A clutch is designed to bring two rotating mechanisms togeth

A clutch is designed to bring two rotating mechanisms together in order to transmit a torque. For the system shown in the following diagram determine the equation of motion.

Solution

Uniform Pressure Theory :

Assuming uniform pressure and considering an elemental area dA : dA = 2.r dr

The normal force on this elemental area is : dN = 2.r.dr.p

The frictional force dF on this area is therefore : dF = f.2.r.dr.p

T = dF. r => f.dN. r => f.p.A.r    => f.p.2..r. dr .r

T = f . F_a (2/3) .R

Where R is the radius of clutch plate