Question

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

• A. $46MPa$
• B. $58MPa$
• C. $70MPa$
• D. $32MPa$

Answer 1

The correct option is A $46MPa$

Given :
$P=3kW=3000W$
$N=20rps$
Form factor , $y=0.3$
Face width, $b=36mm$
Velocity factor, $C_v=1.5$
Module, $m=3mm$
Teeth , $Z=16$
$F_t=\frac{2T}{D_1}$
$D=mZ$
$=3\times 16=48mm$
$P=2\pi NT$ where $N$ is in rps
$T=\frac{P}{2\pi N}=\frac{3000}{2\pi \times 20}$
$=23.8732Nm$
$=23.8732\times {10}^{3}Nmm$
We know
$(F_d{)}_{Lewis}\le F_s$
$F_t\times C_v\le ({\sigma }_b.ybm)$
$\frac{2T}{D}\times C_V=\left({\sigma }_b\right)ybm$
$\frac{2\times 23.8732\times {10}^3\times 1.5}{48}=\left({\sigma }_b\right)0.3\times 36\times 3$
${\sigma }_b=46Nm{m}^2$
$=46MPa$