第五篇

J. Hesselbach and C. Abel-Keilhack

Citation: J. Appl. Phys. 93, 8441 (2003); doi: 10.1063/1.1555850 View online: http://dx.doi.org/10.1063/1.1555850

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JOURNALOFAPPLIEDPHYSICSVOLUME93,NUMBER1015MAY2003

Activehydrostaticbearingwithmagnetorheologicalfluid

J.HesselbachandC.Abel-Keilhacka)

InstituteofMachineToolsandProductionTechnology,TechnicalUniversityofBraunschweig,LangerKamp19b,D-38106Braunschweig,Germany

͑Presentedon15November2002͒

Specialbearingsbasedonmagneticfluidsarewellknowninliterature.Thesebearingsusethemagneticpressureinsideaferrofluidthatisexposedtoamagneticfield.Thebiggestdisadvantageofthisprincipleisthesmallloadthatcanbesupported.Inonereference͓B.M.Berkovsky,V.F.Medvedev,andM.S.Krakov,MagneticFluids,EngineeringApplications͑OxfordUniversityPress,Oxford,1993͔͒,thespecificloadisspecifiedas1NcmϪ2.Tosupportheavyloadsverylargesupportareasareneeded.Wewillpresentacompletelydifferentconceptforbearingswithmagnetorheologicalfluids.Hydrostaticbearingsgettheirloadbearingcapacityfromthehydrostaticpressureproducedbyanexternalpumpandshouldnotbeconfusedwithhydrodynamicbearings

¨rWerkzeugmaschinenundpresentedinanotherreference͓R.Patzwald,M.S.thesis,Institutefu

¨t,Berlin͑2001͔͒.ThemaindisadvantageofhydrostaticFabrikbetrieb,TechnischeUniversita

bearingsisthatthebearinggapvarieswiththepayload.Conventionalsystemscompensateforthesevariationswithachangeoftheoilflowrate,thatisdone,forexample,byexternalvalves.Ourcontributionwillpresentahydrostaticbearingthatusesmagnetorheologicalfluids.Duetothefactthatmagnetorheologicalfluidschangetheirrheologicalpropertieswiththechangeofanexternalmagneticfield,itispossibletoachieveaconstantbearinggapevenifthepayloadchanges.Thegreatadvantageofthissystemcomparedtovalvebasedsystemsistheshortresponsetimetopayloadchanges,becausetheactiveelement͑i.e.,thefluid͒actsdirectlyinsidethebearinggap,andnotoutsidelikeinthecaseofvalves.©2003AmericanInstituteofPhysics.͓DOI:10.1063/1.1555850͔

I.PRINCIPLEOFHYDROSTATICBEARINGS

Ahydrostaticbearingconsistsoftwoslidingsurfacesthatareseparatedbyathinfilmofoil.TheoilispressedwithaconstantflowrateQbyanexternalpumpthroughtheevolvinggap.Tomaximizethebearingforce,oneslidingsurfacehasaspecialtopology:Thedepthofthepadismuchbiggerthanthedepthoftheland.Thus,thepressureinsidethepadisconstantanddeclinestotheambientpressurealongtheland.ThisprincipleisshowninFig.1.Theresult-ingpressuredistributionandtheloadstayinequilibrium.Iftheoilflowrateandtheloadareconstant,thegapisalsoconstant.ThebearingforceFsimplydependsonthepressureinthepadptandtheeffectivepadareaAeff

Fϭ

Thisformulademonstratesthemainproblemofhydrostaticbearings:IftheloadFchanges,theflowrateQhastobechangedtoachieveaconstantbearinggaph.Thischangeoftheflowratecanonlybedonewithexternalmechanicalvalves.Thisleadstoapoorresponsetimeofthebearingtoloadchanges.II.FLUIDMODELS

Duetothefactthatmagnetorheologicalfluidschangetheirrheologicalpropertieswithamagneticfield,itispos-

͵͵pϫdAϭptϫAeff.

͑1͒

Theeffectivepadareaisbiggerthanthepadsize,be-causeapartofthelandcontributestothebearingforce.Assumingalineardecreaseofthepressurealongtheland,themeanvalueofthepressureinsidethelandis1/2pt.TocalculateF(Q)somecalculationsareneededbefore.ForNewtonianfluids,thisiswellknown1,2͑␬:viscosity͒:

F͑Q͒ϭ

a͒

12ᐉs␬Q

ϫAeff.bth3͑2͒

Electronicmail:c.keilhack@tu-bs.de

8441

FIG.1.Principleofconventionalhydrostaticbearing.

©2003AmericanInstituteofPhysics

0021-79/2003/93(10)/8441/3/$20.00

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8442J.Appl.Phys.,Vol.93,No.10,Parts2&3,15May2003J.HesselbachandC.Abel-Keilhack

FIG.2.MeasurementoftheflowbehaviorofacommercialMRfluid͑seeRef.7͒,fitoftheBinghammodelandtheHerschel–Bulkleymodel.

sibletoachieveaconstantbearinggapwithoutchangingtheflowrate.Tocalculatethisbehaviorsomeconsiderationsabouttherheologicalbehaviorofmagnetorheologicalfluids͑MRfluids͒havetobedone:AwidelyuseddescriptionforMRfluidsistheBinghamModel3͑␶:Shearstress,␶0:Yieldstress,Ds:Shearrate,andB:Magneticfield͒:

␶͑B͒ϭ␶0͑B͒ϩ␬ϫDsifDsу0.͑3͒

ThecalculationsforahydrostaticbearingbasedonthisfluidmodelcanbefoundinHesselbach.4Butacloserlookattherealfluidshowsthatthismodeliscompletelyinsufficient͑Fig.2͒,especiallyifitistakenintoaccountthatinsidethegapthereisawiderangeofshearrate͑0–50001/s͒.

AmuchmoresuitablefluidmodelforMRfluidsistheHerschel–Bulkleymodel:5

n

␶ϭ␶0ϩ␬ϫDs

FIG.3.ConstructionofathrustbearingwithMRfluids.

ifDsу0.͑4͒

Thismodelintroducesanadditionallyfluidparametern.AsonecanseeinFig.2,thismodelrepresentsthefluidbehaviormuchbetter.Takingthismodelintoconsideration,onegetsanimplicitequation6fortheevolvingbearinggaph:

1F

Ϫ␶ᐉh

2Aeff0s

Qϭ

͑␬ᐉs͒1/nͩͪ1/nϩ1

bAϫ

FAeff

FFϩhnϩ2n␶0ᐉsnhAeffAeff

ϫ.

1ϩ3nϩ2n2ͩͩͪͪ2mm.Thecoil͑100windings,1⍀͒forgeneratingthemag-neticfieldandthesupplyoftheMRfluidareplacedintheframe.Theslidingsurface1canrotateandmovevertically,otherdegreesoffreedomareblockedbyarotarystrokebear-ing.Therotationisgeneratedbyanexternalservomotor͑notshown͒andistransmittedbyatoothedbeltandtwogearwheels.

Togeneratedynamicpayloadchangesupto300N,apiezostackisappliedasaloadingunit͑notshown͒.Tode-

͑5͒

Equation͑5͒showstheadvantageofhydrostaticbearingswithMRfluids:IfthepayloadFchanges,itisconvention-allynecessarytochangetheflowrateQ,ifthegaphshallbeconstant.WiththeMRfluidinsidethegap,achangeinthemagneticfieldcanbeusedtocontrolthebearinggap.III.MEASUREMENTSA.Testsetup

Duetoasimplerealization,athrustbearingwaschosenfortheexperimentalsetup͑Fig.3͒.Thetwoslidingsurfacesareseparatedbyasmallgapofabout300␮m͑gap1͒andhaveadiameterof160mm.Thepadhasadiameterof54

FIG.4.Changeofbearinggapwiththecoilcurrent.nistherotatingveloc-ityofthebearingandF0istheloadduetotheself-weightofthebearing.Therewasnoadditionalloadonthebearing.

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J.Appl.Phys.,Vol.93,No.10,Parts2&3,15May2003J.HesselbachandC.Abel-Keilhack8443

to700␮m,withonlyamoderatecurrentandaverysmalluseofpower͑roundabout1W͒.Figure5showsthedecreaseofthebearinggapwiththeincreaseofthepayload.Furtheron,onecanseehowaconstantbearinggapcanbeachieved:Forapayload,e.g.,25Nandagapof310␮m,acertainvalueofthemagneticfieldisnecessary͑markerAinFig.5͒.Whenthepayloadchangesto160N,thebearinggapremainsconstantifthemagneticfieldischangedtoanothervalue͑markerB͒.Inaclosedloopcontrol,anearlyinfinitestiff-ness,onlylimitedbytheresolutionofthemeasuringsystem,canbeachieved.

TheseresultsshowthattheconceptofahydrostaticbearingwithMRfluidspresentedherecanovercomethedrawbacks͑stiffnessandresponsetime͒ofconventionalhy-drostaticbearings.ACKNOWLEDGMENT

FIG.5.Changeofbearinggapwiththepayloadfordifferentmagneticfields͑exceptforthepayloadF,theparametersarethesameasinFig.4͒.

ThisprojectispartofthePriorityProgramSPP1104oftheGermanResearchFoundation͑DFG͒withthetitle‘‘Col-loidalMagneticFluids:Basics,DevelopmentandApplica-tionofNewFerrofluids.’’

1

coupletherotationoftheshaftfromtheloadingunit,ajour-nalbearingisused.Aperistalticpumpisusedtogeneratetheconstantflowrate͑0.01–0.81/min͒.ThistypeofpumpischosentopreventtheMRfluidtobepollutedbyabrasionandlubricantofthepump.Themaximumpressureofthispumpis3bar.Tomeasurethechangeofthegap,apreciselasertriangularmeasurementsystemwitharesolutionof1␮misused.AllmeasurementsweremadewithastandardcommercialMRfluid͑MRF132-LD,LordCooperation͒.7B.Results

TheinfluenceofthemagneticfieldonthebearinggapisshowninFig.4inthecaseofaconstantload.8AsonecanseeinFig.4,thegapcanbevariedinawiderangefrom200

W.Rowe,HydrostaticandHybridBearingDesign͑Butterworth,Wash-ington,DC,1983͒.2¨nshoff,Werkzeugmaschinen(Grundlagen)͑Springer,Berlin,H.-K.To1995͒.3

B.F.Spencer,Jr.,S.J.Dyke,M.K.Sain,andJ.D.Carlson,J.Eng.Mech.123,230͑1997͒.4

J.HesselbachandC.Abel-Keilhack,ProceedingsofEighthInternationalConferenceonNewActuators,2002,pp.343–346.5

W.H.HerschelandR.Bulkley,Kolloid-Z.39,291͑1926͒.6

TheapproachforthiscalculationisthesameasinthecaseofNewtonian

¨nshoff,Werkzeugmaschinenfluids,whichcanbefoundinH.K.To

͑Grundlagen͒͑Springer,Berlin,1995͒.Theonlyassumptionneededisalaminarflowofafluidthroughagapresultinginalineardecreaseofpressure.Therefore,thisequationisapplicableinawiderangeofsitua-tions.7

TechnicalReportLordCooperation,Cary,2002.8

Figure4showsthecoilcurrent,becausethemagneticfieldcannotbemeasuredduetothesmallbearinggap.

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