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Modelling and assembly of the full vehicle 343
J is the second moment of area (mm 4 )
L is the length of the anti-roll bar (mm)
Note that the length L used in equation (6.3) is the length of the bar subject
to twisting. For the configuration shown in Figure 6.17 this is the transverse
length of the anti-roll bar across the vehicle and does not include the
fore–aft lengths of the system that connect to the drop links. These lengths
of the bar provide the lever arms to twist the transverse section of bar and
are subject to bending rather than torsion. An externally solved FE model
could be used to give an equivalent torsional stiffness for a simplified
representation such as this.
Given that bending or flexing of the roll bar may have an influence the next
modelling refinement of the anti-roll bar system uses finite element beams,
of the type described in Chapter 3, to interconnect a series of rigid bodies
with lumped masses distributed along the length of the bar. Such sophistication
becomes necessary to investigate anti-roll bar interactions with steer
torque, or anti-roll bar lateral ‘walking’ problems in the vehicle; in general
though, such detail is not required for vehicle behaviour modelling.
Again these joints could be modelled with bushes if needed. Such a model
is shown in Figure 6.18 would be to model the drop links with lumped
masses and beams if the flexibility of these components needed to be
modelled.
The modelling described so far has been for the modelling of the conventional
type of anti-roll bar found on road vehicles. Vehicles with active
components in the anti-roll bar system might include actuators in place of
the drop links or a coupling device connecting the two halves of the system
providing variable torsional stiffness at the connection. Space does not
permit a description of the modelling of such systems here, but with ever
more students becoming involved in motorsport this section will conclude
with a description of the type of anti-roll bar model that might be included
Right anti-roll
bar part
UNIVERSAL
SPHERICAL
REV
Drop link
Revolute joints to
vehicle body
REV
Torsional
spring
Left anti-roll bar part
UNIVERSAL
Drop link
SPHERICAL
Fig. 6.17 Modelling the anti-roll bars using drop links. (This material has
been reproduced from the Proceedings of the Institution of Mechanical Engineers,
K2 Vol. 213 ‘The modelling and simulation of vehicle handling. Part 2: vehicle
modelling’, M.V. Blundell, page 131, by permission of the Council of the
Institution of Mechanical Engineers)