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Modelling and analysis of suspension systems 143
mass centre. Considering the wheel and arm together as a single entity and
noting the ability of the pivot to support no moments, we may draw the
reaction force at the pivot as being on a line between the contact patch and
the pivot. The horizontal magnitude is the same as the applied longitudinal
force at the wheel, giving a full solution for the force at the inboard pivot.
The reaction on the sprung mass is equal and opposite to the force on the
pivot, with a line of action passing directly through the mass centre. This is
widely recognized as a ‘no-dive’ (no pitch) type of suspension. Although
there is no body pitch, this does not mean there is no load transfer between
rear and front wheels. We may therefore conclude that the braking load is
carried to the vehicle mass centre entirely through the suspension linkage
components and that none is carried in the suspension springs – i.e. via an
‘unsprung’ loadpath.
The second diagram has the swinging arm pivot at ground level. Using similar
logic as before, the force at the pivot may be drawn as purely lateral,
equal and opposite to that at the wheel. This in turn means the horizontal
force is applied to the body at ground level, giving a pitch moment. That
pitch moment cannot be reacted until the suspension has deformed sufficiently
to give an equal and opposite moment on the sprung mass. In this
case, the load transfer between rear and front axles is performed entirely by
the suspension springing and none is carried in the suspension linkage
components – i.e. via a ‘sprung’ loadpath.
The third diagram shows a more typical situation, with some of the pitch
moment carried by an unsprung loadpath and most carried by a sprung loadpath.
Some fraction that is a function of the two angles and may be calculated
and expressed as an ‘anti-dive’ fraction or percentage, or alternatively
the anti-pitch angle may be quoted separately. The authors prefer
Anti-dive % 100()/() (4.30)
Other texts give differing descriptions and definitions. What matters is not
the definition, although it is important to be certain how the quantities in
use are defined if they are to be compared one with another, but the significance
of the sprung and unsprung load transfers themselves:
● Unsprung load transfer occurs via the stiff metallic elements in the system
and is thus very rapid. It is limited in speed by the frequency of the
wheel hop mode, a mode of vibration in which the unsprung mass oscillates
on the tyre stiffness somewhere of the order of 15 Hz.
● Sprung load transfer occurs via the elastic elements of the system and is
limited in speed by the frequency of the primary suspension mode. This
is of the order of 1.5 Hz.
It may be seen then that unsprung load transfer is some 10 times faster than
sprung load transfer. Herein lies the key to understanding some of the most
important effects of the so-called ‘roll centre’. Figure 4.9 is very similar to
Figure 4.8 except that it shows the vehicle from the front instead of the
side. Otherwise, the diagrams are identical. Figure 4.9(a) shows a ‘no-roll’
suspension with load transfer entirely by an unsprung loadpath. Figure 4.9(b)
shows a suspension that transmits load entirely via a sprung loadpath.
The point frequently but ambiguously referred to as the ‘roll centre’ is where
the line of action of the unsprung loadpath crosses the vehicle centre line.