Two 20° involute spur gears have a module of 12 mm. The addendum is equal to 1.5 module. If the larger gear has 40 teeth and the pinion has 20 teeth, find the pressure angle at which interference can be avoided.

Two 20° involute spur gears have a module of 12 mm. The addendum is equal to 1.5 module. If the larger gear has 40 teeth and the pinion has 20 teeth, find the pressure angle at which interference can be avoided. Correct Answer 20.66°

Giveφ = 20°, t = 20, T = 40 and m = 12 mm, addendum = 1.5 x m = 18 mm r = mt/2 = 120 mm and R = mT/2 = 240 mm Ra = R + a = 240 + 18 = 258 mm Ra max = ((R cosφ)2 + (R sinφ + r sinφ)2)0.5 = 256.95mm As the calculated value of the addendum radius exceeds the maximum value of the addendum radius, interference occurs. The new value of φ can be calculated by taking R¬a max equal to Ra. 258 = ((240 cosφ)2 + (240 sinφ + 120 sinφ)2)0.5 66564 = (240 cosφ)2 + (240 sinφ + 120 sinφ)2 66564 = 57600 cos2φ +129600 (1-cos2 φ) 66564 = 129600 – 72000 cos2 φ cos2 φ = 0.8755 cos φ = 0.935 φ = 20.66° If the pressure angle is increased to 20.66°, the interference can be avoided.