## 102 Suspension roll centres

Roll centres (Fig. 10.29) The roll centre of a suspension system refers to that centre relative to the ground about which the body will instantaneously rotate. The actual position of the roll centre varies with the geometry of the suspension and the angle of roll.

Roll axis (Fig. 10.29) The roll axis is the line joining the roll centres of the front and the rear suspension. Roll centre height for the front and rear suspension will be quite different; usually the front suspension has a lower roll centre than that at the rear, causing the roll axis to slope down towards the front of the vehicle. The factors which determine the inclination of the roll axis will depend mainly on the centre of gravity height and weight distribution between front and rear axles of the vehicle.

10.2.1 Determination of roll centre height (Fig. 10.18)

The determination of the roll centre height can be best explained using the three instantaneous centre method applied to the swing axle suspension, which is the basic design used for the development of almost any suspension geometry (Fig. 10.18).

A vehicle's suspension system involves three principal items; the suspended body B, the supporting wheels W and the ground G which provides the reaction to the downward load of the vehicle.

If a body which is suspended between two pairs of wheels is to be capable of rolling relative to the ground, then there must be three instantaneous centres as follows:

1 IBG the instantaneous centre of the body relative to the ground which is more commonly known as the body roll centre,

2 IWB the instantaneous centre of the wheel relative to the body which is the swing arm point of pivot,

3 IWG the instantaneous centre of the wheel relative to the ground which is the contact centre between the tyre and ground. It therefore forms a pivot permitting the top of the wheel to tilt laterally inwards or outwards.

Fig. 10.18 Short swing axle

10.2.2 Short swing arm suspension (Fig. 10.18)

When cornering, an overturning moment is generated which makes the body roll outwards from the centre of turn. The immediate response is that the inner and outer swing arm rise and dip respectively at their pivoted ends so that the inner and outer wheels are compelled to tilt on their instantaneous tyre to ground centres, IWGj and IWG2, in the opposite direction to the body roll.

For effective body roll to take place there must be two movements within the suspension geometry:

1 The swing arm pivot instantaneous centres IWBj and IWB2 rotate about their instantaneous centres IWGj and IWG2 in proportion to the amount of body roll.

2 The swing arm pivot instantaneous centres IWBj and IWB2 move on a circular path which has a centre derived by the intersecting projection lines drawn through the tyre to ground instantaneous centres IWGj and IWG2.

The tilting, and therefore rotation, of both swing arms about the tyre to ground instantaneous centres IWGj and IWG2 will thus produce an arc which is tangential to the circle on which the swing arm pivot instantaneous centres IWBj and IWB2 touch. Therefore, the intersecting point IBG, where the projection lines which are drawn through the wheel to ground contact points and the swing arm pivots meet, is the instantaneous centre of rotation for the body relative to the ground. This point is usually referred to as the body roll centre.

Thus the body roll centre may be found by drawing a straight line between the tyre contact centre and swing arm pivot centre of each half suspension and projecting these lines until they intersect somewhere near the middle of the vehicle. The point of intersection becomes the body roll centre.

The roll centre height may be derived for a short swing arm suspension by consideration of similar triangles:

772 " l where h = Roll centre height t = Track width r = Wheel radius l = Swing arm length tr

10.2.3 Long swing arm suspension (Fig. 10.19) The long swing arm suspension is very similar to the short swing arm arrangement previously described, but the arms extend to the opposite side of the body relative to its wheel it supports and therefore both arms overlap with each other (Fig. 10.19).

The roll centre is determined by joining the tyre contact centre and the swing arm pivot centre by a straight line for each half suspension. The point where these lines meet is the body roll centre and its distance above or below the ground is known as the roll centre height. Because the long swing arm suspension has a much longer arm than used on the short swing arm layout, the slope of the lines joining the tyre contact centre and swing arm pivot is not so steep. Therefore the crossover point which determines the body roll centre height is lower for the long swing arm than for the short swing arm suspension.

The inherent disadvantage of the short swing arm suspension is that there is too much camber change with body roll and there is a tendency for the axle arms to jack the body up when cornering. Whereas the long swing arm suspension would meet most of the requirements for a good quality ride, it is impractical for a front suspension layout as it would not permit the engine to be situated relatively low between the two front wheels.

10.2.4 Transverse double wishbone suspension (Figs 10.20, 10.21 and 10.22)

If lines are drawn through the upper and lower wishbone arms and extended until they meet either inwards (Fig. 10.20) or outwards (Fig. 10.21), their intersection point becomes a virtual instantaneous centre for an imaginary (virtual) triangular swing arm suspension. The arc scribed by the wishbone arms pivoting relative to the body is almost identical to that of the imaginary or virtual arm which swings about the instantaneous virtual centres IBWj

Fig. 10.19 Long swing axle

Fig. 10.20 Inward converging transverse double wishbone
Fig. 10.21 Outward converging transverse double wishbone

Fig. 10.22 Parallel transverse double wishbone

### Fig. 10.19 Long swing axle

Fig. 10.22 Parallel transverse double wishbone and IBW2 for small movements of the suspension. Therefore, the body roll centre for a transverse double wishbone suspension can be derived similarly to a long swing arm suspension.

For inwardly converging transverse upper and lower wishbone arm suspension (Fig. 10.20) the body roll centre can be derived in two stages. Firstly, extend straight lines through the wishbone arms until they meet somewhere on the opposite side of the body at their virtual instantaneous centres IWBj and IWB2. Secondly, draw straight lines between the tyre contact centres IWGj and IWg2 and the virtual centres IBWj and IBW2 for each half suspension. The point where these inclined lines intersect is therefore the body roll centre IBG.

For outward converging transverse upper and lower wishbone arm suspension (Fig. 10.21) the body roll centre is found again by drawing two sets of lines. Firstly project straight lines through the wishbone arms for each side of the vehicle until they meet somewhere on the outside of each wheel at their virtual instantaneous centres IWBi and Iwb2. Next draw straight lines between the tyre contact centres IWGi and IWg2 and the virtual centres IWBi and IWB2 for each half suspension, and at the same time extend these lines until they intersect near the middle of the vehicle. This point therefore becomes the body roll centre IBG. It can be seen that inclining the wishbone arms so that they either converge inward or outward produces a corresponding high and low roll centre height.

With parallel transverse upper and lower wishbone arms suspension (Fig. 10.22) lines drawn through the double wishbone arms would be parallel. They would never meet and so the virtual instantaneous centres IWBi and IWB2 would tend to infinity Under these circumstances, lines normally drawn between the tyre contact centres IWGl and IWg2 and the virtual instantaneous centres IWBi and IWB2 would slope similarly to the wishbone extended lines. Consequently, the downwardly inclined parallel wishbone suspension predicts the tyre contact centre to virtual centre extended lines which meet at the roll centre would meet just above ground level. Therefore if the parallel wishbone arms were horizontally instead of downwardly inclined to the ground then the body roll centre would be at ground level.

10.2.5 Parallel trailing double arm and vertical pillar strut suspension (Figs 10.23 and 10.24) In both examples of parallel double trailing arm (Fig. 10.23) and vertical pillar strut (Fig. 10.24) suspensions their construction geometry becomes similar to the parallel transverse double wishbone layout, due to both vertical stub axle members moving parallel to the body as they deflect up and down. Hence looking at the suspension from the front, neither the double trailing arms (Fig. 10.23) nor the sliding pillar (Fig. 10.24) layout has any trans-

Fig. 10.24 Vertical pillar strut

verse swing tendency about some imaginary pivot. Lines drawn through the two trailing arm pivot axes or sliding pillar stub axle, which represent the principle construction points for determining the virtual swing arm centres, project to infinity. The tyre contact centre to virtual instantaneous centre joining lines projected towards the middle of the vehicle will therefore meet at ground level, thus setting the body roll centre position. Inclining the trailing arm pivot axes or the vertical sliding pillar axis enables the roll centre height to be varied proportionally.

10.2.6 MacPherson strut suspension (Fig. 10.25) To establish the body roll centre height of any suspension, two of the three instantaneous centres, the tyre contact centre and the swing arm virtual centre must first be found. If straight lines are drawn between, and in some cases projected beyond, these instantaneous centres the third instantaneous centre which is the body roll centre becomes the point where both lines intersect.

The tyre contact centres (instantaneous centres IWG1 and IWg2) where the wheels pivot relative to the ground are easily identified as the centres of the tyre where they touch the ground, but the second instantaneous virtual centre can only be found once the virtual or imaginary equivalent swing arm geometry has been identified.

For the MacPherson strut suspension (Fig. 10.25) the vertical swing arm and pivot centres IBW1 and IBWj are obtained for each half suspension by projecting a line perpendicular to the direction

Fig. 10.23 Parallel trailing double arm

iwgi g

Fig. 10.25 MacPherson strut

### Fig. 10.23 Parallel trailing double arm iwgi g

Fig. 10.25 MacPherson strut of strut slide at the upper pivot. A second line is then drawn through and beyond the lower control arm until it intersects the first line. This point is the instantaneous virtual centre about which the virtual swing arm pivots.

Straight lines are then drawn for each half suspension between the tyre contact centre and the virtual swing arm centre. The point of intersection of these two lines will then be the third instantaneous centre IBG, commonly referred to as the body roll centre.

10.2.7 Semi-trailing arm rear suspension

A semi-trailing arm suspension has the rear wheel hubs supported by a wishbone arm pivoted on an inclined axis across the body (Fig. 10.26(a)).

If lines are projected through the wishbone arm pivot axis and the wheel hub axis they will intersect at the virtual instantaneous centres IBWj and IBW2 (Fig. 10.26(a and b)). The distance between these centres and the wheel hub is the transverse equivalent (virtual) swing arm length a. Projecting a third line perpendicular to the wheel hub axis so that it intersects the skewered wishbone arm axis produces the equivalent fore and aft (trailing) swing arm length b for the equivalent (virtual) semi-trailing triangular arm (Fig. 10.26(c)). The movement of this virtual swing arm changes the wheel camber and moves the wheel hub axis forward as the wheel deflects in bump or bounce from the horizontal position.

The body roll centre can now be determined by drawing a rear view of both virtual swing arms (Fig. 10.26(b)) and then drawing lines between each half swing arm instantaneous pivot centres IWB| and IWB, and the tyre contact centres Iwg, and IWg2. The point where these two sloping lines cross over can then be defined as the body roll centre IBG.

Fig. 10.26 Semi-trailing arm

10.2.8 High load beam axle leaf spring sprung body roll stability (Fig. 10.27) The factors which influence the resistance to body roll (Fig. 10.27) are as follows:

a) The centrifugal force acting through the centre of gravity of the body load.

b) The arm length from the centre of load to the effective roll centre h1 or h2.

c) The spring stiffness in Newtons/metre of vertical spring deflection.

d) The distance between the centres of both springs known as the spring stability base ts.

e) The distance between road wheel centres known as the tyre stability base tw.

Considering the same side force acting through the centre of gravity of the body load and similar spring stiffness for both under- and over-slung springs (Fig. 10.27), two fundamental observations can be made.

Firstly it can be seen (Fig. 10.27) that with over-slung springs the body roll centre RC1 is much higher than that for underslung springs RC2 and therefore the overslung springs provide a smaller overturning arm length h1 as opposed to h2 for the underslung springs. As a result, the high roll centre with the small overturning arm length offers a greater resistance to body roll than a low roll centre with a long overturning arm.

Secondly it can be seen (Fig. 10.27) that the triangular projection lines produced from the centre of gravity through the centres of the springs to

Fig. 10.27 Effects of under- and over-slung springs on the roll centre height

### Fig. 10.26 Semi-trailing arm

Fig. 10.27 Effects of under- and over-slung springs on the roll centre height the ground provide a much wider spring stability base for the high mounted springs compared to the low mounted underslung springs. In fact the overslung spring centre projection lines nearly approach the tyre stability base width tw which is the widest possible for such an arrangement without resorting to outboard spring seats.

10.2.9 Rigid axle beam suspension

An axle beam suspension is so arranged that both wheel stub axles are rigidly supported by a common transverse axle beam member which may be a steered front solid axle beam, a live rear axle hollow circular sectioned casing or a DeDion tubular axle beam.

With a rigid axle beam suspension there cannot be any independent movement of the two stub axles as is the case with a split swing axle layout. Therefore any body roll relative to the ground must take place between the axle beam and the body itself. Body roll can only take place about a mechanical pivot axis or about some imaginary axis somewhere near mid-spring height level.

Methods used to locate and control the axle movement are considered as follows:

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