Table Of ContentVehicle/Tire/Road Dynamics
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Vehicle/Tire/Road
Dynamics
Handling, Ride, and NVH
Tan Li
Maxxis Technology Center, Maxxis
International—USA, Suwanee, GA, United States
Elsevier
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Contents
1 Introduction 1
1.1 Background 1
1.2 Literature 2
1.3 Organization 3
References 12
2 Definitions and fundamentals 15
2.1 Multibody dynamics 15
2.2 Vibrations 19
2.3 Control 25
2.4 Structure-borne acoustics 44
2.5 Airborne acoustics 63
2.6 Acoustic resonance 84
References 93
3 Tire and vehicle handlingdynamics 95
3.1 Tire handling theory 95
3.2 Vehicle handling theory 138
3.3 Handling test, measurement, and evaluations 174
3.4 Handling simulation approaches 220
References 270
4 Tire and vehicle ride dynamics 275
4.1 Vehicle ride theory 275
4.2 Tire ride theory 295
4.3 Ride test,measurement, and evaluations 310
4.4 Ride simulation approaches 347
References 356
5 Tire and vehicle NVH 359
5.1 Structure-borne acoustics 360
5.2 Airborne acoustics 372
5.3 Sound quality theory 380
5.4 NVH test, measurement, and evaluations 391
5.5 NVH simulation approaches 434
References 454
vi Contents
6 Dependence betweenhandling, ride, and NVH 459
6.1 Fundamental tire material properties 459
6.2 Stress anddeformation distributionintire contact patch 485
6.3 Conflicts between safety and comfort 512
6.4 Optimization with active suspension control 518
6.5 Braking and corneringnoise 525
References 536
7 Road effect on handling,ride, and NVH 539
7.1 Surface texturecharacterization 539
7.2 Influenceof surface texture ontire grip 539
7.3 Influenceof the road profileon vehicle comfort 559
7.4 Influenceof pavement parameters on NVH 560
7.5 Road dynamics 581
References 584
8 Intelligenttireand autonomous electric vehicle 589
8.1 Vehicle/tire state and parameter estimation 589
8.2 Dynamicscontrol for electric vehicles 600
8.3 Smart tire 603
References 614
Appendix1:Example specifications of differenttypes of vehicles 617
Appendix2:Literature review for tire modal analysis 631
Index 647
1
Introduction
1.1 Background
Kinematics is a subfield of classical mechanics that describes the motion of points,
bodies (objects), and systems of bodies (groups of objects) without considering the
forcesthatcausethemtomove.Dynamicsisthebranchofclassicalmechanicscon-
cernedwiththestudyofforcesandtheireffectsonmotion.Obviously,thetopicinthis
book considers underlying forces and computes motion from initial conditions and
physics,so vehicle dynamics is the correct term.
DynamicsisgovernedbyequationsofmotionorNewton’sSecondLawofMotion.
Inthisbook,dynamicsisanalternativetermtomotion.Inphysics,motionisthephe-
nomenoninwhichanobjectchangesitspositionovertime.Motionismathematically
described intermsofdisplacement, velocity, acceleration, and time.Themotion ofa
bodyisobservedbyattachinga frame ofreferencetoanobserverand measuring the
changeinpositionofthebodyrelativetothatframe.Inthisbook,motioniscategorized
into movement and vibration. In philosophy, everything in the Universe moves and
vibrates. Movement is defined as a continual change of physical location relative to
a reference frame. Generally, the removal of applied external forces will not lead to
the body returning to its original location. For vehicle handling analysis focusing on
planar/horizontalmotion,thevehiclesystemisusuallytreatedasasinglebodyhaving
onlyonemovementwithoutconsideringthewheelmovements.Vibrationisdefinedas
theoscillationofamechanicalorstructuralsystemarounditspointofequilibrium.After
theremovalofexternalexcitations,asystemwilleventuallyreturntoastateofequi-
libriumaslongasdampingexists.Forvehiclerideanalysisfocusingonverticalmotion,
thevibrationsofbodyandwheelsusuallymodeledaslumpedmasses(rigidbodies)are
bothconsidered. Modal analysis techniquesare typicallyapplied tolinear systems to
study their modal properties as described by system natural frequency, mode shape,
anddampingratio.Inthisbook,oscillationisanalternativetermtovibration.
NVHstandsfornoise,vibration,andharshness.Noiseisusuallyconsideredasan
unwantedsound.However,“wanted”or“unwanted”dependsuponthelistenerandthe
circumstances.Forexample,rockmusiccanbepleasurablesoundtoonepersonbutan
annoyingnoisetoanother.Inthisbook,soundisanalternativetermtonoise.Vibration
can generate noise by sound radiation and noise can also cause vibration by fluid-
structureinteraction.Harshnessisthesubjectiveimpressionsofthenoise.Inhandling
andrideanalysis,thevehicleisconsideredasasinglebodyoranintegratedsystemof
multiplebodiesconnectedelasticallywitheachother,thatis,eachbodyisonelumped
masswheremotionsofitspartsareinphase.However,inNVHanalysis,thebodyhas
tobedistributedmasswheremotionsofitspartsarenotinphase,allowingacoustic
waves to propagate inside the structure or radiate into the air. The sound field and
vibration map inthe vehicle cabin are highlynonuniform.Thesoundpressure level
atdriver’searclosertothewindowcanbe3dBhigherthanthatattheotherear;the
Vehicle/Tire/RoadDynamics.https://doi.org/10.1016/B978-0-323-90176-5.00003-6
Copyright©2023ElsevierInc.Allrightsreserved.
2 Vehicle/Tire/RoadDynamics
soundpressurelevelattherearseatcanalsobe3dBhigherthanatthefrontseat.The
vibrationlevelscanalsobedifferentonthefloor,seat,andsteeringwheel,whichis
usuallynotinthescopeofridevibrationsfocusedonsmoothnessatthevehiclecenter
of gravity. It is also implied that NVH is a highly subjective performance, which is
why sound quality becomes more and more important for vehicle product quality.
Similarly, handling quality and ride quality in terms of subjective evaluations have
drawnhigherattentionrecently.
Insummary,thereisaspectrumofvehicleperformanceareas:handlingforlowfre-
quency(<10Hz),rideformiddlefrequency(10–100Hz),andNVHforhighfrequency
(>100Hz).Conventionally,“vehicledynamics”onlyimpliedhandlingthatismostcrit-
icalrelatingtosafety,lateritmergedwithridebecausecomfortbecameimportant,now
NVHhasdrawnhigherattentionforproductquality.Allofthethreeareasareactually
dynamics,butwearenotusedtocallingNVHdynamicsyet.Allthreeareascanbeana-
lyzed in frequency and time domain, though handling is usually analyzed in time
domainwhileNVHinfrequencydomain.Inthisbook,bothfrequencydomainanalysis
andtimedomainanalysiswillbepresentedforallthreeareas.Asummarycomparison
betweenvehiclehandling,ride,andNVHisshowninTable1.1.
Generally,therearefivemajornoisesourcesforavehiclewithinternalcombustion
engine (ICE): powertrain, intake system, exhaust system, aerodynamic turbulence
(wind),andtire-roadinteraction.Foranelectricvehicle(EV),thepowertrainnoisefrom
electricmotorismuchlowerthanICE,andtheintake/exhaustnoiseisremoved.This
bookmainlyfocusesontire-road-inducedNVH,whichisdominantforregularvehicle
speeds.Traditionally,vehicleperformanceislimitedbytheICE,astheenginedeter-
minesthevehicletractioncapabilityandgeneratesmostoftheinteriornoiseunderreg-
ularconditions.However,electricmotorwithhightorqueandlownoisecaneliminate
thosedisadvantagesofICE.Hence,theperformanceofEVswillbelargelydependent
ontiresprovidingsufficientgripandminimizingroadnoise.Vehicleelectrificationcan
also provide more spacious passenger compartment due to compact powertrain/
drivetrainsystemandlowerheightofcenterofgravityduetothebatteryarrangement
underthevehiclebody,whichimprovesridecomfortandrollstability.Theadvanced
suspensiontechnologyalsoputstireinamoreimportantroleinimprovingvehiclecom-
fort. Therefore, tire, as a component of vehicle system, will be critical for the major
vehicle performances including handling, ride, and NVH. The tire contact patch is
theonlyinteractionbetweenavehicleandtheroad;theforcesgeneratedinthispatch
dictatethemovementandvibrationofthevehicle.Fortheautonomousvehicle,dueto
littleornocontrolofthevehicle,occupantsmayhavedifferentperspectivesregarding
handling(lowerrequirementsforsteeringfeelbuthigherrequirementsforsafety/stabil-
ity)andhigherstandardsforridecomfortandNVH.
1.2 Literature
Acomprehensivesearchforpublishedbooksonvehiclehandling/ride/NVHhasbeen
performed,aslistedinTable1.2.Thesearegoodreferencesforreaderstodelveinto
specificareasofinterest.However,itcanbeseenthatthereisaneedtoputtogethera
book coveringall the areas.
Introduction 3
Table1.1 Comparisonsbetweenvehiclehandling,ride,andNVH.
Handling Ride NVH
Vehicle Onelumpedmass Multiple Multipledistributed/
model lumped/discrete continuousmasses
masses(rigid (flexiblecomponent)
body)
Tiremodel Spring Springorfinite Finiteelement
element
Driver Steeringwheel,throttle/ Mostlycruise Mostlycruise/coast
input brake,gear
Excitation Tire-roadfriction Road Tire-pavement
irregularity roughness
impact
Motion Movement Movementand Vibration
category vibration
Vibration NA Freeresponse Forcedresponse
response
Typical Time Timeand Frequency(above
analysis frequency 100Hz)
domain (below100Hz)
Time Maxperformance Impactpeakand Soundquality:
domain damping fluctuation,
scope roughness
Frequency Stabilitycontrol Modal Spectraldistribution
domain oscillation andweighting
scope
State Steady-stateortransient Mostlytransient Mostlysteady-state
Parameters Maxvehiclelongitudinal/ Roll/pitchangle, Soundpressure,rms
ofinterest lateralacceleration/ max,andrmsof ofaccelerations
velocity,yawrate,sideslip accelerations
angle
Implication Safety,stability,reliability Comfort,ease Pleasantness,
quality,identity
1.3 Organization
Tofilltheknowledgegapbetweendifferentareas,Chapter2presentedthebasicdef-
initions and fundamentals relatedto vehicle handling, ride, andNVH.
Inthegeneralizedvehicle/tiredynamics,thesteadystateortheshort-timetransient
tireforcesdominatethevehiclehandlingbehavior(Chapter3);then,thefluctuationof
thereactionforcesinfluencestheridequality(Chapter4);finally,thestabilizedoscil-
lationofeachvehicle/tirecomponentrelatestoNVHperformance(Chapter5).How-
ever, there are no clear-cut boundaries between vehicle handling, ride, and NVH.
