Question

A spur gear has a module of 4 mm, number of teeth 21, a face width 25 mm and a pressure angle of 20°. It is transmitting a power of 4 kW at 25 rev/s. Taking a velocity factor of 1.5 and a form factor of 0.3, the stress in the gear tooth is about

Answer 1

m = 4 mm, T = 21,
b = 25 mm, $\varphi$ = 20°,

$F_t=\frac{P}{V}=\frac{4000}{\pi \times \frac{mT}{1000}\times N}$

$=\frac{4000}{\pi \times \frac{4\times 21}{1000}\times 25}\Rightarrow F_t=606.3N$

$606.3=\frac{{\sigma }_{b}mby}{c_v}\Rightarrow {\sigma }_b=\frac{606.3\times 1.5}{4\times 25\times 0.3}=30.3MPa$