Anti-lock braking system and electronic brake distribution

Why it matters

A locked wheel slides: it can no longer steer the car, it usually gives less braking force than a wheel still rolling with a little slip, and a locked rear axle can spin the vehicle. ABS prevents lock-up by modulating each wheel's brake pressure many times a second, and EBD uses the same hardware to share braking between front and rear according to the actual load. Both are now mandatory on new cars and two-wheelers above a size class in India.

Key ideas

Longitudinal slip. A braked tyre turns slightly slower than it would if free-rolling. Slip ratio λ = 0 means free rolling; λ = 1 (100 %) means a locked wheel. The braking force coefficient rises with slip to a peak (μ_p) at roughly 10–30 % slip on most surfaces, then falls to the lower sliding value (μ_s) at lock. Lateral (cornering) grip also collapses as slip approaches 100 %, which is why a locked front wheel cannot steer.

What ABS does. It keeps every wheel near the slip of peak friction, so the car (1) stays steerable, (2) stays directionally stable, and (3) usually stops in a shorter distance than with locked wheels on hard surfaces. On loose gravel or deep snow a locked wheel builds a wedge of material, so ABS stopping distance can be longer — ABS is primarily about control.

Components.

• Wheel-speed sensors — inductive (toothed tone ring and coil) or active Hall-effect / magneto-resistive sensors at each wheel.
• Electronic control unit (ECU) — computes each wheel's speed and deceleration, estimates vehicle speed from all wheels, and detects incipient lock (wheel deceleration above a threshold, or slip above a threshold).
• Hydraulic control unit (modulator) — for each channel an inlet valve (normally open) and an outlet valve (normally closed), a low-pressure accumulator, and an electric return pump that sends released fluid back towards the master cylinder (felt as pedal pulsation).

Control cycle (per wheel).

1. Pressure build — inlet open, outlet closed: normal braking.
2. Pressure hold — the wheel decelerates too fast: inlet closes, pressure is held.
3. Pressure release — the wheel still tends to lock: outlet opens, fluid goes to the accumulator, pressure drops and the wheel speeds up.
4. Re-apply — pressure is built up again in steps. The cycle repeats several times per second.

Channels. Modern cars use four sensors and four channels. Some systems control the two rear wheels together on the select-low principle (pressure set by the wheel with less grip), which keeps the rear stable on split-friction roads. Two-wheelers use single- or dual-channel ABS.

Electronic brake-force distribution (EBD). Without ABS hardware, a mechanical pressure-limiting (proportioning) valve reduces rear pressure above a set value. EBD does this electronically using the ABS sensors and valves: it compares rear-wheel slip with front-wheel slip and, if the rears start to slip more, closes the rear inlet valves to hold rear pressure. Because it reacts to actual slip, it adapts automatically to payload, deceleration and road friction, so the vehicle can use more rear braking when laden while never locking the rears first. It works below the ABS threshold; ABS takes over if a wheel nears lock. Some systems also vary left/right distribution when braking in a curve.

Built on ABS. Traction control (TCS), electronic stability control (ESC), brake assist and hill-hold all use the same sensors and modulator.

Formulas

λ = (v − ω·r) / v

• λ = longitudinal slip ratio under braking (dimensionless; often ×100 %), v = vehicle (wheel-centre) speed (m/s), ω = wheel angular speed (rad/s), r = tyre rolling radius (m). λ = 0 rolling, λ = 1 locked.

F_x = μ(λ) · N

• F_x = braking force at a tyre (N), μ(λ) = braking-force coefficient at slip λ, N = normal load on the tyre (N).

s = v² / (2·μ_eff·g)

• s = braking distance (m), μ_eff = average effective friction coefficient achieved (μ_s for locked wheels; slightly below μ_p for ABS), g = 9.81 m/s². Constant deceleration, no reaction time.

t = v / (μ_eff·g)

• t = braking time (s).

Worked examples

Example 1 (standard) — slip ratio. A car travels at 20 m/s while braking. A front wheel of rolling radius 0.30 m turns at 55 rad/s. Find the slip ratio and say whether ABS is likely to intervene if its target is 10–25 % slip.

1. Wheel circumferential speed ω·r = 55 × 0.30 = 16.5 m/s.
2. λ = (v − ω·r) / v = (20 − 16.5) / 20 = 0.175. λ = 17.5 % — inside the target band, so ABS holds pressure rather than releasing it.

Example 2 (GATE level) — locked wheels versus ABS. On a dry road the peak braking coefficient is μ_p = 0.8 and the sliding coefficient is μ_s = 0.6. ABS achieves an average of 95 % of μ_p. Find the braking distance from 90 km/h with all wheels locked and with ABS, and the percentage saving.

1. v = 90 / 3.6 = 25 m/s; v² = 625 m²/s².
2. Locked: s = v² / (2·μ_s·g) = 625 / (2 × 0.6 × 9.81) = 625 / 11.77 = 53.1 m.
3. ABS: μ_eff = 0.95 × 0.8 = 0.76; s = 625 / (2 × 0.76 × 9.81) = 625 / 14.91 = 41.9 m.
4. Saving = (53.1 − 41.9) / 53.1 = 21 %. Locked ≈ 53.1 m; ABS ≈ 41.9 m (about 21 % shorter) — and the car can still be steered throughout.

Common mistakes

• Saying ABS always shortens stopping distance; its main job is steerability and stability, and on loose surfaces it can lengthen the stop.
• Defining slip with ω·r in the denominator (that is the traction-slip convention, used when accelerating).
• Thinking EBD measures axle load with load sensors — it infers the right distribution from wheel slip.
• Pumping the brake pedal in an ABS car; the correct action is to press hard and steer.
• Assuming the maximum braking force occurs at lock; it occurs at the peak, usually 10–30 % slip.

For GATE ME

ABS and EBD appear mainly as conceptual questions (slip, μ–slip curve, why steering is retained, what EBD replaces). Numericals use slip ratio, braking distance and time with a given friction coefficient, and the load-transfer and brake-distribution results from the brake-fundamentals topic. Practise with consistent units and the correct slip definition.

Quick check

1. What is the slip ratio of a locked wheel?
2. Roughly at what slip does the braking coefficient peak on dry asphalt?
3. What device did EBD replace?
4. Why does a locked front wheel lose steering?
5. What causes the pulsation felt in the pedal during ABS operation?

Answers: 1. 1 (100 %). 2. About 10–30 %. 3. The mechanical rear pressure-limiting (proportioning) valve. 4. A sliding tyre can generate almost no lateral force. 5. The return pump pushing released fluid back towards the master cylinder.