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Tyre characteristics and modelling 295
from the wheel centre such as the height, camber angle, slip angle, spin
velocity and so on are the inputs to the tyre model at each point in time and
will dictate the calculation of the new set of forces at the contact patch.
These newly computed tyre conditions are then fed back to the vehicle model
at each wheel centre. This will produce a change in the vehicle position at
the next solution point in time. The conditions at each wheel centre will
change and will be relayed back to the tyre model again. A new set of tyre
forces and moments will then be calculated and so the process will continue.
The treatment of tyre models that follows in this section is based on methods
that have been developed for vehicle handling simulations. A later section
will deal with tyre models for durability analysis. As stated earlier the computation
of vertical force is straightforward based on the equations in section
5.4.2. For the handling models described here the ‘model’ focuses on the
calculation of longitudinal driving or braking forces and lateral forces. The
formulation of rolling resistance and aligning moments is also covered.
Before discussing individual tyre models it is necessary to describe the calculations
carried out in the main MBS program to provide the tyre model
with the necessary position, orientation and velocities of the road wheel.
5.6.2 Calculation of tyre geometry and velocities
A tyre model, for handling or durability analysis, requires input regarding
the position and orientation of the wheel relative to the road together with
velocities used to determine the slip characteristics. The implementation of
these computations as a tyre model with an MBS program is best described
using the full three-dimensional vector approach outlined in Chapter 2. The
following description is based on the methods used in MSC.ADAMS but is
applicable to any vehicle simulation model requiring tyre force and moment
input. As a starting point the tyre can be modelled using the input radii R 1
and R 2 as shown in Figure 5.52.
Using the tyre model geometry based on a torus it is possible to determine
the geometric outputs that are used in the subsequent force and moment
Tyre dimensions
Model geometry
2R 2
R 1 R 1
R 2
Fig. 5.52 Tyre model geometry. (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 6, by permission of the Council of the Institution of Mechanical Engineers)