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318 Multibody Systems Approach to Vehicle Dynamics
Fig. 5.71
Computer graphics for the tyre rig model
5.8 Examples of tyre model data
The results obtained from a series of tyre tests (Blundell, 2000a) have been
used to set up the data needed for the various modelling approaches
described here. In summary the following procedure was followed:
(i) For the Interpolation method the measured numerical values were
reformatted directly into the SPLINE statements within an
MSC.ADAMS data file as shown in Table 5.5. For each spline shown
in Table 5.5 the X values correspond to either the slip or camber angle
and are measured in degrees. The first value in each Y array corresponds
to the vertical load measured in kg. The following values in
the Y arrays are the measured lateral forces (N) or the aligning
moments (Nm) which correspond with the matching slip or camber
angles in the X arrays. All the required conversions to the vehicle
model units are carried out in the FORTRAN subroutine for the
Interpolation tyre model listed in Appendix B.
(ii) The coefficients for the ‘Magic Formula’ model were provided by
Dunlop Tyres using in-house software to fit the values. The ‘Magic
Formula’ tyre model (version 3) parameters are shown in Table 5.9. It
should be noted that the parameters due to camber effects were not
available from this set of tests.
(iii) The parameters for the Fiala model were obtained by simple measurements
from the plots produced during tyre testing. The Fiala model
requires a single value of cornering stiffness to be defined although in
reality cornering stiffness varies with tyre load. For the purposes of
comparing the tyre models the parameters for the Fiala tyre model
shown in Table 5.6 have been derived from the test data at the average
of the front and rear wheel loads of the vehicle considered in this
study. Fiala parameters obtained at front and rear wheel loads are
given in Tables 5.7 and 5.8. Using the data for each of these models
the tyre rig model described in the previous section was run for vertical
loads of 200, 400, 600 and 800 kg. In each case the slip angle was
varied between plus and minus 10 degrees.