Question

A spur gear has a module of 3 mm, number of teeth 20, and a face width of 40 mm. It is transmitting power of 5 kW at 20 rev/s. Taking velocity factor of 1.5, form factor of 0.3 and permissible bending stress in gear teeth of 100 MPa, the factor of safety for the gear is _______.

Answer 1

m = 3 mm, T = 20, b = 40 mm,
P = 5 kW, $C_v=1.5$,
y = 0.3,

${\sigma }_b=100$

$N_s=20$ rev/s

$F_t=\frac{P}{2\pi N_s}\times \frac{2}{D}=\frac{5000\times 2}{2\pi \times 20\times 3\times 20}$

$F_t=1326.3N$

$F_t=\frac{({\sigma }_b.b.my)}{C_v.FOS}$

$FOS=\frac{100\times 40\times 3\times 0.3}{1.5\times 1326.6}=1.8$