Clutch types: single plate, multi-plate, diaphragm and centrifugal

Why it matters

A friction clutch lets the driver start from rest, change gear and stop without stalling the engine, by connecting and disconnecting a spinning engine from a stationary or differently-moving gearbox. Choosing the clutch type and sizing its friction surfaces and springs decides whether it slips under full torque, how heavy the pedal feels and how long the facings last. Clutch torque capacity is also one of the most common numerical topics in machine design and automotive exams.

Key ideas

• Function. The clutch transmits engine torque by dry (or oil-wetted) friction between rotating discs pressed together by springs. It must transmit maximum engine torque with a margin (typically 1.2–1.5 times, the "clutch reserve factor") without slipping, take up drive smoothly, disengage completely, and dissipate the heat of slipping.
• Single-plate clutch. One driven disc (friction plate), splined to the gearbox input (clutch) shaft, is clamped between the engine flywheel and a pressure plate. Both faces of the disc carry linings, so there are two friction surfaces. Torsional damper springs in the disc hub soften torque pulses, and cushion springs between the linings give progressive engagement. Used in almost all manual-gearbox cars and light commercial vehicles.
• Coil-spring clutch. The pressure plate is loaded by several helical springs around its periphery and released through three or more release levers. Clamp load falls as the linings wear (springs extend), and at high speed the springs can bow under centrifugal force.
• Diaphragm-spring clutch. A single dished (Belleville-type) steel spring with radial fingers does the job of both the coil springs and the release levers. Its non-linear load–deflection curve gives an almost constant (even slightly rising) clamp load as the linings wear, and a falling release load as the pedal is pressed, so pedal effort is low. It is compact, balanced and unaffected by centrifugal force. It is now the standard car clutch; note that it is still a single-plate clutch – "diaphragm" describes the spring, not the number of plates.
• Multi-plate clutch. Alternate plates are splined to the driving drum and the driven hub. With n₁ plates on one member and n₂ on the other, the number of friction surfaces (pairs of contacting surfaces) is n = n₁ + n₂ − 1. More surfaces give more torque in a smaller diameter, so multi-plate clutches are used in motorcycles, heavy vehicles, automatic transmissions (clutch packs) and limited-slip differentials. They may run dry or wet (in oil); wet clutches have a lower friction coefficient (about 0.05–0.10) but cool well and engage smoothly.
• Centrifugal clutch. Weighted shoes on the driving member are held inward by springs. As speed rises, centrifugal force overcomes the spring force and presses the shoes against a drum, so the clutch engages automatically above a set speed and slips progressively. Used in mopeds, scooters (with a CVT), lawn equipment and some small vehicles; some older car clutches combined centrifugal weights with springs to raise clamp load at speed.
• Design assumptions for plate clutches. A new clutch is analysed with uniform pressure across the lining. After initial wear, the wear rate (proportional to pressure × rubbing velocity) becomes uniform, so p·r = constant – the uniform wear theory, which gives slightly lower torque and is used for design because it is safer.

Formulas

n = n₁ + n₂ − 1

• n: number of friction surfaces (pairs of contacting surfaces); n₁, n₂: plates on the driving and driven members. A single-plate clutch with both sides lined has n = 2.

Uniform pressure (new clutch): W = p · π · (R₁² − R₂²) T = n · μ · W · R_m, with R_m = (2/3) · (R₁³ − R₂³) / (R₁² − R₂²)

Uniform wear (worn clutch, design case): W = 2π · C · (R₁ − R₂), with C = p_max · R₂ (maximum pressure at the inner radius) T = n · μ · W · (R₁ + R₂) / 2

• W: axial spring (clamp) force (N); p: pressure (Pa); R₁, R₂: outer and inner radii of the lining (m); μ: coefficient of friction (–); R_m: mean friction radius (m); T: torque capacity (N·m).
• For uniform wear and a given outer radius and p_max, torque is maximum when R₂ = R₁/√3 ≈ 0.577·R₁; in practice R₂/R₁ is about 0.6–0.8.

P = 2π · N · T / 60

• P: power (W); N: speed (rev/min).

Centrifugal clutch (z shoes): F_c = m · ω² · r_g, T = z · μ · (F_c − S) · R

• m: mass of one shoe (kg); ω: angular speed (rad/s); r_g: radius of the shoe's centre of gravity (m); S: spring force on each shoe at the engaging position (N); R: inner radius of the drum (m). Engagement begins when m · ω_e² · r_g = S.

Worked examples

Example 1 (standard). A single-plate clutch, both sides effective, has outer diameter 300 mm and inner diameter 200 mm. μ = 0.3 and the maximum permissible lining pressure is 0.1 MPa. Using uniform wear, find the clamp force, the torque capacity and the power it can transmit at 2000 rev/min.

1. R₁ = 0.15 m, R₂ = 0.10 m, n = 2.
2. C = p_max · R₂ = 0.1 × 10⁶ × 0.10 = 10 000 N/m.
3. W = 2π · C · (R₁ − R₂) = 2π × 10 000 × 0.05 = 3141.6 N.
4. T = n · μ · W · (R₁ + R₂)/2 = 2 × 0.3 × 3141.6 × 0.125 = 235.6 N·m.
5. P = 2π × 2000 × 235.6 / 60 = 49 348 W.

Answer: W ≈ 3.14 kN, T ≈ 236 N·m, P ≈ 49.3 kW.

(With uniform pressure and the same W, R_m = 0.1267 m and T = 238.8 N·m – only about 1.3% higher, which is why uniform wear is the safe design assumption.)

Example 2 (GATE level). A wet multi-plate clutch must transmit 25 kW at 3000 rev/min. It has 3 steel plates on the driving drum and 2 lined plates on the driven hub, lining radii 80 mm and 50 mm, μ = 0.1. Using uniform wear, find the axial force needed and the maximum lining pressure.

1. Torque: T = 60 P / (2π N) = 60 × 25 000 / (2π × 3000) = 79.58 N·m.
2. Friction surfaces: n = 3 + 2 − 1 = 4.
3. W = T / [n · μ · (R₁ + R₂)/2] = 79.58 / (4 × 0.1 × 0.065) = 3060.7 N.
4. C = W / [2π (R₁ − R₂)] = 3060.7 / (2π × 0.03) = 16 237 N/m.
5. p_max = C / R₂ = 16 237 / 0.05 = 3.25 × 10⁵ Pa.

Answer: W ≈ 3.06 kN; p_max ≈ 0.32 MPa (at the inner radius).

Example 3 (centrifugal clutch). Four shoes, each 0.3 kg with centre of gravity at 100 mm radius, engage a drum of inner radius 120 mm. μ = 0.3. Engagement is to start at 800 rev/min. Find the spring force per shoe and the torque at 2000 rev/min.

1. ω_e = 2π × 800/60 = 83.78 rad/s; S = m · ω_e² · r_g = 0.3 × 83.78² × 0.10 = 210.6 N.
2. At 2000 rev/min, ω = 209.44 rad/s; F_c = 0.3 × 209.44² × 0.10 = 1315.9 N.
3. T = z · μ · (F_c − S) · R = 4 × 0.3 × (1315.9 − 210.6) × 0.12 = 159.2 N·m.

Answer: S ≈ 211 N per shoe; T ≈ 159 N·m.

Common mistakes

• Using n = 1 for a single-plate clutch; with linings on both faces there are two friction surfaces.
• Counting plates instead of surfaces in multi-plate clutches; use n₁ + n₂ − 1.
• Taking p_max at the outer radius in uniform-wear problems; it occurs at the inner radius.
• Mixing up the friction radii: (R₁ + R₂)/2 belongs to uniform wear, (2/3)·(R₁³ − R₂³)/(R₁² − R₂²) to uniform pressure.
• Diameters instead of radii, and mm instead of m, in torque formulas.
• Forgetting the spring force in a centrifugal clutch: only F_c − S presses the shoe on the drum.
• Saying a diaphragm clutch is "self-adjusting"; it maintains clamp load over wear, but the free play in the linkage may still need adjustment unless a self-adjusting mechanism is fitted.

For GATE ME

Clutch questions are usually numericals: torque capacity under uniform pressure or uniform wear, axial force for a required power, number of friction surfaces in a multi-plate clutch, maximum pressure location, and engagement speed or torque of a centrifugal clutch. Short conceptual questions ask why uniform wear is used for design and why a diaphragm spring gives low pedal effort. Practise switching between power, speed and torque quickly.

Quick check

1. How many friction surfaces does a clutch with 4 driving and 3 driven plates have?
2. Where is the pressure highest in a worn (uniform-wear) clutch?
3. A single-plate clutch (both sides) has W = 2 kN, μ = 0.25 and mean radius 0.1 m (uniform wear). What torque does it carry?
4. Why does the clamp load of a coil-spring clutch fall as the linings wear?
5. At what speed does a centrifugal clutch begin to transmit torque?

Answers: 1. 6. 2. At the inner radius. 3. T = 2 × 0.25 × 2000 × 0.1 = 100 N·m. 4. The pressure plate moves toward the flywheel, the springs extend and their force falls in proportion to stiffness × extension. 5. When the centrifugal force on each shoe equals its spring force, m·ω²·r_g = S.