Bending Stresses in Gears

Gear Stresses Gears experience two principal types of stresses; bending stress at the root of the teeth due to the transmitted load and contact stresses on the flank of the teeth due to repeated impact, or sustained contact, of one tooth surface against another. A simple method of calculating bending stresses is presented below. Bending Stresses The calculation of bending stress in gear teeth can be based on the Lewis formula

where W_t = transmitted load (N), F = face width (m or mm), m = module (m or mm), and Y = the Lewis form factor and can be found from the below table. When teeth mesh, the load is delivered to the teeth with some degree of impact. The velocity factor is used to account for this and is given, in the case of cut or milled profile gears, by the Barth equation.
where V is the pitch line velocity which is given by
where d is in mm and n is in rpm. Introducing the velocity factor into the Lewis equation gives
This equation forms the basis of a simple approach to the calculation of bending stresses in gears.

*N, Number of Teeth*	Y *Φ = 20°* *a = 0.8 m* *b = m*	Y *Φ = 20°* *a = m* *b = 1.25 m*
12	0.33512	0.22960
13	0.34827	0.24317
14	0.35985	0.25530
15	0.37013	0.26622
16	0.37931	0.27610
17	0.38757	0.28508
18	0.39502	0.29327
19	0.40179	0.30078
20	0.40797	0.30769
21	0.41363	0.31406
22	0.41883	0.31997
24	0.42806	0.33056
26	0.43601	0.33979
28	0.44294	0.34790
30	0.44902	0.35510
34	0.45920	0.36731
38	0.46740	0.37727
45	0.47846	0.39093
50	0.48458	0.39860
60	0.49391	0.41047
75	0.50345	0.42283
100	0.51321	0.43574
150	0.52321	0.44930
300	0.53348	0.46364
Rack	0.54406
Note: a = addendum; b = dedendum; Φ = pressure angle, and m = module

References:

CHILDS, PETER R. N. MECHANICAL DESIGN ENGINEERING HANDBOOK. BUTTERWORTH-HEINEMANN LTD, 2018.