Calculation of Gear Tooth Strength

Reliance develops and produces various gear for many years, with extensive experience and knowledge in the technical background. 

In purpose to calculate the forces and strength of the gear teeth, Reliance has developed a formula for calculating forces or torque, to make sure the customer choose the correct gear for his application. The calculation is relatively simple and does not take much time. 

Reliance considers two forces: 

Fb – Allowable force on the tooth for bending 

Fbw – Force required for tooth wear 

Usually, we want to calculate the smaller force, which is typically the force for wear. 

Both calculations below should be performed, and the lower value should be considered: 

Formula for calculating gear tooth strength: 

For strength: Fbs = 177.7 x J x F x M x Kv x Km [N] 

For wear: Fbw = 14.64 x N x I x F x M x Kv [N] 

Calculation and explanation of the above values: 

N - Teeth Number  

F - Tooth Width  in mm 

M – Module  

Kv – Dynamic speed safety factor, Kv calculation: 

Vt  = values in (m/s) 

For AQME 10 gear wheels 

Km - Safety factor according to the material of the gear, chosen from the table below: 

J – Geometric bending safety factor, taken from the table below: 

I – Geometric wear safety factor, taken from the table below: 

To complete the calculation, another safety factor can be added according to the calculation below: 

For tooth root strength: Fts = Fbs/Ka, where Ka & Ca are Application factors 

For tooth flank pitting (wear): Ftw = Fbw/Ca 

To find the allowable Torque, multiply the force by the radius of the gear wheel. 

For further calculation details, refer to section T4-11.