4569846498

262 Multibody Systems Approach to Vehicle Dynamics
Undeformed
tyre
Deformed
tyre
Rear
Front
Lateral slip movement (Moore, 1975)
Squirm through the contact patch
(Gillespie, 1992)
Fig. 5.16
Lateral distortion of the contact patch for a free rolling tyre
that the radius has reduced to a value equivalent to the effective rolling
radius R e resulting in the rearward tangential velocity matching the forward
vehicle velocity and theoretically producing a point of zero slip in the tyre.
Over the central region of the contact patch between C and D the radius
reduces to a value below the effective rolling radius reversing the slip in the
tyre to the forward direction. At the centre of the patch P the radius reduces
to the loaded radius R l . In theory this point would produce the lowest tangential
velocity and the highest forward slip although experimental observations
(Moore, 1975) indicate that the tangential speed does not reduce to
this level. Between point D and B the radius recovers to a value greater than
the effective rolling radius causing the direction of slip to reverse again to a
rearward direction.
It is clear that the direction of slip changes several times as tread moves
through the contact patch resulting in the distribution of longitudinal shear
stress of the type shown at the bottom of Figure 5.15. The shear stress is
plotted to be consistent with the SAE reference frame and is not symmetric
with the net effect being to produce an overall force, the rolling resistance,
acting in the negative X SAE direction.
It should be noted that the two-dimensional model presented is not
fully representative as components of lateral slip are also introduced in
a free rolling tyre due to deformation of the side walls as shown in
Figure 5.16.
As the tyre carcass deforms in the vicinity of the contact patch the deformation
of the side walls creates additional inwards movement of the tread
material (Moore, 1975). This causes the contact patch to assume an hourglass
shape creating an effect referred to as ‘squirm’ (Gillespie, 1992) as
the tread material moves through the contact patch.
Before moving on to consider the driven or braked tyre we will now consider
the rolling resistance forces generated in a free rolling tyre. Rolling
resistance results from energy losses in the tread rubber and side walls.
Energy loss in the tread rubber is produced by hysteresis. If we refer again
to Figure 5.9 it is clear for a block of rubber, or tread material, that there is
more force required at any given displacement during the loading phase
than the unloading phase. As tread material moves through the contact