Advanced Vehicle Technology Episode 2 Part 10 pdf

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 IBGthe instantan

times tending to align themselves with the wheels

rolling when the steering has been turned to one

lock As a result the trailing or leading offset x

produces a self-righting effect to the steered wheels

The greater the angle the wheels have been steered,

the larger the pivot centre to contact patch centre

offset x and the greater the castor self-centring

action will be The self-righting action which

tends to straighten out the steering after it has

been turned from the straight position, increases with both wheel traction and vehicle speed 10.1.5 Swivel joint positive and negative offset (Figs 10.10±10.15)

When one of the front wheels slips during a brake application, the inertia of the moving mass will tend to swing the vehicle about the effective wheel which is bringing about the retardation because

Fig 10.8 Castor angle steering geometry

(a) Rear wheel drive castor angle self-righting torque effect

(b) Front wheel drive castor angle self-righting torque effect

Castor angle self-righting torque (M)

Castor angle self-righting torque (M)

F R

F R

F D

Fig 10.9 (a and b) Illustration of steered wheel castor self-straightening tendency

there is very little opposing resistance from the

wheel on the opposite side (Fig 10.12)

If the offset of the swivel ball joints is on the

inside of the tyre contact patch the swivel

inclin-ation is known as positive offset (Fig 10.10) When

the wheels are braked the positive offset distance

and the inertia force of the vehicle produce a

turn-ing movement which makes the wheels pivot about

the contact patch centre in an outward direction at

the front (Fig 10.10) If the off side (right) wheel

moves onto a slippery patch, the vehicle will not

only veer to the left, due to the retarding effect of

the good braked wheel preventing the vehicle

mov-ing forward, but the near side (left) wheel will also

turn and steer to the left (Fig 10.13) Therefore the

positive offset compounds the natural tendency for

the vehicle to swerve towards the left if the right

hand wheel skids instead of continuing on a stable

straight ahead path

Arranging for the swivel ball joint inclination

centre line to intersect the ground on the outside of

the contact patch centre produces what is known as

negative offset (Fig 10.11) With negative offset the

Fig 10.10 Swivel pin inclination positive offset

Fig 10.11 Swivel pin inclination negative offset

Fig 10.12 Directional stability when one wheel skids whilst being braked

momentum of the vehicle will produce a turning

moment that makes the wheels swivel inwards at

the front about the contact patch centre (Fig 10.11)

because the swivel ball joints and stub axle assembly

are being pulled forwards and around the patch

centre caused by the negative offset distance The

consequence of negative offset is that the effective

braked wheel twists in the opposite direction to that

to which the vehicle tends to veer (Fig 10.14) and so

counteracts the swerving tendency, enabling the

vehicle to remain in a stable straight ahead direction

In both positive and negative offset layouts, the

skidding wheel turns in the same direction as the

initial swerving tendency, but since it is not

con-tributing greatly to the tyre to ground grip, its

influence on directional stability is small

The effect of negative offset is ideal for a split

line braking system where if one brake line should

fail, the front brake on the opposite side will still

operate as normal (Fig 10.14) The tendency for

the car to veer to the side of the braked wheel is

partially corrected by the wheel being turned due to

the negative offset in the opposite direction

(inwards), away from the direction in which the

car wants to swerve

When cornering, the sideways distortion of the tyre walls will misalign the wheel centre to that of the tread centre so that the swivel ball joint inclin-ation offset will alter The outer front wheel which supports the increase in weight due to body roll reduces positive offset (Fig 10.15(a)), while negative offset becomes larger (Fig 10.15(b)) and therefore makes it easier for the car to be steered when negotiating a bend in the road

10.1.6 MacPherson strut friction and spring offset (Figs 10.16 and 10.17)

The MacPherson strut suffers from stickiness

in the sliding motion of the strut, particularly under light load with an extended strut since the cylinder rod bearing and the damper piston will be closer together Because the alignment

of the strut depends upon these two sliding members, extending and reducing their dis-tance will increase the side loading under these conditions

The problem of reducing friction between the inner and outer sliding members is largely over-come in two ways:

Fig 10.13 Directional stability with positive offset when

one wheel skids whilst being braked Fig 10.14 Directional stability with negative offset whenone wheel skids whilst being braked

(a) By reducing the friction, particularly with any initial movement, using a condition which is known as stiction This is achieved by facing the bearing surfaces with impregnated poly-tetra-fluorethytene (PTFE) which gives the rubbing pairs an exceptionally low coefficient

of friction

(b) By eliminating the bending moment on the strut under normal straight ahead driving although there will be a bending moment under cornering conditions

The tendency for the strut to bend arises because the wheel is offset sideways from the strut, causing the stub axle to act as a cantilever from the base of the strut to the wheel it supports, with the result the strut bends in a curve when extended or under heavy loads (Fig 10.16)

A simple solution which is commonly applied to reduce the bending moment on the strut is to angle the axis of the coil spring relative to the swivel joint axis causing the spring to apply a bending moment

in the opposite sense to the vehicle load bending moment (Fig 10.17) Under normal conditions this coil spring axis tilt is sufficient to neutralize the bending moment caused by the inclined strut and the stub axle offset, but the forces involved while cornering produce much larger bending moments which are absorbed by the rigidity of the strut alone

10.2 Suspension roll centres Roll centres (Fig 10.29) The roll centre of a sus-pension system refers to that centre relative to the ground about which the body will instantaneously

Fig 10.15 (a and b) Swivel pin inclination offset change

when cornering

Fig 10.16 Concentric coil spring and swivel pin axes

permit bending moment reaction

Fig 10.17 Coil spring to swivel pin axis offset counteracts bending moment

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

join-ing the roll centres of the front and the rear

suspen-sion 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

distribu-tion 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

support-ing 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 IBGthe instantaneous centre of the body relative

to the ground which is more commonly known

as the body roll centre,

2 IWBthe instantaneous centre of the wheel relative

to the body which is the swing arm point of pivot,

3 IWGthe instantaneous centre of the wheel

rela-tive 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

10.2.2 Short swing arm suspension (Fig 10.18)

When cornering, an overturning moment is gener-ated 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, IWG1and IWG2, in the oppos-ite 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 IWB1

and IWB 2rotate about their instantaneous centres

IWG1and IWG2in proportion to the amount of body roll

2 The swing arm pivot instantaneous centres IWB1

and IWB2move on a circular path which has a centre derived by the intersecting projection lines drawn through the tyre to ground instantaneous centres IWG 1and IWG 2

The tilting, and therefore rotation, of both swing arms about the tyre to ground instant-aneous centres IWG1 and IWG2 will thus produce

an arc which is tangential to the circle on which the swing arm pivot instantaneous centres IWB1

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 draw-ing a straight line between the tyre contact centre and swing arm pivot centre of each half suspension and projecting these lines until they intersect some-where 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:

h t=2ˆ

r l where h = Roll centre height

t = Track width

r = Wheel radius

l = Swing arm length Hence h ˆ2ltr

Fig 10.18 Short swing axle

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

join-ing the tyre contact centre and swjoin-ing 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

iden-tical to that of the imaginary or virtual arm which

swings about the instantaneous virtual centres IBW1

and IBW2 for small movements of the suspension Therefore, the body roll centre for a transverse double wishbone suspension can be derived simi-larly 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 IWB1and IWB2 Secondly, draw straight lines between the tyre contact centres IWG 1and IWG 2and the virtual centres IBW1 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 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

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 IWB1and IWB2

Next draw straight lines between the tyre contact

centres IWG1and IWG2and the virtual centres IWB1

and IWB2for 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

inclin-ing 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

wish-bone arms suspension (Fig 10.22) lines drawn

through the double wishbone arms would be

par-allel They would never meet and so the virtual

instantaneous centres IWB 1 and IWB 2 would tend

to infinity 1 Under these circumstances, lines

normally drawn between the tyre contact centres

IWG1 and IWG2 and the virtual instantaneous

centres IWB1 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

par-allel 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

mov-ing 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-verse swing tendency about some imaginary pivot Lines drawn through the two trailing arm pivot axes

or sliding pillar stub axle, which represent the prin-ciple construction points for determining the virtual swing arm centres, project to infinity The tyre con-tact 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

IWG1and 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

IBW1and IBW2are obtained for each half suspension

by projecting a line perpendicular to the direction

Fig 10.23 Parallel trailing double arm

Fig 10.24 Vertical pillar strut

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

vir-tual swing arm pivots

Straight lines are then drawn for each half

sus-pension between the tyre contact centre and the

virtual swing arm centre The point of intersection

of these two lines will then be the third

instant-aneous centre IBG, commonly referred to as the

body roll centre

10.2.7 Semi-trailing arm rear suspension

(Fig 10.26)

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 IBW 1and 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

inter-sects 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

IWB1 and IWB2 and the tyre contact centres IWG1

and IWG2 The point where these two sloping lines

cross over can then be defined as the body roll

centre IBG.

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 h1or h2

c) The spring stiffness in Newtons/metre of verti-cal 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 RC2and therefore the overslung springs provide a smaller overturning arm length h1as opposed to h2for 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 10.26 Semi-trailing arm Fig 10.27 Effects of under- and over-slung springs onthe 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

(Fig 10.28(a±d))

An axle beam suspension is so arranged that both

wheel stub axles are rigidly supported by a

com-mon 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

There-fore 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

some-where near mid-spring height level

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

Longitudinally located semi-elliptic springs (Fig 10.28(a)) When semi-elliptic leaf springs support the body, the pivoting point or body roll centre will be roughly at spring-eye level but this will become lower as the spring camber (leaves bow) changes from positive upward bowed leaves when unloaded to negative downward bowed leaves with increased payload

Transverse located Panhard rod (Fig 10.28(b)) The use of coil springs to support the body requires some form of lateral body to axle restraint if a torque tube type axle is to be utilized This may

be provided by a diagonally positioned Panhard rod attached at its ends to both the axle and body When the body tilts it tends to move side-ways and either lifts or dips depending which way the side force is applied Simultaneously the body will roll about the mid-position of the Panhard rod Diagonally located tie rods (Fig 10.28(c)) To pro-vide both driving thrust and lateral support for

Fig 10.28 (a±d) Body roll centres for rigid beam axle suspensions

a helical coil spring live axle layout, a trailing four

link suspension may be adopted which has a pair of

long lower trailing arms which absorb both the

driving and braking torque reactions and a pair of

short upper diagonally located tie rods to control

any lateral movement Any disturbing side forces

which attempt to make the body tilt sideways will

cause it to roll about a centre roughly in line with

the upper tie rod height

Transverse Watt linkage (Fig 10.28(d)) An

alter-native arrangement for controlling the sideways

movement for a coil spring suspension when used

in conjunction with either a live axle or a DeDion

tube is the Watt linkage Suspension linkages of

this type consist of a pair of horizontal tie rods

which have their outer ends anchored to the body

and their inner ends coupled to a central balance

lever which has its pivot attachment to the axle

beam If the body is subjected to an overturning

moment it will result in a body roll about the Watt

linkage balance lever pivot point This

instant-aneous centre is therefore the body roll centre

10.3 Body roll stability analysis

When a vehicle turns a corner the centrifugal force

produced acts outwards through the centre of

grav-ity of the sprung mass, but it is opposed by the tyre

to ground reaction so that the vehicle will tend to

overturn An overturning moment is therefore gen-erated which tends to transfer weight from the inner wheels to the outside wheels At the same time due to the flexibility and softness of the sus-pension, the body rolls so that in effect it overhangs and imposes an additional load to the outer wheels The opposition to any body roll will be shared out between the front and rear suspension accord-ing to their roll resistance Thus if the front suspen-sion roll stiffness with an anti-roll bar is twice that

of the rear, then the front wheels will sustain two thirds of the roll couple while the rear ones only carry one third

10.3.1 Body roll couple (Fig 10.29) The body roll couple (moment) M consists of two components:

Centrifugal moment about the roll centre ˆ

Fa …Nm†

Transverse displacement moment ˆ w a tan 

°Wa (Nm) where1F = centrifugal side force

a = distance between the centre of gravity and roll centre

w = unsprung weight

 = angle of body roll Hence

Total roll movement or couple M ˆ Fa ‡ Wa

ˆ (F ‡ W) a (Nm)

Fig 10.29 Body roll centres and roll axis