Design a compound reverted gear train that will provide exac

Design a compound reverted gear train that will provide exactly a 48:1 increase in angular velocity from the input gear to the output gear while maintaining minimum diameter pinions. Provide both the number of teeth and the pitch diameters for a required diametral pitch of 3 teeth/inch for all gears. List all assumptions.

Solution

GIVEN:- e = 48:1

SOLUTION:- In order to obtain integers, factor the overall ratio into two integer stages.

e = 48 = 8 x 6

N2/N3 = 8 and N4/N5 = 6,

We choose N3 and N5 to be minimum. Assuming a 20° pressure angle, we obtain we get N3 = N5 = 16

That is N2 = 8x16 = 128 & N4 = 6x16 = 96 (ANSWERS) and so e = (128 / 16) x (96 / 16) = 48

and since diametrical pitch P = N/d where P = 3, we obtain pitch diameters as follows-

d2 = 128/3 = 42.66 inch, d3 = 16/3 = 5.33 inch, d4 = 96/3 = 32inch and d5 = 16/3 = 5.33 inch (ANSWERS)