Wheel alignment and wheel balancing

Why it matters

Even a perfectly designed suspension only works if the wheels are set to the angles the designer intended and spin without wobbling. Wrong alignment makes a car pull, wander and wear tyres in a few thousand kilometres; an unbalanced wheel shakes the steering at motorway speed and hammers the suspension. Both are everyday workshop jobs and favourite interview questions.

Key ideas

Wheel alignment means checking and setting the angles of all four wheels and the steering axis to the vehicle maker's specification. The angles themselves (camber, caster, kingpin inclination, toe) are defined in the steering-geometry topic.

What is measured.

• Front: camber, caster, kingpin (steering-axis) inclination, included angle, toe, toe-out on turns (turning angle), and setback (one front wheel behind the other).
• Rear: camber and individual toe of each wheel.
• Thrust line — the direction in which the rear axle points, bisecting the total rear toe. The angle between the thrust line and the vehicle's geometric centreline is the thrust angle. A non-zero thrust angle makes the car "crab" and puts the steering wheel off-centre when driving straight.

Order of adjustment. Check tyre pressures, ride height, worn ball joints, bushes and wheel bearings first — aligning worn parts is pointless. Then set the angles in the order caster → camber → toe, because changing caster or camber changes toe, and toe is always set last. In four-wheel alignment the rear is set first and the front toe is then set relative to the thrust line, so the steering wheel is centred.

How the angles are adjusted. Toe by turning tie-rod or track-rod sleeves (equally on both sides). Camber and caster by shims at the upper-arm pivots, eccentric cams or bolts, slotted strut-top mounts, or adjustable strut rods; on many MacPherson cars caster is fixed and only camber may be adjustable. KPI and the included angle are fixed by the parts — if they are wrong, a part is bent.

Equipment. Turntables under the front wheels and slip plates under the rear, sensor heads or camera targets on the wheels (3D optical systems), a computer that compares readings with the specification; simpler garages use optical or laser gauges and a toe trammel.

Symptoms. Pull to one side (unequal camber or caster side to side), wander (low caster, worn joints), feathered tread (toe), one-edge wear (camber), off-centre steering wheel (thrust angle or unequal toe).

Wheel balancing. A tyre-and-wheel assembly is never perfectly uniform; any uneven mass rotating at radius r produces a centrifugal force m·r·ω² that rotates with the wheel.

• Static unbalance — a heavy spot in the wheel's centre plane. The wheel, free on its bearings, settles heavy-side down. Running, it causes vertical wheel hop (tramp). Corrected by a weight opposite the heavy spot.
• Dynamic (couple) unbalance — heavy spots on opposite sides in different planes; the wheel may be statically balanced but the two forces form a rotating couple that makes the wheel wobble about the steering axis — shimmy felt in the steering wheel.
• Dynamic balancing on a spin balancer measures both force and couple and gives two correction weights, one on the inner and one on the outer rim flange (two-plane balancing). Balance is needed after fitting a new tyre or repairing a puncture.
• The vibration frequency equals the wheel's rotational frequency; it becomes noticeable around the speed at which this matches the wheel-hop natural frequency of the unsprung mass (roughly 10–15 Hz, around 80–110 km/h for a car).

Formulas

γ ≈ (x_t − x_b) / D (radians, small angle; exact: tan γ = (x_t − x_b) / D)

• γ = camber, x_t and x_b = horizontal distances of the top and bottom of the rim from a vertical reference (m), D = vertical distance between the measuring points (m). Positive when the top is further outboard.

total toe = B − A, θ_toe ≈ (B − A) / D (total toe angle, radians)

• A, B = front and rear rim distances at hub height (m), D = rim diameter at the measuring points (m). Each wheel's toe angle is half of the total when toe is equal.

thrust angle = (θ_RL − θ_RR) / 2

• θ_RL, θ_RR = individual toe angles of the rear-left and rear-right wheels (toe-in positive). The thrust line points towards the side with less toe-in.

F = m_u · r · ω², ω = v / R

• F = rotating unbalance force (N), m_u = unbalanced mass (kg), r = its radius (m), ω = wheel angular speed (rad/s), v = vehicle speed (m/s), R = tyre rolling radius (m).

m_i·r_c + m_o·r_c = m_u·r and m_o·r_c·a_o − m_i·r_c·a_i = m_u·r·z (two-plane correction, both weights 180° opposite the unbalance)

• m_i, m_o = inner and outer correction masses (kg), r_c = radius of the correction planes (m), a_i, a_o = distances of the correction planes from the centre plane (m), z = axial position of the unbalance (m, positive outboard).

Worked examples

Example 1 (standard) — force from a static unbalance. A wheel has an unbalance of 30 g at a radius of 200 mm. The tyre rolling radius is 0.30 m. Find the rotating force at 100 km/h and its frequency.

1. v = 100 / 3.6 = 27.78 m/s; ω = v / R = 27.78 / 0.30 = 92.6 rad/s.
2. F = m_u · r · ω² = 0.030 × 0.20 × 92.6² = 0.006 × 8573 = 51.4 N.
3. Frequency f = ω / 2π = 92.6 / 6.283 = 14.7 Hz. F ≈ 51 N at 14.7 Hz — small beside the wheel load, but at that frequency it excites wheel hop.

Example 2 (GATE level) — two-plane balancing. A 30 g unbalance sits at a radius of 200 mm in a plane 30 mm inboard of the wheel centre plane. Correction weights can be clipped on the inner and outer rim flanges, at radius 190 mm and 100 mm either side of the centre plane. Find both correction masses (placed opposite the unbalance).

1. Force balance: (m_i + m_o) × 190 = 30 × 200 = 6000 g·mm → m_i + m_o = 31.58 g.
2. Moment balance about the centre plane (outboard positive): the unbalance moment is 6000 × (−30) = −180 000 g·mm². The corrections must give the same moment so that, being opposite in direction, they cancel it: 190 × (100·m_o − 100·m_i) = −180 000 → m_o − m_i = −9.47 g.
3. Solve: m_i = (31.58 + 9.47) / 2 = 20.53 g; m_o = (31.58 − 9.47) / 2 = 11.05 g. Inner flange ≈ 20.5 g, outer flange ≈ 11.1 g. A single 31.6 g weight in one plane would remove the force but leave a couple — static balance only.

Common mistakes

• Setting toe before caster and camber — toe must be last.
• Aligning a car with worn ball joints or bushes, or at the wrong tyre pressures.
• Adjusting front toe to the centreline instead of the thrust line, leaving the steering wheel off-centre.
• Thinking a statically balanced wheel is fully balanced; couple unbalance still causes shimmy.
• Using vehicle speed directly as ω, instead of ω = v / R.
• Expecting alignment faults to cause speed-related vibration; vibration usually points to balance, run-out or worn parts.

For GATE ME

The calculation side is rotating unbalance (F = m·r·ω²) and static/dynamic balancing of masses in different planes — standard theory-of-machines balancing applied to a wheel. Expect conceptual questions on static versus dynamic unbalance, wheel hop versus shimmy, and the effects of alignment angles. Practise two-plane balancing with masses at different radii.

Quick check

1. In what order are caster, camber and toe set?
2. What symptom does couple unbalance cause in a front wheel?
3. Rear individual toe is +0.20° (left) and 0.00° (right). What is the thrust angle?
4. Doubling the speed changes the unbalance force by what factor?
5. Which alignment angle is changed by turning the tie-rod sleeves?

Answers: 1. Caster, then camber, then toe. 2. Shimmy (wobble felt in the steering wheel). 3. (0.20 − 0)/2 = 0.10°. 4. Four times. 5. Toe.