If the pinion rotates at 120 rpm. Determine;

i) The minimum number of teeth on each wheel to avoid interference.

ii) The number of pairs of teeth in contact.

Subject: Kinematics of Machinery

Topic: Gears and Gear Trains

Difficulty: High

Given $\phi=20^{\circ}$; $N_{P}$=120 rpm; VR=3; Addendum=1.1 m, m=3mm, $\alpha_{w}$=1.1

(i) $T=\frac{2a_{w}}{\sqrt{1+\frac{1}{G}(\frac{1}{G}+2)\sin^{2}\phi-1}}=\frac{2\times1.1}{\sqrt{1+\frac{1}{3}(\frac{1}{3}+2)\sin^{2}20^{\circ}-1}}$=49.44

Taking the higher whole number divisible by the velocity ratio,

i.e T = 51, and t=51/3 =17

(ii) Number of pairs of teeth in contact,

n= Arc of contact / circular pitch = (Path of contact / $\cos\phi$) $\times …