1. Chapter 11 Design of Worm Gearing
Key Terms:
worm
worm gear
heat balance
middle plane

2. 11.1 Types and Characteristics of Worm Gearing

4. 1. Characteristics 1) A large speed ratio is obtained; (i=5~80)
2) Smooth and silent operation;
3) Self-locking will occur when a lead angle is smaller than equivalent friction angle;
4) Low efficiency and expensive antifriction materials necessary.

5. Sliding Velocity Where d1——the worm diameter n1——the speed for worm
——lead angle of worm

7. 2.Applications
Used in low power, intermittent operation case.
reducer

8. winch

10. 3.Types of Worm Gearing
a) Cylindrical Worm b) Circular Worm c) Cone Worm

14. Principle Types of Cylindrical Worms
Involute helicoidal Worms (ZI)
Archimedes Worms (ZA)

15. Convolute Worms (ZN)

16. 4. Forms of Worm and Worm Gear

17. 2 Principle Parameters and Geometrical Calculations of Worm Gearing
middle-plane

18. 1. Principle Parameters of Worm Gearing
Module m & normal pressure angle 
Requirements for Right Mesh
m: table 11.1，=200
ma1=mt2=m (table11.1)
a1=t2=(=200)
1= 2

19. (2) Worm diameter d1 & worm diameter factor q
d1: table 11.2
q=diameter factor ,q=d1/m,
d1=mq

20. (3) Speed ratio i, number of start z1and number of teeth z2 in worm gearing
standard speed ratio:
5, 7.5, 10, 12.5, 15, 20, 25, 30, 40, 50, 60, 70, 80
z1=1, 2 , 4, 6 z1  , i ,  
z2=iz1 26 z2 80 table 11.3

21. (4) Lead Angle 

22. (5) Standard Center Distance
Standard center distance series：
40．50．63．80．100．125．160．
（180）200．250. （280）
2. The Geometrical Calculation of Worm Gearing
table 11.4

26. 11.3 Causes of Worm Gear Failure and Principle of Design
1. Failure Modes wear, seizing, pitting
2. Principle of Design of Worm Gearing Contact Strength & Bending Strength of Worm gear
For Enclosed Gears Contact Strength: H [H]　　
Heat Calculation: t0 [t]
Bending Strength(z2>80): F [F]
2) For Opened Gears Bending Strength: F [F]

27. 3. Materials
• Worm
General : 45, 35SiMn, 40Cr, 40CrNi, 45~55HRC High speed & heavy load: Cr, 15Cr, 20CrMnTi, 56~62HRC Low speed & Low power: 45, 40, 220~300HBS
• Worm gear
High speed: ZCuSn10P1, ZCuSn5Pb5Zn5
Low speed & Heavy Load: ZCuAl10Fe3
Low speed & Light Load: HT150, HT200, QT

28. 4 Strength Calculations of Worm Gearing
1. Force Analysis
Normal Force: Fn
Radial Force: Fr
Tangential Force: Ft
Axial Force: Fa
(Right or Left Hand Law)
Ft1
Fa2
Fa1
Ft2
Fr2
Fr1
Ft1 = -Fa2
Fa1 = -Ft2
Fr1 = -Fr2

29. Magnitude:

30. Example
A worm gearing set is shown below. Draw the radial forces, tangential forces and axial forces of worm and worm gear on the sketch. Draw the rotational speed direction of worm. Determine the hand helix of the worm, draw on the sketch.

31. Solution

32. Design Load: K=KA Kv K KA——application factor, table 11.5
Kv——dynamic factor, Kv=1.0~1.1, Kv=1.1~1.2
K——load distribution factor, K=1, K=1.3~1.6

33. 2. Strength Calculation
1) Contact strength calculations

34. x——the length shifty factor, x=0.75;
——the overlap coefficient on transverse , =2;
——the conditional face angle, =1000 So

35. Check formula
Design formula
ZE——elasticity factor, table 11.6

36. 2) Tooth beam strength calculations
Check formula
Design formula
YF——profile factor, selected according to
zv2=z2/cos3 and x2 from Fig.11.5
Y——helix angle factor,

37. 3) Allowable stresses of worm gears
a. The allowable contact stresses:
ZN——The life factor of contact strength,

38. [OH]——Basic allowable contact stress,
table 11.7
for casting bronze worm gear, b<300MPa, design on contact fatigue strength.
table 11.8
for casting ampco or gray iron worm gear, b>300MPa, design on seizing strength.

39. b. The allowable bending stresses:
YN——the life factor of bending strength
[OF]——basic allowable bending stress,
table 11.9

40. 11.5 Efficiency, Lubrication and Thermal Capacity of Worm Gearing
1. Efficiency of Worm Gearing
——lead angle
v——equivalent friction angle, obtained according to sliding velocity vs from table 11.10

41. 2. Thermal Capacity of Worm Gearing
1) Cause of heat balance
2) Principle: Q1=Q2
heat amount: Q1=1000P(1-)
heat removed: Q2=KtA(t-t0)
3) Check working temperature of the oil:
Kt——the heat transfer coefficient, Kt=14~17.5
A——the area of surface of the housing,
t0——the temperature of the surrounding air, t0=200C

42. 1) Fins
1) Fins
2) Fan
3) Coils

43. Homework: A worm gearing set is shown below
Homework: A worm gearing set is shown below. Draw the radial forces, tangential forces and axial forces of worms and worm gears on the sketch. Draw the rotational direction of each shafts, Determine what the hand helix is of worm gear, draw on the sketch.

44. Solution
Right hand helix

45. Fig.11.5

49. Table11.7 Basic allowable contact stress for the worm gear that is made of casting bronze [OH]

50. Unilateral
Bilateral

51. The end Thanks!