Question

$\text{A spur pinion of pitch diameter 50 mm rotates at 200 rad/s and transmits 3 kW power. The pressure angle of the tooth of the pinion is}{20}^{\circ }\text{. Assuming that only one pair of the teeth is in contact,the total force (in Newtom) exerted by a tooth of the pinion on the tooth on a mating gear is}$

Answer 1

Given, $d=50mm;\omega =200rad/s$
$P=3000W;\varphi ={20}^{\circ }$
$T=\frac{P}{\omega }=\frac{3000}{200}=15N.m$

$F_T\times r=T$
$\therefore F_T=\frac{T}{r}=\frac{15}{0.025}=600N$
$F=\frac{600}{\cos {20}^{\circ }}=638.5N$