Question

The housing for a Spur gear set is manufactured with a center distance that is 0.25mm too large. The gears have 20 and 33 teeth respectively, a module of 6mm and a pressure angle of 22.5°

Calculate the pressure angle (degrees):

Calculate the backlash (mm)

What is the change in speed ratio resulting from the additional center distance.

Answer 1

Firstly, the initial center distance between the two gears is calculated which will be the sum of the radius of both the gears. Since the module and the number of teeth in each gear is given, the radius of each gears can be obtained. From the given pressure ratio, the base circle of any one gear is calculated (All the calculations can be done w.r.t. one gear). The new center distance can be obtained which will be the sum of the old center distance and the given offset. The new radius can also be obtained by incorporating the given offset. Then, new pressure angle can be calculated as the radius of base circle will remain but the radius of pitch circle will change. Once new pressure angle is obtained, then, using the formula for backlash, the backlash can be obtained (All the angles in the formula for backlash are in radians). The new speed ratio will be the ratio of the radius of the pitch circle of larger gear to the radius of the pitch circle of smaller (Here it will be the new pitch circle radius).