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Tyre characteristics and modelling 293
Fig. 5.50 A radial spring terrain enveloping tyre model. (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 4, by permission of the Council of the Institution
of Mechanical Engineers)
ground surface inputs. An example of this sort of tyre model is described
by Davis (1974) where a radial spring model was developed to envelop
irregular features of a rigid terrain. The tyre is considered to be a set of
equally spaced radial springs that when in contact with the ground will
provide a deformed profile of the tyre as it envelops the obstacle. The
deformed shape is used to redefine the rigid terrain with an ‘equivalent
ground plane’. The concept of an equivalent ground plane model was used
in the early ADAMS/Tire model for the durability application but has the
main limitation that the model is not suitable for very small obstacles that
the tyre might completely envelop. This is clarified by Davis (1974) where
it is stated that the wavelength of surface variations in the path of the tyre
should be at least three times the length of the tyre to ground contact patch.
The other and most basic limitation of this type of model is that the simulation
is restricted to straight-line motion and would only consider the vertical
and longitudinal forces being generated by the terrain profile. An
example of a radial spring tyre model is shown in Figure 5.50.
The work carried out by Kisielewicz and Ando (1992) describes how two
different programs have been interfaced to carry out a vehicle simulation
where the interaction between the tyre and the road surface has been calculated
using an advanced non-linear finite element analysis program.
For vehicle handling studies we are generally concerned with the manoeuvring
of the vehicle on a flat road surface. The function of the tyre model is
to establish the forces and moments occurring at the tyre to road contact
patch and resolve these to the wheel centre and hence into the vehicle as
indicated in Figure 5.51.
For each tyre the tyre model will calculate the three orthogonal forces and
the three orthogonal moments that result from the conditions arising at the
tyre to road surface contact patch. These forces and moments are applied
at each wheel centre and control the motion of the vehicle. In terms of