Spring into Action.
(c) Tony Foale 1988-1998
This article was originally written for "Performance Tuning &Sports Car"
and appeared in the March 1988 issue.
The recent development of the Lotus active suspension system has proved that
car body movements such as pitch and roll can be precisely controlled. Unfortunately
it will take some time before we can all take advantage of these developments,
and in the meantime we are stuck with the conventional springs and suspension
that seems to have changed little since the days of the horse drawn carriage.
Every enthusiast knows that the roll characteristics of a car have considerable
influence on its dynamic behaviour as well as the comfort of its occupants.
The parameters that control these characteristics are numerous, terms such as
roll centre, roll stiffness, roll axis and roll couple are often bandied about
but seldom adequately explained. I have often seen, in books and magazine articles,
geometric constructions that can be used to determine roll centres and axis
for different suspension layouts, but I have never seen an explanation of why
these methods actually provide this information. It seems to be taken for granted
that the reader will just accept it on face value, or is it because the writer
is unsure himself and is just repeating that which he has read elsewhere. Anyway
let's break with tradition and see if we can untangle the subject.
Firstly, we must understand the terminology. The roll axis is an imaginary line
running through the car from end to end; when the car rolls, whilst cornering
on a smooth road, it rotates about this axis. Any part of the vehicle not on
this axis bodily moves, either up or down, side to side or both. Fig 1 shows
the motion, as well as the longitudinal position of the roll centres, these
usually being points on the roll axis in line with the wheels. Note that there's
no theoretical reason why the roll centre heights should be at the same level
at each end, and indeed they rarely are.
Now before going into the details of determining the roll centre and axis location,
it must be understood that these parameters are not fixed in relation to the
car's chassis, but move about depending on the deflection of the suspension
and therefore vary depending on the roll angle which is influenced by the cornering
force. When the car rolls the suspension on one side is compressed and on the
other it becomes extended, for the purposes of analysis it matters not whether
we consider the wheels as fixed and the body as capable of movement relative
to them, or the body as fixed with wheels capable of moving. But as it is easier
to visualise the motion with a fixed chassis we will go with that.
Let's now consider the case of a double wishbone suspension system as in Fig
2. If we allow a very small vertical wheel displacement to take place, then
the path of this movement (at the wheel end of the wish- bones) is at right
angles to the wishbones, therefore the length of the wishbone does not affect
the geometry of movement of the upright and wheel (for small displacements).
So if the wishbones were extended in length until their inner pivots coincide
then the motion of the wheel would be unaffected, but as the two wishbones now
pivot around the same axis, we could replace them with a single arm fixed to
the wheel axle, thus in effect creating an equivalent swing axle suspension
system.
Because this new swing axle is only a figment of our imagination, let's call
it a 'virtual swing axle' and its pivot a 'virtual pivot'.
Now, we need to consider the motion of the wheel at the tyre contact patch because
this is our only connection with terra-firma, the reference from which we measure
the roll. The diagram shows that this motion is at right angles to the line
connecting the virtual pivot and the contact patch. Again for small deflections,
this motion is unchanged as long as the effective pivot is located anywhere
along this line. A mirror image of this applies to the wheel at the other side
also. Thus the only common pivot point that satisfies both sides is the one
at the junction of these lines, through the contact patches to the respective
virtual pivots.
So if there is one pivot point that can relate the motion of both tyre contact
patches relative to the chassis, then that same point locates the chassis relative
to the wheels. It is the point about which the body will pivot should the suspension
on one side be compressed by the same amount as the suspension on the other
side be extended, in other words it is the roll centre.
I have emphasised the point about small wheel displacements, this is very important
because the roll centre may vary its position enormously throughout the range
of normal wheel movement. As the car rolls, its roll centres may change not
only in height but also from side to side, as Fig 3, demonstrates.
Even though we have used a double wishbone system to explain the method of determining
the roll centre position, it is very easy to apply the method to any other suspension
configuration. It is only necessary to determine the directions of movement
of the contact patches, and draw lines at right angles to these through the
contact patches, the point at which these last two lines cross is the roll centre.
Fig 4, shows the method for several different systems.
All of the above makes one big assumption (anyone spot it?)
that the effective spring rates at the wheels are equal side to
side. But aren't they, I hear you ask. No, not always: what if
you have progressive rate springing? The effective spring rate
will be increasing on the side that is compressing and will be
reducing on the other. To understand the effect that this may
have, let's look at the extreme case of a car with a rigid
suspension on one side only and with a normal spring on the
other. The chassis is thus completely tied to one contact patch
and so this is the only point about which it can roll. Thus the
roll centre is at ground level directly under the wheel with the
infinitely stiff springing. Obviously this situation is unreal
but demonstrates how the actual roll centre moves away from the
geometrically constructed one, if the springing is not
symmetrical.
It is all very well knowing where the roll centres and thus the
roll axis are but what use is that knowledge, how can we use it
and where should they be anyway? To answer this, we need to look
at the superficially obvious question, 'Just what causes roll?'.
As we negotiate a curve the car is subject to centrifugal force,
which is equal to the lateral acceleration multiplied by the mass
of the machine (for a 1000Kg car cornering at 0.5g. The
centrifugal force is 500Kg). This force is distributed throughout
the car but for most analysis purposes can be considered to be
acting only through the centre of gravity (C of G). Fig 5, shows
that unless the C of G is level with the roll axis, a torque or
couple (the roll couple) will be created, tending to make the
machine roll about the roll axis.
There is another equally valid way of considering the roll
mechanism. The centrifugal force acting through the C of G
produces a torque about ground level and is resisted by weight
transfer to the outside wheels, that is, the outside wheels
support a greater proportion of the car's weight and the inside
wheels a lesser proportion.
This change of load on each wheel normally causes the suspension
to adopt a new position, or to put it another way the car rolls.
It may have occurred to some of you that if the roll axis is made
to coincide with the C of G then there will be no roll couple and
hence no roll or, to take things a step further, if the roll axis
is above the C of G then the roll couple will be in a direction
which makes the car lean inward like a motorbike. Indeed it is
quite possible to design the suspension layout to achieve these
effects. If this is so, why do we need active suspension to do it
for us? Well, because if we use the high roll axis necessary,
then the suspension layout will cause a jacking up effect under
cornering conditions, a phenomenon experienced with some swing
axle designs in the past.
One important point to note, one which is often misunderstood, is
that regardless of the amount of roll allowed by the suspension
design, the actual degree of weight transfer remains unchanged.
This is only affected by the track, C of G height and cornering
acceleration.
So, as with most design features in anything mechanical, the
selection of roll axis position is a compromise: too low and we
get excessive roll, too high and other undesirable handling
traits surface. In practice, the com- promise varies with
different types of car but always such that some roll occurs.
Lowering the C of G is another technically possible way of
reducing the roll couple, but this can only be done to a certain
extent, due to the boring necessity of leaving comfortable space
for the occupants.
The roll couple that such compromise leaves must be resisted by
the car's springs, which leads us to roll stiffness. This term is
defined such that the degree of roll is equal to the roll couple
divided by the roll stiffness. Stiff springing obviously reduces
roll and hence increases the roll stiffness, but if this is the
criterion for selecting spring rates we will usually end up with
an uncomfortable ride over normal road irregularities, so the
anti-roll bar was developed to ease the situation.
The anti-roll bar is a torsion bar (torsion spring) connecting
the suspension systems on each side of the vehicle in such a way
as to allow both wheels to respond unhindered to two-wheel bumps,
such as a ridge across the road. But if the wheels try to move
independently, as with a single-wheel bump, or in opposite
directions when the car rolls then the anti-roll bar resists this
tendency. Roll is reduced as intended but comfort suffers as the
effective spring rate of each wheel is increased in the
individual single-wheel bumps, although the combined spring rate
of the two wheels is unchanged over joint disturbances.
Again a compromise must be reached between the requirements of
minimum roll and good response to road shocks. Roll bars, unlike
the springs, are undamped (theoretically damping could be
incorporated, although the manufacturers have generally concluded
that it is not worthwhile). This is another reason for limiting
the influence of the anti-roll bar, as oscillations might occur
if the undamped bar is too stiff.
It is well known that the under/over steering characteristics of
a car can be substantially modified by tuning the springing and
anti-roll bar stiffnesses, altering the roll stiffnesses of each
end.
While the vehicle as a whole has a certain roll stiffness, this
is made up of the separate roll stiffnesses at the front and
back, which may be quite different. For example, let's consider
the case of a beam axle pivotted on the chassis at its mid point,
and devoid of any form of springing. As unlikely as this layout
seems, you may see it fitted to the front of some tractors,
because it has good terrain-following properties. Now, because
the chassis is completely free to rotate about the pivot point of
this beam axle, then no roll stiffness is provided at this end of
the machine and so all the stiffness needed must be available
from the other end.
This lack of any roll stiffness means that body roll cannot cause
any weight transfer to the outside wheel, and hence as the total
weight transfer must be the same anyway, the other end must
obviously be subjected to proportionally more.
Tyres have the interesting property that although they are
capable of supporting higher cornering forces when subject to
higher vertical loading, this does not go up in proportion. In
other words, the co-efficient of friction is reduced as more
weight is placed on them. In practice this means that weight
transfer reduces the combined cornering force capable of being
developed by the pair of tyres at one end of the car. Now as we
have seen, the weight transfer at either end of the vehicle can
be controlled to some extent by altering the roll stiffnesses of
one or other, or both ends. Therefore, the tyre slip angles
needed to produce the required cornering forces can be adjusted
by modifications to the wheel springing, thus giving us the means
to alter the under/over steering properties.
Dampers, too, have their part to play in the extremely complex
interrelations between the various forces acting on the car.
During the transitional period between initiating a turn and it
becoming fully established, the dampers will affect the dynamic
roll stiffnesses. Because the dampers only contribute whilst the
suspension is actually moving, however, they have no effect once
the car has settled down to a steady state turn.
So now you know why racers spend so much time setting up the
suspension rates on their machines, when at first sight it would
appear that the suspension is there only to cushion the bumps.
Many competition cars have facilities for altering roll bar
stiffness whilst on the move, making it quicker to achieve the
desired performance but also allowing adjustments during a race
as tyres wear and fuel weight reduces.
So how will active suspension improve the situation? The computer
program controlling the system could, for example, be set to
apportion the front/rear roll stiffness.
Assuming, that the system is set to give zero roll (this is by no
means certain to be the aim of future manufacturers) then it is
very interesting to follow through the implications for geometric
roll centres, etc. Basically if we have no roll then the term
roll axis becomes irrelevant, as does the need to have suspension
link layouts that try to keep the outside wheels upright under
cornering roll rather than under all conditions. Perhaps active
suspension means a return to parallel equal length wishbones or
perhaps better still, true trailing or leading arm systems.
Normally, these designs suffer because of vast changes in roll
centre positions, and because the camber angle varies with the
roll angle of the body, the wheels always being held parallel to
it. Straight line stability would be improved as bump induced
wheel deflections would not cause any of the bump steer which
comes from changing wheel camber. That's a desirable state of
affairs that is hard, if not impossible to achieve with
conventional springs and dampers as we have seen.