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78 Mutibody Systems Approach to Vehicle Dynamics
structural parts of the system may be represented in modal form to study
the influence of its flexibility on the behaviour of the system as a whole.
A disadvantage of this method of working is the opportunity to consume large
amounts of computing resources solving these models if care is not taken to
ensure the flexibility is germane to the task at hand. Where a full representation
of the flexibility of the structure is unnecessary, a simpler representation
is possible using joints, ‘hinges’ and an associated stiffness at keypoints in the
structure. This is the authors’ preferred compromise between accuracy and
computational efficiency. This level of abstraction requires a high degree of
understanding of the structural behaviour of elements of the system and
can easily lead to poorly conditioned numerical problems if carelessly performed,
raising solution times drastically. Worse still, it can lead to ‘plausible
but wrong’ answers, particularly if mass properties are poorly distributed.
Using component mode synthesis, a complete set of modal components
can be used with a full vehicle comprehensive model. This approach confuses
accuracy with usefulness in a manner that is becoming increasingly
common. The use of such models works against volatility of design, and
such models cannot be effectively used with an emerging design but belong to
a new generation of mathematical prototypes for use in a later vehicle program.
The notion that too much complexity is a bad thing has already been
discussed in Chapter 1.
For full vehicle applications it is important to obtain an accurate model for
the tyres and the associated forces generated at the tyre–road surface contact
patch. For each tyre on the vehicle model the program will calculate the
three orthogonal forces and three orthogonal torques acting at the wheel
centre as a result of the conditions at the tyre–road surface contact patch. In
order to perform these calculations it is necessary to continuously update
the tyre model regarding the position, velocity and orientation of the wheel
centre marker and any changes in the topography of the road surface. Once
this information has been received the tyre model must then calculate the set
of forces acting at the contact patch. Once these forces have been calculated
they can be resolved back to the wheel centre. The multibody systems
analysis program will then integrate through time to find the new position
and orientation of the vehicle and then repeat the process.
A more detailed description of the modelling features available in a typical
multibody systems analysis program such as the MSC.ADAMS program
follows. It should be noted that commercial software is undergoing continual
development and as such the description provided here is limited to the
software features required to carry out the simulations described in this text.
Elements such as springs, dampers, bushes and bump stops are described in
this chapter as these are considered fundamental components of an MBS
modelling system.
3.2 Modelling features
3.2.1 Planning the model
Before progressing to detail the methods used to describe the typical
elements of a multibody systems model it is necessary to outline some of
the planning that goes into the development of the model. The first step
should be to sketch out a system schematic which would typically illustrate