Bebek,BearingloadBendingstressbeamisrate,parameterwiththemostimportantinfluenceondesignofthecrankshaft.Resultsofbearingloadsandwebbendingstressesaretabulated.mustoverallsystemsonparametersofthecrankshaftsystem.Studiesoncrankshaftofinternalcombustionenginesmainlyfo-cusonvibrationandstressanalyses19.Althoughstressanaly-sesofcrankshaftsareavailableinliterature,therearefewstudiesontheeffectofcounterweightconfigurationonmainbear-ingloadsandcrankshaftstresses.Sharpeetal.10studiedbalanc-ingofthecrankshaftofaV-8engineusingarigidcrankshaftmodeltionsarecarriedoutatenginespeedrangeof10002000rpm.Bendingstressesatthecentresofeachwebarealsocalculated.2.EnginespecificationsThespecificationsofin-linesix-cylinderdieselenginearegiveninTable1.The9.0Lenginecrankshafthaseightcounterweightsatcrankwebs1,2,5,6,7,8,11and12.3Dsolidmodelofthecrank-shaftisobtainedusingPro/EngineerandisshowninFig.1.Sche-maticrepresentationofthecrankshaftisgiveninFig.2.Static*Correspondingauthor.Tel.:+902123597534；fax:+902122872456.AdvancesinEngineeringSoftware40(2009)95104ContentslistsavailableE-mailaddress:.tr(Y.Yilmaz).beingthemainpartresponsibleforpowerproduction.Crankshaftsystemmainlyconsistsofpiston,pistonpin,con-nectingrod,crankshaft,torsionalvibration(TV)damperandfly-wheel.Counterweightsareplacedontheoppositesideofeachcranktobalancerotatinginertiaforces.Ingeneral,counterweightsaredesignedforbalancingratesbetween50%and100%.Foracceptablemaximumandaveragemainbearingloads,massofcounterweightsandtheirpositionsareimportant.Maximumandaveragemainbearingloadsofanenginedependoncylinderpres-sure,counterweightmass,enginespeedandothergeometricstudyoneffectofcounterweightconfigurationonmainbearingloadsandcrankshaftstressesisstillneeded.Inthisstudy,counterweightpositionsandmassesofanin-linesix-cylinderdieselenginecrankshaftsystemarestudied.Maxi-mumandaveragemainbearingforcesandcrankshaftbendingstressesarecalculatedfor12-counterweightconfigurationswithazerodegreecounterweightangle,andforeight-counterweightconfigurationswith30C176counterweightanglefor0%,50%and100%counterweightbalancingrates.AnalysesarecarriedoutusingMultibodySystemSimulationProgram,ADAMS/Engine.Simula-1.IntroductionNewinternalcombustionenginespower,goodfueleconomy,smallengineharmlessaspossibletotheenvironment.eachcomponentoftheengineonitsbeinvestigatedindetail.Crankshafttionengineshaveimportantinfluence0965-9978/$-seefrontmatterC2112008ElsevierLtd.Alldoi:10.1016/j.advengsoft.2008.03.009C2112008ElsevierLtd.Allrightsreserved.havehighenginesize,andshouldbeasTherefore,theeffectofperformanceshouldofinternalcombus-engineperformanceandoptimizedcounterweightstominimizemainbearingloads.StanleyandTaraza11obtainedmaximumandaveragemainbearingloadsoffourandsix-cylindersymmetricin-lineenginesusingarigidcrankshaftmodelandestimatedidealcounterweightmassthatresultedinacceptablemaximumbearingload.Rigidcrankshaftmodelsthatareusedincounterweightanalysesdonotconsidertheeffectofcrankshaftflexibilityonmainbearingloadsandcanleadtoconsiderableerrors.Therefore,anextensiveCrankshaftmodelsBalancingrateBothconfigurationsshowthesametrend.TheloadfromgaspressureratherthaninertiaforcesistheAninvestigationoftheeffectofcounterweightloadandcrankshaftbendingstressYasinYilmaz*,GunayAnlasDepartmentofMechanicalEngineering,FacultyofEngineering,BogaziciUniversity,34342articleinfoArticlehistory:Received11February2008Receivedinrevisedform17March2008Accepted24March2008Availableonline6May2008Keywords:CounterweightconfigurationabstractInthisstudy,effectsofcounterweightstressofanin-linesix-cylinderADAMS.Intheanalysis,rigid,rigid,beamand3Dsolidmodelsanalyses.Twelve-counterweightterweightconfigurationswithingrates,areconsidered.ItwithincreasingbalancingAdvancesinEngineeringjournalhomepage:/lorightsreserved.configurationonmainbearingIstanbul,TurkeymassandpositiononmainbearingloadandcrankshaftbendingdieselengineisinvestigatedusingMultibodySystemSimulationProgram,and3Dsolidcrankshaftmodelsareused.Mainbearingloadresultsofarecomparedandbeammodelisusedincounterweightconfigurationconfigurationswithazerodegreecounterweightangleandeight-coun-30C176counterweightangle,eachfor0%,50%and100%counterweightbalanc-foundthatmaximummainbearingloadandwebbendingstressincreaseandaveragemainbearingloaddecreaseswithincreasingbalancingrate.atScienceDirectSoftwarecate/advengsoftunbalanceofeachcrankthrow(withandw/ocounterweights)isdeterminedusingPro/EngineerandisgiveninTable2.Thebalanc-ingsystemdataforthecranktrainaregiveninTable3.3.ModelingofcrankshaftsystemUsingADAMS/Engine,acrankshaftcanbemodeledinfourdif-ferentways:rigidcrankshaft,torsionalflexiblecrankshaft,beamcrankshaftand3Dsolidcrankshaft.Rigidcrankshaftmodelismainlyusedtoobtainfreeforcesandtorques,andforbalancingpurposes.Torsionalflexiblecrankshaftmodelisusedtoinvesti-gatetorsionalvibrationswhereeachthrowismodeledasonerigidpart,andspringsareusedbetweeneachthrowtorepresenttor-sionalstiffness.Beamcrankshaftmodelisusedtorepresentthetorsionalandbendingstiffnessofthecrankshaft.Usingbeammod-elbendingstressesatthewebscanbecalculated12.Table1EnginespecificationsUnit9.0LengineBorediametermm115Strokemm144Axialcylinderdistancemm134PeakfiringpressureMPa19RatedpoweratspeedkW/rpm295/2200Max.torqueatspeedNm/rpm1600/12001700Mainjournal/pindiametermm95/81Firingorder1-5-3-6-2-4Flywheelmasskg47.84Flywheelmomentofinertiakgmm21.57E+9MassofTVdamperringkg4.94MassofTVdamperhousingkg6.86Momentofinertiaoftheringkgmm21.27E+5Momentofinertiaofthehousingkgmm20.56E+5MainBearing#1MainBearing#2MainBearing#3MainBearing#4MainBearing#5MainBearing#6MainBearing#7CounterweightsFig.1.3Dsolidmodelofthecrankshaft.C3,C4,C5,C6C1,C2,C7,C81,63,42,5C1C2C3C4C5C612Fig.2.Eight-counterweightarrangementTable2PropertiesofthecrankthrowsThrow1Throw2Mass(kg)12.509.25CGpositionfromcrankrotationaxis(mm)12.42331.435Staticunbalance(kgmm)155.265290.76796Y.Yilmaz,G.Anlas/AdvancesinEngineeringSoftware40(2009)95104C7C83456ofthe9.0Lenginecrankshaft.Throw3Throw4Throw5Throw612.5012.509.2812.5511.96711.96631.02711.702149.734149.734287.871146.856Elastic3Dsolidmodelofthecrankshaftcanbeobtainedusinganadditionalfiniteelementprogram.Theprocedureislengthyandtimeconsumingandusuallyoneendsupwithdegreesoffree-dominorderofmillions.Tosimplifythefiniteelementmodel,modalsuperpositiontechniqueisused.Theelasticdeformationofthestructureisapproximatedbylinearcombinationofsuitablemodeswhichcanbeshownasfollows:uUq1whereqisthevectorofmodalcoordinatesandUistheshapefunc-tionmatrix.Table3CrankshaftsystemdataCrankradius(mm)72Connectingrodlength(mm)239Massofcompletepiston(kg)3.42Connectingrodreciprocatingmass(kg)0.92Reciprocatingmass(totalpercylinder)(kg)4.32Connectingrodrotatingmass(kg)2.01Y.Yilmaz,G.Anlas/AdvancesinEngineeringAnelasticbodycontainstwotypesofnodes,interfacenodeswhereforcesandboundaryconditionsinteractwiththestructureduringmultibodysystemsimulation(MSS),andinteriornodes.InMSSthepositionoftheelasticbodyiscomputedbysuperposingitsrigidbodymotionandelasticdeformation.InADAMS,thisisperformedusingComponentModeSynthesis”techniquebasedonCraigBamptonmethod13,14.Thecomponentmodescontainstaticanddynamicbehaviorofthestructure.Thesemodesarecon-straintmodeswhicharestaticdeformationshapesobtainedbygivingaunitdisplacementtoeachinterfacedegreeoffreedom(DOF)whilekeepingallotherinterfaceDOFsfixed,andfixedboundarynormalmodeswhicharethesolutionofeigenvalueproblembyfixingtheentireinterfaceDOFs.Themodaltransforma-tionbetweenthephysicalDOFandtheCraigBamptonmodesandtheirmodalcoordinatesisdescribedby15uuBuIC26C27I0UCUNC20C21qCqNC26C272whereuBanduIarecolumnvectorsandrepresentboundaryDOFandinteriorDOF,respectively.I,0areidentityandzeromatrices,respectively.UCisthematrixofphysicaldisplacementsoftheinte-riorDOFintheconstraintmodes.UNisthematrixofphysicaldis-Fig.3.Modelofthecrankshaftsystem.placementsoftheinteriorDOFinthenormalmodes.qCisthecolumnvectorofmodalcoordinatesoftheconstraintmodes.qNisthecolumnvectorofmodalcoordinatesofthefixedboundarynor-malmodes.Toobtaindecoupledsetofmodes,constrainedmodesandnormalmodesareorthogonalized.Elastic3Dsolidcrankshaftmodelofthe9.0LengineisobtainedinMSC.Nastranusingmodalsuperpositiontechnique.First,3Dso-lidmodelofthecrankshaftthatisshowninFig.1isexportedtoMSC.Nastranandfiniteelementmodelofthecrankshaft,whichischaracterizedbyapproximately300,000ten-nodetetrahedralele-mentsand500,000nodesisobtained.Themodalmodelofthecrankshaftisdevelopedwith32boundaryDOFsassociatedwith16interfacenodes.Constrainedmodesobtainedfromstaticanaly-siscorrespondtotheseDOFs.Flexiblecrankshaftmodelisobtainedthroughmodalsynthesisconsideringthefirst40fixedboundarynormalmodes.Thereforeflexiblecrankshaftmodelischaracter-izedbyatotalof72DOFs.ThismodelisexportedtoADAMS/En-gineandcrankshaftsystemmodelthatisshowninFig.3isobtained.3DfiniteelementmodelisrunwithADAMS.4.ForcesactingoncrankshaftsystemandbalancingForcesinaninternalcombustionenginemaybedividedintoinertiaforcesandpressureforces.Inertiaforcesarefurtherdividedintotwomaincategories:rotatinginertiaforcesandreciprocatinginertiaforces.Therotatinginertiaforceforeachcylindercanbewrittenasshownbelow:FiR；jmRC1rRC1x2C1C0sinhjjcoshjk3wheremRistherotatingmassthatconsistsofthemassofcrankpin,crankwebsandmassofrotatingportionoftheconnectingrod；rRisthedistancefromthecrankshaftcentreofrotationtothecentreofgravityoftherotatingmass,xisangularvelocityofthecrankshaft,andhjistheangularpositionofeachcrankthrowwithrespecttoTopDeadCentre”(TDC).Iftherearetwocounterweightspercrankthrow,eachcounterweightforceisgivenby11FCWi；jC0mCWi；jC1rCWi；jC1x2C1C0sinhjci；jjcoshjci；jkhi；i1；2j1；2；.；64whereci,jistheoffsetangleofcounterweightmassfrom180C176oppo-siteofcrankthrowj”.Therearetwocounterweightsperthrow.i”denotesthecounterweightnumber.ThecounterweightsizethatisrequiredtoaccomplishanassessedbalancingrateisUCWKC1UCrankthrowmcr-rC1rC1cosc25whereUCWisthestaticunbalanceofeachcounterweight,UCrank_throwisthestaticunbalanceofeachcrankthrow,mcr-risthemassofconnectingrodrotatingportion,risthecrankradiusandKisthebalancingrateoftheinternalcoupleduetorotatingforces.Fromthisformulafollowsthebalancingrateforagivencrankshaftandagivencounterweightsize:K2C1UCWUCrankthrowmcr-rC1rC1cosc6Forastandardin-linesix-cylinderenginecrankshaftwiththreepairsofcrankthrowsdisposedatanglesof120C176thatarearrangedsymmetricaltothecrankshaftcentre,rotatingforces,andfirstandsecondorderreciprocatingforcesarenaturallybalanced.ThiscanbeexplainedbythefirstandsecondordervectorstarsshowninFig.4.Thesix-cylindercrankshaftgeneratesrotatingandfirstSoftware40(2009)9510497andsecondorderreciprocatingcouplesineachcrankshafthalfthatbalanceeachotherbutwhichresultininternalbendingmoment.Athighspeeds,thetwoequallydirectedcrankthrows,3and4yieldahighrotatingloadoncentremainbearing.Therotatinginertiaforceofeachcylinderisusuallyoffsetatleastpartiallybycounterweightsplacedontheoppositesideofeachcrank.Ingen-eral,thecounterweightsaredesignedforbalancingratesbetween50%and100%oftheinternalcouple.Gasforcesincylindersareactingonpistonhead,cylinderheadandonsidewallsofthecylinder.Thesefor