16 Suspension 2

8/3/2019 16 Suspension 2

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Determinationofantipitchgeometry

acceleration[1 3]

Oppositedirectionof

DAlembertsforces.

FrontwheelforcesandeffectivepivotlocationsFigurefromSmith,2002


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2 of39


acceleration[2 3]

is:

wherekf =frontsuspensionstiffness.


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3 of39


acceleration[3 3]Pitchangle

Zeropitchoccurswhen =0,i.e.whentheterminsquarebracketsiszero.

properties suspensiongeometry,

suspensionstiffnesses(frontandrear)and

Tract ve orce str ut on.

Forasolidaxlethedrivetorqueisreactedwithinthewheelassembly,i.e.itisaninternalmomentasfarasthefreebodyisconcerned. Inthiscase M=0ande uationsmodifiedb settin r=0forthea ro riate

solidaxle(s)


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Notationandassumptionsintheanalysisare:

Gisthesprungmasscentreofgravity;

ThetransverseaccelerationatGdueto

corneringisa;

abouttherollaxis;

Thecentrifugal(inertia)forceonthe

sprungmassmsaactshorizontallythrough

Thegravityforceonthesprungmassmsg

actsverticallydownwardsthroughG;

Theinertiaforcesmufaandmuraact

directlyontheunsprungmassesatthefrontandrearaxles.Eachtransfersload

onlybetweenitsownpairofwheels.Steadystatecorneringanalysis

FigurefromSmith,2002


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5 of39

Loadtransferduetotherollmoment

[1 2]

Re lace the two forces at G with the same forces at

A plus a moment (the roll moment) Ms about theroll axis, i.e

AssuminglinearrelationshipbetweenM and M =ks

ks =totalrollstiffness


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6 of39

Loadtransferduetotherollmoment

[2 2]

ksf +ksr =ks oa rans ers n woax esare

TfandTr arethefrontandreartrackwidthsofthe


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7 of39

Loadtransferduetosprungmass

inertiaforce

Thes run massis

distributedtotherollcentersatfrontandrear.

distributionis

Correspondingloadtransfersare


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8 of39

Loadtransferduetotheunsprung

massinertiaforces

Totalloadtransfer


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9 of39

Needforcompliancebetweenunsprungandsprungmass.

Requirements: Goodisolationofthebody(Goodride) Softresponse

Rollstiffeningusingantrollbars

Springcanhitlimits

Preventhighfrequencyvibrationfrombeingtransmitted Userubberbushconnections

oo roa gr p oo an ng ar response


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10 of39

Semielliptic springs

ear iest eve opments in

motor vehicle Robust and simple used

or eavy app cat ons

Hotchkiss type to provide

both vertical compliancean a era cons ra n orthe wheel travel

change in length of the

loading is accommodatedby the swinging shackle

Leafspringdesign



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11 of39

Wheel load FW , is vertical.

FC

is parallel to the shackle

Two load member

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

Angling of the shackle linkused to give a variable rate

When the an le < 90 ,

the spring rate will increase(i.e. rising rate) with bumploading



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Lightandcompactformofcomplianceforweightand

packagingconstraints

Littlemaintenanceandprovides

Variableratespringsproducedeitherbyvaryingthe

coildiameterand/orpitchofthecoilsalongitslengthDisadvantages:

Lowlevelsofstructuraldamping,thereisapossibility

Springasawholedoesnotprovideanylateralsupportforguidingthewheelmotion.


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Very simple form of

spring and consequentlyvery cheap

The rinci le of o erationis to convert the appliedload FW into a torque FW R producing twist in thebar

Stiffness related todiameter len th of the

torsion bar and thetorsion modulus of thematerial



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Spring is produced by a

cons an mass o gas yp ca y

nitrogen) in a variable volumeenclosure

Basicdiaphragmaccumulatorspring

,the piston moves upwardstransmitting the motion to the

fluid and compressing the gasv a e ex e ap ragm

The gas pressure increases asits volume decreases to

characteristic Systems are complex (and

expensive) and maintenance

Principlesofahydropneumatic

suspensionspring



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15 of39

Reduce body roll

Ends of the Ushaped barconnected to the wheelsu orts and

Central length of bar

attached to body of the

Attachment points needto be selected to ensure

Torsional loading withoutbending

Antirollbarlayout



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16 of39

Conditions: Totalrollstiffnesskrs isequaltothesum

Onewheelsisliftedrelativeto

theother,halfthetotalantirollstiffnessactsdownwardsonthewheelandthereactiononthe

suspensionspringskr,sus andthe

roll

stiffnessoftheantirollbarskr,ar,

vehiclebodytendstoresistbodyroll.

Ifbothwheelsliftbythesameamountthebarisnottwistedandthereisnotransferofloadtothevehiclebody.

Ifthedisplacementsofthe

(onewheelupandtheotherdownbythesameamount),thefulleffectoftheantirollstiffness Rollbarcontributiontototalrollstiffness

.



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absorbers Mainener dissi ators

inavehiclesuspension

Twotypes:dualtube,Monotube.

Inmonotube

Surplusfluid

accommodatedbygasDampertypes,(a)dualtubedamper,

reepistonmonotu e amper



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18 of39

In dealing with road surface

un u ations in t e ump

direction (damper beingcompressed) relatively low

required compared with therebound motion (damperbein extended

These requirements lead todamper characteristicswhich are as mmetrical

when plotted on forcevelocity axes

Ratios of 3:1 Dampercharacteristics



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19 of39

Damperdesignsare

achievedbyacombinationoforificeflowandflowsthroughspring oa e onewayvalves Atlowspeedsorificesare Shapingofdampercharacteristics

e ect ve

Athigherpressurevalvesopenup

o o scope ors ap ngandfinetuningofdampercharacteristics

Typicalcurvesforathreeposition

(electronically)adjustabledamperFigurefromSmith,2002


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20 of39

Roadsurfaceroughnessandvehicle

excitation

deterministic.

PowerspectraldensityS(n)oftheheightvariationsasa unctiono t espatia

frequencyn

=therou hnesscoefficient


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21 of39

Roadsurfaceroughnessandvehicle

excitation

ThevariationofS(f)fora

minorroadat20m/sis

shown



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22 of39

Humanresponsetowholebody

vibration

Humanbod com lexassembla eoflinearandnon

linearelements Rangeofbodyresonances 1to900Hz

Foraseatedhuman

12Hz(headneck)

Perceptionofvibrationmotionsdiminishesabove25Hzandemergesasaudiblesound.

Dualperception(vibrationandsound)uptoseveralhundredHzisrelatedtothetermharshness


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23 of39


vibration Motionsickness(kinetosis) lowfrequency,normallyin

ships

ISO2631(ISO,1978)andtheequivalentBritishStandardBS6841(BSI,1987)

wholebodyvibrationfromasupportingsurfacetoeitherthefeetofastandingpersonorthebuttocksofaseated

personThecriteriaarespecifiedintermsof

Directionofvibrationinputtothehumantorso

Frequencyofexcitation

Exposureduration


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vibration Most sensitive frequency range

or ver ca v ra on s rom

Hz corresponding to the thoraxabdomen resonance

transverse vibration is from 1 to2 Hz corresponding to head

neck resonance ISO 2631 discomfort boundaries

0.1 to 0.63 Hz for motionsickness.

RCB

Reduced

Comfort.

to 0.315 Hz

WholebodyRCBvibrationcriteria,(a)RCBfor

vertical(zaxis)

vibration

(b)

RCB

for

lateral (x

andyaxisvibration)FigurefromSmith,2002


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25 of39

Analysisofvehicleresponsetoroad

excitation Most comprehensive of these

as seven egrees o ree om

Three degrees of freedom forthe vehicle body (pitch,

Vertical degree of freedom ateach of the four unsprung

masses. This model allows the pitch,

bounce and roll

The suspension stiffness and

amp ng rates are er vefrom the individual spring anddamping units Fullvehiclemodel



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Analysisofvehicleresponsetoroad

excitation Muchusefulinformationcanbe

models. Thetwomostoftenusedfor

passengercarsarethehalfvehiclemodel andthequartervehiclemodel.

Thesehavefourandtwodegreesoffreedomres ectivel .

Reducednumberofdegreesoffreedom

Inthecaseofthehalfvehicle Halfandquarter,

forthequartervehiclemodelpitchinformationisalsolost

ve c emo e s, a

halfvehiclemodel,

(b)quartervehicle

model



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27 of39

Pitchandbouncecharacteristics

Equivalentstiffnessis

Generalizedcoordinatesarezand

Notationforpitchbounceanalysis



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28 of39

IfB=0 theequationsareuncoupled

Onabumponlypitchingoccurs notdesired

,n bounce =

,n pitch C =


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29 of39

DistanceofO1 &O2 (Oscillationcentres)fromG



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30 of39

O1 andO2 areatsuspensioncenters

(0.8forsportscars,1.2forsomefrontdrivecars)Ifwnf

Tnr

andonabump

Nocouplingoffrontandrearsuspensions

Twoequivalentmasses

andminimalpitching

betterride

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16 Suspension 2