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274 Multibody Systems Approach to Vehicle Dynamics
Slip angle = 0
F z = 8 kN
Lateral force F y (N)
F z = 6 kN
F z = 4 kN
F z = 2 kN
φ
Camber stiffness
C = tan φ
Camber angle (degrees)
Fig. 5.27
Plotting lateral force versus camber angle
If the tyre is inclined at a camber angle , then deflection of the tyre and the
associated radial stiffness will produce a resultant force, F R , acting towards
the wheel centre. Resolving this into components will produce the tyre load
and the camber thrust.
An alternative explanation provided in Milliken and Milliken (1995) compares
a stationary and rolling tyre. For the stationary tyre experimental
observations of tread in the contact patch indicate a curved shape. As the
tyre rolls the tread moving through the contact patch is constrained by the
road to move along a straight line, the net reaction of these forces being
the camber thrust.
Figure 5.27 shows a typical plot of lateral force F y with camber angle for
increasing tyre load with the slip angle set to zero. From the plot it can be
seen that the camber stiffness C is the gradient of the curve measured at
zero camber angle at a given tyre load.
In order to understand why a cambered tyre rolling at zero slip angle produces
an aligning moment, it is useful to consider the effect of the shape of
the contact patch. Consider the situation shown in Figure 5.28 where the
wheel and tyre are rolling at a camber angle with the slip angle equal to
zero. The lower part of Figure 5.28 is a plan view on the tyre contact patch.
The three points A, B and C, shown in Figure 5.28, are initially in line
across the centre of the contact patch. If the tyre rolls so that point B moves
to B at the rear of the contact patch then the rubber in the centre line is not
subjected to any longitudinal stress.
Due to the camber the tyre will corner and point A on the inside of the tyre
will roll at a smaller radius of bend to point C on the outside of the tyre. If
the tyre rubber was not subject to any longitudinal stress these points would
move to A and C respectively. If it is assumed that the stiffness of the tyre
restricts this and the points remain in line across the rear of the contact
patch (A, B and C) then a longitudinal tensile stress acts on the inner
A side and a compressive stress acts on the outer C side.