How this calculation works
A disc clutch or brake transmits friction at a range of radii. Replacing that range by the outer radius overestimates torque. This calculator uses an effective radius derived from either uniform pressure or uniform wear across an annular contact face.
T = interfaces × μ × axial force × effective radius; uniform pressure R = 2(ro³−ri³)/[3(ro²−ri²)]A worked example
With radii 50 and 100 mm, uniform pressure gives an effective radius of 77.7778 mm. At 1000 N, coefficient 0.3 and two working interfaces, ideal torque is 46.6667 N m. The uniform-wear alternative gives 45 N m.
Good to know
Constant entered friction and ideal contact distribution only. The calculation omits heat, fading, wear evolution, actuation geometry and dynamic stopping behavior. It does not approve a vehicle brake, lifting brake or machine clutch design.
Reference: RoyMech — engineering mechanics and friction context (opens in a new tab) ↗
What this model answers
A disc clutch or brake transmits friction at a range of radii.
Replacing that range by the outer radius overestimates torque. This calculator uses an effective radius derived from either uniform pressure or uniform wear across an annular contact face.
The Capstan wrap angle and limiting tension calculator models friction accumulated around a wrap. An annular disc instead integrates friction over radial contact and uses a different effective radius.
Keep the input conventions consistent
Enter axial force through the stack, which is also the force at each ideal interface.
Count working friction interfaces separately; do not multiply the force by that count before entering it. Dimensions are radii, not diameters.
Read the result carefully
Uniform pressure and uniform wear imply different radial distributions and therefore different effective radii.
The average pressure output is force divided by annular area for one interface. It is not multiplied by the interface count and is not a temperature-dependent friction estimate.
The pressure distribution assumption changes the effective friction radius even when inner and outer radii are identical. Compare the uniform-pressure and uniform-wear cases as separate models, not as interchangeable names. Friction coefficient and normal force still require an appropriate basis outside the geometric effective-radius calculation.
Work through the numbers
With radii 50 and 100 mm, uniform pressure gives an effective radius of 77.7778 mm.
At 1000 N, coefficient 0.3 and two working interfaces, ideal torque is 46.6667 N m. The uniform-wear alternative gives 45 N m.
Where the calculation stops
Constant entered friction and ideal contact distribution only.
The calculation omits heat, fading, wear evolution, actuation geometry and dynamic stopping behavior. It does not approve a vehicle brake, lifting brake or machine clutch design.
A few questions, answered
Does doubling working interfaces double contact pressure?
No. In this ideal stack the same axial force passes through each interface; torque doubles but per-interface pressure stays fixed.
What should I change in the comparison?
Compare uniform wear with uniform pressure at the same geometry and axial force.