Multiple Disk Clutch⚠ unverified
Mechanical / Clutches Brakes · Compute the torque capacity of a multiple-disk clutch
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| F | F | N | 1.0 | Axial clamping force |
| mu | μ | — | 1.0 | Coefficient of friction between the facings (dimensionless) |
| R_i | Ri | m | 1.0 | Inner friction radius |
| R_o | Ro | m | 1.0 | Outer friction radius |
| n | n | — | 1.0 | Number of friction surfaces (pairs of contact) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | T | N*m | Torque capacity, in newton-metres (N*m) |
The science & history
Understanding the Parameters
-
Number of friction surfaces $n$ — the multiplier that makes multi-plate clutches powerful. The same clamp force $F$ is reacted at every interface in the stack (the force passes through them in series), so each interface contributes its full $\mu F R_{mean}$ and the torques add. A pack with 5 driving and 5 driven plates has $n = 9$ working faces — nine times the capacity of a single face.
-
Clamping force $F$ — note it is not multiplied by $n$: the same axial force presses the whole stack, transmitting through each plate to the next. Only the torque multiplies, not the force.
-
Mean radius $R_{mean}$ — the effective friction radius, $(R_i + R_o)/2$ under uniform wear (see Clutch Torque Capacity Uniform Wear).
-
Why multi-plate — packing capacity into a small diameter, and (in wet clutches) running the plates in oil to carry away heat, enabling smooth, repeated engagement in automatics and motorcycles.
Derivation (Approaching a Proof)
Each friction interface in the stack behaves as a single disk clutch and transmits (uniform wear)
$$T_1 = \mu F R_{mean}, \qquad R_{mean} = \frac{R_i + R_o}{2},$$
derived in Clutch Torque Capacity Uniform Wear. The crucial observation is how the stack combines: the axial clamp force $F$ is transmitted through every plate (equal force at each interface, in series), but the friction torques are all reacted about the same axis and therefore add (in parallel). With $n$ interfaces,
$$T = n\, T_1 = n F \mu R_{mean}.$$
So the plate count multiplies torque without multiplying the required clamp force — the whole point of the multi-plate design. The limit is heat: all $n$ interfaces dissipate slip energy into the same small volume, which is why high-cycle multi-plate clutches run wet (oil-cooled).
Dimensional check. $[T] = \text{N}\cdot\text{m}$. ✓
History and Development
Multi-plate clutches became essential with motorcycles, automatic transmissions, and heavy machinery needing high torque in small diameters. Wet multi-plate packs (running in transmission oil) are standard in automatics and motorcycle primary drives for their heat capacity and smooth engagement. The torque-adds / force-shared analysis is standard in Shigley.
Related Concepts: Clutch Torque Capacity Uniform Wear, Disk Clutch Torque, Cone Clutch Torque, Clutch Facing Pressure, Disk Clutch Heat Generation
Notes: Duplicate of Clutch Torque Capacity Uniform Wear ($R_{mean}=(R_i+R_o)/2$). Interfaces $n = N_{driving} + N_{driven} - 1$. Force is shared (not multiplied); torque adds. Heat limits high-cycle use — run wet.