Question

4. An electric motor rotates at 1000 rpm and drives a pump through a soft start disc clutch. The pump has rotating mass of 250 kg and radius of gyration 0.5 m. The clutch has 5 friction surfaces having inner and outer radii of 250 mm and 350 mm respectively. The friction coefficient of the clutch material is 0.1. (a) For the first 5 seconds of operation, an axial force of 1 kN is applied through the clutch. Calculate the torque transferred through the clutch, the angular acceleration of the pump during this time and the speed of the pump after 5 seconds. (10 Marks) (b) After the first 5 seconds of operation, the pump takes a further 20 seconds to reach the motor speed from the speed calculated in (a), with constant angular acceleration. Calculate the required axial force operating through the clutch mechanism during this 20 second period. (10 Marks) (c) Sketch the graphs of torque vs speed and speed vs time for the clutch-pump system during the 25 seconds of operation as given in parts (a) and (b). (5 Marks) (Total 25 Marks)

Answer 1

We considering the clutching is uniform wear process

a)

Torque transmitted by the clutch (Uniform wear )

Torque equation of the pump can be written as

Angular acceleration till t=5 s

Angular speed

At t=5 s

b)

Take angular acceleration as

The equation of angular speed

Angular acceleration to reach the final angular speed

Torque equation

Torque transmitted by the clutch

We need 1.937 kN axial to achieve the final speed in 20 seconds after 5 seconds

c)

Torque vs angular speed

Speed VS time