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Tyre characteristics and modelling 281
Fig. 5.34
Race car simulation model (provided courtesy of MSC.Software)
a moment that would add to the aligning moment due to the product of lateral
force and pneumatic trail. At higher braking forces the effect may
cause the aligning moment to go negative.
The friction circle or ellipse is also a way to monitor the performance of a
race car driver using instrumented measurements of lateral and longitudinal
accelerations, sometimes called the ‘g–g’ diagram. Comparing this diagram
with known tyre data it is possible to see how well the driver performs
keeping the vehicle close to the friction limits of the tyres.
A similar exercise is possible using an MBS model of a vehicle with a road
model to represent the circuit. With the MBS model, extraction of longitudinal
and lateral tyre force time histories is possible for a simulated lap of
the circuit. This in theory allows investigation into the influence of tyre
or vehicle model parameter changes and steering inputs on tyre limit
behaviour.
5.4.12 Relaxation length
For cornering it has been shown that the generation of lateral force due to
slip angle is of prime importance. In practice the generation of lateral force
is not instantaneous but is subject to a delay generally referred to as ‘tyre
lag’. Without modelling some form of time lag a tyre model will compute
the force and pass this to the MBS vehicle model so that the lateral force is
applied instantly at that integration time step. It has been shown (Loeb
et al., 1990) that the tyre must roll a certain distance, ‘relaxation length’,
for the tyre to deflect sufficiently to generate the lateral force.
A possible method to measure relaxation length is to set the tyre up at a
given slip angle in a test rig with the drum or belt not yet moving. On starting
the machine the distance rolled before the forces and moments reach
steady state can be recorded, hence giving a measure of relaxation length.
An improved method for vehicle dynamics (Loeb et al., 1990) is to start
the test with the tyre running at low speed in the straight ahead configuration
and apply a rapid step input of steer angle to the tyre producing a time