TheanalysisanddesignofMagnetorheologicalFluidDampe

TheanalysisanddesignofMagnetorheologicalFluidDamperAbstract:Magnetorheological(MR)FluidDamperisadevicetogivedampingbythetheshearforceofMRfluid,AMRdamperhasthepropertythatitsdampingchangesquicklyinresponsetoanexternalmagneticfieldstrength.Inthispaper,thedesignmethodoftheMRfluiddamperisinvestigatedtheoretically.TheequationofthedamptingbytheMRfluidwithinthedamperisderivedtoprovidethetheoreticalfoundationsinthedesignofthedamper.Basedonthisequation,aftermathematicalmanipulation,thecalculationsofthevolume,thicknessandwidthoftheannularMRfluidwithintheMRfluidsdamperareyielded.Keywords:MRfluiddamper;constitutiveequationIntroductionMagnetorheological(MR)fluidsconsistofstablesuspensionsofmicro-sized,magnetizableparticlesdispersedinacarriermediumsuchassiliconoilorwater.Whenanexternalmagneticfieldisapplied,thepolarizationinducedinsuspendedparticlesresultsinthemagnetorheologicaleffectoftheMRfluids.ThemagnetorheologicaleffectisdirectinfluencesonthemechanicalpropertiesoftheMRfluids.ThesuspendedparticlesintheMRfluidsbecomemagnetizedandalignthemselves,likechains,withthedirectionofthemagneticfield.TheformulationoftheseparticlechainsrestrictsthemovementoftheMRfluids,therebyincreasingtheyieldstressofthefluids.Thechangeisrapid,reversibleandcontrollablewiththemagneticfieldusedintheconstructionofmagneticallycontrolleddevicessuchasdamper,brake,cluch,etc.TodesigntheMRfluiddamperforagivenspecification,onemustestablishtherelationshipbetweentheshearstressdevelopedbyMRfluidsandtheparametersofthestructureandthemagneticfieldstrength.Inthispaper,thefundamentaldesignmethodoftheMRdamperisinvestigatedtheoretically.BinghammodelisusedtocharacterizetheconstitutivebehavioroftheMRfluidssubjecttoanexternalmagneticfieldstrength.ThetheoreticalmethodsisdevelopedtoanalyzetheshearstressbytheMRfluidwithinthedamper.Anengineeringexpressionfortheshearstressisderivedtoprovidethetheoreticalfoundationsinthedesignofthedamper.Basedonthisequation,bealgebraicallymanipulated,thevolumeandthicknessoftheannularMRfluidwithinthedamperisyielded.OperationalPrincipleMRfluiddamperisadevicetogivedampingbytheshearstressofMRfluid.AMRdamperhasthepropertythatitsdampingchangesquicklyinresponsetoanexternalmagneticfieldstrength.TheoperationalprincipleofthecylindricalMRdamperisshowninFig.1.TheMRfluidisfilledintheworkinggapbetweenthefixedoutercylinderandinnercylinder.TheinnercylindermovesataspeedV.Intheabsenceofanappliedmagneticfield,thesuspendedparticlesoftheMRfluidcannotrestricttherelativemotionbetweenthefixedoutercylinderandinnercylinder.Howover,inthecourseofoperation,themagneticfluxpathisformedwhentheelectriccurrentputthroughthesolenoidalcoil.Asaresult,theparticlesaregatheredtoformthechain-likestructures,withthedirectionofthemagneticfluxpath.Thesechain-likestructuresrestrictthemotionoftheMRfluid,therebyincreasingtheshearstressofthefluid.ThedampercanbeachievedbyutilizingtheshearforceofMRfluid.Thedampingvaluescanbeadjusredcontinuouslybychangingtheexternalmagneticfieldstrength.PropertiesofMRFluidsMRfluidsaresuspensionsofmicron-sized,magnetizableparticlesinacarrierfluid.Theymainlyconsistofthefollowingthreecomponents:magnetizableparticles,acarrierfluid,andsomeadditionaladditives.ThemagnetizableparticlesinMRfluidsinducepolarizationbyapplicationofanexternalmagneticfield,whichresultsinthemagnetorheologicaleffectoftheMRfluids.Thecarrierfluidservesasadispersedmediumandensurestheparticlesinthefluidhomogeneity.Theadditionaladditivesincludethestabilizersandsurfactants.Thestabilizersservetokeeptheparticlessuspenedinthefluid.Thesurfactantsareadsorbedonthesurfaceofthemagneticparticlestoenhancethepolarizationinducedinsuspendedparticlesbyapplicationofamagneticfield.Intheabsenceofanappliedmagneticfield,theparticlesinMRfluiddisperserandomlyinacarrierfluid.MRfluidflowsfreelythroughtheworkinggapbetweenthedixedoutercylinderandrotor.MRfluidexhibitsNewtonian-likebehaviorandtheshearstressofMRfluidscanbedescribedas:τ=ηγ′(1)whereτistheshearstress,ηistheviscosityofMRfluidwithnoappliedmagneticfieldandγ′istheshearrate.Whenthemagneticfieldisapplied,thebehaviorofthefluidsisoftenrepresentedasaBinghamfluidhavingthevariableyieldstrength.Inthismodel,theconstitutiveequationisderivedbytheleastsquaremethod.τ=ηγ′+τB(2)whereτBistheyieldstressdevelopedinresponsetoanappliedmagneticfield.ItsvaluesaredependentuponthemagneticinductionfieldB.Fig.2showstherelation,obtainedfromtheexperiment,betweenshearrateandshearstressdependingupontheappliedmagneticfieldstrength.Ascanbeseen,theMRfluidshavethevariableyieldstrength.Theshearstressincreasesastheappliedmagneticfieldstrength.Theshearratehaslittleinfluenceontheshearstress.ThisresultindicatesthattheMRfluidexhibitsBinghamplasticmodel.DampingofMRdamperThekeyquestioninthedesignofMRfluiddamperistoestablishtherelationbetweenthedamperandtheparametersofthestructureandmagneticfieldstrength.ASthemagneticfieldisapplied,thedampingFdevelopedbyMRfluidcanbecalculatedby:F=12ηLπr2πRh3V+(k0LτBπr2h+ƒ)sgn(V)(3)WhereVisthespeedofpiston;ƒisfrictionofpistonandcylinder;k0isacoefficient(0.8～1);histhethicknes