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Bebek,BearingloadBendingstressbeamisrate,parameterwiththemostimportantinfluenceondesignofthecrankshaft.Resultsofbearingloadsandwebbendingstressesaretabulated.mustoverallsystemsonparametersofthecrankshaftsystem.Studiesoncrankshaftofinternalcombustionenginesmainlyfocusonvibrationandstressanalyses1–9.Althoughstressanalysesofcrankshaftsareavailableinliterature,therearefewstudiesontheeffectofcounterweightconfigurationonmainbearingloadsandcrankshaftstresses.Sharpeetal.10studiedbalancingofthecrankshaftofaV8engineusingarigidcrankshaftmodeltionsarecarriedoutatenginespeedrangeof1000–2000rpm.Bendingstressesatthecentresofeachwebarealsocalculated.2.EnginespecificationsThespecificationsofinlinesixcylinderdieselenginearegiveninTable1.The9.0Lenginecrankshafthaseightcounterweightsatcrankwebs1,2,5,6,7,8,11and12.3DsolidmodelofthecrankshaftisobtainedusingPro/EngineerandisshowninFig.1.SchematicrepresentationofthecrankshaftisgiveninFig.2.StaticCorrespondingauthor.Tel.902123597534fax902122872456.AdvancesinEngineeringSoftware40200995–104ContentslistsavailableEmailaddressyasin.yilmazboun.edu.trY.Yilmaz.beingthemainpartresponsibleforpowerproduction.Crankshaftsystemmainlyconsistsofpiston,pistonpin,connectingrod,crankshaft,torsionalvibrationTVdamperandflywheel.Counterweightsareplacedontheoppositesideofeachcranktobalancerotatinginertiaforces.Ingeneral,counterweightsaredesignedforbalancingratesbetween50and100.Foracceptablemaximumandaveragemainbearingloads,massofcounterweightsandtheirpositionsareimportant.Maximumandaveragemainbearingloadsofanenginedependoncylinderpressure,counterweightmass,enginespeedandothergeometricstudyoneffectofcounterweightconfigurationonmainbearingloadsandcrankshaftstressesisstillneeded.Inthisstudy,counterweightpositionsandmassesofaninlinesixcylinderdieselenginecrankshaftsystemarestudied.Maximumandaveragemainbearingforcesandcrankshaftbendingstressesarecalculatedfor12counterweightconfigurationswithazerodegreecounterweightangle,andforeightcounterweightconfigurationswith30C176counterweightanglefor0,50and100counterweightbalancingrates.AnalysesarecarriedoutusingMultibodySystemSimulationProgram,ADAMS/Engine.Simula1.IntroductionNewinternalcombustionenginespower,goodfueleconomy,smallengineharmlessaspossibletotheenvironment.eachcomponentoftheengineonitsbeinvestigatedindetail.Crankshafttionengineshaveimportantinfluence09659978/seefrontmatterC2112008ElsevierLtd.Alldoi10.1016/j.advengsoft.2008.03.009C2112008ElsevierLtd.Allrightsreserved.havehighenginesize,andshouldbeasTherefore,theeffectofperformanceshouldofinternalcombusengineperformanceandoptimizedcounterweightstominimizemainbearingloads.StanleyandTaraza11obtainedmaximumandaveragemainbearingloadsoffourandsixcylindersymmetricinlineenginesusingarigidcrankshaftmodelandestimatedidealcounterweightmassthatresultedinacceptablemaximumbearingload.Rigidcrankshaftmodelsthatareusedincounterweightanalysesdonotconsidertheeffectofcrankshaftflexibilityonmainbearingloadsandcanleadtoconsiderableerrors.Therefore,anextensiveCrankshaftmodelsBalancingrateBothconfigurationsshowthesametrend.TheloadfromgaspressureratherthaninertiaforcesistheAninvestigationoftheeffectofcounterweightloadandcrankshaftbendingstressYasinYilmaz,GunayAnlasDepartmentofMechanicalEngineering,FacultyofEngineering,BogaziciUniversity,34342articleinfoArticlehistoryReceived11February2008Receivedinrevisedform17March2008Accepted24March2008Availableonline6May2008KeywordsCounterweightconfigurationabstractInthisstudy,effectsofcounterweightstressofaninlinesixcylinderADAMS.Intheanalysis,rigid,rigid,beamand3Dsolidmodelsanalyses.Twelvecounterweightterweightconfigurationswithingrates,areconsidered.ItwithincreasingbalancingAdvancesinEngineeringjournalhomepagewww.elsevier.com/lorightsreserved.configurationonmainbearingIstanbul,TurkeymassandpositiononmainbearingloadandcrankshaftbendingdieselengineisinvestigatedusingMultibodySystemSimulationProgram,and3Dsolidcrankshaftmodelsareused.Mainbearingloadresultsofarecomparedandbeammodelisusedincounterweightconfigurationconfigurationswithazerodegreecounterweightangleandeightcoun30C176counterweightangle,eachfor0,50and100counterweightbalancfoundthatmaximummainbearingloadandwebbendingstressincreaseandaveragemainbearingloaddecreaseswithincreasingbalancingrate.atScienceDirectSoftwarecate/advengsoftunbalanceofeachcrankthrowwithandw/ocounterweightsisdeterminedusingPro/EngineerandisgiveninTable2.ThebalancingsystemdataforthecranktrainaregiveninTable3.3.ModelingofcrankshaftsystemUsingADAMS/Engine,acrankshaftcanbemodeledinfourdifferentwaysrigidcrankshaft,torsional–flexiblecrankshaft,beamcrankshaftand3Dsolidcrankshaft.Rigidcrankshaftmodelismainlyusedtoobtainfreeforcesandtorques,andforbalancingpurposes.Torsional–flexiblecrankshaftmodelisusedtoinvestigatetorsionalvibrationswhereeachthrowismodeledasonerigidpart,andspringsareusedbetweeneachthrowtorepresenttorsionalstiffness.Beamcrankshaftmodelisusedtorepresentthetorsionalandbendingstiffnessofthecrankshaft.Usingbeammodelbendingstressesatthewebscanbecalculated12.Table1EnginespecificationsUnit9.0LengineBorediametermm115Strokemm144Axialcylinderdistancemm134PeakfiringpressureMPa19RatedpoweratspeedkW/rpm295/2200Max.torqueatspeedNm/rpm1600/1200–1700Mainjournal/pindiametermm95/81Firingorder–153624Flywheelmasskg47.84Flywheelmomentofinertiakgmm21.57E9MassofTVdamperringkg4.94MassofTVdamperhousingkg6.86Momentofinertiaoftheringkgmm21.27E5Momentofinertiaofthehousingkgmm20.56E5MainBearing1MainBearing2MainBearing3MainBearing4MainBearing5MainBearing6MainBearing7CounterweightsFig.1.3Dsolidmodelofthecrankshaft.C3,C4,C5,C6C1,C2,C7,C81,63,42,5C1C2C3C4C5C612Fig.2.EightcounterweightarrangementTable2PropertiesofthecrankthrowsThrow1Throw2Masskg12.509.25CGpositionfromcrankrotationaxismm12.42331.435Staticunbalancekgmm155.265290.76796Y.Yilmaz,G.Anlas/AdvancesinEngineeringSoftware40200995–104C7C83456ofthe9.0Lenginecrankshaft.Throw3Throw4Throw5Throw612.5012.509.2812.5511.96711.96631.02711.702149.734149.734287.871146.856Elastic3Dsolidmodelofthecrankshaftcanbeobtainedusinganadditionalfiniteelementprogram.Theprocedureislengthyandtimeconsumingandusuallyoneendsupwithdegreesoffreedominorderofmillions.Tosimplifythefiniteelementmodel,modalsuperpositiontechniqueisused.Theelasticdeformationofthestructureisapproximatedbylinearcombinationofsuitablemodeswhichcanbeshownasfollowsu¼Uqð1ÞwhereqisthevectorofmodalcoordinatesandUistheshapefunctionmatrix.Table3CrankshaftsystemdataCrankradiusmm72Connectingrodlengthmm239Massofcompletepistonkg3.42Connectingrodreciprocatingmasskg0.92Reciprocatingmasstotalpercylinderkg4.32Connectingrodrotatingmasskg2.01Y.Yilmaz,G.Anlas/AdvancesinEngineeringAnelasticbodycontainstwotypesofnodes,interfacenodeswhereforcesandboundaryconditionsinteractwiththestructureduringmultibodysystemsimulationMSS,andinteriornodes.InMSSthepositionoftheelasticbodyiscomputedbysuperposingitsrigidbodymotionandelasticdeformation.InADAMS,thisisperformedusingComponentModeSynthesistechniquebasedonCraig–Bamptonmethod13,14.Thecomponentmodescontainstaticanddynamicbehaviorofthestructure.ThesemodesareconstraintmodeswhicharestaticdeformationshapesobtainedbygivingaunitdisplacementtoeachinterfacedegreeoffreedomDOFwhilekeepingallotherinterfaceDOFsfixed,andfixedboundarynormalmodeswhicharethesolutionofeigenvalueproblembyfixingtheentireinterfaceDOFs.ThemodaltransformationbetweenthephysicalDOFandtheCraig–Bamptonmodesandtheirmodalcoordinatesisdescribedby15u¼uBuIC26C27¼I0UCUNC20C21qCqNC26C27ð2ÞwhereuBanduIarecolumnvectorsandrepresentboundaryDOFandinteriorDOF,respectively.I,0areidentityandzeromatrices,respectively.UCisthematrixofphysicaldisplacementsoftheinteriorDOFintheconstraintmodes.UNisthematrixofphysicaldisFig.3.Modelofthecrankshaftsystem.placementsoftheinteriorDOFinthenormalmodes.qCisthecolumnvectorofmodalcoordinatesoftheconstraintmodes.qNisthecolumnvectorofmodalcoordinatesofthefixedboundarynormalmodes.Toobtaindecoupledsetofmodes,constrainedmodesandnormalmodesareorthogonalized.Elastic3Dsolidcrankshaftmodelofthe9.0LengineisobtainedinMSC.Nastranusingmodalsuperpositiontechnique.First,3DsolidmodelofthecrankshaftthatisshowninFig.1isexportedtoMSC.Nastranandfiniteelementmodelofthecrankshaft,whichischaracterizedbyapproximately300,000tennodetetrahedralelementsand500,000nodesisobtained.Themodalmodelofthecrankshaftisdevelopedwith32boundaryDOFsassociatedwith16interfacenodes.ConstrainedmodesobtainedfromstaticanalysiscorrespondtotheseDOFs.Flexiblecrankshaftmodelisobtainedthroughmodalsynthesisconsideringthefirst40fixedboundarynormalmodes.Thereforeflexiblecrankshaftmodelischaracterizedbyatotalof72DOFs.ThismodelisexportedtoADAMS/EngineandcrankshaftsystemmodelthatisshowninFig.3isobtained.3DfiniteelementmodelisrunwithADAMS.4.ForcesactingoncrankshaftsystemandbalancingForcesinaninternalcombustionenginemaybedividedintoinertiaforcesandpressureforces.Inertiaforcesarefurtherdividedintotwomaincategoriesrotatinginertiaforcesandreciprocatinginertiaforces.TherotatinginertiaforceforeachcylindercanbewrittenasshownbelowFiRj¼mRC1rRC1x2C1ðC0sinhjjþcoshjkÞð3ÞwheremRistherotatingmassthatconsistsofthemassofcrankpin,crankwebsandmassofrotatingportionoftheconnectingrodrRisthedistancefromthecrankshaftcentreofrotationtothecentreofgravityoftherotatingmass,xisangularvelocityofthecrankshaft,andhjistheangularpositionofeachcrankthrowwithrespecttoTopDeadCentreTDC.Iftherearetwocounterweightspercrankthrow,eachcounterweightforceisgivenby11FCWij¼C0mCWijC1rCWijC1x2C1C0sinðhjþcijÞjþcosðhjþcijÞkhii¼12j¼12...6ð4Þwhereci,jistheoffsetangleofcounterweightmassfrom180C176oppositeofcrankthrowj.Therearetwocounterweightsperthrow.idenotesthecounterweightnumber.ThecounterweightsizethatisrequiredtoaccomplishanassessedbalancingrateisUCW¼KC1ðUCrankthrowþmcrrC1rÞC1cosc2ð5ÞwhereUCWisthestaticunbalanceofeachcounterweight,UCrank_throwisthestaticunbalanceofeachcrankthrow,mcrristhemassofconnectingrodrotatingportion,risthecrankradiusandKisthebalancingrateoftheinternalcoupleduetorotatingforces.FromthisformulafollowsthebalancingrateforagivencrankshaftandagivencounterweightsizeK¼2C1UCWðUCrankthrowþmcrrC1rÞC1coscð6ÞForastandardinlinesixcylinderenginecrankshaftwiththreepairsofcrankthrowsdisposedatanglesof120C176thatarearrangedsymmetricaltothecrankshaftcentre,rotatingforces,andfirstandsecondorderreciprocatingforcesarenaturallybalanced.ThiscanbeexplainedbythefirstandsecondordervectorstarsshowninFig.4.ThesixcylindercrankshaftgeneratesrotatingandfirstSoftware40200995–10497andsecondorderreciprocatingcouplesineachcrankshafthalfthatbalanceeachotherbutwhichresultininternalbendingmoment.Athighspeeds,thetwoequallydirectedcrankthrows,3and4yieldahighrotatingloadoncentremainbearing.Therotatinginertiaforceofeachcylinderisusuallyoffsetatleastpartiallybycounterweightsplacedontheoppositesideofeachcrank.Ingeneral,thecounterweightsaredesignedforbalancingratesbetween50and100oftheinternalcouple.Gasforcesincylindersareactingonpistonhead,cylinderheadandonsidewallsofthecylinder.TheseforcesareequaltoFpj¼C0pD24C1½PcyljðhÞC0PccjðhÞC138kj¼12...6ð7Þ1,62,53,43,41,62,5Fig.4.Firstandsecondordervectorstars.020406080100120140160180200090180270360450540630720CrankAngledegreePressurebar1000rpm1200rpm1350rpm1675rpm2000rpmFig.5.Gaspressurevaluesatdifferentenginespeedsforthe9.0Lengine.Bearing102550751001251500120240360480600720CrankAngledegForcekNRigidBeam3DsolidFig.6.Forcesactingonmainbearing1forrigid,beamand3Dsolidcrankshaftmodelsat1000rpmenginespeed.Bearing202550751001251501750120240360480600720CrankAngledegForcekNRigidBeam3DsolidFig.7.Forcesactingonmainbearing2forrigid,beamand3Dsolidcrankshaftmodelsat1000rpmenginespeed.Bearing302550751001251500120240360480600720CrankAngledegForcekNRigidBeam3DsolidFig.8.Forcesactingonmainbearing3forrigid,beamand3Dsolidcrankshaftmodelsat1000rpmenginespeed.Bearing402550751001251500120240360480600720CrankAngledegForcekNRigidBeam3DsolidFig.9.Forcesactingonmainbearing4forrigid,beamand3Dsolidcrankshaftmodelsat1000rpmenginespeed.Bearing5125150RigidBam3Dsolid98Y.Yilmaz,G.Anlas/AdvancesinEngineeringSoftware40200995–10402550751000120240360480600720CrankAngledegForcekNFig.10.Forcesactingonmainbearing5forrigid,beamand3Dsolidcrankshaftmodelsat1000rpmenginespeed.
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