Design the torque a disc (plate) friction clutch can transmit. Adjust the inner and outer friction diameters, axial force, friction coefficient and number of faces to see the effective friction radius, transmitted torque and maximum contact pressure update in real time, and find clutch dimensions that neither slip nor scorch.
Parameters
Wear model
Model for the effective radius and pressure distribution
Friction outer diameter Do
mm
Friction inner diameter Di
mm
Must be smaller than the outer diameter
Axial clamping force F
N
Force the pressure plate applies to the faces
Friction coefficient μ
Dry organic ~0.3, sintered metal ~0.4
Number of friction faces n
1 for a single-plate clutch, 2+ for multi-plate
Results
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Transmitted torque T (N·m)
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Effective radius R_e (mm)
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Max contact pressure p_max (MPa)
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Total friction area A (cm²)
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Radius ratio Di/Do
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Pressure verdict
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Face-on view — contact pressure animation
The rotating annular friction face. Redder means higher pressure — concentrated at the inner edge for uniform wear, even for uniform pressure. The dashed circle is the effective friction radius R_e.
Transmitted torque vs axial force F
Transmitted torque vs radius ratio Di/Do (at constant p_max)
Maximum contact pressure for the uniform-wear model. Wear makes p·r constant, so the pressure peaks at the inner radius r_i.
The uniform-wear model has a smaller effective friction radius and gives a conservative (smaller) torque, so it is the model used for strength design in practice.
What is a Friction Clutch?
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A "clutch" is that pedal you press when driving a car, right? What is actually happening inside it?
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Exactly — the car clutch is the most familiar example. The mechanism is simple: a disc on the engine side and a disc on the gearbox side are pressed firmly together by a spring. Torque is transmitted by the friction between those two clamped discs. "Disengaging" the clutch just means releasing the clamping force, pulling the two discs apart and reducing the friction to zero.
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It transmits power through friction alone? What decides how much torque it can carry?
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As a formula it is T = μ·F·R_e·n — a product of four things: the friction coefficient μ, the clamping force F, the effective friction radius R_e and the number of friction faces n. The key term is R_e, which represents the radius at which the friction force acts on average. The friction face has width from the inner to the outer diameter, so you take a representative radius somewhere in between. Raise the "friction outer diameter Do" on the left and you will see R_e grow and the transmitted torque jump up.
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There is a "wear model" selector. Why is the R_e formula different for uniform wear and uniform pressure?
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Good question. A new clutch has roughly uniform pressure over the friction face — that is the "uniform pressure" model. But as it is used, the outer region, which slides faster, wears more. After wear has progressed, the product of pressure and radius, p·r, settles to a constant. That is the "uniform wear" model. Uniform wear gives a slightly smaller effective friction radius, so it predicts a smaller torque. That is why, in practice, engineers use the conservative uniform-wear model.
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I see. So when I want more torque, can I just keep raising the clamping force F?
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That is the trap. Raising F does increase torque, but it also raises the contact pressure. If the pressure exceeds the allowable value of the friction material, the heat from a slip moment concentrates at one spot and scorches or chars the surface. So rather than relying on F alone, the classic move is to increase the number of friction faces n — go "multi-plate". Double the friction faces and the torque doubles, while the pressure stays the same. That is why the wet clutches in motorcycles and construction machinery are multi-plate.
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One last thing. The "radius ratio Di/Do" chart has a peak. A smaller inner diameter should give more torque, so why is there a maximum?
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That is the interesting part. Shrinking the inner diameter Di does tend to grow R_e, but with the clamping force F fixed, you are concentrating the load onto a narrow face, and the contact pressure shoots up. Torque is the product F·R_e, so squeezing the inner diameter too far backfires. With the uniform-wear model, torque is maximised around Di/Do ≈ 0.577 (1/√3). It is a handy number to remember — when the outer diameter is fixed, it tells you the most efficient inner diameter.
Frequently Asked Questions
The transmitted torque of a disc friction clutch is T = μ·F·R_e·n, where μ is the friction coefficient, F is the axial clamping force, R_e is the effective friction radius and n is the number of friction faces. The effective radius depends on the wear model: for uniform wear R_e = (r_o+r_i)/2, and for uniform pressure R_e = (2/3)·(r_o³−r_i³)/(r_o²−r_i²). For a worn-in clutch, the uniform-wear model is the standard design choice because it gives a smaller, conservative torque.
A new clutch is close to the uniform-pressure model, where the pressure is assumed uniform over the friction face. A worn-in clutch approaches the uniform-wear model, where wear has progressed until the product p·r is constant. The uniform-wear model has a smaller effective friction radius and therefore predicts a smaller transmitted torque. Because it is the conservative estimate, the uniform-wear model is the standard choice for strength design in practice.
If the contact pressure exceeds the allowable value of the friction material (lining), the heat generated during slipping concentrates locally and causes scorching, charring and rapid wear. In the uniform-wear model the pressure is highest at the inner radius: p_max = F / (2π·r_i·(r_o−r_i)). The allowable pressure for organic linings is roughly 1.0–1.7 MPa. If the pressure is too high, lower it by enlarging the friction area or by increasing the number of friction faces (going multi-plate).
Since T = μ·F·R_e·n, consider in this order: (1) raise the axial force F (watching the pressure limit), (2) increase the number of friction faces n to make a multi-plate clutch, (3) enlarge the outer diameter to gain effective friction radius R_e, and (4) switch to a friction material with a higher μ. Going multi-plate raises torque without raising the contact pressure, so it is widely used in wet clutches where torque capacity must be reached within a limited outer diameter.
Real-World Applications
Automotive manual transmissions: The dry single-plate clutch is the most typical use. A diaphragm spring clamps the flywheel and the clutch disc together to transmit engine torque to the gearbox. In design, the target torque capacity is the engine's maximum torque multiplied by a margin (the clutch factor, usually 1.3–2.0), and from that the inner and outer friction diameters and the clamping force are chosen.
Multi-plate clutches in motorcycles and construction machinery: To transmit large torque within a limited outer diameter, several friction plates are stacked into a multi-plate clutch. Increasing the number of friction faces n raises the torque capacity in proportion without raising the contact pressure. Wet multi-plate clutches running in oil cool well and resist scorching even when the half-clutch is used heavily.
Safety clutches and torque limiters in industrial machinery: A torque limiter that deliberately slips to protect the drivetrain when an excessive torque is applied works on the same principle as a friction clutch. The clamping force (spring force) is tuned so that slipping begins above a set torque. The formula T = μ·F·R_e·n in this tool is exactly the equation for that set torque.
Pre-study for CAE and thermal analysis: Before running a detailed thermal analysis of a clutch (a coupled analysis of slip heating and temperature rise), a closed-form formula like this tool gives a first read of the transmitted torque and the contact pressure. Knowing how many times the allowable pressure the design is at lets you revise the friction-face dimensions before investing in mesh and material models. Conversely, if the FEM result differs from this estimate by an order of magnitude, it is a sanity check that points to a contact-setup mistake.
Common Misconceptions and Pitfalls
The biggest misconception is designing with the uniform-pressure model of a new clutch. The uniform-pressure model has a slightly larger effective friction radius and overestimates the transmitted torque. But as the clutch is used and wear progresses, it shifts toward the uniform-wear state, the effective friction radius drops and the torque capacity falls. Designing with the new-clutch value leaves a worn clutch slipping. In practice, the rule is to estimate torque capacity consistently with the conservative uniform-wear model.
Next, assuming the friction coefficient μ is a fixed number. μ varies strongly not only with the material pairing but also with temperature, sliding speed, contact pressure and the presence of oil. At high temperature in particular, "fade" occurs — μ drops and the transmitted torque falls sharply. A clutch used while still hot can begin to slip even when the calculation says it is adequate. In design, do not use the catalogue μ directly; check with the effective or lower-bound value at the expected operating temperature.
Finally, looking only at torque capacity and ignoring heat generation. At the moment of engagement there is a speed difference between the engine side and the gearbox side, so a clutch always transmits torque while slipping. The frictional heat generated during this slip is the other main concern in clutch design. Even with ample torque capacity, heavy use of the half-clutch or frequent repeated starts can overwhelm heat dissipation and overheat the friction face. Alongside the torque calculation, always check the heat generated per engagement and the available cooling capacity.
How to Use
Enter outer diameter (Do) in mm and inner diameter (Di) in mm to define the friction disc geometry; Di/Do ratio should typically be 0.4–0.8 for single-plate clutches.
Input axial clamp force (F) in kN and coefficient of friction (μ) for your friction material (dry sintered bronze μ ≈ 0.35–0.45; wet paper μ ≈ 0.25–0.35).
Click Calculate to obtain transmitted torque T, effective radius R_e, contact pressure p_max, and total friction area A; verify p_max stays below material limits (typically 1.0–1.5 MPa for sintered metal).
Worked Example
A heavy-duty industrial clutch with Do = 200 mm, Di = 100 mm, F = 8 kN, and μ = 0.40 (sintered bronze). Effective radius R_e = (2/3) × (Do³ − Di³)/(Do² − Di²) = 127 mm. Friction area A = π(Do² − Di²)/2 = 23,562 mm² ≈ 235.6 cm². Transmitted torque T = 2 × μ × F × R_e = 2 × 0.40 × 8000 × 0.127 = 813 N·m. Contact pressure p_max = F/A = 8000/(23,562) = 0.34 MPa, well within sintered limits.
Practical Notes
Increasing Do relative to Di improves torque capacity and reduces contact pressure—use Di/Do ≈ 0.5 for optimal strength-to-wear trade-off in automotive applications.
Wet clutches (oil-cooled, μ ≈ 0.25) require higher clamp forces than dry types for equivalent torque; cool-down time extends engagement duration.
Monitor p_max; exceeding 1.5 MPa causes accelerated wear, glazing, and chatter; reduce F or increase disc area if pressure verdict shows critical.
Double-disc clutches (two friction surfaces) double torque capacity without increasing external size; common in motorcycles and racing transmissions.