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342 Multibody Systems Approach to Vehicle Dynamics
complicated by the need to model the interleaf contact forces between the
lumped masses with any associated components of sliding friction.
6.6 Anti-roll bars
As shown in Figure 6.16 anti-roll bars may be modelled using two parts connected
to the vehicle body by revolute joints and connected to each other by
a torsional spring located on the centre line of the vehicle. In a more detailed
model the analyst could include rubber bush elements rather than the revolute
joints shown to connect each side of the anti-roll bar to the vehicle. In
this case for a cylindrical bush the torsional stiffness of the bush would be
zero to allow rotation about the axis, or could have a value associated with
the friction in the joint. In this model the connection of the anti-roll bars to
the suspension system is not modelled in detail, rather each anti-roll bar part
is connected to the suspension using an inplane joint primitive that allows the
vertical motion of the suspension to be transferred to the anti-roll bars and
hence produce a relative twisting motion between the two sides.
A more detailed approach, shown in Figure 6.17, involves including the
drop links to connect each side of the anti-roll bar to the suspension systems.
The drop link is connected to the anti-roll bar by a universal joint and
is connected to the suspension arm by a spherical joint. This is similar to
the modelling of a tie rod as discussed in Chapter 4 where the universal
joint is used to constrain the spin of the link about an axis running along its
length, this degree of freedom having no influence on the overall behaviour
of the model.
The stiffness K T of the torsional spring can be found directly from fundamental
torsion theory for the twisting of bars with a hollow or solid circular
cross-section. Assuming here a solid circular bar and units that are
consistent with the examples that support this text we have
GJ
KT
(6.3)
L
where
G is the shear modulus of the anti-roll bar material (N/mm 2 )
Right anti-roll
bar part
Revolute joints to
vehicle body
REV
INPLANE
REV
Torsional
spring
Left anti-roll bar part
Front wheel
knuckle
INPLANE
Front wheel
knuckle
Fig. 6.16
Modelling the anti-roll bars using joint primitives