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Modelling and analysis of suspension systems 147
15
10
5
0
5
10
15
Half-track change (mm)
Anti-roll angle (degrees)
20
150 100 50 0 50 100 150
Bump travel (mm)
Slope of half-track change
at this point in travel
Calculated half-track
characteristic, to scale
Fig. 4.11
Relationship between calculated half-track change and anti-roll angle
the outside. Were the wheels to remain perpendicular to the vehicle platform
at all times, they would be presented to the road with a camber angle
equal to the vehicle roll angle. For most independent suspension types,
the wheels camber somewhat with respect to the body such that they are
presented to the road at something less than the vehicle roll angle. This is
referred to as ‘camber compensation’. Were the wheels to remain upright
with respect to the road, this would be 100% or ‘full’ camber compensation.
As the wheel is presented to the road progressively more and
more upright, the tyre is loaded more and more evenly across its width and
lasts longer. This is of primary concern for competition vehicles. Camber
angles also generate forces in their own right and the tendency of a tyre
leaned ‘out’ of the turn is to reduce the cornering forces generated by tyre
slip angles; therefore by balancing camber compensations front to rear
some influence may be exerted on the overall handling balance of the
vehicle.
(iii) It is typical for independent suspensions to move the contact patch of
the tyre laterally as they articulate. Although less intuitively direct than the
toe change mechanism, half-track change (lateral displacement) influences
the lateral velocity of the tyre contact patch via roll rate. Hence the slip
angle of the tyre is affected, since the angle is defined as the arctangent of
lateral and longitudinal velocities; an increase in lateral velocity directly
increases slip angle. If the track change is plotted against bump travel, with
both measured at the contact patch, a direct indication of the anti-roll angle
is obtained with no need for knowledge of construction methods for any
particular type of suspension, as shown in Fig. 4.11.
Equally, there is often a desire to calculate some of these measures, particularly
camber values and anti-roll elements, with respect to the ground.
Unfortunately the location and orientation of the ground cannot reliably be
determined using only a quarter vehicle model. Non-linear force-deflection
characteristics are typical for the suspension elements and so the frequently
used ‘symmetric roll’ presumption is often flawed. The amount of roll generated
for a particular lateral loading varies with suspension calibration and
the amount of roll moment carried on a particular axle varies with suspension
calibration. Thus the boundary conditions cannot be known for a quarter
vehicle model with any useful degree of certainty except for symmetric