## 1031 Body roll couple Fig 1029

The body roll couple (moment) M consists of two components:

Centrifugal moment about the roll centre = Fa (Nm)

Transverse displacement moment = w a tan 0

— Wa0 (Nm) where F = centrifugal side force a = distance between the centre of gravity and roll centre w = unsprung weight 0 = angle of body roll

Hence

Total roll movement or couple M = Fa + Wa0

Fig. 10.29 Body roll centres and roll axis

The sum of these couples are resisted by the springs in proportion to their torsional stiffness at the front and rear.

Body roll stiffness (Fig. 10.29) The body roll stiffness is defined as the roll couple produced per degree of body roll.

Roll angle v ' BJ

where S = roll stiffness (Nm/deg) M = roll couple (Nm) © = angle of roll (deg)

The fraction of torsional stiffness for the front and rear suspensions will therefore be:

where SF = fraction of front torsional stiffness SR = fraction of rear torsional stiffness

10.3.2 Body overturning couple (Fig. 10.30) The centrifugal force F created when a vehicle is travelling on a circular track acts through the body's centre of gravity CG at some height h and is opposed by the four tyre to ground reaction forces F1; F2, F3 and F4.

Consequently an overturning couple Fh is produced which transfers weight W from the inside wheels to the outer wheels which are spaced the track width t apart. Thus the overturning couple will also be equivalent to Wt, that is, Wt = Fh.

It should be noted that the centre of gravity height h is made up from two measurements; the distance between the ground and the body roll centre b and the distance between the roll centre and the centre gravity a.

Therefore

Total body roll couple = Fh = F(a + b) (N) M = Fa + Fb (N)

10.3.3 Body roll weight transfer (Fig. 10.31)

The product Fa is the overturning couple rotating about the roll centre which causes the body to roll. This couple is opposed by a reaction couple Rt where R is the vertical reaction force due to the weight transfer and t is the wheel track width.

Therefore Rt = Fa

This shows that as the distance between the ground and the body roll centre known as the couple arm becomes smaller, the overturning couple and therefore the body roll will also be reduced in the same proportion. Thus if the couple arm a is reduced to zero the reaction force R will likewise approach zero. A small couple is desirable so that the driver experiences a sense of body roll as a warning for cornering stability. If both roll centre and centre of gravity height coincided there would be no indication to the driver that the lateral forces acting on the body were reaching the limit of the tyre to ground sideway grip. Consequently suspensions in which the centre of gravity and the roll centre are at the same height can cause without warning a sudden tyre to ground breakaway when cornering at speed.

10.3.4 Body direct weight transfer couple

If the centrifugal force acted through the roll centre axis instead of through the centre of gravity, a

Fig. 10.32 Direct weight transfer

moment Fb about the ground would be produced so that a direct transference of weight from the inner to the outer wheels occurs. The reaction to this weight transfer for a track width t is a resisting moment Rt which is equal but opposite in sense to the moment Fb.

Hence

If the fore and aft weight distribution is proportional between the front and rear axle roll centres, the centrifugal force F acting through the roll centre axis would be split into two forces Ff and FR which act outwards from the front and rear roll centres.

Rr t

= Total, front and rear vertical reaction forces respectively

Thus lowering the body roll centre correspondingly reduces the vertical reaction force R and by having the roll centre at ground level the direct weight transfer couple will be eliminated.

Therefore if the roll axis slopes from the ground upwards from front to rear, all the direct weight transfer couple will be concentrated on the rear wheels.

10.3.5 Body roll couple distribution (Fig. 10.29) The body roll couple on the front and rear tyres is proportional to the front and rear suspension stiffness fraction.

i.e. Roll couple on front tyres

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