Question

A ${20}^{\circ }$ full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.

Given thatthe tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material is

• A. $242.0$
• B. $166.5$
• C. $121.0$
• D. $74.0$

Answer 1

The correct option is B $166.5$

Tooth geometry factor, $Y=0.32$
Combined effect of dynamic load and allied factors intensifying the stress is $f_s=1.5$
$F_t=\frac{{\sigma }_{b}b{Y}_m}{f_s}$
$\Rightarrow 3552N=\frac{{\sigma }_b\left(25mm\right)\left(0.32\right)\left(4mm\right)}{1.5}$
$\Rightarrow {\sigma }_b=166.5Mpa$