1. Introduction
The plate clutch is used in automotive and industrial service to connect and disconnect the transmission of rotation / torque / power.

This picture shows a typical automotive clutch (49 kb).

In conveyor systems it is common to fit a clutch designed to slip and warn the operator if a jam occurs so corrective action can be taken before expensive gearboxes or conveyor belts brake.

To determine the torque transmitted it is necessary to make an assumption about the pressure distribution over the friction surfaces. For perfectly aligned new surfaces, it could be assumed that the pressure is uniformly distributed over the entire surface. However once the system has had some use, a better assumption is that the rate of wear is uniform over the friction surfaces. As a first approximation it can be assumed that the wear rate is proportional to the product of the velocity of sliding and the pressure. Since the sliding velocity is proportional to the radius r to the annular element dr, the following can be written:

wear = k p r, since the wear is constant for the entire face, the maximum pressure will occur at the inner radius, ri hence wear = k pmax ri

Eliminating wear and the constant, k, gives the pressure at any radius, p

p = pmax ri/r

The total force Fn which must be exerted by the actuating spring, is found by multiplying the element area 2 x 3.142 x r x dr, by the pressure and integrating over the surface. This gives

Fn = 2 x 3.142 x pmax ri(ro - ri)

The torque is found by multiplying the force on the element by the coefficient of friction, f, and the radius, and integrating over the area. This gives:

T = 3.142 x f x pmax x ri ( ro2 - ri2) = 0.5 f (ro + ri)Fn

Single plate clutches have lining on both sides of the plate. Multiple plate disc clutches have friction linings on both sides of alternate plates. The above gives the torque for a single face, thus this quantity must be multiplied by the number of friction faces to find the torque for the entire clutch.

2. Cone clutch
The cone clutch utilises the wedging action of the parts to increase the normal force on the lining for a given spring force, thus an increase in the tangential friction and the torque results. Uniform wear is assumed. Values of included semi - angle vary from about 8o upwards. Smaller angles can lead to jamming and a jerky take up.

3. Lining Pressure
Typical lining pressures (in N/mm2) and dry coefficients of friction are shown below:

MaterialWorking PressureCoefficient of friction
Moulded materials and sintered metals1 to 2
Cast iron on cast iron1 to 1.70.15 - 0.2
Steel on cast iron0.8 to 1.40.2 - 0.3
Bronze on cast iron0.5 to 0.8
Wood on cast iron0.4 to 0.60.2 - 0.25
Cork on metal0.05 to 0.10.35
Asbestos blocks on metal0.25 to 1.10.4 - 0.48

For clutches running in oil the coefficient of friction will typically be in the range 0.05 to 0.15.

Example clutch calculation

4. Torque Transmitted by Clutch: Calculator
This section calculates the maximum torque that can be transmitted by a clutch that is undergoing 'uniform wear' using the formula above. Enter appropriate values in the boxes below then click on the 'calculate' box. Torques of less than 0.001 Nm will not be correctly displayed.

Clutch plate outer diameter, mm:
Clutch plate inner diameter, mm:
Coefficient of friction:
Maximum permitted lining pressure, N/mm2:
Number of friction surfaces:

Answer - Maximum clutch torque, Nm:

David J Grieve. Revised: 18th February 2010, 12th August 2004. Original: 13th November 2001.