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272 Multibody Systems Approach to Vehicle Dynamics
Camber angle = 0
Lateral force F y (N)
F z = 8 kN
F z = 6 kN
F z = 4 kN
F z = 2 kN
φ
Cornering stiffness
C = tan
Fig. 5.24
Slip angle (degrees)
Plotting lateral force versus slip angle
origin. In practice a small offset in lateral force will be apparent at zero slip
angle due to the effects of conicity and plysteer discussed earlier.
Looking back to Figure 5.23 it can be seen that as the shape of the lateral stress
distribution is approximately triangular the lateral force F y acts through the
centroid of this area that is to the rear of the wheel centre line by a distance
referred to as the pneumatic trail. Inspection of Figure 5.23 should indicate
that as the slip angle increases the line of action of F y moves forward reducing
the pneumatic trail eventually to zero. The aligning moment M z is the
product of the lateral force and the pneumatic trail and will reduce accordingly
eventually becoming negative usually for lightly loaded tyres at high
slip angles. In these situations the extent of sliding occurs to such an extent
throughout the contact patch that the lateral stress distribution approaches
the shape of the p curve moving the centroid through which F y acts forward
of the centre. A typical plot of aligning moment with slip angle, for a
given tyre load and zero camber angle, is shown in Figure 5.25. From the
plot it can be seen that the aligning moment stiffness is the gradient of the
curve measured at zero slip angle at a given tyre load.
The aligning moment curve is nearly linear at low slip angles and reaches
a maximum value for most tyres at a slip angle of 4 to 6 degrees. The gradient
of the curve measured at a zero slip angle is the aligning moment
stiffness. In Figure 5.25 the curves are shown to pass through the origin. In
practice a small offset in aligning moment will be apparent at zero slip
angle due to the effects of conicity and plysteer discussed earlier.
5.4.8 The effect of camber angle
The lateral force that arises due to an inclination of the tyre from the vertical
is referred to as camber thrust. The SAE definition of positive camber
angle is taken for the top of the tyre leaning outwards relative to the vehicle.
The fact that this differs from side to side does not lead to consistency when
developing a tyre model. For understanding it is useful to remember that