FRICTION CLUTCHES

In the majority of engineering applications we aim to reduce friction to an absolute minimum in order to minimise wear and energy losses. In the case of a clutch however the opposite is true as without friction it would be unable to function. Maximising the coefficient of friction and keeping it reasonably constant over a wide range of operating conditions are two prime considerations in clutch design.

The purpose of a clutch is to allow smooth and gradual engagement and disengagement of two revolving members sharing a common axis of rotation. Although there are a number of arrangements of friction clutches only the disc type will be considered here.

Figure 1 shows a basic disc clutch which consists of one driving and one driven face. As the two surfaces are forced together, most often by means of a spring, a frictional driving force is developed between them.

Figure 1 Basic disc clutch

Friction clutches are commonly used in the transmission of most automobiles, a typical example of which is the BORG­WARNER arrangement shown in fig.2 .

The clutch cover, pressure plate and flywheel rotate with the crankshaft, while a set of radially spaced springs push the pressure plate towards the flywheel clamping the clutch plate, or friction plate, between them. A mechanical drive, between the clutch hub and the transmission input shaft, is achieved by means of splines which permit relative axial motion between the two components. When the clutch pedal is depressed an intermediate actuating mechanism, typically hydraulic or cable, rotates the release arm ever about its pivot point. This in turn pushes the clutch release bearing against a set of radially orientated release levers that lift the pressure plate away from the flywheel.

Note that this clutch has two driving surfaces, one on the pressure plate and one on the flywheel, and two driven surfaces, the two sides of the clutch plate. Also note that the clutch release bearing is a thrust bearing taking a purely axial load. The left side bears against the clutch release levers which rotate with the crankshaft while the right bears against the release mechanism which does not rotate at all.

Figure 2 Arrangement of a BORG­WARNER automotive­type disc clutch

Figure 3 Hydraulically operated multi­disc clutch

Figure 3 shows a multi­disc clutch, sometimes referred to as a multi­ plate clutch. The discs 'a' are constrained by means of splines to rotate with the input shaft while the discs 'b', by similar means, are constrained to rotate with the output shaft. When the oil pressure is released and the clutch is disengaged the disc are free to slide axially to separate themselves. When the clutch is engaged the discs are tightly clamped together thus providing a number of driving and driven surfaces; in this case six of each. To avoid the need for a thrust bearing to transmit the clamping force the two end discs, which have only their inner faces acting as friction surfaces, have been made members of the same set.

Disc clutches can be designed to work either wet, in an oil bath, or dry. Automotive clutches such as that shown in Fig 2 are dry clutches and will cease to function satisfactorily if oil comes into contact with the friction material. Multi­disc clutches such as that in Fig 3 will most often be run wet. The oil serves as an effective coolant during clutch engagement and the use of multiple discs compensates for the reduced coefficient of friction.

Two sets of equations have been developed which relate clutch size, friction coefficient, torque capacity, axial clamping force and interface pressure. Each set uses a different basic assumption. One assumes that the distribution of interface pressure is uniform while the other assumes a uniform rate of wear at the interface. Each is now looked at in turn.

1 ASSUMING A UNIFORM DISTRIBUTION OF INTERFACE PRESSURE. This assumption is valid for a new, accurately produced clutch with rigid discs. Referring to Figure 1 the Normal Force acting on a ring element of radius r is

dF = (2πr dr)p (a)

where p is the uniform level of interface pressure. The total Normal Force acting on the area of contact is

F = ∫2πpr dr between the limits ri and ro

F = πp(ro 2 – ri 2 ) (1)

where F is also the axial force clamping the driving and driven discs together. The Friction Torque that can be developed on a ring element is the product of the Normal Force, Coefficient of Friction and radius

i.e. dT = (2πr dr) p fr

where f is the coefficient of friction.

The total torque that can be developed over the entire surface is

T = ∫2πpfr 2 .dr between the limits ri and ro

T = ⅔ πpf (ro 3 – ri 3 ) N (2)

Solving Eqn (1) for p and substituting its value into Eqn (2) gives an equation for the torque capacity as a function of the clamping force:

T = 2Ff (ro 3 – ri 3 )N (3) 3(ro 2 – ri 2 )

2 ASSUMING A UNIFORM RATE OF WEAR AT INTERFACE Wear rate is proportional to the rate of friction work, i.e. friction force multiplied by the rubbing velocity. With a uniform coefficient of friction the wear rate is proportional to the product of pressure times sliding velocity. On a clutch face the velocity of sliding is proportional to radius. Thus the frictional work is proportional to the product of pressure and radius. On the above basis a new clutch would experience greater initial wear at the outside radius. From this it will be seen that a new clutch, which has a uniform distribution of interface pressure, will undergo greatest INITIAL wear at its outer radius. After this initial wearing­in period the friction lining tends to wear at a uniform rate as though it were being 'ground' between the two outer steel plates which are assumed to be parallel and rigid. The uniform wear rate is believed to result from a uniform rate of friction work across the lining; that is to say the product of PRESSURE and VELOCITY is constant which in turn means that the product of PRESSURE and RADIUS is constant.

i.e. pr = C (where C is a constant)

The greatest interface pressure, pmax, occurs at the inside radius, ri , and has a limiting value determined by the characteristics of the friction lining material. Thus, for a clutch of inside radius ri and a friction lining with an allowable maximum pressure of pmax, the clutch design is based on

pr = C = pmax ri ( 4 )

Using Eqn (4) and following the method of derivation for Eqns (1) to (3) we obtain:

F = ∫ 2π pmax ri dr between the limits ri and ro F = 2π pmax ri (ro – ri) (5)

and

T = ∫ 2π pmax ri fr dr N between the limits ri and ro

T = π pmax ri f(ro 2 – ri 2 )N (6)

T = Ff(ro – ri)N (7) 2

where N is the number of of friction interfaces. Note the simple physical interpretation of Eqn (7)

The assumption of a uniform wear rate results in a lower calculated clutch capacity than that based upon the assumption of uniform pressure. This must be so because the wear at the outer radius effectively shifts the centre of pressure towards the centre, resulting in a smaller torque arm. Clutch design is, therefore, usually based upon the uniform wear assumption and will consequently have a slightly higher torque capacity when new.

Using Eqn (6) it can be shown that the maximum torque capacity for a clutch with a given outside radius is achieved when:

ri = √⅓ (ro) (8)

Proportions commonly used range from O.45ro < ri < O.80ro