262KSMEInternationalJournal,VoL18No.2,pp.262-271,2004StudyonDampingCharacteristicsofHydropneumaticSuspensionUnitofTrackedVehicleJin-RaeCho*,Hong-WooLee,Wan-SukYooSchoolofMechanicalEngineering,PusanNationalUniversity,Jangjeon-Dong,Kumjung-Ku,Pusan609-735,KoreaJin-KyuLeeTongMyungHeavyIndustriesCo.,Changwon,Kyungnam641-050,KoreaHydropneumaticsuspensionunitisanimportantpartoftrackedvehiclestoabsorbexternalimpactloadexertedfromthenon-pavedroadandthecannondischarge.Itsabsorptionperformanceisstronglyinfluencedbybothdampingandspringforcesoftheunit.Inthispaper,wenumericallyanalyzethedampingcharacteristicsofthein-arm-typehydropneumaticsuspensionunit(ISU)byconsideringfourdistinctdynamicmodesoftheISUdamper:jounce-loading,jounce-unloading,rebound-loadingandrebound-unloading.Theflowratecoefficientsdeterminingtheoilflowratethroughthedamperorificearedecidedwiththehelpofin-dependentexperiments.Thewheelreactionforce,theflowrateatcrackingandthedampingenergyareparametricallyinvestigatedwithrespecttotheorificediameterandthewheelmotionfrequency.KeyWords:ISU,DampingCharacteristics,DamperDynamicMode,DamperOrifice,FlowRateCoefficients,FlowRateatCracking,DampingEnergyvehiclethroughthesuspensionunitinordertoabsorbtheexternalimpactload.Here,theabsorptionprocessofahydropneu-maticsuspensionunitisaccomplishedbyacom-binationofspringanddampingforces(TongMyungTechnicalReports1996,2000).Ingener-al,theabsorptionperformanceismostlycharac-terizedbythekeycomponentcalledthedampercomposedofanorificeanddiscspringsinstalledwithinthesuspensionunit.Thus,anappropriatehydrodynamicmodelingofthedamperisessen-tialfortheaccuratepredictionofthedynamicdampingperformance(TongMyungTechnicalReports2002).Hydropneumaticsuspensionunitisclassifiedintotwotypes,ISU(in-arm-typehydropneu-maticsuspensionunit)andHSU(hydro-pneu-maticsuspensionunit)accordingtothelayoutofthearm.Intheformercasearmandmainhousingareunifiedintoabody(refertoFig.2),butthearmispositionedoutsidethemainhousinginthelattercase.Therefore,bothshowremarkable1.IntroductionDifferingfromgeneralvehiclesrunningonwell-pavedroad,heavy-weightedtrackedvehicletravelsonnon-pavedruggedroadwithrelativelyhighspeed.Furthermore,itissubjectedtoaverybigreboundingimpactatthetimeofthecannondischarge.Asaresult,oscillatoryimpactloadsexertedfromsuchanon-pavedroador/andthecannondischargemay,butfrequently,causethevehicledamage,therunningperformancedegra-dationandthelossofmaneuverability.ReferringtoFigs.Iand2representingtheschematicviewsofgeneralarmedtrackedvehicleandthesuspen-sionunit,eachwheelisassembledintothetracked•CorrespondingAuthor,E-mail:jrcho@hyowon.pusan.ac.krTEL:+82-51-510-2467;FAX:+82-51-514-7640SchoolofMechanicalEngineering,PusanNationalUniversity,Jangjeon-Dong,Kumjung-Ku,Pusan609-735,Korea.(ManuscriptReceivedAugust29,2003;RevisedNovember14,2003)StudyonDampingCharacteristicsofHydropneumaticSuspensionUnitofTrackedVehicle263fueltankl\\Fig.1Majorcomponentsofarmedtrackedvehicledifferencesinthekinematicmotionaswellasthestructuralcomposition.RegardingthedynamiccharacteristicsandthedesignofHSUthereadermayrefertotheTongMyungtechnicalreport(2002inKorean).Themainpurposeofthispaperistoinvesti-gatethedampingcharacteristicsofISU.Thedy-namicmotionofISUissplitintofour;jounce-loading,jounce-unloading,rebound-loadingandrebound-unloading,sothatfourdistinctdynamicmodesshouldbeconsideredforthedamper.Here,jounceandreboundaredistinguishedwhetherthewheelmovesupwardordownwardfromitsstationaryposition(SP),meanwhileloadingandunloadingarejudgedbycompressionorreleaseofdiscspringsinthedamper,whichwillbeclearinfollowingsections.Inordertoaccuratelycal-culatetheoilnowratethroughthedamperori-fice,wedeterminetheflowcoefficientsusingex-perimentalresults.Afterconstructingthemathe-maticaldampingmodels,weperformthepara-metricexperimentstoexaminetheeffectsoftheorificediameterandthewheelmotionfrequencyontheISUdampingperformance.2.StructureandKinematicsofISU2.1StructureandoperatingmechanismofISUReferringtoFig.2(a),anISUisattachedtothetrackedvehicleviaamountingplateandavehiclewheelisassembledintoISU.But,theassemblyofISUandwheelispermittedtorotateaboutthefixedarmaxis,sothatthevehiclewheelmovesupward(jounce)ordownward(rebound)(a)mainpistonmainCYiilder,llCCUTlUi.t\Pfessurepiston(b)Fig.2ISU:(a)assembledconfiguration;(b)sche-maticviewofitscomponentsfromthestationaryposition.Then,referringtoFig.2(b),themainpistonmovesrelativelyinthedirectioncompressingoilcontainedinthemaincylinderwhenISUisinthejouncemode,andviceversa.ThemaincylinderandthePA(pressureaccumulator)cylinderareopen-channeledalongthemanifoldsuchthatoilcannowfromtherightsideofthemainpistonuptotheleftsideofthePA(pressureaccumulator)piston.Differingfromthedamperfixedattherightendofthemaincylinder,thePApistonmoveshorizontallyac-cordingtooilandgaspressures.Ofcourse,theleftendofthePAcylinderisclosed.WhenISUisinthejouncemode,therelativerotationofISUhousingabouttherotatingcentermakesthemainpistoncompressoil.Then,oilisforcedtopassthroughthedamperandcompressthePApistonuntiltheforcebalancebetweengasandoilisreached.Ontheotherhand,inthereboundmodeISUrotatesdownbytheexpan-sionofgasinthePAcylinder.Inthismanner,264Jin-RaeCho,Hong-WooLee,Wan-SukYooandJin-KyuLee(il)f----Ih(ll)nulouteredgeInneredgediscsprings(2x3EA)gapFig.3Damperassemblytheexternaloscillatoryimpactcanbeabsorbed.ReferringtoFig.3,thedamperiscomposedofanorifice,openingholes,pre-compresseddiscsprings,adisc-typegap,anutandaninsert.Regardlessoftheoilpressuremagnitude,themainflowpath(I)fromtheorificetothedamperexitthroughinnerholesofdiscspringsandgapisopened.Ontheotherhand,oilcanflowalongthesecondarypath(II)onlywheneitherdiscspringsarecompressedtowardsthegaphingedatthespringouteredgeorexpandedfromthegaphingedaboutthespringinneredge.Initially,anassemblyofdiscspringsisforcedtotightlycon-tactwithboththeorificecoreplateandtheinsertsurface.However,sufficientlyhighoilpressurecompressesthediscspringstowardsthegapinthejouncemodeandexpandstheouteredgeofdiscspringsfromthegap,whileopeningthesecon-daryoilpath,sothatoilflowsalongbothpath(I)andpath(II).Here,wedefinetwonomencla-tures,crackingandchoking.Theformerindicatesthetimewhendiscspringsstarttocompressorexpand,whilethelatteriscalledwhendiscspringsarecompletelycompressedorexpanded.Furthermore,thedamperiscalledinloadingstatuswhendiscspringsmovefromcrackingtochokingandinunloadingstatuswhenthosere-leasefromchokingtocracking.2.2KinematicsofISUThewheellocationsatthestationaryposition(SP),thefulljounce(FJ)andthefullrebound(FR)arerepresentedinFig.4.Forthekinema-ticsanalysis,weusethelocalcoordinatesx-ycrankshaft(radiusLy2)h~-+-fulljounce-rr-(FJ)rolalingp.....-I--+stationarycenter(SP)x-Y;fixedglobalx-y;rotatinglocalFig.4CoordinatedefinitionandthewheellocationrotatingwiththeISUarmwithrespecttothefixedglobalcoordinatesX-YoHere,bothcoordi-natesystemsareoriginatedattherotatingcenter.Atthestationaryposition,thearmandthefixedcrankshaftarealignedwithpresetanglesaand/3,respectively,withrespecttothehorizontalline(i.e.theX-axis),Forthearminarbitrarywheellocation,wedefinetwoangles,81fromthestationaryarmpositionandfh.fromthefixedcrankshaft.Sincebothanglesshouldsatisfytherelation:fA+fh.=a+/3,wehavee2=-el8and2=-81•Figure5showsthegeometricrelationshipbe-tweenISUcomponentsatarbitrarywheelposi-tion,whereDmandDparethediametersofthemainandthePApistonswhiled«anddparetheirdisplacementsfromthestationaryposition,respectively.Meanwhile,thehorizontaldistanced,ofthemainpistonandthedeviationangle8aareimportantparameterstobecalculated.Toderivetheseparameters,weusethefollowinggeometricrelationforthepositionvectorrm:(1)where,r2=L2(cosfh.i+sinfh.j)andr3=L2(cos8ai+sin8aj).Then,wecanderivefollowingrelationsgivenbyd,=L2cosfh.+[(L2cosfh.)2_ik]112(2)withA=LHH2-H-2L2sinfh.,and8a=tan-1[Hd-L2sinfh.]1-L2cosfh.UsingEqs.(I)and(2),wecanalsoderivethemainpistonvelocityVm(=dl=-dm)givenbyStudyonDampingCharacteristicsofHydropneumaticSuspensionUnitofTrackedVehicle265ymaincyHnder.---:,..:.,_.\"'---',6,·\"olinePIlf8lleJtoISUarmIIISPPAcylinderFig.5AnglesandpositronvectorsatarbitrarywheelpositionFurthermore,(5)Wenoteherethatbothpistonvelocitiesareposi-tivewhenbothpistonsareinthejouncemode.Fig.6depictsforcesactingonISU,wheretheoilpressurepisthesumoftheoilpressuredropPdthroughthedamperandthegaspressureinthePAcylinder:P=Pd+p}[lgl(lg-dp)]1.4(6)Inwhich,19indicatesthePAcylinderlengthfilledwithgaswhichisassumedtobeanidealgas,atthestationaryposition.Thederivationoftheoilpressuredropwillbegiveninthenextsection.Whentheoilpressureisknown,forcesactingontheconnectingrodandthewheelcanbederived.First,theconnectingrodforceFeiscalculatedthroughFe=[Fptan\"fk+(Fp+Ff)2]lI2(7)withFp=;rR'f\"PandFf=sgn(Vm)J.l1FptanfkI.Then,themomentequilibriumabouttherotatingcentergivesusthenormalforceFwactingonthewheelgivenbyFw=FcLzsinefJz-fk)ILlcos(8l-a)(8)ReferringtoFig.4,weassumeinthecurrentstudythetimehistoryofthewheelverticaldis-placementthatbringstheISUmechanisminmotion:WurnurFRDrYD+2urFRvrDsin(2;r!t-r!»+urnrYD;rrD(9)Thefrequencyandthephaseangleinthewheelverticalmotionarederivedrespectivelybymainpistonp(Jounce)Fig.6Forcesactingonthemainpistonandthewheel!;r(We!wmax~weR),r!>=sin-1[W;FJwt!-+wtW;FR]R(10)And,thearmangleOrisrelatedtothewheelverticaldisplacementWD:2.3SpringforceReferringtoFig.7(a),thespringforceF.actingonasinglediscspringiscalculatedac-cordingto(Wahl,1963)whereEistheYoung'smodulusandlJisthePoisson'sratioofdiscspring.Ontheotherhand,Ks=[(I;-I)/I;]ZI;r[(I;+I)/(I;-l)-21m1;]intermsoftheratioI;definedbyI;=dold;Meanwhile,discspringsinthedampershowninFig.3areconnectedsuchthateachthreespringsareinparallelconnectionandtwosetscomposedofthreespringsareinserialconnection.Then,thetotalspringforceFeombandthedisplacementScombarecalculatedusing(13)wherenpandnsarespringnumbersinparallelandtheserialconnectionnumber,respectively.And,J.lcomb=1±(1-np)J.listhetotalfrictionbetweenspringswhenJ.lisdenotedbythefrictioncoefficientbetweenanytwodiscspringsinparallelconnection(+:loading,coefficient266Jin-RaeCho,Hong-WooLee.Wan-SukYooandJin-KyuLee(a)F.....c;JjJ:kj(Jounce)(b)Fig.7Discspring:(a)edgeforce;(b)equivalentforceanditsactingpositionunloading).ReferringtoFig.7(a),theequivalentcon-centrationforceFeqoftotaloilpressureactingondiscspringsisFeq=7CPd(d~-d'f)/4anditsactingpositionreqis(d~-d'f)/3(d~-d'f).Then,thetotalspringforceFcombcanbedeterminedusingthemomentequilibriumsuchthat(14)whereais(do-2req)inthejouncemodeand(2req-di)inthereboundmode.Ascanbein-ferablefromEqs.(13)and(14),theISUdamperexhibitsfourdistinctdampingcharacteristicsaccordingtofourdampermodes:jounce-loa-ding,jounce-unloading,rebound-loadingandrebound-unloading.Meanwhile,thecrackingpointofthedampervarieswiththespringpre-loadFpreactingexertedbynutinthedamper,sothatthedampingcharacteristiccanbecontrolledbyadjustingthespringpre-displacementSpre.Inthiscase,theactualspringdisplacementSdmbecomes(15)3.OilFlowRateandPressureDropThroughDamperInthissection,wederivethepressuredropthroughthedamperinthreespringmotions,beforecracking,fromcrackingtochoking,andafterchoking.WedenotetheparametersusedfortheflowandpressuredropanalysisinFig.8,where1JJ.andQoaretheoilpressureandtheoilflowrateinthemaincylinder.Here,Qoiscal-culatedfromthemainpistonvelocity(+:Vmsuchthatjounce,-:rebound)Qo=±7Cd~IVm1/4(16)Assumingincompressibleoilflow,pressuredrops(Gerhartetal.1992)throughindividualdamperpartsareLlpI2=1JJ.-P2=p(QI/CIAI)2/2(17a)Ll/J32.=/>3-P2=p(~/C~2)2/2(17b)LlP43=P4-/>3=P(Qa/CaAa)2/2(l7c)whereC,aretheflowratecoefficientstobedeter-mined,andAiareareasofindividualflowholes.Here,A3isvariabledependingontheactualspringdisplacementSdm.Then,thepressuredropthroughthedamperPdbecomes(18)Meanwhile,thecontinuityconditionrequires:QO=QI+Q4=QI+Qa=Q2,butQ3(=Q4)andQ4vanishwhencrackingdoesnotoccur,sothatthepressuredropbeforecrackingbecomesOntheotherhand,discspringsstarttocrackwhenFcombreachesthespringpre-loadFpre,thenthepressuredropatthecrackingpointiscal-culatedusingEq.(14):(20)And,theflowrateQgrainthemaincylindercanbederivedusingEq.(19)suchthatQgra=jp~ra/~2[(_1_)2+CAl(_I_)2JCA(21)2OilflowrategraduallyincreasesaftercrackinganddiscspringsreachthechokingpointwhenStudyonDampingCharacteristicsofHydropneumaticSuspensionUnitofTrackedVehicle267Fig.8ParametersfortheflowandpressureanalysisSdmbecomesh(refertoFig.7(a)).Aftercrac-king,itisconvenientforcalculatingQIandQatointroducetheratioTJbetweenQIandQs(=Q4)whichisderivedusingtherelationLl/JJ.a=LlPI4+LlP43:7i=IQIQs=CIAI[(C~1)2+(C~1)2J1/2(22)SinceAsvarieswiththeactualspringdisplace-ment,theratioTJisalsoinfunctionofSdm.So,weapproximateTJasaquadraticfunctionofSdmusingthreeTJvaluesatSdm=O,h/2andh.Next,wederivethepressuredropsatchokingandafterchoking.FromEq.(14),thepressuredropfromtheopeningholestodiscspringsbecomes--,..---...,..,..--4sa(do+di)Fg3i!.b(23)Usingtherelation(13),togetherwithQI=Qo-QaandQ2=QO,wehavethepressuredropthroughthedamperatchoking:PdChO=2-2[(Qgho_QfhOCIAI)2+(CzA2QghO)2J(24)Inthesamemanner,thepressuredropPdafterchokingisalsocalculatedusingEq.(15)bysubstitutingtheflowratesatchokingwithQoandQs.WeremindherethatQoandQsarecalculatedusingEqs.(16)and(22),respectively.4.NumericalResultsAccordingtothetheoreticalderivationdes-cribedsofarwecodedatestFortranprogramwhichiscomposedofthreepartsforanalyzingTable1Damperparametersfornumericalexperi-mentsParametersValuesSpringthicknesstandh2.35mm/1.8mmSpringdiametersdo,d,63.0mm/31.0mmPre-displacementSPre2.35mmFrictioncoefficientjJ.0.0012Connectionnumbernp,n.3/2SpringYoung'smodulusE204GPaSpringPoisson'sratioII0.3Diametersd2•d;28.0mm/17.0mmFlowratecoefficientsC2,C.1.0/1.0Oildensityp947.0kg/m3theISUkinematics,calculatingdisc-springforcesandcomputingoilflowratesandpressuredrops.ThewheelverticalmotionoperatingISUisgivenaccordingtoEqs.(9)and(10),whereweRweIandaresetrespectivelyby362.7mmand120.2mm.Thewheelmotionfrequencyt,aswellastheorificediameterdlandtwoflowratecoefficientsCIandCa,ischosenvariable;0.5,0.7and1.0Hzfortheparametricdampingan-alysis.OthersimulationparametersarerecordedinTable1.4.1FlowratecoefficientsTherearefourflowratecoefficientstobedeterminedinorderfortheflowanddynamicdampinganalyses;twoforthemainflowpathandtheothertwoforthesecondaryflowpath.ReferringtoEq.(16),thepressuredropisinreverseproportionaltotheproduct(CA)2sothatthedampingcharacteristicislessinsensitivetotheflowpathoflargersectionarea.Mean-while,bothfourcoefficientsarenotindependentvariables,butdependentsuchthatCIandC2areinthemainpathwhileCaandC4areinthesecondarypath,respectively.Byvirtueofthesefeatures,weletC1andCaareunknowntobedeterminedusingexperimentalresultswhileset-tingC2andC4byunity.Sincethesecondarypathactivatesaftercrac-king,ClandCacanbeseparatelydeterminedsuchthatCIbeforecrackingandCaaftercrac-king.Fig.9(a)showsthecomparisonofthepres-suredropwiththeexperimentalresultsconducted268Jin-RaeCho,Hong-WooLee,Wan-SukYooandJin-KyuLeem.,.....------------------,o10020ooElcpII'ln1llft1.Experlnllll'·U0+-\"\"\"\"'o..........,..-...,..-T\"'\"\"-..--r--.,...~~25Sl75........--110)flowrateinmaincylinderOoCelmin)(a)l00,----------\"\"?===r-....,oQEx!lerimt11l1Elqlerlment2«1+---...-----,..----..--.....,..---.----15055EOfl5flowrateInmaincyl1nderOoCelmln)(b)Fig.9FlowratecoefficientC1:(a)wholeperiod;(b)beforecracking(C3=0.5)byTongMyung.EventhoughC3istentativelysetby0.5itdoesnotaffectthepressuredropbeforecracking.FromthedetailedcomparisonbeforecrackinginFig.9(b),wefoundthatC1of0.63isappropriateforthecurrentISU.WithCdeterminedwecomparethepressuredropaftercrackingwiththeexperimentalresults,whilevaryingtheflowratecoefficientC3•Asrepre-sentedinFig.9(b),thechoiceofC3=0.35showsaquiteconsistentcurvewiththeexperimentalone.Itisworthtonotethatthevalue0.06and0.35arenotuniquesolutionsbutratherthosevarywiththepresetvaluesofC2andC4•WecomputethepressuredropPDthroughthedamperwiththeflowratecoefficientsdeterminedm.,.....---------,10020nElqIeJ1InRnt1O~ZOf-..::=;---.-.--....,..-...,....--,r-----r--...--jo2550~10)~flowrateInmaincYlinderOo(e/min)(a)110.,.----------------,-0-Experiment1-0-Expennent290100110.1201:30flowratainmaincylinderaoU!min)(b)Fig.10FlowratecoefficientC3:(a)wholeperiod;(b)aftercracking(Cl=0.63)200.,....-----------------...,orificediameterd,=4mmjounce-loading~..a100\".~=-Jounce-\\c.~\"eunloading0e:J(J)rebound-unloading(J)l5.·100lrebound-loading\\-1600-1200-800-4000400600flowrateinmaincylinderaoCe/rntn)Fig.11Pressuredropversusflowrate(Cl=0.63,C3=0.35)StudyonDampingCharacteristicsofHydropneumaticSuspensionUnitofTrackedVehicle269andpresentitsvariationinFig.IItotheoilflowrateQointhemaincylinder.WheretherighthandsidecenteringaboutQoisforthejouncemodewhilethelefthandsideisforthereboundmode.Wefirstobservethedifferenceinthecurvebetweenloadingandunloadingintheflowrateregionstartingfromcrackingtochoking,owingtothedifferenceinthehingepointofdiscsprings.Second,weclearlyseethefourdistinctfeaturesofdynamicdampingofISUforfourdifferentdampermodes,jounce-loading,jounce-unloa-ding,rebound-loadingandrebound-unloading.4.2DampingcharacteristicsWenextperformtheparametricanalysisforinvestigatingtheISUdampingperformancetothewheelmotionfrequencyandtheorificediameter.Here,thewheelmotionfrequencyisinpropor-tionalrelationwiththetrackedvehiclevelocitythroughruggedroad.Figure12(a)representsorbitsofthewheelreactionforceFw,duringaperiodofwheelverti-calmotion,forthreedifferentfrequenciesf=0.5,0.7and1.0Hz,whentheorificediameterd,issetby4.0mm.ThereactionforceFwiscalculatedusingEq.(6)andtheundampedspringforceisdueonlytothegaspressureinthePAcylinder.WeseethesignificanteffectofthewheelmotionfrequencyontheISUdampinginbothfulljounce(FJ)andfullrebound(FR)regionssuchthatthedampingforceincreasesinproportionaltothefrequency.Here,thedampingforceincreasesastheareainsidetheclosedcurvebecomeslarger.Thisisbecauseofthedifferenceincrackingoc-currenceandremovalpointsaccordingtothedifferenceinoilflowratemagnitudecausedbywheelmotionfrequency.FourvertexpointsineachclosedcurveinFig.12(a)indicatethecrackingoccurrenceorcrackingremovalpoints.Figure12(b)showsthedependenceofthewheelreactionforceontheorificediameterforafixedwheelmotionfrequency(i.e.velocity).Wefirstobservethatthedampingforcedecreasesinproportionaltotheorificediameter.Furthermore,theredoesnotoccurcrackingeitherinjounceorreboundmodewhentheorificediameterreaches5mm.Theflowratecausingcrackingincreasesas140.,.....------------------,orificediameterd,=4mm120-0-f=0.5Hz-A-f=0.7Hz~zu!100-0-f=1.0HzQ)--springforce~e800g§60al~40Cii~~20orebound-200-1000100200300400wheelverticaldisplacementWD(mm)(a)frequencyf-O.5Hz120z-0-orificediameterd,3mm-i1-orificediameterd,=4mm=~loo\"'\"-0-orificediameterd,=5mm
--springforce.2!:!80~g60~40CiiIII~20o-200·1000100200300400wheelverticaldisplacementwD(mm)(b)Fig.12Dampingcharacteristics:(a)tothewheelmotionfrequency;(b)totheorificediame-tertheorificediameterbecomeslarger,asrepresentedinFig.13(a),sothatthewheelverticalvelocityshouldincreaseforproducingthesamepressuredropthroughthedamper.Inotherwords,foragivenexternalimpactthereactingwheelverticalvelocityincreasesinproportionaltotheorificediameter.Asaresult,onecancontrolthereactingwheelverticalvelocitybyadjustingtheorificeFig.13(b)representstheparametricvariationthedampingenergyEDabsorbedbytheofwheelverticalmotion,whereEDisdefinedbytheinsideareaoftheofFwsuchthatdiameter.ofdamper,duringaperiodhysterisiscurve270Jin-RaeCho,Hong-WooLee,Wan-SukYooandJin-KyuLeec:110-a-Jounce-loading~-0-lounce-unloadlng-4-rebound-loadingJ...-V-rebound-unloading~50~co'\"o70(jj~50~;;::o~303.03.54.04.55.0orificediameterd,(mm)(a)20ECZ18uJQ~16<»eGlC.e014~E12---0-f;;O.5Hzf;;0.7Hz-A-f=1.0HZ10-+--,...._--r-~-,....---r-~-,....-l3.03.54.04.55.0orificediameterd.Irnrn)(b)Fig.13(a)Flowrateatcrackingtotheorificediameter;(b)dampingenergyduringonecycle(25)Togetherwiththeorificediameterincreasethedampingenergymonotonicallydecreases,andthedecreaseratebecomesconsiderableasthewheelmotionfrequencygoeslower.Fromthisparame-tricfeature,wecaninferthefollowings.Whentheorificediameteristoosmall,thedamperstronglyresiststothesmallexternalimpactbeforethespringforcebygasinthePAcylinderisnotfullydeveloped.Onthecontrary,whentheorificedi-ameteristoolargetheexternalimpactdirectlytransferstothePApistonowingtotheinsuffi-cientimpactabsorptionbythedamper,andwhichmakesthewheelverticaldisplacementbesignificantlylarge.Thus,thecrackingpressureshouldbesimultaneouslycontrolledbyadjustingthepre-displacementSpreofdiscspringswhentheorificediameterischanged,inordertopreventthesecriticaldefects.5.ConclusionThedynamicmodelingandnumericalinvesti-gationfortheISUdampingcharacteristicshasbeenaddressed.Byclassifyingthedamperdy-namicmodeintofourdistinctones,theoilflowrateandthepressuredropwerederivedforindividualmodes.Theflowratecoefficientsofthedamperweredeterminedwiththehelpofindependentexperiments.Fromtheparametricnumericalresults,wefoundthatthedampingperformanceandthegasspringforcearestronglyinfluencedbythewheelmotionfrequencyandtheorificediameter,whilebothareinreciprocalrelationtotwoparameters.Thelargerdampingforceisproducedforeitherhigherfrequencyorsmallerorificediameter.Onthecontrary,thegasspringforcebecomeslargerforeitherlowerfre-quencyorwiderorificediameter.Incidentallywefoundthatthedamperperformancewiththesuitablewheelverticaldisplacementcanbeachi-evedbyadjustingboththeorificediameterandthepre-displacementofdiscsprings.AcknowledgmentThefinancialsupportsforthisworkbyTongMyungHeavyIndustriesCo.,Ltd.andtheKoreaScience&EngineeringFoundation(GrantNo.:ROI-2001-00383)aregratefullyacknowledged.Aswell,twoauthors(WSYandHWL)wouldliketothanktheMinistryofScienceandTech-nologyofKoreaforthefinancialsupportbyagrant(MI-0203-00-0017-02JOOOO-00910)undertheNRL(NationalResearchLaboratory).ReferencesBlack,W.Z.andHartley,J.G.,1996,Ther-modynamics,HarperCollins,NewYork.Gerhart,P.M.,Gross,R.J.andHochstein,J.I.,StudyonDampingCharacteristicsofHydropneumaticSuspensionUnitofTrackedVehicle2711992,FundamentalsofFluidMechanics,Addi-son-WesleyPublicationCompany.Kim,H.O.,Lee,H.W.,Cho,J.R.,Lee,J.K.andChang,M.S.,2002,\"StudyontheKinematicDesignoftheHydropneumaticSuspensionUnit,\"Proc.KSME2002FallAnnualMeeting(PusanBranch),pp.87-92.Lee,H.W.,Cho,J.R.,Lee,J.K.andLee,K.Y.,2003,\"StudyonDynamicDesignofRecipro-catingHydropneumaticSuspensionUnit,\"Proc.KSME2003SpringAnnualMeeting(PusanBranch),pp.83-88.Lee,H.W.,Kim,H.0.,Cho,J.R.,Lee,J.K.andChang,M.S.,2002,\"CharacteristicAnalysisofSpringandDampingoftheHydropneumaticSuspensionUnit,\"Proc.KSME2002FallAnnualMeeting(PusanBranch),pp.93-98.Press,W.H.,Teukolsky,S.A.,Vetterling,W.T.andFlannery,B.P.,1992,NumericalRecipesinFortran:TheArtofScientificComputing,CambridgeUniversityPress.TongMyungHeavyIndustriesCo.,Ltd.,R&DCenter,1996,TechnicalReport:AnalysisofDynamicBehaviorandHeatTransferofHSU.TongMyungHeavyIndustriesCo.,Ltd.,R&DCenter,2000,TechnicalReport:TheDesignofERSU.TongMyungHeavyIndustriesCo.,Ltd.,R&DCenter,2oo2,TechnicalReport:TheDesignandComputationalAnalysisofHSUBack-UpModelofNIFVISU.Wahl,A.M.,1963,MechanicalSprings,Mc-Graw-Hill.