Hydraulic and electric power steering

Why it matters

Wider tyres, heavier front ends and front-wheel drive make manual steering too heavy when parking, while a very high manual ratio makes the car sluggish. Power steering supplies most of the force so the ratio can stay quick. Hydraulic systems still dominate heavy vehicles; electric power steering (EPS) is now standard on cars and is the actuator that lane-keeping and parking assistance work through.

Key ideas

What any power steering must do. Add force in the direction the driver steers, in proportion to how hard the driver is steering. Leave some road feel. Stay mechanically connected so the car can still be steered (with more effort) if the assistance fails.

Hydraulic power steering (HPS).

• Pump — a vane pump driven by the engine belt, with a flow-control valve (steady flow at all engine speeds) and a pressure-relief valve (limits maximum pressure; the value is in the maker's specification). Reservoir, pressure and return hoses, often a fluid cooler.
• Control (rotary) valve — sits in the pinion (or screw) input. A slim torsion bar joins the input shaft from the steering wheel to the pinion. Driver torque twists the bar a few degrees; this relative rotation between the valve spool and sleeve opens ports that send pressure to one side of the power cylinder and connect the other side to return. With no torque the valve is open-centre: oil circulates freely back to the reservoir at low pressure.
• Power cylinder — a double-acting piston built into the rack housing (or around the nut of a recirculating-ball gear, "integral" type for trucks). Pressure on one side of the piston pushes the rack.
• Feel — because assistance rises with the twist of the torsion bar, the driver's torque still rises with steering load, so some feel remains.
• Drawbacks — the pump runs whenever the engine runs, absorbing power even when driving straight (roughly a few percent fuel penalty); hoses, leaks and fluid maintenance; assistance is not easily made speed-sensitive (needs an extra valve).
• Electro-hydraulic (EHPS) — the pump is driven by an electric motor only on demand; a halfway step.

Electric power steering (EPS).

• Torque sensor on a torsion bar in the column or pinion measures driver torque (and usually steering angle).
• ECU reads driver torque and vehicle speed and sets the motor's assist torque from a map: high assist when parking, low at speed.
• Brushless DC (or induction) motor adds torque through a reduction gear. Layouts: column-assist (motor and worm gear on the column — small cars), pinion-assist, dual-pinion, and rack-assist (motor drives a ball nut on the rack through a belt — large cars and SUVs, highest force).
• Benefits — energy used only when steering (typically 2–3 % fuel saving over HPS), no fluid, compact, speed-sensitive assistance, active return-to-centre, damping and pull compensation in software, and the motor can steer the car for lane-keeping and automated parking.
• Limitations — limited rack force on 12 V systems for very heavy vehicles; feel depends on software calibration; motor inertia and friction can dull feedback; needs functional-safety design so a sensor fault cannot cause unwanted steering.

Fail-safe. Both systems keep a mechanical link from steering wheel to rack, so a failure means heavy steering, not loss of steering.

Formulas

F_a = p · A, A = π·(D² − d²) / 4

• F_a = assist force on the rack (N), p = pressure difference across the piston (Pa), A = effective piston area (m²) — for the rod (annulus) side of a double-rod cylinder use D = piston diameter and d = rod diameter (m).

F_rack = η·T_d / r_p + F_a

• F_rack = total rack force (N), T_d = driver torque (N·m), η = gear efficiency, r_p = pinion pitch radius (m).

T_d = k_tb · Δθ

• k_tb = torsion-bar stiffness (N·m/rad or N·m/deg), Δθ = twist of the torsion bar.

P_h = p · Q

• Hydraulic power (W), Q = flow rate (m³/s).

T_m = T_a / (i · η_g), ω_m = i · ω_sw

• EPS motor torque (N·m) and speed (rad/s) for an assist torque T_a at the column, reduction ratio i, gear efficiency η_g, steering-wheel speed ω_sw.

P_m = T_m · ω_m, P_e = P_m / η_m, I = P_e / V

• Motor mechanical and electrical power (W), motor efficiency η_m, current I (A) at supply voltage V (V).

Worked examples

Example 1 (standard) — HPS cylinder pressure. Parking needs a rack force of 9.0 kN. The pinion pitch radius is 8 mm, gear efficiency 0.85, and the driver applies 5 N·m. The power piston is 45 mm in diameter on a 22 mm rack (rod) diameter. Find the pressure needed.

1. Driver's share: η·T_d / r_p = 0.85 × 5 / 0.008 = 531 N.
2. Assist needed: F_a = 9000 − 531 = 8469 N.
3. A = π·(D² − d²)/4 = π × (45² − 22²) / 4 = π × 1541 / 4 = 1210 mm².
4. p = F_a / A = 8469 / 1210 = 7.0 N/mm². p ≈ 7.0 MPa — the relief valve must be set above this.

Example 2 (GATE level) — sizing a column-type EPS motor. A column EPS assists with T_a = 3 × driver torque when parking. The driver applies 4 N·m. The torsion bar stiffness is 2 N·m/degree. The motor drives the column through a worm gear of ratio 16.5 and efficiency 0.8; motor efficiency is 0.8 and supply 12 V. The steering wheel is turned at 360°/s. Find the torsion-bar twist, motor torque, motor speed and current.

1. Twist: Δθ = T_d / k_tb = 4 / 2 = 2.0°.
2. Assist torque at the column: T_a = 3 × 4 = 12 N·m.
3. T_m = T_a / (i·η_g) = 12 / (16.5 × 0.8) = 0.909 N·m.
4. ω_sw = 2π rad/s → ω_m = i·ω_sw = 16.5 × 2π = 103.7 rad/s (990 rpm).
5. P_m = T_m·ω_m = 0.909 × 103.7 = 94.2 W; P_e = P_m / η_m = 94.2 / 0.8 = 117.8 W.
6. I = 117.8 / 12 = 9.8 A. Δθ = 2°, T_m ≈ 0.91 N·m, n_m ≈ 990 rpm, I ≈ 9.8 A. Total column torque is 4 + 12 = 16 N·m, four times what the driver supplies.

Common mistakes

• Saying the HPS valve is worked by vehicle speed; it is worked by the twist of the torsion bar, i.e. by driver torque.
• Forgetting the rod area on the annulus side of the piston.
• Thinking EPS uses no energy at all: it uses electrical energy, but only when assisting.
• Dividing by efficiency in the wrong direction: torque out = torque in × ratio × efficiency.
• Claiming loss of power steering means loss of steering — the mechanical link remains.
• Confusing electro-hydraulic steering (electric pump) with EPS (electric motor on the column or rack).

For GATE ME

Questions are usually simple hydraulics and torque/power chains: force from pressure and piston area, torque multiplication through a reduction gear with efficiency, motor power and current, plus conceptual comparison of HPS and EPS. Practise chaining driver torque → torsion bar → gear → rack force with consistent units.

Quick check

1. What senses driver effort in both HPS and EPS?
2. Why does HPS consume power when driving straight?
3. Name the EPS layout suited to the heaviest cars.
4. A cylinder of effective area 1000 mm² sees 6 MPa. What is the assist force?
5. What is an open-centre valve?

Answers: 1. The twist of a torsion bar between the steering wheel and the pinion. 2. The engine-driven pump circulates oil continuously. 3. Rack-assist (belt and ball-nut on the rack). 4. 6000 N. 5. A valve that, in neutral, lets oil flow straight back to the reservoir at low pressure.