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Q2. A single plate clutch with both sides effective has an outside diameter of 400 mm and an inside diameter of 180 mm. The clutch is designed to transmit 20 kW at 720 rev/min when new. In this condition the coefficient of friction between the clutch contact surfaces can be assumed to be 0.6.

Once the clutch starts to wear and the surfaces become contaminated, the maximum power that the clutch can transmit will be reduced. The axial thrust on the clutch faces is provided by eight identical springs placed in parallel, each with a spring stiffness of 16 kN/m. Maximum wear of the clutch plates is limited to 0.6 mm at each contact surface. Calculate EACH of the following:

(a) The total spring load (W) required when the clutch is new;

(b) The minimum coefficient of friction of the worn clutch plates if 80% of the original maximum power can be transmitted.

Note: For constant pressure T =  (2μW(r₁³- r₂³)/(3(r₁²- r₂² )

For constant pressure T = μNW(r₁+ r₂ )/2

n = Number of surfaces in contact