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310 Multibody Systems Approach to Vehicle Dynamics
active chassis control systems and optimizing vehicle ride properties with
capabilities including:
(i) The use of the ‘Magic Formula’ for slip force calculations
(ii) A sophisticated contact for short wavelength slip variations
(iii) An effective method to model road obstacles (durability)
(iv) A rigid ring model to accommodate tyre belt vibrations to 80 Hz
(v) Tyre characteristics that can vary with speed and load
The model has been validated through the extensive tyre test capabilities at
TNO and has been shown (van Oosten and Jansen, 1999) to be accurate for
durability applications, such as rolling over cleats and enveloping steps in the
road surface, when comparing simulations with experimental measurements.
A comprehensive description of this complex tyre model is not possible
here. Rather the reader is referred to the companion text in this series
(Pacejka, 2002) where a complete chapter is dedicated to describing the
formulations within the SWIFT tyre model.
The MSC.ADAMS durability tyre model (Vesimaki, 1997) was originally
developed to deal with off-road applications. An example of this would be
the simulation of very large vehicles used by the timber industry in the
forests of the author’s home country, Finland. The tyre model developed
for such an application would be required to deal with a vehicle cornering
on a steep uneven slope where the tyres are going to encounter obstacles
such as tree stumps. The requirements for such a tyre model are summarized
by the author as:
(i) to enable handling simulation on an uneven 3D road surface
(ii) to allow a road/terrain definition based on geometry
(iii) to accommodate varying friction over the terrain
(iv) to account for the cross-sectional tyre dimension and geometry
Such a model requires a physical representation of the tyre profile in order to
model the boundaries of the tyre carcass as they envelop obstacles. The tyre
model input consists of points that model one half of the tyre profile, as shown
on the left side of Figure 5.64. The tyre model uses the input geometry to
compute interpolated internal points, each of which defines the radius and
lateral position of a disc representing a slice of the tyre cross-section.
As with any model based on a physical discretization, the model refinement
or number of cross-sectional elements must be such that the width of
the ‘slices’ is sufficiently small to deal with obstacles that are narrow compared
with the overall width of the tyre. The road model is based on the
finite element representation described in section 5.6.3.
The algorithm developed carries out initial iterations to identify road elements
that are subject to potential contact, at the current integration time
step, before evaluating the position of each tyre element slice with each of
the candidate road elements. An example of this is shown schematically in
Figure 5.65 where one tyre cross-sectional element is seen to intersect a
step defined by a number of triangular road elements.