AutoMobile Suspension

7/30/2019 AutoMobile Suspension

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Determination of anti-pitch geometry

acceleration [1/3]

Similar to anti-squat

Opposite direction of

DAlemberts forces.

Front wheel forces and effective pivot locationsFigure from Smith,2002


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acceleration [2/3]

It follows that the change in the front spring force

is:

where kf= front suspension stiffness.

Similarly for the rear wheels.


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acceleration [3/3]Pitch angle

Zero pitch occurs when = 0, i.e. when the term in squarebrackets is zero.

anti-squat and anti-pitch performance depends on thefollowing vehicle properties suspension geometry,

suspension stiffnesses (front and rear) and

Tractive force distribution.


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Lateral load transfer during cornering

Notation and assumptions in the analysis are:

G is the sprung mass centre of gravity;

The transverse acceleration at G due to

cornering is a;

The sprung mass rolls through the angle

about the roll axis; The centrifugal (inertia) force on the

sprung mass msa acts horizontally through

G;

The gravity force on the sprung mass msg

acts vertically downwards through G;

The inertia forces mufa and mura actdirectly on the unsprung masses at the

front and rear axles. Each transfers load

only between its own pair of wheels.Steady-state cornering analysis

Figure from Smith,2002


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Load transfer due to the roll moment

[1/2]

Replace the two forces at G with the same forces atA plus a moment (the roll moment) Ms about theroll axis, i.e

Assuming linear relationship between M and

M = ks

ks = total roll stiffness


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Load transfer due to the roll moment

[2/2]

ksf+ ksr = ks Load transfer sin two axles are

Tfand Tr are the front and rear track widths of thevehicle


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Load transfer due to sprung mass

inertia force

The sprung mass isdistributed to the rollcenters at front and rearaxles.

Centrifugal forcedistribution is

Corresponding loadtransfers are


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Load transfer due to the unsprung

mass inertia forces

Total load transfer


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Suspension components

Need for compliance between unsprung and sprung mass.

Requirements:

Good isolation of the body(Good ride) Soft response Inconsistent with roll resistance in cornering

Roll stiffening using ant-roll bars Spring can hit limits

Additional springs as bump stops

Prevent high frequency vibration from being transmitted Use rubber bush connections

Good road grip (Good handling) Hard response


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Steel springs

Semi-elliptic springs earliest developments inmotor vehicle

Robust and simple usedfor heavy applications

Hotchkiss type- to provideboth vertical complianceand lateral constraint forthe wheel travel

change in length of thespring produced by bumploading is accommodatedby the swinging shackle

Leaf spring design



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Leaf spring analysis

Wheel load FW , is vertical.

FC is parallel to the shackle

Two load member

The stiffness (rate) of the

spring is determined by thenumber, length, width andthickness of the leaves

Angling of the shackle linkused to give a variable rate

When the angle < 90 ,the spring rate will increase(i.e. rising rate) with bumploading



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Coil springs

Light and compact form of compliance for weight andpackaging constraints

Little maintenance and provides

Opportunity for co-axial mounting with a damper

Variable rate springs produced either by varying thecoil diameter and/or pitch of the coils along its length

Disadvantages:

Low levels of structural damping, there is a possibility

of surging (resonance along the length of coils) Spring as a whole does not provide any lateral support

for guiding the wheel motion.


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Torsion bars

Very simple form ofspring and consequentlyvery cheap

The principle of operation

is to convert the appliedload FW into a torque FW R producing twist in thebar

Stiffness related to

diameter, length of thetorsion bar and thetorsion modulus of thematerial Principle of operation of a torsion bar spring



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Hydro-pneumatic springs

Spring is produced by aconstant mass of gas (typicallynitrogen) in a variable volumeenclosure

As the wheel deflects in bump,

the piston moves upwardstransmitting the motion to thefluid and compressing the gasvia the flexible diaphragm

The gas pressure increases asits volume decreases to

produce a hardening springcharacteristic

Systems are complex (andexpensive) and maintenance

Principles of a hydro-pneumatic

suspension spring

Basic diaphragm accumulator spring



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Anti-roll bars (stabilizer)

Reduce body roll

Ends of the U-shaped barconnected to the wheelsupports and

Central length of barattached to body of thevehicle

Attachment points needto be selected to ensure

that bar is subjected toTorsional loading withoutbending

Anti-roll bar layout



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Anti-roll bars (stabilizer)

Conditions:

One wheels is lifted relative tothe other, half the total anti-rollstiffness acts downwards on thewheel and the reaction on thevehicle body tends to resist body

roll. If both wheels lift by the same

amount the bar is not twisted andthere is no transfer of load to thevehicle body.

If the displacements of the

wheels are mutually opposed(one wheel up and the otherdown by the same amount), thefull effect of the anti-roll stiffnessis produced.

Roll bar contribution to total roll stiffness

Total roll stiffness krs is equal to the sum

of the roll-stiffness produced by the

suspension springs kr,sus and the roll

stiffness of the anti-roll bars kr,ar,



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Dampers types and characteristics

Frequently called shock

absorbers

Main energy dissipators

in a vehicle suspension Two types: dual tube,

Mono tube.

In mono tube Surplus fluid

accommodated by gas

pressurized free pistonDamper types, (a) dual tube damper,

(b) free-piston monotube damper


f


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In dealing with road surfaceundulations in the bumpdirection (damper beingcompressed) relatively lowlevels of damping are

required compared with therebound motion (damperbeing extended)

These requirements lead todamper characteristics

which are asymmetricalwhen plotted on force-velocity axes

Ratios of 3:1 Damper characteristics


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Damper designs areachieved by acombination of orificeflow and flows throughspring-loaded one-wayvalves At low speeds orifices are

effective

At higher pressure valvesopen up

lot of scope for shapingand fine tuning of dampercharacteristics

Shaping of damper characteristics

Typical curves for a three position

(electronically) adjustable damperFigure from Smith,2002

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Road surface roughness and vehicle

excitation

Road surfaces have random profiles -> non-

deterministic.

Methods based on the Fourier transform

Power spectral density S(n) of the height

variations as a function of the spatial

frequency n

= the roughness coefficient

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Road surface roughness and vehicle

excitation

Substituting

The variation of S( f ) for a

vehicle traversing a poorminor road at 20 m/s is

shown


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Human response to whole body

vibration

Human bodycomplex assemblage of linear and non-linear elements

Range of body resonances - 1 to 900 Hz

For a seated human 12 Hz (headneck)

48 Hz (thoraxabdomen)

Perception of vibration motions diminishes above 25

Hz and emerges as audible sound. Dual perception (vibration and sound) up to several

hundred Hz is related to the term harshness

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vibration Motion sickness (kinetosis) low frequency , normally in

ships

ISO 2631 (ISO, 1978) and the equivalent British Standard BS6841 (BSI, 1987)

whole-body vibration from a supporting surface to eitherthe feet of a standing person or the buttocks of a seatedperson

The criteria are specified in terms of

Direction of vibration input to the human torso

Acceleration magnitude Frequency of excitation

Exposure duration

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vibration Most sensitive frequency range

for vertical vibration is from 48Hz corresponding to the thoraxabdomen resonance

most sensitive range for

transverse vibration is from 1 to2 Hz corresponding to headneck resonance

ISO 2631 discomfort boundaries 0.1 to 0.63 Hz for motion

sickness.

most sensitive range is from 0.1to 0.315 Hz

Whole-body RCB vibration criteria, (a) RCB for

vertical (z-axis) vibration (b) RCB forlateral (xand y axis vibration)Figure from Smith,2002

RCB

Reduced

Comfort

Boundary

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Analysis of vehicle response to road

excitation Most comprehensive of these

has seven degrees of freedom

Three degrees of freedom forthe vehicle body (pitch,bounce and roll)

Vertical degree of freedom ateach of the four unsprungmasses.

This model allows the pitch,bounce and roll

The suspension stiffness anddamping rates are derivedfrom the individual spring anddamping units Full vehicle model


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Analysis of vehicle response to road

excitation Much useful information can be

derived from simpler vehiclemodels.

The two most often used forpassenger cars are the half-vehicle model and the quarter

vehicle model. These have four and two degrees

of freedom respectively.

Reduced number of degrees offreedom

In the case of the half vehicle

model, roll information is lost andfor the quarter vehicle modelpitch information is also lost

Half and quarter

vehicle models, (a)

half vehicle model,

(b) quarter vehicle

model


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Response to road excitation

Pitch and bouncecharacteristics

Equivalent stiffness iscalculated as

Generalized co-ordinatesare z and

Notation for pitchbounce analysis


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Equations simplify as

If B=0 the equations are uncoupled

On a bump only pitching occurs not desired

,

,

n bounce

n pitch

A

C

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Roots of the equation are

Distance of O1 & O2 (Oscillation centres)from G



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If inertia coupling ratio is

O1 and O2 are at suspension centers

it becomes a 2 DOF (2 mass) system

(0.8 for sports cars ,1.2 for some front drive cars)

No coupling of front and rear suspensions

Two equivalent masses

Tnr and on a bump

one gets a feeling of in phase motion

and minimal pitching

better ride

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Suspension performance analysis

Quarter car model

Frequency ranges

Low - 1 to 2 Hz resonance of sprung mass

High - 1011 Hz resonance of un-sprung orwheel hop

Suspension designer has selection of

characteristics and parameter values forsuspension springs and dampers to achievethe desired suspension performance

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Suspension performance analysis

Lowest transmissibility(best ride) is producedwith the softestsuspension

good road holdingrequires a hardsuspension

low transmissibility at thewheel-hop frequency andin the mid-frequency rangebetween the tworesonances Effect of suspension stiffness on sprung and

unsprung mass transmissibilities, (a) sprung

mass transmissibility, (b) unsprung mass

transmissibility

(a)

(b)


rs = kt/ks

ride

Road

holding

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Effect of Suspension Damping

sprung and

unsprung mass

transmissibilities,

(a) sprung mass

transmissibility,

(b) unsprung

mass

transmissibility

Control of the sprung mass resonance requires high levels ofdamping, but results in poor isolation in the mid-frequency

Wheel-hop resonance also requires high levels of damping for itscontrol, but with the same penalties in the mid-frequency range

0.3 used for passenger cars


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Refined non-linear analysis

suspension spring and dampernon-linearities,

random road excitation

assessment of ride, tyre forcefluctuation and clearance

space limitations highly non-linear analysis

Requires simulations in thetime domain

ISO weighted acceleration

response of the sprung massdenoted by the DiscomfortParameter D is evaluated

ISO weighting characteristic for

vertical vehicle body acceleration


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Controllable suspensions

Hydraulic Control Speed of response, high

bandwidth, up to 60 Hz

Actuator is driven by an on-boardpump controlled by signalsderived from transducers fitted to

the sprung and unsprung masses. Signals are processed in a

controller according to somecontrol law to produce acontrolled force at the actuator

With practical limitations taken

into account, ride can beimproved by 2030% for thesame wheel travel and dynamictire load when compared with apassive suspension Fully active suspension


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Slow active controlled suspensions

Low bandwidth (up to approximately6 Hz).

The aim of this form of suspension isto control the body mode to improveride.

Above its upper frequency limit it

reverts to a conventional passivesystem which cannot be bettered forcontrol of the wheel-hop mode.

Such systems require much lesspower than the fully active system,with simpler forms of actuation.

The potential performance gains are

less than those for a fully activesystems, but the viability is muchimproved.

Slow active suspension


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Another Controllable suspension

Passive damper is replaced with acontrollable one.

Designed to produce a controlledforce when called upon to dissipateenergy and then switches to anotional zero damping state whencalled upon to supply energy.

Performance potential of thissuspension closely approaches thatof a fully active system under certainconditions, but the hardware andoperational costs of this type ofsuspension are considerably less

Performance is impaired by changesin payload which alter the suspensionworking space : overcome bycombining the controllable damperwith some form of self-levelingsystem

Semi-active suspension

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