Clamping Force and Clutch Calculation

Question

A multiple clutch has to transmit 90kW from an engine running at 3500 rpm.

Clutch lining outer diameter is 200mm and inside diameter is 160mm. Spring pressure on clutch is 170kPa and it's coefficient of friction is 0.28.

a)Calculate the minimum clamping force required

b) Calculate the no. of clutch plates.

Answer 1

Hi Ashley,

Lets begin by finding the force and then determine number of clutch plates.

Step #1 - Find the Force

1. F = Pπ(D_o²-D_i²)/4
2. Where P = pressure, D₀ = outer diameter, and D_i is inner diameter.
3. F = 170,000π(0.2²-0.16²)/4 = 1923 N

Step #2 - Find the Torque

1. Where ω = angular velocity, P = power, and τ = torque.
2. ω = 2πRPM/60 = 2π3500/60 = 366.5 rad/s
3. τ = P/ω = 90,000/366.5 = 245.6 N-m

Step #3 - Find Friction Radius

1. For this equation we are not told if the contract pressure is uniform or if wear is uniform.
2. For uniform pressure: R_f = (2/3)[(R_o³-R_i³)/(R_o²-R_i²)] = (2/3)[(0.1³-0.08³)/(0.1²0.08-²)] = 0.0903 m
3. For uniform wear: R_f = (R_o+R_i)/2 = (0.1+0.08)/2=0.09 m

Step #4 - Find the Number of Clutch Plates

1. The number of plates is found with the following equation: n = τ/(F*f*R_f).
2. Where n = number of plates, F = force, f = friction coefficient, τ = torque, and R_f = friction radius.
3. Using the prior equation for uniform pressure: n = 245.6/(1923*0.28*0.0903) = 5.05 plates
4. Using the prior equation for uniform wear: n = 245.6/(1923*0.28*0.09) = 5.07 plates

Conclusion

At this point one has to make the decision of designing of a 5 or 6 plate clutch.