Clutches, Brakes and Couplings
Friction torque with uniform pressure and wear, engagement time and heating, brake sizing and flexible couplings.
What clutches and brakes do
A clutch connects and disconnects two shafts, so a motor can run while the load rests (and so the load can be brought up to speed gradually). A brake slows or holds a rotating part by converting its kinetic energy into heat. Both rely on friction between surfaces pressed together; the design questions are the torque capacity, the engagement time and the heat that has to be dissipated.
Friction torque: uniform pressure and uniform wear
For an annular friction disc of inner radius ri and outer radius ro pressed by an axial force F, the torque depends on how the pressure is distributed. A new disc has about uniform pressure; once it has run in, the wear equalizes and the distribution becomes uniform wear (higher pressure at the inner radius). The second is the safe design value because it is the lower:
Uniform wear: T = μ F n (ro + ri) ÷ 2 Uniform pressure: T = (2 ÷ 3) μ F n (ro³ − ri³) ÷ (ro² − ri²)
Worked example: a disc clutch for the press drive
Worked example: a single-plate dry clutch between the 11 kW motor and a flywheel press
- Torque to transmit: T = 9 549 × P ÷ n = 9 549 × 11 ÷ 1 470 = 71.5 N·m (the motor of Induction Motors and Drives); with a service factor of 1.5: 107 N·m design torque.
- Clutch size: ro = 100 mm, ri = 60 mm (ratio 0.6), μ = 0.30, axial spring force 3 000 N, two surfaces.
- Uniform wear: T = 0.30 × 3 000 × 80 mm × 2 = 144 N·m; uniform pressure: 147 N·m. Capacity 144 N·m against 107 N·m required: margin 1.34. Good.
- Lining pressure (uniform wear, maximum at ri): pmax = F ÷ (2π ri (ro − ri)) = 3 000 ÷ (2π × 60 × 40) = 0.20 MPa: under the 0.3 to 1 MPa a dry organic lining accepts.
Engagement time and heat
While the clutch slips, the friction torque accelerates the load and the difference between the input and the output energy goes into heat in the plates. For a load inertia J from rest to ω with a clutch torque T and a constant load torque TL: t = J ω ÷ (T − TL) and the energy dissipated is E = ½ J ω² × T ÷ (T − TL) (with no load torque, the slip loss equals the energy stored in the load, whatever the clutch torque).
Worked example: starting the flywheel and a 20 N·m load
- Load inertia J = 0.5 kg·m² to 1 500 rpm (157.1 rad/s) against TL = 20 N·m with a clutch torque of 144 N·m: t = 0.5 × 157.1 ÷ (144 − 20) = 0.63 s.
- Energy dissipated E = ½ × 0.5 × 157.1² × 144 ÷ 124 = 7.2 kJ per engagement.
- Temperature rise of 3 kg of steel plates: ΔT = E ÷ (m c) = 7 163 ÷ (3 × 460) = 5.2 K per start. At 6 engagements a minute the average heating is 716 W, which the clutch must lose by convection and conduction. Frequent starts need a bigger or a wet (oil-cooled) clutch; the heat per start grows with the load inertia and the square of the speed.
- Faster engagement means more shock; slower means more heat. A smooth, controlled engagement (a pneumatic valve, a pressure ramp) protects the drive train.
Brakes
A brake dissipates the kinetic energy ½ J ω² (and any potential energy of a lowered load). The brake torque sets the stopping time t = J ω ÷ Tb. For a disc brake with caliper pads at an effective radius rb and clamp force F on n friction surfaces: Tb = n μ F rb.
Worked example: stopping the 1.22 kg·m² flywheel
- Stored energy ½ J ω² = 15.0 kJ at 1 500 rpm. A brake torque of 100 N·m stops it in t = 1.22 × 157.1 ÷ 100 = 1.9 s.
- A disc brake with two pads (n = 2, μ = 0.35) at an effective radius of 120 mm needs a clamp force of 100 ÷ (2 × 0.35 × 0.12) = 1 190 N.
- Heat: 15.0 kJ into a 4 kg steel disc raises it by 8.2 K in one stop; repeated stops need a bigger disc or cooling. Brake fade (a loss of friction when hot) and thermal cracking limit the temperature to about 300 to 600 °C.
- Safety: a brake that holds a load must be fail-safe (spring-applied, released by power or air) and its torque must exceed the largest load torque with a safety factor (typically 1.5 to 2.5); for machines see the stopping-distance rules in System Integration.
Types of clutch and brake
| Type | How it works | Use |
|---|---|---|
| Single-plate dry clutch | spring-loaded friction disc between the flywheel and a pressure plate | vehicles, machines |
| Multi-plate wet clutch | many steel and friction plates in oil | high torque in a small space, motorcycles, transmissions, industrial drives |
| Electromagnetic clutch and brake | a coil pulls the armature to the friction face | precision on-off control: packaging, printers, servo holding brakes |
| Dog, jaw and tooth clutch | positive engagement with no slip; engage at rest or at synchronous speed | gearboxes, machine axes |
| Centrifugal clutch | shoes thrown out by speed engage the drum | chain saws, small engines, soft starting |
| Overrunning (freewheel) clutch | sprag or roller wedges one way | one-way indexing, backstops |
| Torque limiter (slip clutch) | friction or ball detent slips at a set torque | overload protection on machines |
| Drum, band and disc brake | shoes, a band or pads press on a drum or disc | vehicles, winches, conveyors |
| Spring-applied holding brake | springs clamp; power releases it | servo motors, lifts, cranes |
| Eddy-current, hydrodynamic and regenerative braking | no wear: the energy is dissipated in a field or returned to the supply | dynamometers, trains, drives (see drives) |
Shaft couplings
A coupling joins two shafts and passes the torque, ideally while accepting some misalignment (the shafts are never exactly aligned), absorbing shock and vibration and protecting the machines. Choose it from the torque (with a service factor) and the misalignment, then check the speed, the torsional stiffness and the environment. The design torque for the press motor is 71 × 1.5 = 107 N·m: choose a coupling rated at 120 N·m or more (the next size up), for example a jaw coupling.
| Coupling | Construction | Misalignment it accepts (typical) | Notes |
|---|---|---|---|
| Jaw / spider | elastomer star between two jaws | 0.2 to 0.4 mm; 1° | cheap, damps vibration; backlash; limited speed and temperature |
| Disc (steel membrane) | thin flexible steel discs | 0.1 to 0.5 mm; 0.5 to 1° | zero backlash, high speed, no lubrication; stiff in torsion |
| Gear coupling | crowned teeth inside a sleeve | 0.5 to 3 mm; 1° per mesh | heavy torque, needs oil; mills, rolling equipment |
| Bellows | thin metal bellows | 0.1 to 0.3 mm; 1 to 2° | servo and encoder drives; torsionally stiff; light |
| Oldham | two hubs and a sliding disc | 1 to 3 mm; 1° | large parallel offset, low torque |
| Rigid (flange, sleeve) | bolted solid connection | none: aligned shafts only | cheap; every misalignment becomes a bearing load |
| Fluid coupling | oil-filled impeller and turbine | slips 2 to 5 % | soft start, overload protection |
Align the shafts with a laser or a dial indicator to well under the coupling’s rating: the allowed misalignment is a capability, not a target, and every bit of it becomes a bearing load and a vibration at twice running speed. Check a rigid coupling’s alignment to 0.05 mm; a flexible one to 0.1 to 0.2 mm. Guard every rotating shaft and coupling (see Workshop Safety).
Related
- Previous: Vibration, Isolation and Noise. Next: Flywheels, Balancing and Rotors.
- Gears and Power Transmission and Motion Control and Actuators for brakes on motors.
- Machine Design: the whole guide.
FAQ
Why design on uniform wear?
A new lining wears in towards uniform wear, which gives the lower torque. Designing on that value gives a clutch that still transmits the load after the break-in period.
What is brake fade?
A fall in the friction coefficient when the pads and the disc get too hot (the lining outgasses or the pad glazes). Size the brake for the energy and the heat dissipation of the worst stop sequence.
Why is a wet clutch smoother?
The oil film cushions the engagement and carries the heat away, but lowers the friction coefficient, so it needs more plates for the same torque.
Can I use a clutch as a torque limiter?
Yes: a friction clutch slips at its set torque and protects the drive. It heats if it slips for long, so add a sensor to stop the machine.
References
- Shigley, J. E., Mischke, C. R., Budynas, R. G., Mechanical Engineering Design, McGraw-Hill (clutches, brakes, couplings, flywheels); Norton, R. L., Machine Design, Pearson.
- Orthwein, W. C., Clutches and Brakes: Design and Selection, CRC Press; Machinery’s Handbook, Industrial Press.
- DIN 740 (torsionally flexible couplings), ISO 14691 (flexible couplings for general use); coupling manufacturers’ catalogs (KTR, Rexnord, R+W).
Last reviewed: October 2026. Friction coefficients and pressures are typical for the lining material.