Question

Two standard spur gears have a diametrical pitch of 10, a center distance 3.5 inches and a velocity ratio of 2.5. How many teeth are on each gear?

Answer 1

Answer:50 , 20

Explanation:

Given

Diametrical Pitch$\left ( P_D\right )=\frac{T}{D}$

where T= no of teeths

D=diameter

module(m) of gears must be same

$m=\frac{D}{T}=\frac{1}{P_D}=0.1$

Let $T_1 & T_2$be the gears on two gears

Therefore Center distance is given by

$m\frac{\left ( T_1+T_2\right )}{2}=3.5$

thus

$0.1\frac{\left ( T_1+T_2\right )}{2}=3.5$

$T_1+T_2=70----1$

and Velocity ratio is given by

$VR=\frac{No\ of\ teeths\ on\ Driver\ gear}{No.\ of\ teeths\ on\ Driven\ gear}$

$2.5=\frac{T_1}{T_2}----2$

From 1 & 2 we get

$T_1=50, T_2=20$