Question

A spur gear has a module of 3 mm, a number of teeth 16, a face width of 36 mm, and a pressure angle of ${20}^0$. it is transmitting power of 3 kW at 20 rev/s. Taking a velocity factor of 1.5 and a form factor of 0.3, the stress in the gear tooth in MPa, is about

• A. 32
• B. 70
• C. 58
• D. 46

Answer 1

The correct option is D 46

Beam strength $S_b={\sigma }_{b}bmY$

$={\sigma }_b\times 36\times 3\times 0.3d_g=m\times t_g=3\times 16=48mm{M}_t=\frac{3\times 1000}{2\pi \times 20}N-m{M}_t=\frac{3\times {10}^3}{2\pi \times 20}\times {10}^{3}N-m$

=23873.241 N-mm

Tangential force due to torque,

$P_t=\frac{2\times 23873.241}{48}=994.718N{P}_{eff}=P_t\times C_V=994.718\times 1.51492.0775={\sigma }_b\times 36\times 3\times 0.3{\sigma }_b=46MPa$