Clutches and brakes

In short

A clutch connects and disconnects two coaxial shafts while they may be rotating at different speeds; a brake absorbs kinetic or potential energy from a moving system and dissipates it as heat. Both are friction devices, so both are designed by the same two ideas - torque capacity from a friction area under pressure, and heat dissipation from the rubbing surface. Clutches and brakes are examined every year in GATE (ME) and in university machine design papers, and are core knowledge at Maruti Suzuki, Tata Motors, Mahindra, Ashok Leyland, Bajaj, TVS, Brakes India, Endurance, Sundaram-Clayton and Bosch. Design work follows IS 2742 (industrial shoe brakes for cranes and hoists), IS 3177, and automotive AIS/CMVR braking requirements.

Explained

Friction fundamentals common to both

• Friction torque on a ring element of radius r, width dr, pressure p: dT = μ p (2πr dr) r. Integrating gives torque; the pressure law chosen decides the answer.
• Uniform pressure theory: valid for a new, rigid, accurately machined lining - p = constant = F/[π(R₁²−R₂²)]. Gives higher torque, used for new clutches/light duty.
• Uniform wear theory: wear ∝ p·v ∝ p·r, so p·r = constant = p_max·R₂ - the inner edge carries maximum pressure. Standard design assumption because a clutch spends its life worn-in; gives lower (safe) torque.
• Mean radius R_m = (R₁+R₂)/2 for uniform wear; R_m = (2/3)(R₁³−R₂³)/(R₁²−R₂²) for uniform pressure.
• Number of friction pairs i: a single plate clutch with lining on both faces has i = 2; a multi-plate clutch with n₁ driving and n₂ driven plates has i = n₁+n₂−1.
• Lining materials: moulded/woven asbestos-free composites (μ ≈ 0.3-0.4 dry), sintered metal (μ ≈ 0.2-0.3), cork, cast iron on steel (μ ≈ 0.15-0.2), wet clutches in oil (μ ≈ 0.06-0.1). Permissible pressure 0.1-0.5 N/mm² dry, up to 1-2 N/mm² sintered.
• Service factor: design torque = rated engine torque × factor (1.3-1.75 for cars, up to 3 for construction machinery) to cover slip, overload and lining fade.

Types of clutches

• Positive (jaw/spline) clutches - mesh teeth; no slip, no heat, but engage only at rest or near-equal speeds.
• Single plate (dry) clutch - one friction disc between flywheel and pressure plate; coil-spring or diaphragm spring type; standard in cars and LCVs.
• Multi-plate clutch - several plates stacked alternately multiply torque for the same diameter; usually wet (oil-cooled) in motorcycles and automatic transmissions.
• Cone clutch - conical surfaces give a wedge action: normal force F_n = F/sin α, so torque is boosted by 1/sin α. Semi-cone angle α = 12.5° typical; below ~8° it will not disengage.
• Centrifugal clutch - shoes thrown outward by centrifugal force engage automatically above a set speed; used in scooters, mopeds, small compressors.
• Electromagnetic, hydraulic (fluid coupling), and one-way (freewheel) clutches - no friction-area design; selected from catalogues.
• Requirements of a good clutch: adequate torque capacity, smooth gradual engagement, good heat dissipation, low inertia of driven member (for fast gear change), easy adjustment and low pedal effort, dynamic balance.

Types of brakes

• Single block/shoe brake - one shoe pressed on a drum. Braking torque T = μ R_n r. The lever equation changes with the line of action of the friction force and the offset of the pivot; with a short shoe, μ acts tangentially at the rim.
• Double block brake - two shoes on opposite sides cancel the bearing load on the shaft; standard on crane and hoist motors with electromagnetic/thruster release (designed to IS 2742).
• Simple band brake - a flexible band wrapped over angle θ; T₁/T₂ = e^{μθ}, braking torque = (T₁−T₂)r.
• Band and block brake - blocks on the band; tension ratio per block = (1+μ tan θ)/(1−μ tan θ), raised to the number of blocks n. Lining wears instead of band.
• Internal expanding shoe (drum) brake - two shoes expand inside a drum by cam or hydraulic wheel cylinder; the leading shoe self-energizes, the trailing shoe de-energizes. Still used on rear wheels of small Indian cars and most two-wheeler rear wheels.
• Disc brake - calliper pads clamp a rotor; T = 2 μ F R_m (two pads). Better cooling, far less fade, uniform wear, linear response; no self-energization so it needs a booster.
• Other types - internal/external shoe, cone and plate brakes (same equations as clutches), plus non-friction types: eddy-current, hydrodynamic retarder, and regenerative braking in EVs (energy returned to the battery, not dissipated).

Self-energization, self-locking and braking sense

• Self-energizing: the friction force itself increases the applied normal force, so required actuating force falls. In a band brake, anchoring the tight end to the pivot makes it self-energizing for one direction of rotation.
• Self-locking: the brake grips with zero external effort - occurs when the actuating force computes to zero or negative. Desirable only in back-stops/hoist holding devices; dangerous in vehicles because it means uncontrollable grab.
• Reversing the drum direction converts a self-energizing shoe into a de-energizing one - hence a brake must be checked for both directions and designed for the worse case.
• A band brake's two ends: tight-side tension T₁ = T₂ e^{μθ}; whichever end feeds the lever decides effort.

Energy, heat and thermal design

• Energy absorbed = change in KE (½mv² or ½Iω²) + change in PE (mgh, for hoists) + work done against the brake by the driving torque during braking.
• Temperature rise: ΔT = E/(m c), with m the mass of the drum/disc and c ≈ 0.46 kJ/kg·K for steel/cast iron. Cast-iron drums are normally limited to about 300-400 °C; organic linings fade above ~350 °C.
• Continuous rating uses the energy dissipation rate per unit area, H_g = μ p v (W/mm²), and the heat rejection capacity C = h·A·ΔT. Typical permissible p·v: 1.0 N/mm²·m/s intermittent, 0.3 for continuous service.
• Brake fade - loss of μ when the lining overheats or gases form between lining and drum; water fade when wet. Ventilated/drilled discs, fins on drums and larger thermal mass are the cures.
• Clutch slipping energy E = T × relative slip angle; for accelerating an inertia from rest through slip the heat equals the final kinetic energy ½ I_e ω². A bus clutch in city traffic is a thermal design, not a torque design.

Standards and Indian practice

• IS 2742 (Parts 1-4) - electrically operated shoe/thruster brakes for cranes and hoists; IS 3177 - design of EOT cranes, prescribes brake torque as a multiple of full-load torque (commonly ≥150%, holding ≥125%, and 125-150% for hoists per the applicable part - check the current part and edition, as values differ by class).
• CMVR 1989 and AIS-015 / AIS-011 cover automotive braking: service, secondary and parking brake performance, stopping distances, and dual-circuit requirements. ABS has been mandatory on two-wheelers of 125 cc and above (CBS below 125 cc) since 2019, extended to all new two-wheelers from 1 January 2026, and is required on cars sold in India.
• Linings must be asbestos-free in Indian OEM supply (asbestos exposure is regulated under the OSH Code, 2020 — which replaced the Factories Act and its schedules from 21 November 2025 — and allied rules).
• Parking brakes on vehicles must hold on a specified gradient (commonly 18% laden, 12% for a vehicle-trailer combination - confirm against the current standard edition).

Key points

• Clutch - transmits torque between coaxial shafts and allows deliberate disconnection; brake - absorbs energy and dissipates it as heat.
• Uniform wear - p·r = p_max·R₂, lower torque, used for design; uniform pressure - p constant, higher torque, for a new lining.
• Single plate clutch torque T = i·μ·F·R_m, with i = 2 for both faces lined.
• Multi-plate clutch - i = n₁+n₂−1; torque multiplies without increasing diameter.
• Cone clutch - torque gains the factor 1/sin α; α too small prevents disengagement.
• Centrifugal clutch - engages automatically above a cut-in speed; force ∝ ω².
• Diaphragm spring clutch - lighter pedal effort, clamp force stays steady as the lining wears, so modern cars use it over coil-spring types.
• Ratio R₂/R₁ - torque peaks near R₂/R₁ ≈ 0.577 for a given outer radius and p_max; practical designs use 0.5-0.8.
• Band brake - T₁/T₂ = e^{μθ}; braking torque (T₁−T₂)r; simplest and cheapest.
• Band and block brake - ratio per block (1+μ tanθ)/(1−μ tanθ); lining is replaceable.
• Self-energizing - friction increases the applied force, reducing the effort needed; direction-dependent.
• Self-locking - zero or negative required effort; wanted in back-stops, forbidden in vehicles.
• Leading shoe self-energizes, trailing shoe de-energizes in an internal expanding brake.
• Disc brake - uniform wear, fade-resistant, cools well, needs servo assistance; drum brake - self-energizing, cheaper, poorer cooling.
• Energy absorbed = ½mv² + ½Iω² + mgh + driving work during the stop.
• ΔT = E/(mc), c ≈ 0.46 kJ/kg·K for cast iron; permissible p·v limits continuous rating.
• Fade - loss of friction coefficient on overheating; the main reason brakes are sized thermally, not just by torque.
• Service factor 1.3-3 on rated torque covers slip, overload and lining variation.

Formulas and examples

Example 1 - single plate clutch (uniform wear). A single plate clutch, both sides effective, transmits 25 kW at 1,500 rpm. μ = 0.3, p_max = 0.1 N/mm², R₁ = 1.25 R₂. Service factor 1.25. Find radii and the axial force.

• Torque T = 60 × 25,000/(2π × 1500) = 159.2 N·m; design torque = 159.2 × 1.25 = 199 N·m = 1.99 × 10⁵ N·mm.
• F = 2π p_max R₂ (R₁ − R₂) = 2π(0.1)R₂(0.25R₂) = 0.1571 R₂².
• R_m = (1.25R₂ + R₂)/2 = 1.125 R₂.
• T = 2 × 0.3 × 0.1571R₂² × 1.125R₂ = 0.1061 R₂³ = 1.99 × 10⁵ → R₂³ = 1.876 × 10⁶ → R₂ = 123.3 mm, R₁ = 154.2 mm.
• F = 0.1571 × 123.3² = 2,389 N.

Example 2 - multi-plate wet clutch. A multi-plate clutch has 5 driving and 4 driven plates, R₁ = 100 mm, R₂ = 70 mm, μ = 0.1 (oil), axial force 800 N, uniform wear. Find torque and power at 2,000 rpm.

• i = 5 + 4 − 1 = 8; R_m = (100+70)/2 = 85 mm.
• T = 8 × 0.1 × 800 × 85 = 54,400 N·mm = 54.4 N·m.
• P = 2π × 2000 × 54.4/60 = 11.4 kW.

Example 3 - cone clutch. Cone clutch, α = 12.5°, R₁ = 150 mm, R₂ = 130 mm, μ = 0.25, p_max = 0.1 N/mm², uniform wear, one pair of surfaces.

• F = 2π × 0.1 × 130 × (150−130) = 1,634 N.
• R_m = 140 mm; sin 12.5° = 0.2164.
• T = 0.25 × 1,634 × 140/0.2164 = 264,200 N·mm ≈ 264 N·m.
• An equal-size plate clutch (i = 1) would give 0.25 × 1,634 × 140 = 57.2 N·m - the cone gives 4.6× more for the same axial force.

Example 4 - simple band brake. A band brake has drum diameter 400 mm, wrap angle 240°, μ = 0.3, lever 500 mm long with the tight end pinned at the fulcrum and the slack end attached 80 mm from it. Find the effort for a braking torque of 300 N·m.

• θ = 240° = 4.189 rad; e^{0.3 × 4.189} = e^{1.2566} = 3.513.
• T₁ − T₂ = T_b/r = 300/0.2 = 1,500 N; with T₁ = 3.513 T₂ → T₂(2.513) = 1,500 → T₂ = 597 N, T₁ = 2,097 N.
• Moments about the fulcrum: P × 500 = T₂ × 80 → P = 597 × 80/500 = 95.5 N (self-energizing arrangement; reversing the drum would need P = 2,097 × 80/500 = 335 N).

Example 5 - thermal check on a vehicle brake. A 1,200 kg car stops from 80 km/h. Four cast-iron discs of 4 kg each, c = 0.46 kJ/kg·K. Find energy and temperature rise, ignoring losses.

• v = 80/3.6 = 22.22 m/s; E = ½ × 1200 × 22.22² = 296 kJ.
• Total disc mass = 16 kg → ΔT = 296/(16 × 0.46) = 40.2 °C per stop.
• Ten repeated stops with no cooling would add ~400 °C - which is why fade begins and why ventilated discs and cooling time matter.

Where it is used

• Automotive transmissions: dry single plate / diaphragm clutches in cars and LCVs; wet multi-plate clutches in motorcycles and automatics - Maruti Suzuki, Tata Motors, Mahindra, Bajaj, TVS, Hero.
• Braking component industry: Brakes India (Chennai), Sundaram-Clayton, Endurance Technologies, Bosch and Rane supply discs, drums, callipers, master cylinders and ABS modules to Indian OEMs and for export.
• Material handling and cranes: double-shoe electromagnetic/thruster brakes on hoist and travel motors, designed and tested to IS 2742 and IS 3177; also band brakes on winches.
• Machine tools and presses: electromagnetic clutch-brake units for rapid start-stop and emergency stopping; flywheel presses use band or plate brakes.
• Agriculture and construction: tractor PTO clutches, dual clutches, oil-immersed multi-disc brakes in backhoe loaders - Mahindra, Escorts Kubota, JCB, Tata Hitachi.
• Job roles: design engineer (driveline/brakes), NVH and judder investigation, brake test engineer running fade and recovery tests, validation to AIS/CMVR, and after-market lining development.

Interview questions

• Q: Why is uniform wear theory preferred for clutch design? A: A clutch spends most of its life with a worn-in lining; uniform wear predicts a lower torque capacity, so designing on it is conservative and safe.
• Q: Where is the pressure maximum under uniform wear, and why? A: At the inner radius, because p·r is constant - the smallest radius must carry the highest pressure.
• Q: Why does a multi-plate clutch use many plates instead of a bigger single plate? A: Torque scales with the number of friction pairs, so plates let a compact, low-inertia clutch carry high torque in a small diameter.
• Q: What limits how small the cone angle of a cone clutch can be? A: Below about 8° the wedge action makes disengagement difficult or impossible, and the clutch sticks, so 12.5° is the usual choice.
• Q: What is a self-locking brake and is it desirable? A: One that grips with no external force; it is wanted only in back-stops and holding devices, and must be avoided in vehicles where it would cause grabbing and loss of control.
• Q: Why does a drum brake have a leading and a trailing shoe? A: The friction force on one shoe adds to its application force (leading, self-energizing) while on the other it opposes it (trailing), so their torques differ.
• Q: Why are disc brakes used on front wheels and drums often retained at the rear? A: Weight transfer makes the front do most of the braking so it needs fade resistance and cooling, while the lighter rear duty is met more cheaply by a drum that also integrates the parking brake.
• Q: What is brake fade and how is it reduced? A: Loss of friction coefficient from overheating or gassing of the lining; reduced by larger thermal mass, ventilated/drilled discs, better lining material and adequate cooling area.
• Q: Why is a wet clutch's coefficient of friction so much lower? A: Oil separates the surfaces and much of the torque is transmitted through shear of the film; μ falls to about 0.06-0.1 but cooling and life improve greatly.
• Q: How does a centrifugal clutch engage without a pedal? A: Shoes are thrown outward by force m ω² r; when this exceeds the retaining spring force at the cut-in speed, they press on the drum and transmit torque.
• Q: Why does the diaphragm spring clutch dominate modern cars? A: Its non-linear characteristic keeps clamp load almost constant as the lining wears, needs lower pedal effort and is compact and better balanced at high speed.
• Q: A brake has to stop a hoisting load being lowered - what extra energy must it absorb? A: The potential energy released, mgh, in addition to the kinetic energy of the load and the rotating parts, plus any motor torque still applied.

Common mistakes

• Taking i = 1 for a single plate clutch when both faces are lined - the torque is double.
• Using R_m = (R₁+R₂)/2 with the uniform pressure formula, or constant p with the uniform wear formula - the pressure law and the radius expression must match.
• Writing i = n₁ + n₂ for a multi-plate clutch instead of n₁ + n₂ − 1.
• Forgetting 1/sin α in the cone clutch, or using the full cone angle instead of the semi-angle.
• Using θ in degrees in e^{μθ} for a band brake, and mixing up the tight and slack ends when taking moments.
• Checking a brake for only one direction of rotation and missing the de-energizing (or self-locking) case.
• Sizing a brake on torque alone and ignoring heat - the p·v limit and temperature rise usually decide the size.

Related topics

Machine design: failure theories and fatigue · Design of shafts, keys, bearings and springs · Bearings, lubrication and tribology · Gear design · Theory of machines: friction and power transmission · Automobile engineering: transmission and braking systems