How to use this calculator
Enter the tooth size (module or diametral pitch), the teeth on each gear, the face width and the pinion speed, then the power or torque. Add an allowable bending stress to get the safety factor and the power rating.
Formulas
Worked example
Shigley Example 14-1: 16 teeth, Pd = 8, 20°, F = 1.5 in, 1200 rpm, σall = 10 kpsi (cut teeth)
- d = 16/8 = 2 in, V = π(2)(1200)/12 = 628 ft/min.
- Kv = (1200 + 628)/1200 = 1.52; Y = 0.296 for 16 teeth.
- Wt = FYσall/(KvPd) = 1.5(0.296)(10 000)/(1.52 × 8) = 364 lbf.
- Power = WtV/33 000 = 6.93 hp.
Frequently asked questions
Why is the pinion the critical gear?
With fewer teeth its teeth are thinner at the root, so its Lewis form factor Y is smaller and its bending stress higher for the same load.
What does the velocity factor account for?
Dynamic loads from tooth spacing and profile errors, which grow with pitch-line speed. Better-made (hobbed, shaved, ground) teeth have smaller factors.
Is the Lewis equation enough for design?
It is the starting point. The AGMA method adds factors for load distribution, size, rim thickness and reliability, and checks surface (pitting) stress as well.