

64. 4) Quality Classes of Gears
P200, Table 10.8

65. 10.6 Design of helical Gears
Right hand helix
Key Terms:
virtual spur gears
virtual number of teeth
Left hand helix

66. 1. Forces on Helical Gear Teeth
Pinion
Normal Forces Fn :
Radial Force Fr
Tangential Force Ft
Axial Force Fa
(Right or Left Hand Law)

67. Right or Left Hand Law
Ft1= -Ft Fr1= -Fr Fa1= -Fa2

68. Magnitude: Where: b——base helix angle
n——normal pressure angle , n=200
t——transverse pressure angle

69. Example 3
The pinion of a pair of helical gears (shown below) has a normal module of 2, a normal pressure angle of 200, 32 teeth, and a helix angle of 150. If the pinion is rotating at 750 rpm while transmitting 20kW, draw and compute the tangential force, the axial force, and the radial force.

70. Solution

71. 2. Contact Fatigue Strength of Helical Gear Teeth
Check Formula:
Z——helix angle factor,
ZH——zone factor, Fig.10.12
Z——coefficient of contact ratio, Z=0.75~0.88

72. Design Formula:

73. Y——contact ratio factor,
3. Bending Fatigue Strength of Helical Gear Teeth
Check Formula:
Y——helix angle factor, Y=0.85~0.92
YFa——tooth form factor, table 10.4,
YSa——stress concentration factor, table 10.4
Y——contact ratio factor,

74. Design Formula:

75. 10.7 Design of Straight Bevel Gears
large end

76. 1. Straight Bevel Gear Geometry
Ov2
d1——reference diameter
dm——mean reference diameter
dv——reference diameter of virtual spur gears

78. 2. Forces on Straight Bevel Gear Teeth
Normal Force Fn:
Radial Force Fr
Tangential Force Ft
Axial Force Fa
(point to the large end)
Ft1= -Ft2 Fr1= -Fa2 Fa1= -Fr2

80. Example 3
A bevel-helical gear-type speed reducer is shown below, in order to counteract the axial forces on the shaft II, draw tangential forces, radial forces, axial forces on bevel gears and helical gears. determine left hand helix or right hand helix on helical gears.

82. 3. Contact Fatigue Strength on Straight Bevel Gear Teeth

84. ZE——elastic coefficient, table 10.3 ZH——zone factor, ZH=2.5
K=KA Kv KK
KA——application factor, table 10.2
Kv——dynamic factor, Kv=1.1~1.4
K—— load partition factor, K=1;
K——load distribution factor, K=1.1~1

85. 4. Bending Fatigue Strength on Straight Bevel Gear Teeth

86. YFa, Ysa—according to ,
obtained from table10.4

87. Conclusion 1)Failure modes of gears; 2) Force analysis of gear tooth;
3) Design criteria of Gears;
4) Design of contact fatigue strength
& bending fatigue strength.

88. Fig.10.14

89. Fig.10.15

92. Fig.10.12

95. The end Thanks!