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20 Multibody Systems Approach to Vehicle Dynamics
1986, 1989; Pacejka and Bakker, 1993) and is known to give an accurate
representation of measured tyre characteristics. The model uses modified
trigonometric functions to represent the shape of curves that plot tyre
forces and moments as functions of longitudinal slip or slip angle. In recent
years the work of Pacejka has become well known throughout the vehicle
dynamics community. The result of this is a tyre model that is now widely
used both by industry and academic institutions and is undergoing continual
improvement and development. The complexity of the model does,
however, mean that well over 50 or more parameters may be needed to define
a tyre model and that software must be obtained or developed to derive the
parameters from measured test data.
(ii) The second model considered here is known as the Fiala tyre model
(Fiala, 1954) and is provided as the default tyre model in MSC.ADAMS.
This is a much simpler model that also uses mathematical equations to represent
the tyre force and moment characteristics. Although not so widely
recognized as Pacejka’s model the fact that this model is the default in
MSC.ADAMS and is simpler to use led to its inclusion. The advantage of
this model is that it only requires 10 parameters and that the physical significance
of each of these is easy to comprehend making this a good starting
point for students and newcomers to the discipline. The parameters can
also be quickly and easily derived from measured test data without recourse
to special software. It should also be noted, however, that this model unlike
Pacejka’s is not suitable for combined braking and cornering and can only
be used under pure slip conditions. The Fiala formulation also has some
limitations at high slip angles and is thus unsuitable for limit manoeuvres
even when pure slip conditions are included.
(iii) The fourth modelling approach is to use a straightforward interpolation
model. This was the original tyre modelling method used in MSC.ADAMS
(Ryan, 1990). This methodology is still used by some companies but has,
to a large extent, been superseded by more recent parameter-based models.
The method is included here as a useful benchmark for the comparison of
other tyre models in Chapter 5.
Another tyre model is provided for readers as a source listing in Appendix
B. This model (Blundell, 2003) has been developed by Harty and as with
the Fiala model has the advantage of requiring only a limited number of
input parameters. The implementation is more complete, however, than the
Fiala model and includes representation of the following:
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Comprehensive slip
Load dependency
Camber thrust
Post limit
It has been found that the Harty model is robust when modelling limit behaviour
including, for example, problems involving low grip or prolonged
wheelspin.