A V belt and V pulleys with alpha=53 degrees are used to transmit a couple from

Question

A V belt and V pulleys with alpha=53 degrees are used to transmit a couple from pulley A to pulley B. The radius of each pulley is 56 mm and a force of magnitude P=835 N is applied as shown to the axle of pulley A. Knowing that the coefficient of static friction is 0.41, determine (a) the largest couple that can be transmitted. (b) the corresponding maximum value of the tension in the belt.

Distance between A and B is 240 mm.

Thanks for your help!!

A V belt and V pulleys with alpha=53 degree s are used to transmit a couple from pulley A to pulley B. The radius of each pulley is 56 mm and a force of magnitude P=835 N is applied as shown to the axle of pulley A. Knowing that the coefficient of static friction is 0.41, determine (a) the largest couple that can be transmitted. (b) the corresponding maximum value of the tension in the belt. Distance between A and B is 240 mm. Thanks for your help!!

Explanation / Answer

Angle of wrap, theta = 180 deg = pi rad = 3.14 rad

T1 / T2 = e^(u*theta*Cosec alpha/2)

T1 / T2 = e^(0.41*3.14*Cosec 53/2)

T1 / T2 = 17.9

Also, T1 + T2 = P = 835 N

Solving both these eqns, we get T2 = 44.16 N and T1 = 790.84 N

a) Largest couple = (T1 - T2)*r = *0.056 = 41.814 Nm

b) max. Tension = T1 = 790.8 N

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