4569846498

Modelling and analysis of suspension systems 229
BUSH
BUSH
SPHERICAL
SPHERICAL
(a)
REVOLUTE
(b)
SPHERICAL
INLINE
(c)
Fig. 4.74 Wishbone mount modelling strategies: (a) wishbone mounted by
two bushes; (b) wishbone mounted by two spherical joints; (c) wishbone
mounted by a single revolute joint; (d) wishbone mounted by a spherical joint
and inline joint primitive.
(d)
is that the wishbone initially has 6 degrees of freedom and the two spherical
joints remove three each leaving for the wishbone body a local balance
of zero degrees of freedom. This is clearly not valid as in the absence of
friction or other forces the wishbone is not physically constrained from
rotating about an axis through the two spherical joints.
This is a classic MBS modelling problem where we have introduced a
redundant constraint or overconstrained the model. It should also be noted
that this is the root of our requirement for two more equations for the manual
analysis, each equation being related to the local overconstraint of each
wishbone. Early versions of MBS programs such as MSC.ADAMS were
rather unforgiving in these circumstances and any attempt to solve such a
model would cause the solver to fail with the appropriate error messages.
More modern versions are able to identify and remove redundant constraints
allowing a solution to proceed. While this undoubtedly adds to the
convenience of model construction it does isolate less experienced users
from the underlying theory and modelling issues we are currently discussing.
In any event if the required outcome is to predict loads at the
mount points the removal of the redundant constraints, although not affecting
the kinematics, cannot be relied on to distribute correctly the forces to
the mounts.
In Figure 4.74(c) the two wishbone mount connections are represented by
a single revolute joint. This is the method suggested earlier as a suitable
start for predicting the suspension kinematics but will again not be useful
for prediction the mount reaction forces. In this model the single revolute
joint will carry the combined translational reaction forces at both mounts
with additional moment reactions that would not exist in the real system.
The final representation shown in Figure 4.74(d) allows a model that uses
rigid constraint elements and can predict reaction forces at each mount
without using the ‘as is’ approach of including the bush compliances or
introducing redundant constraints. This is achieved by modelling one