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340 Multibody Systems Approach to Vehicle Dynamics
Equivalent spring
acting at the wheel
centre
k w
l w
F s
k s
F w
δ s
δ w
l s
Fig. 6.14
Equivalent spring acting at the wheel centre
problem can be overcome as shown in Figure 6.14 by using an ‘equivalent’
spring which acts at the wheel centre.
As an approximation, ignoring exact suspension geometry, the expression
(6.2) can be used to represent the stiffness k w of the equivalent spring at the
wheel:
k F / ( l / l ) F/( l / l ) ( l / l ) 2 k
w w w s w s w s s s w s
(6.2)
The presence of a square function in the ratio can be considered a combination
of both the extra mechanical advantage in moving the definition of
spring stiffness to the wheel centre and the extra spring deflection at the
wheel centre.
6.5.2 Modelling leaf springs
Although the modelling of leaf springs is now rare on passenger cars they
are still fitted extensively on light trucks and goods vehicles where they
offer the advantage of providing relatively constant rates of stiffness for
large variations in load at the axle. The modelling of leaf springs has
always been more of a challenge in an MBS environment when compared
with the relative simplicity of modelling a coil spring. Several approaches
may be adopted the most common of which are shown in Figure 6.15.
Early attempts at modelling leaf springs utilized the simple approach based
on equivalent springs to represent the vertical and longitudinal force–
displacement characteristic of the leaf spring. On the actual vehicle the
leaf springs also contribute to the lateral positioning of the axle, with
possible additional support from a panhard rod. Although not shown in
Figure 6.15 lateral springs could also be incorporated to represent this.