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Tyre characteristics and modelling 285
The measurements of forces and moments were taken using the SAE
co-ordinate system for the following configurations:
(i) Varying the vertical load in the tyre 200, 400, 600, 800 kg.
(ii) For each increment of vertical load the camber angle is varied
from 10 to 10 degrees with measurements taken at 2 degree intervals.
During this test the slip angle is fixed at 0 degrees.
(iii) For each increment of vertical load the slip angle is varied from 10
to 10 degrees with measurements taken at 2 degree intervals. During
this test the camber angle is fixed at 0 degrees.
(iv) For each increment of vertical load the slip and camber angle are
fixed at zero degrees and the tyre is gradually braked from the free
rolling state to a fully locked skidding tyre. Measurements were
taken at increments in slip ratio of 0.1.
The test programme outlined here can be considered a starting point in the
process of obtaining tyre data to support a simulation exercise. In practice
obtaining all the data required to describe the full range of tyre behaviour
discussed in the preceding sections will be extremely time consuming and
expensive. The test programme described here does not, for example, consider
effects such as varying the speed of the test machine, changes in tyre
pressure or wear, changes in road texture and surface contamination by
water or ice. The testing is also steady state and does not consider the transient
state during transition from one orientation to another.
Most importantly the tests do not consider the complete range of combinations
that can occur in the tyre. The longitudinal force testing described is
limited by only considering the generation of braking force. To obtain a
complete map of tyre behaviour it would also, for example, be necessary to
test not only for variations in slip angle at zero degrees of camber angle but
to repeat the slip angle variations at selected camber angles. For comprehensive
slip behaviour it would be necessary at each slip angle to brake or
drive the tyre from a free rolling state to one that approaches the friction
limit, hence deriving the ‘friction circle’ for the tyre.
Extending a tyre test programme in this way may be necessary to generate
a full set of parameters for a sophisticated tyre model but will significantly
add to the cost of testing. Obtaining data requires the tyre to be set up at
each load, angle or slip ratio and running in steady state conditions before
the required forces and moments can be measured. By way of example the
basic test programme described here required measurements to be taken
for the tyre in 132 configurations. Extending this, using the same pattern of
increments and adding driving force to consider combinations of slip angle
with camber or slip ratio would extend the testing to 1452 configurations.
In practice this could be reduced by judicious selection of test configurations
but it should be noted the tests would still be for a tyre at constant
pressure and constant speed on a given test surface. Examples of test results
for a wider range of tyres and settings can be obtained by general reference
to the tyre specific publications quoted in this chapter and in particular to
the textbook by Pacejka (2002).
For the tyre tests described here the following is typical of the series
of plots that would be produced in order to assess the force and moment