Three gears with a module m 10mm and a pressure angle of Ph

Three gears with a module m = 10mm and a pressure angle of Phi = 14.50 degree are in mesh. The pinion is turning at 1800r pm with an input power of 7460W. The pinion has 24 teeth, the idler has 12 teeth, and the final gear has 48 teeth. What is the speed ratio between the pinion and the final gear? What are the center distances between the gears? What separating forces will need to be reacted by the structure h gears? What is the output torque on the final gear?

Solution

Speed ratio of a gear system = No. of teeth on the output gear/No. of teeth on the input gear.

Since we have a train of gears, we have the input-idler system and the idler output system and the final ratio being the multiplication of them both.

Hence, speed ratio of the system = 48/12 *12/24 = 2

Hence for every two rotations of the input shaft, the output shaft rotates once.

Given input speed = 1800 rpm

Therefore, the output speed is 900 rpm = 2pi x 900/60 =30pi

But the power transmitted = 7460 watt = torque x angular velocity

Hence, torque = 7460/30pi = 79.12 N-m

Given module of the gear = 10 mm = D/T

where D = diameter and T = No. of teeth

Hence, diameter of pinion = 10x24 = 240 mm

Diameter of idler gear = 10x12 = 120 mm

Diameter of final gear = 10x48 = 480 mm

Hence, the center distance = 240/2 + 120 + 480/2 = 480 mm