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Tyre characteristics and modelling 269
A measure of the slip generated for the driven tyre can be defined by a further
modification to the slip ratio S:
S
D
0
0
(5.21)
where
0 is the angular velocity of the free rolling wheel
D is the angular velocity of the driven wheel
For driving a slip ratio of 1.0 is sometimes taken to define the onset of
wheel spin. From equation (5.21) this will occur when the angular velocity
of the driven wheel reaches a value of twice that for free rolling. Unlike
braking, the slip ratio in driving can exceed 1.0 as the wheel angular velocity
continues to increase. This definition of ‘spin’ is somewhat arbitrary.
For both tractive and braking cases the relationship between longitudinal
force and slip ratio is such that the wheel behaviour converges for slip
ratios smaller than those at which peak force is produced. However, for
larger slip ratios the wheel behaviour diverges rapidly. For spin in particular,
angular velocity increases very quickly until torque is reduced.
5.4.6 Generation of lateral force and aligning moment
The generation of lateral force and aligning moment in the tyre results from
combinations of the same mechanisms and are thus treated together here.
As a starting point it is helpful to consider Figure 5.22, which is adapted
from the sketches for forces and torques provided by Olley (1945). Figure
5.22 is particularly useful for relating the sign convention for the lateral
forces and aligning moments plotted and discussed throughout this chapter.
From Figure 5.22 it can be seen that for a tyre rolling with a slip angle at
zero camber angle the lateral force generated due to the distribution of
shear stress in the contact patch acts to the rear of the contact patch centre
creating a lever arm known as the pneumatic trail. This mechanism introduces
the aligning moment and has a stabilizing or ‘centring’ effect on the
road wheel. This is an important aspect of the steering ‘feel’ that is fed
back to the driver through the steering system.
Similarly it can be seen from Figure 5.22 that for a tyre rolling with a camber
angle at zero slip angle the lateral force generated is called camber thrust.
Due to the conditions in the contact patch the camber thrust acts in front
of the contact patch centre creating a mechanism that creates a moment.
Although this is referred to here as an aligning moment it has the opposite
effect of the aligning moment resulting from slip angle and is sometimes
called the camber torque as there is no resultant aligning action on the
road wheel.
5.4.7 The effect of slip angle
In order to understand the mechanisms that lead to the generation of lateral
force and aligning moment resulting due to slip angle it is useful to start
with Figure 5.23 showing the distribution of pressure p, and the lateral
stress in the contact patch. The upper part of the figure provides a side view