4569846498

140 Multibody Systems Approach to Vehicle Dynamics
O 1
X 1
GRF
O 2 G 2
Y 1
Y 2
X 2
V x 2
F y
V y 2
z2
F y
Fig. 4.6 The simplest possible representation of a vehicle manoeuvring in the
ground plane
divided by the mass of the vehicle. The additional term in the lateral
force expression reflects a body-centred formulation, which is more convenient
when the model is expanded to more than the 2 degrees of freedom
shown.
The two equations are correctly referred to as a 2-degree-of-freedom (‘2
DOF’) model; they are sometimes referred to as a ‘bicycle’ model but the
authors dislike this description since it implies that the description may be
suitable for two-wheeled vehicles, which it most certainly is not.
Even with this simplest possible representation, it can be seen that the
vehicle may be thought of as a free-floating ‘puck’ (as used in ice hockey), to
which forces are applied by the tyres in order to manipulate its heading and
direction. To many casual observers it appears that the vehicle runs on little
‘rails’ provided by the tyres and that the function of the tyres is simply
to provide a cushion of air beneath the steel wheel rims. This is simply not
so, and examination of the behaviour of rally cars in the hands of skilled
drivers reveals behaviour which visually resembles that of a hovercraft. All
vehicles on pneumatic tyres behave as the rally cars behave, adopting a
sideslip angle to negotiate even the slightest curve. Since this angle is typically
less than a degree it is not always apparent to the untrained observer;
it may, however, be seen on high speed, steady corners such as motorway
interchanges if vehicles are observed attentively.
The generation of the forces necessary to initiate the turn, to constrain the
vehicle at the correct sideslip angle and to return it to the straight-running
condition is the role of the tyres. In order to successfully control the vehicle,
however, those loads must be transmitted to the sprung mass. This is a key
role for the vehicle suspension system.
Close examination of the vehicle behaviour described by the equations
above can demonstrate the slight phasing of the forces necessary to allow
the vehicle to accelerate in yaw and be constrained to the desired yaw