Clutches

Clutches connect and disconnect shafts while running. Learn plate clutches (single and multi-plate), uniform-pressure vs uniform-wear theory, cone and centrifugal clutches, engagement energy, and one-way and dog clutches.

A car clutch lets the engine keep spinning while the wheels stop, then smoothly joins them. Motorcycles, automatic gearboxes, power tools and industrial drives all use clutches.

Friction clutches transmit torque by pressing friction surfaces together; their design follows the same physics as brakes, but the goal is smooth engagement and no slip once engaged.

An analogy

Two spinning plates pressed together: at first they slip against each other, then friction drags them to the same speed and they rotate as one.

Types

Single-plate dry (cars with manual gearbox), multi-plate wet (motorcycles, automatic transmissions, DCTs), cone (compact, high torque for size), centrifugal (engage automatically with speed — scooters, chainsaws), electromagnetic (industrial), and positive clutches: dog clutches (no slip, engage only at matched speeds) and one-way/sprag clutches (starters, freewheels).

Uniform pressure vs uniform wear

A new clutch has roughly uniform pressure. As it wears, the outer area (sliding faster) wears more until pressure × radius is constant — uniform wear. Uniform wear gives slightly lower torque, so designers use it as the conservative assumption. The optimum r/R ≈ 0.577 maximises torque for a given outer radius in uniform wear.

Multi-plate clutches

Each extra plate pair adds two friction faces, multiplying torque without increasing diameter — essential in compact automatic transmissions. Oil cooling in wet clutches allows repeated slipping.

Engagement dynamics and control

During slip, energy equal to the relative kinetic energy plus work done against the load is dissipated as heat. Dual-clutch transmissions and launch control modulate clamp force precisely using hydraulic or electromechanical actuators; judder arises from μ–slip-speed characteristics (negative slope).

Formulas

• Uniform wear (worn clutch): T = μ F n (R + r)/2
• Uniform pressure (new clutch): T = μ F n · (2/3)(R³ − r³)/(R² − r²)
• Cone clutch: T = μ F r_m / sin α
• Slip energy (constant torque): E ≈ ½ I_eq ω_rel²·(T_c/(T_c − T_load))

Worked example: Car clutch capacity

Given: μ = 0.3, F = 4 kN, R = 100 mm, r = 60 mm; Single plate, 2 faces

Find: Torque by both theories.

• Uniform wear: 0.3 × 4000 × 2 × 0.08 = 192 N·m
• Uniform pressure: r_f = (2/3)(0.001 − 0.000216)/(0.01 − 0.0036) = 0.0817 m → 196 N·m

Answer: 192 N·m (worn) / 196 N·m (new)

Worked example: Required clamp force

Given: Engine torque 180 N·m, margin 1.3; Same geometry, uniform wear

Find: Spring force.

• T_req = 234 N·m
• F = 234/(0.3 × 0.08 × 2) = 4875 N

Answer: ≈ 4.9 kN diaphragm spring force

Common mistakes

• Wrong: Designing on new-clutch (uniform pressure) capacity. — Right: Use uniform wear — it's lower and represents service life.
• Wrong: Ignoring heat from slipping. — Right: Check energy per engagement and cooling for frequent starts.

Applications

• Manual & DCT transmissions: Dry single-plate and wet/dry dual clutches.
• Motorcycles: Wet multi-plate clutches in oil.
• Industrial & tools: Electromagnetic clutches, centrifugal clutches, sprag freewheels.

Key takeaways

• T = μFn(R + r)/2 (uniform wear).
• Multi-plate multiplies torque in a compact space.
• Slip energy becomes heat — check cooling.
• Positive clutches (dog, sprag) have no slip.

Going further

• Clutch judder: A falling μ-vs-slip curve excites drivetrain oscillations; friction material and oil additives control it.
• Torque converters: Hydrodynamic couplings with torque multiplication and lock-up clutches in automatic transmissions.
• Launch control: Closed-loop clamp-force control maximises acceleration without excessive slip.