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附录AMulti-DomainSimulation:MechanicsandHydraulicsofanExcavatorHirokazuAraya,MasayukiKagoShimaMechanicalEngineeringResearchLaboratoryKobesteel,Ltd,Nishi-KvKobeHyogo6512271,JapanAbstractItisdemonstratedhowtomodelandsimulateanexcavatorwithModelicaandDymolabyusingModelicalibrariesformulti-bodyandforhydraulicsystems.Thehydraulicsystemiscontrolledbya“loadsensing”controller.Usually,modelscontaining3-dimensionalmechanicalandhydrauliccomponentsaredifficulttosimulate.AthandoftheexcavatoritisshownthatModelicaiswellsuitedforsuchkindsofsystemsimulations.1.IntroductionThedesignofanewproductrequiresanumberofdecisionsintheinitialphasethatseverelyaffectthesuccessofthefinishedmachine.Today,digitalsimulationisthereforeusedinearlystagestolookatdifferentconcepts.Theviewofthispaperisthatanewexcavatoristobedesignedandseveralcandidatesofhydrauliccontrolsystemshavetobeevaluated.Systemsthatconsistof3-dimensionalmechanicalandofhydrauliccomponents–likeexcavators–aredifficulttosimulate.Usually,twodifferentsimulationenvironmentshavetobecoupled.Thisisofteninconvenient,leadstounnecessarynumericalproblemsandhasfragileinterfaces.InthisarticleitisdemonstratedathandofthemodelofanexcavatorthatModelicaiswellsuitedforthesetypesofsystems.The3-dimensionalcomponentsoftheexcavatoraremodeledwiththenew,freeModelicaMultiBodylibrary.Thisallowsespeciallytouseananalyticsolutionofthekinematicloopatthebucketandtotakethemassesofthehydrauliccylinders,i.e.,the“forceelements”,directlyintoaccount.Thehydraulicpartismodeledinadetailedway,utilizingpump,valvesandcylindersfromHyLib,ahydraulicslibraryforModelica.Forthecontrolpartageneric“loadsensing”controlsystemisused,modeledbyasetofsimpleequations.Thisapproachgivestherequiredresultsandkeepsthetimeneededforanalyzingtheproblemonareasonablelevel.2.ModelingChoicesThereareseveralapproacheswhensimulatingasystem.Dependingonthetaskitmaybenecessarytobuildaveryprecisemodel,containingeverydetailofthesystemandneedingalotofinformation,e.g.,modelparameters.Thiskindofmodelsisexpensivetobuildupbutontheotherhandveryusefulifparametersofawelldefinedsystemhavetobemodified.Atypicalexampleistheoptimizationofparametersofacounterbalancevalveinanexcavator(Kraft1996).Theotherkindofmodelisneededforafirststudyofasystem.Inthiscasesomepropertiesofthepump,cylindersandloadsarespecified.Requiredisinformationabouttheperformanceofthatsystem,e.g.,thespeedofthepistonsorthenecessaryinputpoweratthepumpshaft,tomakeadecisionwhetherthisdesigncanbeusedinprincipleforthetaskathand.Thismodelhasthereforetobe“cheap”,i.e.,itmustbepossibletobuilditinashorttimewithoutdetailedknowledgeofparticularcomponents.Theauthorsintendedtobuildupamodelofthesecondtype,runitandhavefirstresultswithaminimumamountoftimespent.ToachievethisgoalthemodelinglanguageModelica(Modelica2002),theModelicasimulationenvironmentDymola(Dymola2003),thenewModelicalibraryfor3-dimensionalmechanicalsystems“MultiBody”(Otteretal.2003)andtheModelicalibraryofhydrauliccomponentsHyLib(Beater2000)wasused.Themodelconsistsofthe3-dimensionalmechanicalconstructionoftheexcavator,adetaileddescriptionofthepowerhydraulicsandageneric“loadsensing”controller.ThismodelwillbeavailableasademointhenextversionofHyLib.3.ConstructionofExcavatorsInaschematicdrawingofatypicalexcavatorunderconsiderationisshown.Itconsistsofachaintrackandthehydraulicpropeldrivewhichisusedtomanoeuvrethemachinebutusuallynotduringaworkcycle.Ontopofthatisacarriagewheretheoperatorissitting.Itcanrotatearoundaverticalaxiswithrespecttothechaintrack.ItalsoholdstheDieselengine,thehydraulicpumpsandcontrolsystem.Furthermore,thereisaboom,anarmandattheendabucketwhichisattachedviaaplanarkinematiclooptothearm.Boom,armandbucketcanberotatedbytheappropriatecylinders.Figureshowsthattherequiredpressuresinthecylindersdependontheposition.Forthe“stretched”situationthepressureintheboomcylinderis60%higherthanintheretractedposition.Notonlythepositionbutalsothemovementshavetobetakenintoaccount.Figure3showsasituationwherethearmhangsdown.Ifthecarriagedoesnotrotatethereisapullingforcerequiredinthecylinder.Whenrotating–excavatorscantypicallyrotatewithupto12revolutionsperminute–theforceinthearmcylinderchangesitssignandnowapushingforceisneeded.Thischangeisverysignificantbecausenowthe“active”chamberofthecylinderswitchesandthatmustbetakenintoaccountbythecontrolsystem.Bothfiguresdemonstratethatasimulationmodelmusttakeintoaccountthecouplingsbetweenthefourdegreesoffreedomthisexcavatorhas.Asimplermodelthatusesaconstantloadforeachcylinderandtheswiveldriveleadstoerroneousresults4.LoadSensingSystemExcavatorshavetypicallyoneDieselengine,twohydraulicmotorsandthreecylinders.Thereexistdifferenthydrauliccircuitstoprovidetheconsumerswiththerequiredhydraulicenergy.AtypicaldesignisaLoadSensingcircuitthatisenergyefficientanduserfriendly.Theideaistohaveaflowratecontrolsystemforthepumpsuchthatitdeliversexactlytheneededflowrate.Asasensorthepressuredropacrossanorificeisused.Thereferencevalueistheresistanceoftheorifice.Aschematicdrawingisshowninfigure4,agoodintroductiontothattopicisgivenin(anon.1992).Thepumpcontrolvalvemaintainsapressureatthepumpportthatistypically15barhigherthanthepressureintheLSline(=LoadSensingline).Ifthedirectionalvalveisclosedthepumphasthereforeastand-bypressureof15bar.Ifitisopenthepumpdeliversaflowratethatleadstoapressuredropof15baracrossthatdirectionalvalve.Note:Thedirectionalvalveisnotusedtothrottlethepumpflowbutasaflowmeter(pressuredropthatisfedback)andasareference(resistance).Thecircuitisenergyefficientbecausethepumpdeliversonlytheneededflowrate,thethrottlinglossesaresmallcomparedtoothercircuits.Ifmorethanonecylinderisusedthecircuitbecomesmorecomplicated,seefigure5.E.g.iftheboomrequiresapressureof100barandthebucketapressureof300barthepumppressuremustbeabove300barwhichwouldcauseanunwantedmovementoftheboomcylinder.Thereforecompensatorsareusedthatthrottletheoilflowandthusachieveapressuredropof15baracrosstheparticulardirectionalvalve.Thesecompensatorscanbeinstalledupstreamordownstreamofthedirectionalvalves.Anadditionalvalvereducesthenominalpressuredifferentialifthemaximumpumpflowrateorthemaximumpressureisreached(seee.g.Nikolaus1994).5.ModelofMechanicalPartInFigure6,aModelicaschematicofthemechanicalpartisshown.Thechaintrackisnotmodeled,i.e.,itisassumedthatthechaintrackdoesnotmove.Components“rev1”,...,“rev4”arethe4revolutejointstomovethepartsrelativetoeachother.Theiconswiththelongblacklineare“virtual”rodsthatareusedtomarkspecificpointsonapart,especiallythemountingpointsofthehydrauliccylinders.Thelightbluespheres(b2,b3,b4,b5)arebodiesthathavemassandaninertiatensorandareusedtomodelthecorrespondingpropertiesoftheexcavatorparts.Thethreecomponents“cyl1f”,“cyl2f”,and“cyl3f”arelineforcecomponentsthatdescribeaforceinteractionalongalinebetweentwoattachmentpoints.Thesmallgreensquaresatthesecomponentsrepresent1-dimensionaltranslationalconnectorsfromtheModelica.Mechanics.Translationallibrary.Theyareusedtodefinethe1-dimensionalforcelawactingbetweenthetwoattachmentpoints.Here,thehydrauliccylindersdescribedinthenextsectionaredirectlyattached.Thesmalltwospheresintheiconsofthe“cyl1f,cyl2f,cyl3f”componentsindicatethatoptionallytwopointmassesaretaken
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