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The pressure angle of two gears in a mesh is φ = 22.5°. The number of teeth on the pinion is 25 and the gear ratio is 2. The module is 7 mm and addendum = 1 module. Find the angle of action of these two gears.

The pressure angle of two gears in a mesh is φ = 22.5°. The number of teeth on the pinion is 25 and the gear ratio is 2. The module is 7 mm and addendum = 1 module. Find the angle of action of these two gears. Correct Answer 22.72°

φ = 22.5°, t = 25 and T = 25 x 2 = 50, m = 7 mm and addendum = 7 mm. r = mt/2 = 87.5 mm and ra = r + a = 94.5 mm R = mT/2 = 175 mm and Ra = R + a = 182 mm Path of contact = (Ra2 – R2cos2 φ)0.5 + (ra2 – r2cos2 φ)0.5 – (R + r)sinφ = 32.056 mm Arc of contact = Path of contact/cos φ = 32.056/cos 22.5° = 34.697 mm. Angle of action = Arc of contact / r = 0.3965 rad = 22.72°.

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