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

Step-by-step explanation:

Given

Diametrical Pitch
`\left ( P_D\right )=(T)/(D)`

where T= no of teeths

D=diameter

module(m) of gears must be same

`m=(D)/(T)=(1)/(P_D)=0.1`

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

Therefore Center distance is given by

`m(\left ( T_1+T_2\right ))/(2)=3.5`

thus

`0.1(\left ( T_1+T_2\right ))/(2)=3.5`

`T_1+T_2=70----1`

and Velocity ratio is given by

`VR=(No\ of\ teeths\ on\ Driver\ gear)/(No.\ of\ teeths\ on\ Driven\ gear)`

`2.5=(T_1)/(T_2)----2`

From 1 & 2 we get

`T_1=50, T_2=20`