Question

A steel pinion has module of 4 mm, pressure angle ${20}^{\circ }$ and has 22 teeth. This pinion runs at 900 rpm and transmits 10 kW power to a 60 tooth gear. The bending stress on the pinion tooth using Lewis beam strength, by assuming the face width of the gear tooth as 38 mm and the velocity & Lewis form factors as 0.59 and 0.32, respectively is

• A. 120.4 MPa
• B. 67.7 MPa
• C. 132.5 MPa
• D. 83.3 MPa

Answer 1

The correct option is D 83.3 MPa

$m=4mm,\varphi ={20}^{\circ },t=22,N=900rpm$
P = 10 kW T = 60 b = 38 mm y = 0.59
$c_v=0.32$

Power = $F_t\times V=F_t\times \frac{\pi \times DN}{60}$

$=F_t\times \pi \times \frac{4\times 22}{1000}\times \frac{900}{60}$

$F_t=2.411kN$
$2411N={\sigma }_b\times m\times b\times y\times c_v$
$2411={\sigma }_b\times 4\times 38\times 0.59\times 0.32$
${\sigma }_b=84MPa$