I have this self study question, can anyone provide some guidance?...
A pulley 150 mm diameter is driven directly by an electric motor at 250 revs min–1. A V-belt is used to transmit power from this pulley to a second pulley 400 mm diameter against a load of 200 Nm.
The distance between the centre of the pulleys is 600 mm, the included angle of the pulley groove = 40°, the coefficient of friction between the belt and pulley is 0.4 and the ultimate strength of the belt is 8 kN.
(a) Calculate the actual power transmitted to the second pulley.
(b) Calculate the power which can be transmitted if the maximum tension in the belt is limited to half of the ultimate strength of the belt.
(c) What would be the effect of the following factors on the maximum power which can be transmitted (give reasons for your answer):
(i) increasing the coefficient of friction
(ii) increasing the included angle of the pulley groove.
(d) What would be the effect on the following if the load torque is increased and the speed maintains constant (give reasons for your answer):
(i) the tension in the tight side of the belt
(ii) the tension in the slack side of the belt
(iii) the power transmitted.
P(t) = τ.ω (power is the product of the torque τ and angular velocity ω)
The Attempt at a Solution
Driver speed = 250 revs min-1 = 25pi/3 rad s-1 = 26.18 rad s-1
Driven Speed (angular Velocity) = (25pi/3) * (0.075/0.2) = 25pi/8 rad s-1 = 9.817 rad s-1
Power dissipated at pulley 2 = (25pi/8) * 200 = 625*pi W
= 9.817 * 200 = 1963.4 W = 1.9634 kW