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 Wt = 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.
