A conical friction clutch is used to transmit 75 kW at 1500 r.p.m. The semi cone angle is 20° and the coefficient of friction is 0.3. If the mean diameter of the bearing surface is 500 mm and the intensity of normal pressure is not to exceed 0.1 N/mm2, find the dimensions of the conical bearing surface.

A conical friction clutch is used to transmit 75 kW at 1500 r.p.m. The semi cone angle is 20° and the coefficient of friction is 0.3. If the mean diameter of the bearing surface is 500 mm and the intensity of normal pressure is not to exceed 0.1 N/mm2, find the dimensions of the conical bearing surface. Correct Answer 131.93 mm, 118.07 mm

Given : P = 75 kW = 75 × 103 W ; N = 1500 r.p.m. or ω = 2 π × 1400/60 = 157.08 rad/s ; α = 20° ; µ = 0.3 ; D = 500 mm or R = 250 mm ; pn = 0.1 N/mm2 Power transmitted (P) = 75 × 103 = T.ω = T × 157.08 T = 75× 103/157.08 = 477.4 N-m = 477.4× 103 N-mm Torque transmitted (T) = 477.4 × 103 = 2 π µ pn.R2.b = 2π × 0.3 × 0.1 (250)2 b = 11780.97 b b = 40.52 mm We know that, r1+r2 = 250 and r1-r2 = 40.52 sin 20 = 13.86 Therefore, r1 = 131.93 mm, r2 = 118.07 mm.
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