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300 Multibody Systems Approach to Vehicle Dynamics
data that were used directly by the tyre model to interpolate the lateral force
and aligning moment at the contact patch. Figure 5.56 illustrates a sample
of some results which might typically be obtained from a tyre rig test
where for variations in vertical load F z the lateral forces F y are plotted as a
function of slip angle at zero camber angle.
For this set of data the independent variables that are set during the test are
the camber angle, the vertical force, and the slip angle. The measured
dependent variable is the lateral force. Using this measured data the tyre
model, really a method rather than a model, uses a curve fit to obtain a value
for the lateral force for the value of F z and slip angle determined by the wheel
centre position and orientation. If the instantaneous camber angle lies between
two sets of measured data at different camber angles set during the test then
the tyre model can use linear interpolation between the two camber angles.
If the instantaneous camber angle is, for example, 2.4 degrees and measured
data is available at 2 and 3 degrees, then the curve fitting as a function of F z
and slip angle is carried out at the two bounding camber angles and the linear
interpolation is carried out between these two points. The approach
described here for lateral force is applied in exactly the same manner when
determining by interpolation a value for the aligning moment. There are
some disadvantages in using an interpolation tyre model:
(i) The process of interpolating large quantities of data at every integration
step in time may not be an efficient simulation approach and is
often considered to result in increases in computer solution times for
the analysis of any given manoeuvre.
(ii) This sort of model does not lend itself to any design modification or
optimization involving the tyre. The tyre must already exist and have
been tested. In order to investigate the influence of tyre design
changes on vehicle handling and stability then the tyre model must be
reduced to parameters that can be related to the tyre force and moment
characteristics. This has led to the development of tyre models represented
by formulae that will now be discussed.
Camber angle = 0
Lateral force measurements
F z 8 kN
F y (N)
F z 6 kN
F z 4 kN
F z 2 kN
Slip angle (degrees)
Fig. 5.56 Interpolation of measured tyre test data. (This material has been
reproduced from the Proceedings of the Institution of Mechanical Engineers,
K1 Vol. 214 ‘The modelling and simulation of vehicle handling. Part 3: tyre
modelling’, M.V. Blundell, page 14, by permission of the Council of the Institution
of Mechanical Engineers)