845Cornering stiffness cornering power

When a vehicle travels on a curved path, the centrifugal force (lateral force) tends to push sideways each wheel against the opposing tyre contact patch to ground reaction. As a result, the tyre casing and tread in the region of the contact patch very slightly deform into a semicircle so that the path followed by the tyre at ground level will not be quite the same as the direction of the wheel points. The resistance offered by the tyre crown or belted tread region by the casing preventing it from deforming and generating a slip angle is a measure of the tyre's cornering power. The cornering power, nowadays more usually termed cornering stiffness, may be defined as the cornering force required to be developed for every degree of slip angle generated.

Cornering stiffness

Cornering force Slip angle

In other words, the cornering stiffness of a tyre is the steepness of the cornering force to slip angle curve normally along its linear region (Fig. 8.32). The larger the cornering force needed to be generated for one degree of slip angle the greater the cornering stiffness of the tyre will be and the smaller the steering angle correction will be to sustain the intended path the vehicle is to follow. Note that the supple flexing of a radial ply side wall should not be confused with the actual stiffness of the tread portion of the tyre casing.

8.4.6 Centre ofpressure (Fig. 8.35) When a wheel standing stationary is loaded, the contact patch will be distributed about the geometric centre of the tyre at ground level, but as the wheel rolls forward the casing supporting the tread is deformed and pushed slightly to the rear (Fig. 8.35). Thus in effect the majority of the cornering force generated between the ground and each element of tread moves from the static centre of pressure to some dynamic centre of pressure behind the vertical centre of the tyre, the amount of displacement corresponding to the wheel construction, load, speed and traction. The larger area of



/ \ «

/ Cornering stiffness


Slipangle <deq)

Fig. 8.32 Effect of slip angle on cornering force o 2 a 6

Slipangle <deq)

Fig. 8.32 Effect of slip angle on cornering force

Fig. 8.33 Effect of tyre vertical load on cornering force

tread to ground reaction will be concentrated behind the static centre of the wheel and the actual distribution of cornering force from front to rear of the contact patch is shown by the shaded area between the centre line of the tyre and the cornering force plotted line. The total cornering force is therefore roughly proportional to this shaded area and its resultant dynamic position is known as the centre of pressure (Fig. 8.35).

The cornering force generated at any one time will be approximately proportional to the shaded area between the tyre centre line and the cornering force plotted line so that the resultant cornering force (centre of pressure) will act behind the static centre of contact. The distance between the static and dynamic centres of pressure is known as the pneumatic trail (Fig. 8.35), its magnitude being dependent upon the degree of creep between tyre and ground, the vertical wheel load, inflation pressure, speed and tyre constriction. Generally with the longer contact patch, radial ply tyres have a greater pneumatic trail than those of the cross-ply construction.

8.4.8 Self-aligning torque (Fig. 8.35)

When a moving vehicle has its steering wheels turned to negotiate a bend in the road, the lateral (side) force generates an equal and opposite s

Inflation pressure (bar)

Fig. 8.34 Effect of tyre inflation pressure on cornering force reaction force at ground level known as the cornering force. As the cornering force centre of pressure is to the rear of the geometric centre of the wheel and the side force acts perpendicularly through the centre of the wheel hub, the offset between the these two forces, known as the pneumatic trail, causes a moment (couple) about the geometric wheel centre which endeavours to turn both steering wheels towards the straight ahead position. This self-generating torque attempts to restore the plane of the wheels with the direction of motion and it is known as the self-aligning torque (Fig. 8.35). It is this inherent tyre property which helps steered tyres to return to the original position after negotiating a turn in the road. The self-aligning torque (SAT) may be defined as the product of the cornering force and the pneumatic trail.

Higher tyre loads increase deflection and accordingly enlarge the contact patch so that the pneumatic trail is extended. Correspondingly this causes a rise in self-aligning torque. On the other hand increasing the inflation pressure for a given tyre load will shorten the pneumatic trail and reduce the self-aligning torque. Other factors which influence self-aligning torque are load transfer during braking, accelerating and cornering which alter the contact patch area. As a general rule, anything which increases or decreases the contact patch length raises or reduces the self-aligning torque respectively. The self-aligning torque is little affected with small slip angles when braking or accelerating, but with larger slip angles braking decreases the aligning torque and acceleration increases it (Fig. 8.36).

Fig. 8.35 Illustration of self-aligning torque

Fig. 8.36 Variation of self-aligning torque with cornering force

Static steering torque, that is the torque needed to rotate the steering when the wheels are not rolling, has nothing to do with the generated self-aligning torque when the vehicle is moving. The heavy static steering torque experienced when the vehicle is stationary is due to the distortion of the tyre casing and the friction created between the tyre tread elements being dragged around the wheels' point of pivot at ground level. With radial ply tyres the more evenly distributed tyre to ground pressure over the contact patch makes manoeuvring the steering harder than with cross-ply tyres when the wheels are virtually stationary.

8.4.9 Camber thrust (Figs 8.37 and 8.38) The tilt of the wheel from the vertical is known as the camber. When it leans inwards towards the turning centre it is considered to be negative and when the top of the wheel leans away from the turning centre it is positive (Fig. 8.37). A positive camber reduces the cornering force for a given slip angle relative to that achieved with zero camber but negative camber raises it.

Constructing a vector triangle of forces with the known vertical reaction force and the camber inclination angle, and projecting a horizontal component perpendicular to the reaction vector so that it intersects the camber inclination vector, enables the magnitude of the horizontal component, known as camber thrust, to be determined (Fig. 8.37). The camber thrust can also be calculated as the product of the reaction force and the tangent of the camber angle.

i.e. Camber thrust = Wheel reaction x tan fl

The total lateral force reaction acting on the tyre is equal to the sum of the cornering force and camber thrust.

Where F = total lateral force Fc = cornering force Ft = camber thrust

When both forces are acting in the same direction, that is with the wheel tilting towards the centre of the turn, the positive sign should be used, if the wheel tilts outwards the negative sign applies (Fig. 8.38).

Thus negative camber increases the lateral reaction to side forces and positive camber reduces it.

///////zWA//////// Negative camber Positive cambei Cumber ihrusl

Fig. 8.37 Illustrating positive and negative camber and camber thrust

0 - ve

ß „ Q

S, li J VC

- Ff Fii--7

-Fc 77



w w f

Slip angle (deg)

Fig. 8.38 Effect of slip angle on cornering force with various camber angles

8.4.10 Camber scrub (Fig. 8.39) When a wheel is inclined to the vertical it becomes cambered and a projection line drawn through the wheel axis will intersect the ground at some point. Thus if the wheel completes one revolution a cone will be generated about its axis with the wheel and tyre forming its base.

If a vehicle with cambered wheels is held on a straight course each wheel tread will advance along a straight path. The distance moved along the road will correspond to the effective rolling radius at the mid-point of tyre contact with the road (Fig. 8.39). The outer edge of the tread (near the apex) will have a smaller turning circumference than the inner edge (away from apex). Accordingly, the smaller outer

Fig. 8.39 Illustration of camber scrub

edge will try to speed up while the larger inner edge will tend to slow down relative to the speed in the middle of the tread. As a result, the tread portion in the outer tread region will slip forward, the portion of tread near the inner edge will slip backwards and only in the centre of tread will true rolling be achieved.

To minimize tyre wear due to camber scrub modern suspensions usually keep the wheel camber below 1/2 degrees. Running wheels with a slight negative camber on bends reduces scrub and improves tyre grip whereas positive camber increases tread scrub and reduces tyre to road grip.

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