Page 471 - Automotive Engineering Powertrain Chassis System and Vehicle Body

Modelling and assembly of the full vehicle C HAPTER 15.1

V

X β V y
cm V x

Y

Fig. 15.1-6 Body slip angle.

In the following discussion a vehicle modelled with the The mass is connected to the vehicle body at the wheel
suspension represented in this manner is referred to as centre by a translational joint that only allows vertical
a ‘Linkage model’. sliding motion with no change in the relative camber
Before the advent of computer simulation classical ve- angle between the road wheels and the body. The camber
hicle dynamicists needed to simplify the modelling of the angle between the road wheels and the road will there-
vehicle to a level where the formulation of the equations of fore be directly related to the roll angle of the vehicle.
motion was manageable and the solution was amenable Spring and damper forces act between the suspensions
with the computational tools available at the time. Such an and the body. Such suspensions have been used on early
approach encouraged efficiency with the analyst identify- road vehicles, notably the Lancia Lambda (1908–1927),
ing the modelling issues that were important in repre- where it was termed ‘sliding pillar’.
senting the problem in hand. The use of modern software The front wheel knuckles are modelled as separate
need not discourage such an approach. The following parts connected to the lumped suspension parts by
sections summarize four vehicle models, one of which is revolute joints. The steering motion required for each
based on modelling the suspension linkages with three manoeuvre is achieved by applying time dependent
other models that use alternative simplified implementa- rotational motion inputs about these joints. Each road
tions. All four models have been used to simulate a double wheel is modelled as a part connected to the suspension
lane change manoeuvre and are compared in Case study 7 by a revolute joint. The lumped mass model is shown
at the end of this chapter. The four models described here schematically in Fig. 15.1-7.
involve levels of evolving detail and elaboration and can be
summarized as follows:
15.1.4.3 Equivalent roll stiffness model
(i) A lumped mass model, where the suspensions are
simplified to act as single lumped masses which This model is developed from the lumped mass model by
can only translate in the vertical direction with re- treating the front and rear suspensions as rigid axles
spect to the vehicle body. connected to the body by revolute joints. The locations of
(ii) An equivalent roll stiffness model, where the body the joints for the two axles are their respective ‘roll
rotates about a single roll axis that is fixed and centres’. A torsional spring is located at the front and rear
aligned through the front and rear roll centres. roll centres to represent the roll stiffness of the vehicle.
(iii) A swing arm model, where the suspensions are The determination of the roll stiffness of the front and
treated as single swing arms that rotate about rear suspensions required an investigation as described in
a pivot point located at the instant centres for each the following section. The equivalent roll stiffness model
suspension. is shown schematically in Fig. 15.1-8.
(iv) A linkage model, where the suspension linkages and Note that this model shows the historical background
compliant bush connections are modelled in detail to much of the current unclear thinking about roll centres
in order to recreate as closely as possible the actual and their influence on vehicle behaviour. With beam axles,
assemblies on the vehicle. as were prevalent in the 1920s, this model is a good
equivalent for looking at handling behaviour on flat sur-
faces and ignoring ride inputs. For independent suspen-
15.1.4.2 Lumped mass model sions where the anti-roll geometry remains relatively
consistent with respect to the vehicle and where the roll
For the lumped mass model the suspension components centres are relatively low (i.e. less than around 100 mm for
are considered lumped together to form a single mass. a typical passenger car) – a fairly typical double wishbone

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