A shaft carries a 50tooth 16teethin diametral pitch gear tha

A shaft carries a 50-tooth, 16-teeth/in diametral pitch gear that drives another gear at 400 RPM. How fast does the 50-tooth gear rotate if the shaft center distance is 6 in? What’s the pitch line velocity?

Solution

For the first gear,

Diametral pitch = T/D = 16 teeth/in

Diameter = D

No. of teeth T = 50

Therefore, Diameter of first gear,D = T/16 = 50/16 = 3.125 in

For the second gear,

Diameter = D\', no. of teeth = T\' and speed = N\'

Centre distance between two shaft = 6 in = (D+D\')/2

So, D+D\' = 12 in

And Diameter of second gear D\' =12-D = 12 - 3.125 = 8.875 in

Here the second gear rotates at N\' = 400 RPM

So the 50-tooth gear rotates at N = (D\'/D)*400 [as N/N\' = D\'/D]

= (8.875/3.125)*400

= 1136 RPM

The pitch line velocity = DN/60 = (3.14 x 3.125 x 1136/60) = 185.88 in/s.