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Tyre characteristics and modelling 291
5000.0
TYRE BRAKING FORCE TEST – TYRE B 195/65 R15
Vertical load increments – 1 kN 2 kN 3 kN 4 kN
4000.0
Braking force (N)
3000.0
2000.0
1000.0
0.0
0.1 0.3 0.5
0.0 0.2 0.4 0.6
Slip ratio
0.7
0.8
0.9
1.0
Fig. 5.48 Braking force with slip ratio
of comparable tyre test machines gave differences between minimum and
maximum measured values of up to 46%. Given the complexities of the
tyre models that are described in the following section the starting point
should be a set of measured data that can be used with confidence to form
the basis of a tyre model.
5.6 Tyre modelling
5.6.1 Overview
The modelling of the forces and moments at the tyre contact patch has been
the subject of extensive research in recent years. A review of some of the
most common tyre models was provided by Pacejka and Sharp (1991),
where the authors state that it is necessary to compromise between the
accuracy and complexity of the model. The authors also state that the need
for accuracy must be considered with reference to various factors including
the manufacturing tolerances in tyre production and the effect of wear on
the properties of the tyre. This would appear to be a valid point not only
from the consideration of computer modelling and simulation but also
in terms of track testing where new tyres are used to establish levels of
vehicle performance. A more realistic measurement of how a vehicle is
going to perform in service may be to consider testing with different levels
of wear or incorrect pressure settings.
One of the methods discussed by Pacejka and Sharp (1991) focuses on a
multi-spoke model developed by Sharp where the tyre is considered to be a
series of radial spokes fixed in a single plane and attached to the wheel hub.
The spokes can deflect in the radial direction and bend both circumferentially
and laterally. Sharp provides more details on the radial spoke model
approach in Sharp and El-Nashar (1986) and Sharp (1990, 1993). The other