Question

A spur gear with ${20}^o$ full depth teeth transmits 20 kW at 2000 rad/s. The pitch circle diameter of the gear is 100 mm. The magnitude of the force applied on the gear in the radial direction is

• A. 0.73 kN
• B. 2.78 kN
• C. 1.39 kN
• D. 0.36 kN

Answer 1

The correct option is A 0.73 kN

Given data:

$\varphi ={20}^o,P=20kW,\omega =200\text{rad/s}$

D = 100 mm

We know that:

$\text{Power,}P=T\times \omega$

$20\times {10}^3=T\times 200$

$T=100\text{N-m}$

We know that,

$T=F_t\times r$

$F_t=\frac{2T}{D}=\frac{2\times 100}{100\times {10}^{-3}}=2\text{kN}$

Radial force:

$F_r=F_t\left(tan\varphi \right)$

$=2\times tan{20}^o=0.72794\text{kN}$

$=0.728kN=0.73\text{kN}$