The pressure angle of two gears in a mesh is φ = 25°. The number of teeth on the pinion is 45 and the gear ratio is 2. The module is 6 mm and addendum = 1.1 module. Find the contact ratio of these two gears.

The pressure angle of two gears in a mesh is φ = 25°. The number of teeth on the pinion is 45 and the gear ratio is 2. The module is 6 mm and addendum = 1.1 module. Find the contact ratio of these two gears. Correct Answer 1.7

φ = 25°, t = 45 and T = 45 x 2 = 90, m = 6 mm and addendum = 6.6 mm. r = mt/2 = 135 mm and ra = r + a = 141.6 mm R = mT/2 = 270 mm and Ra = R + a = 276.6 mm Path of contact = (Ra2 – R2cos2 φ)0.5 + (ra2 – r2cos2 φ)0.5 – (R + r)sinφ = 29.068 mm Arc of contact = Path of contact/cos φ = 29.068/cos 25° = 32.073 mm. Contact ratio = Arc of contact / Circular pitch = 32.073 / πm = 32.073 / (πx6) = 1.7.