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Modelling and assembly of the full vehicle 329
Anti-symmetry
constraints along
vehicle centre line
Force input
z
y
Fig. 6.4
x Force input
Finite element model of body-in-white
An example of a vehicle body referenced frame O 2 located at the mass
centre G 2 for Body 2 is shown in Figure 6.3. For this model the XZ plane
is located on the centre line of the vehicle with gravity acting parallel to the
negative Z 2 direction. Using an approach where the body is a single lumped
mass representing the summation of the major components the mass centre
position can be found by taking first moments of mass and the mass moments
of inertia can be obtained using the methods described in Chapter 2. From
inspection of Figure 6.3 it can be seen that a value would exist for the I xz
cross product of inertia but that I xy and I yz should approximate to zero given
the symmetry of the vehicle. In reality there may be some asymmetry that
results in a CAD system outputting small values for the I xy and I yz cross
products of inertia.
The dynamics of the actual vehicle are greatly influenced by the yaw moment
of inertia I zz of the complete vehicle, to which the body and associated masses
will make the dominant contribution. A parameter often discussed
is the ratio k 2 /ab, sometimes referred to as the ‘Dynamic Index’, where k is
the radius of gyration associated with I zz and a and b locate the vehicle mass
centre longitudinally relative to the front and rear axles respectively, as shown
earlier in Figure 4.47. The significance of this is discussed later in Chapter 7.
The assumption so far has been that the vehicle body is represented as a
single rigid body but it is possible to model the torsional stiffness of the
vehicle structure if it is felt that this could influence the full vehicle simulations.
A simplistic representation of the torsional stiffness of the body may
be used (Blundell, 1990) where the vehicle body is modelled as two rigid
masses, front and rear half body parts, connected by a revolute joint aligned
along the longitudinal axis of the vehicle and located at the mass centre.
The relative rotation of the two body masses about the axis of the revolute
joint is resisted by a torsional spring with a stiffness corresponding to the
torsional stiffness of the vehicle body. Typically, the value of torsional stiffness
may be obtained using a finite element model of the type shown in
Figure 6.4. For efficiency symmetry has been exploited here to model with