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Modelling and analysis of suspension systems 183
Once generated the suspension model may be used in two ways. One of
these is to apply the load and carry out a static analysis. This may result in
the suspension system moving through relatively large displacement to
obtain a static equilibrium position for the given load. The static reactions
in joints, bushes and spring seats can then be extracted. It is also possible
to make the load a function of time and then to apply a quasi-static analysis.
This has the advantage that the graphical post-processor can be used to
animate the simulation to demonstrate how the suspension moves under the
given load. An example of this for the 3G bump case would be to apply the
1G load for an initial static analysis at time equal to zero and then to apply
the remaining 2G of the load over, say, 1 second of simulation time.
The use of equivalent static loads to represent real dynamic effects has
been used by the automotive industry for some time. The derivation of
design loads similar to those shown in Table 4.8 can be traced back to a
publication in the early 1950s (Garrett, 1953) in the Automobile Engineer.
The disadvantage of the static analysis is that any velocity dependent forces
will not be transmitted through the damper without the inclusion of some
static equivalent.
The extension of this is to carry out a dynamic simulation if possible. The
model used may be a quarter suspension model or even a simulation of the
complete vehicle. An example of this would be the simulation of a sportsutility
type vehicle in off-road conditions. An early example of this (Rai
and Soloman, 1982) was the use of MSC.ADAMS to carry out dynamic
simulation of suspension abuse tests. The problem for the analyst with the
dynamic approach is the amount of reaction force time history output generated
at bush and joint positions.
The input loads used to represent braking and cornering may be obtained
using basic vehicle data and weight transfer analysis. As an example consider
the free-body diagram shown in Figure 4.47 where the wheel loads
are obtained for a vehicle braking case. Note that in this example we are
ignoring the effects of rolling resistance in the tyre, discussed later in
Chapter 5, and the vehicle is on flat road with no incline.
cm
mA x
Z
A
mg
B
h
X
F Fx
F Rx
Fig. 4.47
F Fz F SFz F B
a
L
Forward braking free-body diagram
b
F Rz F SRz F B