Gear Tooth Strength Calculation and Equation

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The following is general guidelines for determining or estimating your required gear tooth strength. When a more definitive strength calculation is required Engineers Edge suggests that you consult with a knowledgeable engineering professional or any one of the many gear engineering and design handbooks that are readily available.

When a gear train system is transmitting power and motion, it is safe to assume that all of the load is being carried by one tooth.This is most correct because as the load approaches the end of the tooth, where the bending force would be the greatest, a second tooth comes into mesh to share the load. Simple results can be obtained from the Lewis bending strength equation.

Wt = [S x F x Y]/Dp


Wt = Maximum transmitted load (lbs, N)
S = Maximum bending tooth stress taken as 1/3 of the tensile strength (psi, N/mm2)
F = Face width of gear (in, mm)
DP = Diametral Pitch, 1/module for equation only (in, mm).
Y = Lewis Factor (See Lewis Factor for Gears) (no units)

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Spur Gear Tooth Profile

The maximum bending tooth stress (S) is valid for well lubricated, low shock applications. For high shock, poorly lubricated applications, the safe stress could be as low as .025S. If your design calls for an harsh environment for your gear application, you might want to lower S to assure a reasonable amount of gear life.