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sensorLiu,KeywordsInversemagnetostrictiveeffectForcesensorGiantmagnetostrictivematerialrodmagnetostrictiveAHallexpoundedfirstly.ThemagneticcharacteristicsareanalyzedbyFEM.AmodelisdevelopedIfepects,suchascorematerialandexcitingmodeisthefocusofthisresearch.Atpresent,thesensitivematerialcommeasureisneeded.TheemergenceofgiantmagnetostrictivematerialGMMprovidesanewtypeofsensitivematerialforthedevelopmentofmagnetostrictiveforcesensor.Byrightofitsexcellentcharacteristicsoflargemagnetostrictivecoefficientatroomtemperature1500C210C06–2000C210C06whichis100–1000timeshigherthanthatofcommonmagnetostrictivematerial,highelectromechanicalcoupling02632241/seefrontmatterCrownCopyrightC2112010PublishedbyElsevierLtd.Allrightsreserved.⇑Correspondingauthor.AddressSchoolofMechanicalEngineering,DalianUniversityofTechnology,No.2,LinggongRoad,GanjingziDistrict,Dalian,LiaoningProvince116024,PRChina.Tel.8613940925372fax8641184708812.Emailaddresshuifangl163.comH.F.Liu.Measurement44201188–95ContentslistsavailableatScienceDirectMeasuremenjournalhomepagewww.elsevierdoi10.1016/j.measurement.2010.09.031ofsensorsinsystemdesign.Sensoristhefirstlinkformeasuringandautomaticcontrol1.Theforcesensorisoneofthewidelyusedsensors.Inrecentyears,thereisanewtypeofforcesensorwhichismagnetostrictiveforcesensor.Comparedwiththeothertypesofforcesensors,ithasobviousadvantages,suchastheefficientcouplingbetweentheelasticandmagneticstates,withstandingheavyload,shortresponsetime,lowpowerconsumption,bettercapabilitytoadapttoharshworkingenvironment,etc.2.Thus,magnetostrictiveforcesensoranditsrelevantaswasusedasthesensitivematerial.Adetectioncoilproducedaninducedcurrentduetothemagneticfieldtomeasureappliedforce3.BaudendistelandTurnerstudiedaringmagnetostrictiveforcesensor1.However,themagnetostrictivecoefficientofthesematerialsusedinthesesensorsweresmall10C06–10C05andthesensitivitywerepoor.Inaddition,thesesensorswereallbasedonthefaradaylawofelectromagneticinductionandcanonlymeasuredynamicforce.Therefore,amagnetostrictiveforcesensorwithhighsensitivitythatcanbeusedforstaticforce1.IntroductionThewisewordsofanoldengineer,sureit,youcantcontrolitdemonstratbasedonthecoupledlinearmagnetomechanicalconstitutiveequationsandtheexperimentalresultshowsthatthemodelisgoodatreflectingtheforce.Theoptimalbiasmagneticfieldandsensitivityarestudiedthroughexperiments.Thesensorsensitivityis6.14timeshigherthanthatofthesensorwhichdosenothaveastainlesssteelring.Thepaperlaysafoundationforthedevelopmentofmagnetostrictiveforcesensorwithgiantmagnetostrictivematerial.CrownCopyrightC2112010PublishedbyElsevierLtd.Allrightsreserved.youcantmeatheimportancemonlyusedinmagnetostrictiveforcesensoraresiliconsteelsheet,permalloy,electricalpureironandothersoftmagneticmaterials.KleinkeandUrasdevelopedacontactingmagnetostrictiveforcesensorinwhichSAE1018steelAvailableonline21September2010fluxdensityvariationunderforce.AspecialstructuresurroundingHallsensorisproposedtoimprovethesensitivity.ThedesignmethodofthegiantmagnetostrictiveforcesensorisAnovelmagnetostrictivestaticforcemagnetostrictivematerialZhenYuanJia,HuiFangLiu⇑,FuJiWang,WeiKeyLaboratoryforPrecisionandNontraditionalMachiningTechnologyofMinistryarticleinfoArticlehistoryReceived27April2010Receivedinrevisedform6September2010Accepted14September2010abstractInordertorealizestaticforcesensor,anovelrialrodispresented.basedonthegiantChunYaGeofEducation,DalianUniversityofTechnology,Dalian116024,PRChinaforcemeasuringandimprovethesensitivityofmagnetostrictivestaticforcesensorwithgiantmagnetostrictivematesensorintegratedinthesensorisusedtomeasuremagnetict.com/locate/measurementhighsensitivegiantmagnetostrictivestaticforcesensorcircuitisnecessary.DuetoitsquitelowpermeabilityofZ.Y.Jiaetal./Measurement44201188–9589whichusesGMMrodasthesensitiveelement.Aspecialstructurewasproposedtoimprovethesensorsensitivity.First,themeasureprincipleanddesignmethodwereexpounded.Afterwards,FEMsoftwarewasusedtoanalyzemagneticfluxdensityofthesensor.Third,amodelwasestablishedbasedonthecoupledlinearmagnetomechanicalconstitutiveequationsandmagnetostrictionmodelanditwasverifiedbyexperiment.Inaddition,thesensorperformanceunderdifferentbiasmagneticfiled,linearityandsensitivitywereanalyzedthroughexperiment.2.PrincipleofoperationTheoperationprincipleofthemagnetostrictiveforcesensorisbasedontheinversemagnetostrictiveeffect.InversemagnetostrictiveeffectalsoknownastheVillarieffectspecifiesthatunderaconstantmagneticfield,themagneticpermeabilityofGMMchangeswhenitissubjectedtoanexternalforce7.Theessenceofinversemagnetostrictiveeffectisthatunderstress,magneticdomainsinGMMrotate.Thiscausesthechangeofmagnetizationormagneticfluxdensity.Ontheonehand,magneticfieldaroundGMMrodmakesmagneticdomainsrotatetowardsthedirectionparalleltothemagneticfield.Ontheotherhand,stressmakesmagneticdomainsrotatetowardsthedirectionparticulartotheappliedstress.ThechangingprocessisshowninFig.1.Underexternalstress,magneticdomainrotatingleadstothechangeofrelativemagneticpermeabilityofGMMrodlr.ForpositiveGMMinvolvedinthepaper,accordingtothetheoryofferromagnetics,iftheeternalstressiscompressivestress,relativemagneticpermeabilityinthestressorientationisdecreasing.Conversely,ifitistensilestress,relativemagneticpermeabilityisincreasing.Thecalculationformulaofmagneticfluxdensityiscoefficient,fastresponsespeedetc.,GMMattractswideattentioninhomeandabroadacademiccircles,andindustrialcommunity.Atpresent,forthestudyofGMM,itmainlyfocusesontheactuatorswhicharebasedonthemagnetostrictiveeffectathomeandabroadanditisrelativelymature.ForexampleZhejiangUniversityresearchedonmagnetostrictivematerialhighspeedpowerfulsolenoidvalveandactuator.TheUnitedStatesETRAMAdevelopedamagnetostrictivemicroactuator4.GMMhavebeenusedpracticallyinthefieldsofraildieselinjectionsystem,vibrationabsorberofturbopropaircraft,microfeeddevice,etc.5.However,fewinvestigationshavebeendoneonmagnetostrictiveforcesensorwhichusesGMMasthesensitiveelement.Itlacksofthenecessarydesigntheoryanditlimitsthedevelopmentofthisdevice6.Yangetal.developedagiantmagnetostrictiveforcesensorandestablisheditsmagnetomechanicalstronglycoupledmodel2.However,agaussmeterwasusedinthesensortomeasurethemagneticfluxdensityvariationintheairgap.Themeasuringaccuracywasrelativelylowandthemeasuringpositionwashardtocontrol.Thus,thedesignmethodandrelatedtheoryofgiantmagnetostrictivestaticforcesensorwithhighersensitivityandprecisionareneeded.Inordertofillthevacancy,thispaperproposedanovellr5approximately,GMMrodisnotsuitableasfluxguidingelementintheconstructionofthesensor.Therefore,thesurroundingstructureshavetoensureguidingandfocusingofthemagneticfield.TheupperandlowerendplatesandorientationplatesmadeofhighlypermeableelectricalpureironDT4aredesignedtoworkasthefluxguidanceelements.Theprimarypurposeofthemountingcoverandoutersleeveistomakethesensormechanismassembletogether.Theyaremachinedwithinternalandexternalthreadrespectivelyandconnectedtogetherthroughthread.Theotherfunctionispreventingthemagneticcircuitfrominterferingwithexternalenvironment.Thus,antimagneticstainlesssteel1Cr18Ni9Tiisselected.Thediskspringisapreloaddevice.Itprovidesamechanicalpretighteningforcetothewholeinternalstructuretopreventitfromloosening.Thepretighteningforcecanbeadjustedwiththethreadfitdistancebetweenmountingcoverandoutersleeve.TheexertingcompressivestressB¼l0lrHð1Þwherel0isthepermeabilityofvacuumandHisthemagneticfieldintensity.Accordingtotheformula,thechangeoftherelativemagneticpermeabilitycausesmagneticfluxdensitychange.Sincebothl0andHareconstant,magneticfluxdensityinGMMrodchangeswithchangingexternalstress.TheconversionprocessisshowninFig.2.Thus,forcecanbemeasuredbymeasuringmagneticfluxdensity.AccordingtothechangingprocessofmagneticdomaininFig.1,theinversemagnetostrictiveeffectisrelatedtobothmagneticfieldandstress.Therefore,inordertoimprovethesensorssensitivitytheGMMrodmustbepremagnetizationwithabiasmagneticfield.Inaddition,inordertomeasureforceandmakethemagneticfluxdensitybethesinglevaluedfunctionofthestress,themagneticfieldintensitymustbekeptconstant.ThebiasmagneticfieldcanbeappliedviaaconstantDCcurrentthroughexcitationsolenoidorwithpermanentmagnet.3.DesignofthesensorAdetailedcrosssectionalviewofthemagnetostrictiveforcesensorpresentedinthepaperisshowninFig.3.Thesensormainlyconsistsofonemountingcover,oneoutersleeve,twoendplates,onecorewithwirecoils,GMMrod,onepreloaddeviceandexertingcompressivestressmechanism.Thesensorismodularindesignsothateachcomponentcanbefabricatedseparately.ThesensitiveelementGMMrodismadeofTbDyFe,anditslengthanddiameterare44mmand12mm,respectively.Inthesensor,GMMrodmustbeinamagneticfieldtobeinpremagnetizationstatetoimprovethesensitivity.DCexcitationcoilmodeisselectedinthesensortosupplybiasmagneticfield,whichenablesbiasmagneticfieldtobeadjustedconveniently.Thecoreisdesignedasindividualspooltofacilitatethecoilwindingprocess.Thecoreshoulderskeepthewireinplaceafteritiswoundandfunctionsasloadbearingsurfacewhenthesensorisassembledandpreloaded.SinceGMMrodiscostly,itshouldbefullyutilized.Consequently,acarefuldesignofthefluxguiding90Z.Y.Jiaetal./Measurement44201188–95mechanismismadeofstainlesssteel1Cr18Ni9Ti.Astheforceisappliedtoexertingcompressivestressmechanism,itistransferredtoGMMrodinaxisorientationsimultaneously.AspecialfeatureinthedesignofthemagnetostrictiveforcesensorisanintegratedlinearHallsensorallowingustomeasurethevariationofmagneticfluxdensitywithrespecttotheexternalforce.HallsensorisplacedatthebottomofGMMrodandmeasuresamagneticfluxdensityproportionaltothemagneticfluxdensityinGMMrod.InFig.1.ChangingprocessofFig.2.ChangingprocessofFig.3.Structurediagramofthemagnetostrictiveordertoimprovethesensitivityofgiantmagnetostrictiveforcesensor,whichisenhancingtheproportionalcoefficientbetweenthemagneticfluxmeasuredbyHallsensorandtheactualmagneticfluxdensityinGMMrod,aspecialstructurearoundHallsensorisproposedinthepaper.ItissurroundingtheHallsensorwithastainlesssteelring.ThestructureisshownastheamplifyingpartinFig.3.Thestructureresultsfromthefollowingprinciplethemagneticfluxlikeanelectriccurrenttakesthewaywiththeleastresistance.IfthestructurearoundtheHallsensormagneticdomains.magneticfluxdensity.forcesensor.weremadeofthefluxguidingmaterial,themagneticresistanceinthispathwouldhavebeenlowerthanapathcrossingHallsensor.Therefore,themagneticresistancearoundthesensorhastobechangedinsuchawaythatthereisnopathforthefluxhavingalowerresistance.Therelativemagneticpermeabilityofthestainlesssteelringisneartoone,soitmagneticallybehaveslikethesensorandthesurroundingair.Thus,magneticfluxcanpassHallsensor,stainlesssteelringandairaveragely.Therefore,accordingtoinversemagnetostrictivemechanismandGMMsproperties,amagnetostrictiveforcesensorbasedonGMMcomprisesofamagneticcircuithavingmagneticallyconductiveendstructuresconnectedbymagneticallyconductivemembers,atleastoneofthemagneticmembersbeingGMMwhichisthesensitiveelementformagnetostrictiveforcesensormeansforgeneratingasityinGMMrodishomogeneous,andmagneticfluxpassesHallsensor,stainlesssteelringandthesurroundingairZ.Y.Jiaetal./Measurement44201188–9591averagely.TheproportionalcoefficientbetweenmagneticfluxdensitymeasuredbyHallsensorandtheactualinGMMrodis2.Thus,themagneticfluxdensityofGMMrodcanbecalculatedbythemagneticfluxdensitymeasuredbyHallsensorwiththeproportionalcoefficient.AccordingtoHalleffectofHallsensorandtheproportionalcoefficient,magneticfluxdensityinGMMrodisFig.4.Analysisresultofmagneticfluxdensity.magneticfieldinmagneticcircuittomakeGMMbeinpremagnetizationstate,aDCexcitationcoilbeingadoptedinthispapertoprovidethemagneticfieldmeansforsensingthechangeofmagnetizationstate,aHallsensorbeingusedasthesensingdeviceheretomeasurethevariationofmagneticfluxdensityanddeviceforapplyingpretighteningforce.4.FEManalysisformagneticfluxdensityInthispaper,FEMsoftwareANSYSisusedtoanalyzethemagneticfieldcharacteristicoftheforcesensor.AtwodimensionalaxisymmetricgeometricmodelofthesensorisestablishedintheANSYS.Theairfarfieldelementisusedtosimulatefarfielddissipation.AccordingtoMaxwellequations,magneticfieldintensity,magneticfluxandmagneticfluxdensityareanalyzedandcalculated.Amongthem,thecalculatedresultofmagneticfluxdensityisshowninFig.4.TheresultsshowthatMagneticfluxdenBrod¼2BHall¼2UC0U0Kð2ÞInwhichBrodandBHallaremagneticfluxdensityofGMMrodandHallsensorrespectively,UistheoutputvoltageofHallsensor,U0isthequiescentvoltage,KisthesensitivityofHallsensor.AspecifictypeofA1302madebyAllegroMicrosystemsInc.isselectedinthispaperanditssensitivityKis1.3mv/G.Thus,themagneticsignalistransformedtovoltagesignalbyHallsensorandthemagnetostrictiveforcesensoroutputsignalusedinthepaperisthevoltageU.5.ModelofthesensorEqs.3and4arethemagnetostrictiveconstitutiveequationsbasedonGMMworkingattheconstanttemperature4.e¼sHrþdtHð3ÞB¼drþlrHð4ÞInwhicheisstrain,risstress,sHiscompliantcoefficientwithconstantappliedmagneticfieldintensity,dtðdedHjrÞismagnetostrictiveconstant,dtðdBdrjHÞispiezomagneticcoefficient,lrismagneticpermeabilitywithaconstantstress,andBismagneticfluxdensitywithintheGMMrodsubjectedtomagneticfieldandforce.Althoughtheabovevariablesaretensorquantities,fortheforcesensorwhichisunderaxialforceandaxialmagneticfieldonlytheaxialdirectionwillbeconsidered.Twoimportantassumptionsarebuiltintothismodel.First,linearoperationofthesensorisassumed.Althoughthemagnetostrictiveeffectisnonlinear,forlowsignalwhichislessthanapproximatelyonethirdthemaximumstraincapability,thelinearequationsofmagnetostrictionprovideagoodapproximation.Second,themagnetostrictionprocessisassumedtobereversible,thatisd¼dBdrjH¼dedHjr¼dtð5ÞInwhichHisheldconstantforthefirstderivativeandrisheldconstantforthesecond.ThesetwoassumptionsleadtoasimplificationofEqs.3and4,sinceddt.SolvingEq.3forHandsubstitutingitandEq.5intoEq.4yieldsB¼rdC0lrsHdC18C19þlrdeð6Þe¼DLLð7ÞInwhich,DListhelengthvariationofGMMrod,Listheinitiallength.Thispaperproposesusingthemagnetostrictionmodel8whichisbasedonthemagnetizationtocalculatelengthvariation.DLC25LEl0B20ð8ÞInwhichEisyoungmodulus,B0ismagneticfluxdensityoftherodonlysubjectedtoamagneticfield.B0canbecalculatedby