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Modelling and assembly of the full vehicle 339
6.5 Modelling of springs and dampers
6.5.1 Treatment in simple models
The treatment of road springs and dampers in a vehicle where the suspensions
have been modelled using linkages is generally straightforward. A
road spring is often modelled as linear but the damper will usually require
a non-linear representation as discussed in Chapter 3. It is also common for
the bump travel limiter to be engaged early and to have both stiffness and
damping elements to its behaviour; both those aspects may be modelled
using the methods discussed here. The choice of whether to combine them
with the road spring and damper forces is entirely one of modelling convenience;
the authors generally find the ease of debugging and auditing the
model is worth the carriage of two not strictly necessary additional force
generating terms.
For the simplified modelling approach used in the lumped mass and swing
arm models the road springs cannot be directly installed in the vehicle
model as with the linkage model. Consider the lumped mass model when
compared with the linkage model as shown in Figure 6.13.
Clearly there is a mechanical advantage effect in the linkage model that is
not present in the lumped mass vehicle model. At a given roll angle for the
lumped mass model the displacement and hence the force in the spring will
be too large when compared with the corresponding situation in the linkage
model.
For the swing arm model the instant centre about which the suspension pivots
is often on the other side of the vehicle. In this case the displacement in the
spring is approximately the same as at the wheel and a similar problem
occurs as with the lumped mass model. For all three simplified models this
LINKAGE MODEL
LUMPED MASS MODEL
δ s (I s /I w )δ w
δ s
δ w
δ s
l s
δ w
δ s δ w
l w
Fig. 6.13
Road spring in linkage and lumped mass models