Clutch System Simulator

Friction clutch design and take-up lab • single-plate • multi-plate • cone • centrifugal — Simulate • Explore • Practice • Quiz

Mode

Gearbox

Friction

Flywheel 📖 User Guide

Display Controls

Labels & forces Slip heat glow

📖 Understand what you see

Σ Live equations — your numbers substituted

✓ Design checks — what a designer would verify

💡 What-if coach — predictions to test

User Guide — Clutch System Simulator

1 What this clutch simulator does

A free clutch simulator and clutch design calculator for the four friction clutches taught in machine design and automotive courses. For each one you set the design and the tool works out the torque capacity, the pressure on the lining and the design checks; then you press Engage to play a take-up: the clutch is clamped, slips, and locks, and the tool integrates the two sides through the slip to give the slip time, the heat generated and the temperature rise.

Single-plate (dry, car): diaphragm or coil springs, facing wear, uniform wear or uniform pressure, a launch from rest on a level road or a hill.
Multi-plate (wet, motorcycle): how many plates are needed, and how many are fitted.
Cone: the wedge gain 1/sin α, the engaging force and whether the cone self-locks; driven by an induction motor.
Centrifugal (go-kart): spring preload from the engagement speed, torque against speed, shoe pressure and width.

Four modes: Simulate, Explore (22 concept cards in six groups, including dog, one-way and electromagnetic clutches), Practice (15 problem types) and Quiz (5 questions from a pool of 21).

2 How to use it in four steps

Pick a clutch type from the tiles above the canvas. Each tile shows its current torque capacity.
Set the design in the panel: the Design group sizes the clutch; the Take-up group sets the engine (or motor) and the load it starts.
Press Engage. The take-up plays at ½× real time (choose ⅛× to 1×). Rotation is drawn slower than the true speed by a factor printed on the canvas.
Switch to Diagram for the pressure distribution across the face, the design curve (d/D, plate count, cone angle or torque against speed) and the take-up chart.

Keyboard: Space engage / pause, D Real / Diagram, R reset.

3 The Real view: section, end view and chart

Section A–A cuts the clutch on its shaft axis. Cut parts are hatched; shafts are not, as on an engineering drawing. Running clearances are drawn larger than life so you can see them close. Green arrows are the clamp force as it builds. The end view shows the driving member (orange index dot) and the driven member (blue dot): while they turn at different speeds the clutch is slipping and the facing glows with the slip power. The chart plots the engine speed ω₁, the load speed ω₂ and the clutch torque against time; the shaded band between the two speeds is the slip, and its area weighted by torque is the heat.

4 The take-up model

While slipping: I₁·dω₁/dt = T_e − T_c and I₂·dω₂/dt = T_c − T_L. Once the speeds meet the two sides turn as one body, and the clutch carries whatever torque that needs, as long as it is within its capacity. For the plate and cone clutches the clamp force rises linearly over the release time; for the centrifugal clutch the capacity follows the engine speed. A vehicle is reflected to the clutch shaft as I₂ = m·r²/i² with rolling resistance and grade, and its brake holds it until the clutch can move it. The engine stalls below 600 rpm (the centrifugal clutch disengages first, so it never stalls). The slip energy E = ∫T_c(ω₁ − ω₂)dt goes into the metal behind the faces: ΔT = E/(m·c).

5 Readings and design checks

The tiles under the canvas give the headline numbers; the status line states the verdict in words. Live equations substitutes your numbers into every formula used, and Design checks lists what a designer would verify: torque reserve (usually 1.2–1.5 for cars), peak pressure against the lining’s allowable value, faces fitted against faces needed, self-locking of a cone, shoe arcs and pressure, and the take-up. Show working collects them in one window.

6 Explore, Practice and Quiz

Explore has 22 concept cards, each with a drawing, the formula and a worked example; most have a Try it in the simulator button that loads the matching set-up. Practice deals unlimited problems from 15 types (plate torque by both theories, spring force, peak pressure, faces needed, multi-plate torque, cone torque, axial and engaging force, centrifugal engagement speed and torque, slip energy, temperature rise, best inner diameter, electromagnetic force); answers within 2 % count and a worked solution follows. Quiz draws 5 questions from 21 and shuffles the options every time.

7 SI and Imperial units

The SI / Imperial switch sits in the toolbar after Reset. Diameters switch mm ↔ in, forces N ↔ lbf, torques N·m ↔ lbf·ft, pressure MPa ↔ psi, heat kJ ↔ ft·lbf, temperature rise °C ↔ °F, masses kg ↔ lb (shoes g ↔ oz) and inertia kg·m² ↔ lb·ft². Speeds stay in rpm. Practice problems are set in SI. Your choice is remembered across the site.

8 Assumptions and limits

One friction coefficient is used for sliding and for lock-up (real linings have a slightly higher static value, which is one cause of judder). Friction values and allowable pressures are representative design figures; a real design uses the supplier’s data. Spline friction in a multi-plate pack, which lowers the clamp on the faces furthest from the piston, is neglected. Centrifugal shoes are taken as guided radially (no self-energising leading shoe). The cone clutch’s induction motor follows the straight-line part of its torque–slip curve, capped at breakdown torque. The heat estimate is a lumped bulk rise with no cooling during the take-up; the surface runs much hotter for a moment.

Clutch Design Calculator and Clutch Types Simulator

A clutch connects a driving shaft to a driven shaft and lets them be separated while running. A friction clutch does it by pressing surfaces together: while their speeds differ it slips, turning the speed difference into heat, and once they match it locks. This simulator designs the four friction clutches found in machine-design syllabuses and then runs a take-up so you can see the slip, the lock-up and the heat:

the single-plate clutch of a manual car;
the multi-plate clutch of motorcycles and automatic transmissions;
the cone clutch, whose wedge multiplies the spring force;
the centrifugal clutch of go-karts, mopeds and chainsaws, which engages by itself.

Torque capacity of a plate clutch: uniform pressure and uniform wear

On an annular face from inner radius r_i to outer radius r_o, pressed by an axial force F with friction coefficient μ, the torque is T = μ·F·n·R_f, where n is the number of friction faces and R_f the friction radius. Two pressure distributions are used:

Theory	Pressure	Axial force	Friction radius R_f	Default car clutch
Uniform wear (design)	p·r = constant, peak at r_i	2π·p_max·r_i(r_o − r_i)	(r_o + r_i)/2	330.8 N·m
Uniform pressure (new)	p = constant	p·π(r_o² − r_i²)	⅔(r_o³ − r_i³)/(r_o² − r_i²)	335.4 N·m

The default car clutch has 228 × 150 mm organic facings (μ = 0.35) on both sides of the disc (n = 2) and a 5,000 N diaphragm spring. A run-in clutch has worn until the wear rate, proportional to pressure times sliding speed, is the same everywhere, so p·r is constant. That gives the lower torque and is the theory used for design. With the outer diameter and the allowable pressure fixed, the torque is greatest when d/D = 1/√3 ≈ 0.577.

How many plates does a multi-plate clutch need?

In a multi-plate clutch, plates splined to the driving basket alternate with lined plates splined to the driven hub. One actuating force passes through the whole pack, so every face carries the same normal force, and n = n₁ + n₂ − 1. The number of faces follows from the design torque:

n = ⌈ β·T / (μ·F·R_f) ⌉, F ≤ 2π·p_max·r_i(r_o − r_i)

Worked example: 160 N·m at the clutch, reserve β = 1.3, plates 140 × 110 mm, paper lining in oil (μ = 0.12) and 3,000 N of spring force. One face carries 0.12 × 3,000 × 0.0625 = 22.5 N·m. The pack needs 208/22.5 = 9.24, so 10 faces: 5 lined discs and 6 steel plates. The peak pressure is 0.58 MPa, well inside the 2.76 MPa allowed. A dry sintered lining (μ = 0.30) would need only 4 faces. Wet clutches use many plates because oil lowers μ; in return the oil cools them and smooths the engagement.

Cone clutch: wedge action and self-locking

An axial force F on a cone of semi-angle α produces a normal force N = F/sin α, so T = μ·F·R_f/sin α. The default cone (mean diameter 180 mm, α = 20°, 1,000 N, μ = 0.35) carries 92.1 N·m, 2.92 times a flat face at the same radius. Pushing it home while it slides takes N(sin α + μ cos α) = 1,962 N. If tan α ≤ μ, the cone self-locks and must be pulled out with N(μ cos α − sin α). That is why α is kept a little above the friction angle tan⁻¹μ. Gearbox synchronizers are small oil-lubricated cone clutches with α of about 6–7°.

Centrifugal clutch design factors

Each shoe of mass m, with its centre of mass at radius r_g, is held off the drum by a spring preload F_s. It engages when mω²r_g = F_s, at ω_e = √(F_s/(m·r_g)). Above that, T = z·μ·R·(mω²r_g − F_s). The design factors, each a slider in the simulator, are:

the shoe mass and its radius, which set the centrifugal force;
the engagement speed, which sets the spring preload (a common rule puts it near three-quarters of the running speed);
the drum radius, the number of shoes and the lining μ, which set the torque;
the contact arc and the shoe width, which keep the lining pressure N/(θ·R·b) within its limit.

The default kart clutch has three 120 g shoes at 40 mm, engages at 2,800 rpm (F_s = 412.7 N) and carries 15.6 N·m at 3,600 rpm. Under a steady 10 N·m throttle the engine holds 3,336 rpm while the clutch slips and the kart catches up.

Slip energy, temperature rise and the take-up

With no engine or load torque, the heat of a take-up is E = I₁I₂(ω₁ − ω₂)²/[2(I₁ + I₂)], whatever the clutch torque. With the throttle held open the engine keeps supplying energy during the slip. The default car launch (1,400 kg, first gear, 1,500 rpm, 90 N·m of throttle, 1 s pedal release) locks in 0.65 s and makes 8.8 kJ of heat, a 2.2 °C bulk rise in 8 kg of cast iron. A 20 % hill raises that to 11.2 kJ. Dropping the clutch in 0.1 s stalls the engine, and a 2 s release roughly doubles the heat to 16.4 kJ.

Who uses this simulator?

Mechanical and automotive engineering students working clutch problems in machine design (uniform wear and uniform pressure, multi-plate, cone and centrifugal clutches); diploma and vocational learners studying the car clutch and its diaphragm spring; teachers who want to show a clutch slipping, locking and heating up on a projector; and designers who need a quick torque, pressure and plate-count check.

Frequently asked questions

How do you calculate the torque capacity of a plate clutch?

Multiply the friction coefficient, the axial clamp force, the number of friction faces and the friction radius: T = μ·F·n·Rf. By the uniform-wear theory, used for design, Rf = (ro + ri)/2. By the uniform-pressure theory, for a new clutch, Rf = (2/3)(ro³ − ri³)/(ro² − ri²), which is slightly larger. A car clutch disc lined on both sides has n = 2.

How is the number of plates in a multi-plate clutch determined?

Find the largest axial force the lining allows, F = 2π·pmax·ri·(ro − ri) under uniform wear, then the torque one face carries, μ·F·Rf. The number of faces is the design torque (engine torque times a reserve factor) divided by that, rounded up: n = ⌈β·T/(μ·F·Rf)⌉. Taking n even puts steel plates at both ends, giving n/2 lined discs and n/2 + 1 steel plates, since n = n₁ + n₂ − 1.

Why is uniform wear theory used for clutch design?

Wear is proportional to pressure times sliding speed, and sliding speed grows with radius, so a clutch wears in until p·r is constant. That theory gives a smaller torque than uniform pressure (about 1 to 2.5 % less for usual proportions), so designing with it is conservative for a clutch that has run in.

What is the semi-cone angle of a cone clutch and why does it matter?

The axial force F creates a normal force F/sin α on the cone, so the torque is μ·F·Rf/sin α: a smaller angle gives more torque from the same spring. But if tan α is less than or equal to μ the cone self-locks and must be pulled out with a force N(μ cos α − sin α). The angle is chosen a little above the friction angle tan⁻¹μ.

How does a centrifugal clutch work and at what speed does it engage?

Shoes on a hub turned by the engine are held off the drum by springs. The shoe engages when its centrifugal force m·ω²·r_g equals the spring preload Fs, so ωe = √(Fs/(m·r_g)). Above that each shoe presses with N = m·ω²·r_g − Fs and the torque is T = z·μ·R·(m·ω²·r_g − Fs), growing with the square of speed.

Explore Related Simulators

To see where the clutch sits in the driveline, open the Gearbox Simulator; automatic transmissions apply their multi-plate clutches to the sets in the Planetary Gear Simulator. The friction coefficient itself is explored in the Friction & Contact Forces simulator, the engine-side inertia in the Flywheel Dynamics simulator, and the friction that drives a belt in the Belt & Chain Drive simulator.

Updated 11 October 2026