Suspension and Steering

Purposes of suspension

• Isolate the body from road shocks for ride comfort.
• Keep the tyres in contact with the road for good traction and braking.
• Support the vehicle weight and carry loads.
• Maintain correct wheel alignment and control body roll, pitch and squat.
• Transmit driving, braking and cornering forces to the frame.

Types of springs

Telescopic shock absorber (damper)

A spring stores energy and would keep oscillating, so a damper is fitted in parallel to convert oscillation energy into heat.

   top mount (body)
        |
   [ piston rod ]
   |  +--------+  | <- oil
   |  | piston |  |    valves in piston
   |  +--------+  |
   |   oil + gas  |
   bottom mount (axle)

The cylinder is filled with oil. During bump the piston moves down and oil is pushed through small orifices and valves into the upper chamber. During rebound it flows back through other valves, giving more resistance (higher in rebound than bump, typically 2:1). The restriction of oil flow creates the damping force. A gas-charged (monotube) design avoids foaming.

Stabilizer (anti-roll) bar

A U-shaped steel torsion bar connected between the left and right suspension arms. In a corner, the outer wheel moves up and the inner wheel moves down; the bar twists and resists this. It reduces body roll, improves handling and keeps both tyres on the road.

Rack and pinion steering

 Steering wheel
      |
  Steering column (universal joints)
      |
  [Pinion]---meshes--- [Rack]
                      |      |
                tie-rod    tie-rod
                  |            |
              steering arm   steering arm
                  |            |
              left wheel    right wheel

• Turning the wheel rotates a small pinion gear that meshes with a toothed rack; the rotary motion becomes linear motion of the rack.
• The rack moves the tie rods (with ball joints) which turn the stub axle arms of the wheels.
• Steering ratio is typically 14:1 to 20:1 (steering wheel turns vs wheel angle).
• Advantages: simple, compact, direct feel, low cost, few joints. Used in nearly all cars and many SUVs.
• Limitation: passes road shocks back to the driver (kickback), unsuitable for heavy vehicles (a recirculating-ball box is used there).

Hydraulic and electric power steering

Power steering reduces the driver's effort at low speed and for parking.

Condition for correct steering

For pure rolling (no tyre scrub) during a turn, the axes of all four wheels must meet at one point on the extended line of the rear axle (the instantaneous centre). For this the inner wheel turns more than the outer wheel and, with inner angle $\theta$ and outer angle $\phi$,

$$\cot\phi - \cot\theta = \frac{c}{L}$$

where $c$ is the distance between the pivots and $L$ the wheelbase. The Ackermann linkage (trapezium) approximates this.

 Instantaneous centre O ---------- rear axle line
        |   \               |
        |    \  R_in        |  L
        |      \ theta      |
     inner wheel         outer wheel (phi)
        |<-------- c ------->|

Numerical

Given: $L = 2.7$ m, $c = 1.4$ m, $\theta = 20^\circ$.

$$\begin{aligned} \cot 20^\circ &= 2.7475 \\ \frac{c}{L} &= \frac{1.4}{2.7} = 0.5185 \\ \cot\phi &= 2.7475 + 0.5185 = 3.2660 \\ \phi &= \tan^{-1}\left(\frac{1}{3.266}\right) = 17.02^\circ \end{aligned}$$

Turning radii (wheel centre-line to instantaneous centre, $R = L/\sin$ of wheel angle):

$$R_{in} = \frac{L}{\sin\theta} = \frac{2.7}{\sin 20^\circ} = 7.89\ \text{m}, \qquad R_{out} = \frac{L}{\sin\phi} = \frac{2.7}{\sin 17.02^\circ} = 9.22\ \text{m}$$

Check: the difference $R_{out} - R_{in}$ projected along the axle is $9.22\cos 17.02^\circ - 7.89\cos 20^\circ = 8.82 - 7.42 = 1.40$ m $= c$. Correct.

Answer: outer wheel angle $= 17.02^\circ$; $R_{in} = 7.89$ m; $R_{out} = 9.22$ m.