Application of the repulsive-type magnetic bearing technology based on digital control implementation for manufacturing a micro-mass measurement balance system

Application of the repulsive‑type magnetic bearing technology based on digital control implementation for manufacturing a micro‑mass measurement balance system

著者 Hussien Mahmoud Alaa Abdel Moneim

著者別名 ホセイン マハモド, アラー アブディル モーネイ

ム journal or

publication title

博士学位論文要旨 論文内容の要旨および論文審査 結果の要旨／金沢大学大学院自然科学研究科

volume 平成19年9月

page range 16‑30

year 2007‑09‑01

URL http://hdl.handle.net/2297/26679

ＡｍＡＡＡＢＤＥＬＭＯＮｍＭＨＵＳＳＩＥＮＭＯＨＡＭＵＤ 博士(工学）

博甲第８４１号 平成１８年９月２８日

課程博士（学位規則第４条第１項）

ApplicationoftheRepulsive-TypeMagneticBearinglbchnologyBasedon DigitalControllmplementationfbrManufblcturingaMicro-Mass

MeasurementBalanceSystem

．（極微小質量計測天秤へのデジタル制御反発形磁気軸受の応用に関する研究）

山田外史（自然計測応用研究センター・教授）

岩原正吉（自然科学研究科･教授)，上杉喜彦（自然科学研究科･教授)，

神谷好承（自然科学研究科･教授)，滑川徹(自然科学研究科･助教授）

氏名 学位の種類 学位記番号 学位授与の日付 学位授与の要件 学位授与の題目

論文審査委員（主査）

論文審査委員(副主査）

学位論文要旨

Abstract

Therepulsive-typemagneticbearingtechnologyisbecomingattractivefbrmany applicationsinrecentyears，specially，fbrtllehighprecisionmstmnents・Ｔｈｅmost importantfeatureofmagneticbearingingeneralisthecontact-丘eeoperation・Inaddition，

tllerepulsivetypespeciallyofferslnanyotlleradvantagessuｃｈａｓ，slnallnumberof electromagnetsandasmnplifiedschemeareneededfbrcontrol，italsohaveasoftand constantstifnesstothepassivecontrolaxis・so,tllistypeofbearingisriglltsuitedfbr lnanyapplications、Inthisthesis，tllerepulsivetypemagneticbearingbasedondigital controlilnplementationisemployedtomanufactureabalancesystemwhichcanmeasure nncrolnasses､Theproposedsystemconsistsofanaxialshaftandabalancebeam,tlleshaft islevitatedalongtlleradialdirectionbytllerepulsivefbrcesoftllelnagneticbearing sectionandalongtheaxialdirectionbyacontrolledelectromagnet・Thebeamiskeptatan eqUilibriumhorizontalpositionTheprincipleoperationdependsontransfeningtllelnass

valuetotllecurrentofacontrolledactuator・Thefimctionoftllesystelnasamass

measuringdeviceisconfirlnedbyｍｅasunngsomesamplesandevaluatmgtllesystem lneasurelnentcharacteristicssuchassensitivity,controlcurrenthysteresisandlinearity．

１.Introduction

Itiswellknownthatelectronicsnowprovidetlle‘brams，fbrtoday，sadvancedsystems

andproducts,nncromechanicaldevicescanprovidetllesensorandactuator,tlleeycsand ears,handsandfeetwhichinterfacetotlleoutsideworld・Fordevelopmgbothelectronics andnlicrolnechanicalsystems,tllefieldofmaterialsciencehasgivenmuchofinterest､One oftlleimportanttopicsofmaterialscienceistllematerialcharacterizationwhichis perfbrlnedtospecifWllephysicalpropertiesoftllematerials・ThematerialCharacterization canbeachievedthroughsomechelnicalanalysissuchasdifferentialtllermalanalysis (DTA)andtllermogravetencanalysis(TGA)．

Themassmeasurementdeviceswhichhavehighmeasunngsensitivitytodetectthelninute

changeofasa【nplemassarenecessaryfbrperfbrnmngsuchkindofmaterial characterizationanalysis・Insomeapplications,therangeofthatchangereachestllｅｏｒｄｅｒ ｏｆ皿crogramsorevennano-grams・Ｔｈｅｉｍｐｏｒtanttopictobeconsideredwllile lnanufacturinghighsCnsitivitymassmeasurementdevicesistllebearingmetllod、The repulsive-typemagneticbearingisanon-contactoperationmetllod,ｓｏｎｏｐｒｏｂｌｃｍａｎｓｅｓ 丘Cl、随ctionwhichusuallyaffectstllesystemsensitivity・Inaddition,itisasmgle-axis controlledsystelnsotllenumberofperipheraldeviccssuchassensorsandactuatorsare

－１６－

reducedandasaresultsilnpleandsmallsizesystemdesignispossible､Anotllerimportant featureofthattypeOfbearingisthesoftandconstantstifnesstotllepassivecontrolaxis wllichensuresgoodlevitationstabilityalongtheradialdirection［1]-[3]、so,fbrtlle applicationsoftheearlierreqUirements,therepulsive-typemagneticbearingisrightsuited fbrnlanufacturiｎｇｗｈａｔｉｓｃａｌｌｅｄ“Repulsivctypemagneticbearingnucromass

lneasurementsystem.,,

Inthistllesis,theconfigurationoftherepulsivetypemagneticbearingsectionandfbrces analysisisgivenThissectionisemployedfbrmanufacturingtlleproposedbalancesystem whichconsistsoftwomainparts，tlleaxialshaftpartandtllebalancebeampart・The completesetupoftlleproposedbalancesystemandtheoperatmgfeaturesaremcluded

Thesystemmathematicallmearizedmodeisobtamedandcontrollersfbrbothshaftand

beamareimplementedaroundaDSP､Theexperilnentalresultsfbrconfirn血gtllefUnction

oftllesystemasalnassmeasuremelltdeviceandevaluationofitScharacteristicssuchas

linearity,accuracy,andprecisionaregiven[4],[5]．

2.Configurationoftlnerepulsivetypema窪neticlDearingsection

2.ＩＳｍＪｃ"〃qﾊﾉjePMsecがo〃

Thestructureoftherepulsive-typemagneticbeamgsectionisshowniｎＦｉｇｌ（a).It consistsoftwounits，eachunitconsistsofacylindricalstatormagnetandacylmdrical rotorlnagnetmade丘omNeodylniumIron-Boron（Nd-Fe-B）materialbecauseofits excellentmagneticpropertieswhicharementionedearlier,Thedimensionsofbothstator

androtormagnetsisalsoillustratedWhereapieceofmagneticmaterial(，Odeg)covers partoftllestatorlnagnetmordertoinlprovetllerepulsivefbrcecharacteristicsasitwillbe explainedlater・Thestatormagnetconsistsoftwopiecesattachedtogetller、TY1eradial repulsivefbrcesbetweentllestatorandrotormagnetslnaketllerotorlevitatedstablyalong

theradialdirectionwheretheaxialdirectionisunstableandneedsacontrolled electromagnetinordertostabilizetllerotor・Duetosolnemanufacturingdefectsor fabricationdifficulties,thereissomemagnetizationasymnetryofmagnetsandasaresult tllefnbricatedmagnetsOftllesamematerialanddimensionsarenotidentiCaLSo,befbre settingtllemodel,bothofthestatorandrotormagnetsshouldbeselectedtobesinlilari.e‘

manypiecesofrotorandstatormagnetsshouldbepreparedandthefluxdensity

distributionofeachpieceshouldbemeasuredmordertoselecttllerotorandstatorleftand rightmagnetsthathaveconstantfluxdensitydistributionaroundtllesurface,inaddition thefluxdensitiesvaluesofbothleftandrightmagnetsshouldbeascloseaspossibleto

eachotheH

２２Ｆi"舵eﾉe川e"/αＭ)ﾉＩＤ応q/rﾉｶePMsecがo"伽〃

TheFEMmodeloftllePMsectionisshowninFig､１(b)Theaxialrepulsivefbrcesare calculatedusmgtlleMaxwell3-Dprogrａｍｍｏｒｄｅｒｔｏｕｓｅｔｌｌｉｓｄａｔａｆｂｒｄｅｓｉｇningtlle electrolnagnetusedfbrcontrollmgtlleunstabledirectionHowever,ｔｈｅｒａｄｉａｌｆｂｌＣｅｓａｒｅ calculatedinordertoensuretllestabilizationalongtllatdirection.Asshownmthenlodel，

bothoftheleftandri=htstatorconsistsoftwopiecesofNd-Fe-Bperlnanentmagnetand

tllestatoriscOveredbyamagneticshuntmateriaL

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（a)Structureofthesection （b)FEMmodelofthesection

Fig.lConfigurationandFEMmodelofthePMrepulsivetypelnagneticbearing

Thecalculatedaxialrepulsivefbrcesmcaseofusingonepieceandtwopiecesstatorsare showninFig.Ｚ(a)nisclearfiPomtllecalculateddatatllattlleaxialfbrcemcaseofusing twopieceSstatorislessthanthefbrcemcaseofusingonepiece・Inadditiontllerangeof fbrcclmearityiswiderwitlltwopieces・Sotllestatorisdesignedastwopiecesbecausein tlliscasethefbrceneededfbrcontrollingtllatdirectionwillbelesstllanthefbrcemthe caseofusingonepiece,tllatmeanssmallandsnpleelectromagnetdesignisreqUired・Thc surfaceofthe叩perpartofthestatoriscoveredwithironshuntmaterialwithdifIerent centerangles・TWocenteranglesaresimulated,g0degreeand360degree､Attachmgsuch shuntmaterialaffectsbotllaxialandradialfbrcecharacteristics・I、Fig.２(b),theaxial repulsivefbrcewithoutattachmgtheironshuntandwithironshuntofcenterangles90 degrceand360degreeisshownTheironshuntofbotllcenteranglesdecreasestheaxial fiorcc,but90degreeispreferablebecauseofbetterlinearity・Decreasingtlleaxialrepulsive fbrceisdesirablefbrasimplecontroldesign・Furtllerlnore,tllisshuntincreasestlleradial repulsivefbrcealongz-directionandmakesitalwayspositivewhichisdesirablefbrbetter stability・Thisisclearlyillustratedin]Fig.３(a)Wheretlleradialrepulsivefbrcewithout attachingtheshuntandwith90degreeofironshuntisshown､Thenegativegradientofthe radialfbrcecharacteristics(i､e､positivestiffiless)contributetopassivestability・Theradial repulsivefbrcealongy-dircctionisalsocalculatedmbothcases(witllandwitlloutshunt）

andshownmFig､３(b)Ｔｈｅｙ当directionfbrcechangeslinearlywillltlledisplacelnentand

lncreasesalittlewhenthestatoriscoveredwithtllemagneticshunt．

1０

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AxialdispkmcmantOnlm0

(a)Usingoneandtwopiecesstator （b)Withoutandwithmagneticshunt Fi9.2CalculatedaxialrepulsivefbrcescharacteristicsofthePMsection

６

－１８－

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５２５１５０５２１００（巴三国田富②。』巳。昌已三壱塁 ２８４０４８１００心心Ｃｅ一一【田冨の自己の彦窃己（読昌呵弓飼国

-11 ^{０．８－０４} -..、…△･・-1.Ｚ－U､８－０．４００．４０．８､-４ ^と1.2-1.2 -0.8 -0.4

Z-dircctiondisplacement(m､）Ｙ白diIcctiondisplacement(m[I0

lZ-dilectionfbrcecharacteristics （b)Y-directionfbrcecharacteristicｓ

Fig.３CalculatedradialrepulsivefbrcescharacteristicsofthePMsection．

Z-dircctiondisplacementOnm） 1.2

(a)Ｚdilectionfbrcecharacteristics

Pannanent controlled

ｅ

ＪｎＩＰ ^ａ回ｎＥｔ

Gapsensor

uapsensor

Stopperplate

Fig4Configurationoftlleaxialshaftpart、

３.Configurationoftheaxialslmftpart

TheconfIgurationoftheaxialshａｆｔｉｓｓｈｏｗｎｍＦｉｇ４，Wherethetwounitsoftlle

permanentmagnetsareinstalledaroundthecenterpoint；tllestructureoftllissectionis

explainedearlier.BasedonEarnshawtheorem,theaxialshaftisunstablealongtheaxial direction,soacontrolledelectromagnetismstalledtogenerateanattractiveforce，This fbrceismodulatedthroughacontrolsystemwhichreceivestheshaftpositionmfbnnation fomagapsensormstalledtotheleftsideoftheshaft・Theexplanationofeachpart mdividuallyisgivenmtllenextsUbsections、Astopperplateisplacedinordertostopthe

movementoftheshaftwhilenooperationFurtllennoreabalanceweigI1tisplacedatthe otllerendoftheshaftinordertokeCpitmeqUilibriumposition

3・ＩＥﾙc加川cJg7zeM己Sｉｇ７ｚ

ＴheEarnshawtlleoremstatesthat,ａｔleast,onedirectionshouldbeactivelycontrolledin ordertoachieveastablenon-contactlevitationmmagnetstatic・so，anelectrolnagnet

deviceismstalledbesideanironplatefixedintlleshaft・Thedetailsstructureofboth E1ectromagnetandironplatearｅｓｈｏｗｎｉｎＦｉｇ４ＴｈeEMconsistsofanironcoreand０．６

，mndiametercoppercoilof683turn,８．９１ohmresistanceandO・O6Z4henerymductance・

Thisdeviceisusedtogeneratetherequiredstabilizingfblce，IIlfact,theelectromagnet causestheflUxtocirculatemalnagneticloopWhenanalyzingsuchmagneticloop,an

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exacttheoreticalcomputationofthefieldisrarelypossibleandseldomreqUired・One usuallyworkswitllanalyticmetllodsOfapproximation，basedontllesimplifj/ing assumptionthattlleflux,exceptfbrintheairgap,runsentirelythrouglltlleironSmcetlle permeabilityofironisconsiderablylargerthanthatofair,tllemagneticfieldlinesleave theironalmostperpendicularly・TheEMfbrcecanbeexpressedasfbllｏｗｓ

涙―だ

Ｋ一一

涙一万

。〃α４２Ｎ０匹’一乎一一Ｆ

ｗｈｅｒｅＮ,iaretheNoofturnsandcurrentofthecoilrespectively,xistheaxialgap,Aairis tlleareaoftheairgapbetweentheEMandironplate,川istllepemeabilityoftheair．

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+Ｌ

4のＬノ⑪

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（b)Ironplate (a)ControlledEM

Fig､４ConfigurationoftheEMandIronplate．

５３５２５１５０３２Ｌ０（庭）８衿＆］①［助ロ日○垣。①［四

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-I－Ｕ－ｆ

u－－口---口－－乱

Axialgap(m､）

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(a)FEMmodeloftlleEM （b)EMfbrcecharacteristics

Fig・SThecontrolledEMmodelandfbrcecharacteristiCs．

ThefiniteelementlnodeloftheelectrolnagnetdeviceisshowninFi9.5(a)wherethe attractivefbrceiscalculatedasafimctionoftheairgapandthecoilcurrentusingMaxwell 3-Dsoftware・ＴｈｅＥＭｆｂｒｃｅｖｓ・axialairgapcharacteristicsfbrdifferentcoilcurrentsare

showninFig5(b).TheaxialairgapchangesfieolnOto2mnandthefbrceiscalculatedat 0.24Ａ,０．４８Ａａｎｄ0.72Acurrent､TllefbrceisinverselyproportiOnalwiththeairgapand directlyproportionalwitllcoilcurrent､Inordertoachieveastablenon-contactlevitation，

theEMfiDrcecharacteristicsiscomparedwiththePMrepulsivefbrcecharacteristicsfbr

deterIniningtllesteadystateoperatingcurrentandgapThisinfbrlnationisneededfbr implementationofthecontrolsystemwhichisemployedtoadjustthecoilcurrentattlle

－２０－

steadystateoperatingpoint・TheEMsteadystateoperatingcurrcntissetatO48Aandif fbranyreason,tlleairgapischanged,tllecoilcurrentshouldbealsochangedmorderto keeptlleEMfbrceconstantallthetimefbrachievingstablelevitation

3.2dxjZJﾉｇ叩Ｓｃ"so7

Theopticalsensorisfastandhasagoodsensitivity；maddition，itismagnetically mdependent,simpleandcheap､Fortllesereasons,aphotosensorisusedfbrdetectingthe displacementoftheaxialshaft・ThestructureoftllephotosensorisshowninFig､６(a)，

whereitconsistsofaliglltemittingdiode(LED)(GL513F)andaphotodiode(PD)(MI- 33H2D).TheLEDemitsUlelightandtllesllutterobstructstllelight・TheqUantityoftlle

Lightreceptionside 0５ _Ｖ ^０１

iＶＩ２ ゴＩＳｅｃｔｌｏｎｐｈｏｔ⑥。、。［

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（b)Outputcharacteristics Fig､6thephotogapsensorstructureandoutputcharacteristics.

incidentliglltonthebisectionphotodiodeischangedasthepositionoftheshaftis changedandasaresulttlledifferentialoutputvoltageischangedaswelLTllesensor

characteristicsisshowninFig6(b）

4.ＣＯnfHgurationoftllebalmncelDeam

ｲ.ＩＢａｍ"ｃｅ６ｅα〃ＷｉＺﾉbelecかo川ag7zetcMWam7

ThefirsttrailofmanufacturingoftllebalancebeamisshowninFig､７Itconsistsofabrass bar,ａｔｏｎｏｆｉｔｓｅｎｄｓ，ａｎｉｒｏｎｂａｌｌｉｓａｔｔａｃｈｅｄａｎｄａＭｈｅｏｔｈerend,analunmnumSample holderisplaceｄＡｓｍａｌｌｓ]mtterisfixedattheholdersidewhereaverticaldisplacement sensorisalrangedandinstalledbesidetlleholderinordertodetectthedisplacementofthe bearnwhentllesampleisaddedtotlleholder・TY1issensoristllesametypeofUleaxialgap sensorusedfbrdetectingtheaxialshaftdisplacement,butitisonlyarrangedmdifferent waytodetecttheverticaldisplacement・ThemfbrlnationofthebeampoSitionistransfelred mmtllegapsensortoacontrolsysteminordertoadjusttlleattractionfbrceofan electrolnagnetwithironcoremstalledundertheironbalLThisEMattractionfbrCeis

changedaSthepositionofthebearnischangedinordertolKeeptllebeamlnequilibrium

horizontalposition、Asitisexplamedearlier，tlleEMreluclancefbrceneededfior stabilizmgtheaxialshaftisdirectlyprOportionalwiththesqUareoftheEMcurrentanditis

samefbrtheEMusedfbrkeepingthebeamhorizontaL

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－２１－

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Jｅａｎ ｎｎｑｉ囮Iｕｈｕ

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Fig.７BalancebeamwithEMactuator，

Avoicecoilmotor(VCM)actuatorissuggestedtoreplacetheEMwherethestabilizing fbrceisproportionallmearlywithcurrent・ReplacingtheEMwiththisdevicewillincrease thesystemsensitivitywhichisdesiredfbrmeasuringtheslnallsamples・Anotherimportant aspectistllesaturationofEMironcoreandthemagnetichysteresis，itmcreasesthe

measurementerror．

ｲ.２Ｂａﾉ[J"ｃｅ６ｅａ川wjZZlvojcecoﾉﾉ川om7

TllemodifiedbalancebeamconfigurationisshownmFig、８．ＴｈｅＥＭａｎｄｉｒｏｎｂａｌｌａｒｅ

ｒｅｐｌａｃｅｄｂｙａvoicecoillnotorastllebeamactuatortoavoidthedifficultiesmthedesign

andcontroLSomeofthesedifficultiesarethenonlinearityoftlleEMreluctancefbrce,tlle

colnplexdistributionoftllefluxintlleairgap,andthesaturationoftheEMcoremateriaL

TlleVCMattractionfbrceislmearlyproportionalwitlltllecoilcurrentandasaresult,tlle

systemmeasurementsensitivityisbeconlinghigherthanintllecaseofusmgEMwheretlle

fbrceisproportionaltotllesquareoftllecurrent．

手.３８Ｊ'wc〃eqﾉﾝﾉｉｅＦＣＭα"cMie抑ｊＭＣ川ilﾘﾉ伽伽〃o〃

TheconfigurationoftheVCMisshowninFig.９(a)itconsistsofanironyoke,afigureof eigImtcoppercOiloflOturnsand0.61mndiameter,andtwopiecesofpennanentmagnets areattachedtotheinternalsidesoftlleyoke・Thepemanentmagnetisconsideredaｓa sourceofastationeryflux,Thefbrceexertedonthecoilisgiveｎｂｙ

Ｆｃ.〃＝Ｂ､/､lVj

WhereBistllefluxdensityinsidetllegap,Mstllenumberofcoiltums,ノistllelengtllof thepartoftllecoilwllichliesinsidetllegap,andjistllecoilcurrent､AsillustratedmFig、

9(a),thedirectionofthefbrceexertedonthecoilis叩wardaccordmgtolefthandrule・But becausethecoilisfixedandtheyokeisfiPee,tllereisareactiondownwardfbrceexertedon

theyokeasgivcnintheeqUatiOnbelow・Thisattractionfbrceexertedontheyokekeepsthe

balanceofthebeam．

Ｆ,､＝Ｆ"庭＝－Ｆ・ojl

TllesimulatedlnagneticfileddistributionoftlleVCMmodelbyMaxwell2-Dsoftwareis shownmFig.，(b).T11efluxdensityattllelmeW11ichliesmthemiddleoftlleairgap insidetheyokeiscalcUlatedusingtlle2-Dfiniteelementmetllod・Itisclear丘or、Fig.３－１４

thatthefluxdensityattllatlmeisparabolic．

lｅｒｍａｎＣｍ

Ｊｅｒｍａｎｃｍ okc

aIZnI ＴａＥｎＣＩＳＣＵＬ１ｕＬ

Fi窪.SBalancebeamwitllvoicecoilmotor、

－２２－

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mDI

、

（伊日）、｛目呂旨逼

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澪、

DiSplacemBntOnllD

（aWCMconfiguration 化)F1uxdensitydistribution

Fig・DVCMstructureandfluxdensitydistributioninsidetllegapatthecenter ５.ConfigumtionofthecompletesystemandprincipleolDeration

ThetOpviewoftllecompletesetupoftllerepulsivetypemagneticbearingbalancesystem isshowninFiglO・Theaxialshaftandtllebalancebealnareattachedtogetllerattl1e centerpoint・Thehybridlnagneticbearingsystemwhichincludestllepennanentlnagnet unitsandtheelectromagnetwithactivecontrolhelpsthesettobelevitatedstablywitllout

contact・ThelnostconⅡnonproblelnarisesmallconventionalbeambalanceistlleEiction atthefillcnⅡ､;thisproblemdecreasestheequiplnentsensitivity・Thenon-contactlevitation oftheproposedsystemovercomesthefiictionproblemseckingfbrbettersensitivity・

Tlleproposedmagneticlevitationmassmeasurelnentsystenlisbasedoninstallinga controlledbalanceｂｅａｍａｎｄｕｓｅｓｉｔａｓｔｈｅｍｅａｓｕｒｉｎｇｄｅｖice，sotllemeasuremem sensitivityishigherthanthatoftlleconventionalmechanicalbearingsystelns・Also,tllis systemcanbeusedtodetecttherelativevaluewhichismassWheretheeffectofgravityis elinnatedlnsomeapplications,itisneededtodetectthelnasschangeofasamplewhere

tllischangeisresultingffomheatingorpressurizationSincethebalancebeamofthe systemisdesignedsothatthesampleholderandtheactuatoraredistantenough，ｉｔｉｓ ｃｏｎｖｅｍｅｎｔｔｏｂｅｕｓｅｄａｓａｔｈｅｒｍｏbalancewhichiswidelyusedfbrthechenlicalanalysis・

Someoftlleseanalysissuchasdifferentialthennalanalysis(DTA)andthenno-gravimetric analysis(TGA)areusehlfbrmaterialcharacterizationapplicationS

TY1eprincmleoperationoftlleproposedsystemdependsontransfelTingtheadditionalnlass tothcactuatorcontrolcurrent・Ｗｈｅｎｔｌｌｅｓａｍｐｌｅｉｓａｄｄｅｄｔｏｔｌｌｅｈolder，tllebeamis

distUrbedanditspositionischangedTheverticaldisplacementofthebeamisdetectedby thegapsensormstalledbesidetlleholderandbythehemofdigitallyilnplementedcontrol system;tlleactuatorcontrolcurrentischangedinordertogeneratetllefbrcenecdedto keeptllebeamatitsorigmalposition

TllefimctionofmassmeaSuringisconfirmedbyaddingsomesalnplestotheholderand noticingtllevoicecoilcmrentchange、Ｉｎｏｒｄｅｒｔｏｐｒｏｖｅｔｌｌａｔｔｌｌｅｓｙｓｔｅｍｍeasurestlle colTectsamplemass，ｓｏｍｅｓａｍｐｌｅｓｏｆｋｎｏｗｎｍａｓｓｅｓａｒｅａｌｓomeasuredaftercalibrating thesystemThedetailsofexperimentalresultsofmeasurementandtlleevaluationoftlle systemmeasurementperfbnnanccssuchaslincarity,accuracy,precisionandrepeatability

willbegivenlater．

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Aftertheanalyticalmodelsofbothｓｈａｆｔａｎｄｂｅａｍａｒｅｄｅｒｉｖｅｄａｎｄｔｌｌｅｓtatespace equationsareobtained，thecontrollersaredesignedusingthelinearquadraticoptimal controltechniquewheretheblockdiagrarnofshaftandbearncontrolsystemｓａｒｅｓｈｏｗｎｉｎ Ｆｉｇｌ２.TheblockdiagramofthewholesystemwithcontrolisgiveninFig、１３where4- channel，１２bit,２５KHzanalog-to-digitalconverterreceivesthevoltagesignalsfromboth oftheaxialandradialgapsensorswhichexpressthedisplacementofbothshaftandbearn Thesevoltagesignalsarefedtothecontrollerafieritisbeingconvertedintodisplacement signalsThecontrolleroutputispassedtothedigital-to-analogconverterandthenthe controlsignalsarefedtothernagneticbearingactuators(ＥＭａｎｄＶＣＭ)throughpower

amplifiercircuits・

ThecontrolprocessstartswithrunningtheMTALABprogramtocalculatethecontroller feedbackmatricesandthengeneratingthereal-timecontrolsignalsbyexecutingthe

MTALBSIMULmKcontrollermodeLBythehelpofルpasssoftware,theexecuteddata iSsubmittedtotheDSPandafterthatthemagneticbearingsystemisoperatedltis

confirmedtllatthepreviouslydesignedcontrollerscouldachievestablelevitationofthe systemalongtheaxialdirectionwherethebeamCouldbekeptatanequilibriumhorizontal positionevenafteritissubjectedtoextemaldisturbance．

四ｍ：

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7.Massmeasurementmdevaluationofthesystempermrmmces

AfterthesystemismanufacturedandtllecontrollersaredCsignedandimplementedaround aDSP，theexperimentsarecarriedoutonthesystemtoconfinnthefimctionofmass measuringandevaluatetlleperfbrmances・Intllefirstexperiment,somesamplesofequal rnassesareaddedgraduallytotllemassholderandremovedbythesarneway､Ineachtime

tllecontrolcurrentisnoticed,Tllecontrolculrentvs､samplemasscharacteristicsisshoｗｎ

ｉｎＦｉｇｌ４(a)wherethebeamactuatorisanEMwitllironcore・Thecontrolcurrent variationismcreasedasthesamplemassinsidetheholderisincreasedAssｈｏｗｎｍＦｉｇｌ４

〔b),tlledifferencemtllecontrolcurrentbetweentllemcreasingdirectionanddecreaslng whichisdefinedbythellysteresisisinvestigatedbyzoomingintoFigl4(a).Itisfbund tllatthesensitivityisqUitelowandtllevalueoftllellysteresisiseqUivalentto730}L9.and thenon-lmearityerroroftllecharacteristicsisabout５％ofthefilllscalecurrent．

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BecausetheEMfbrceisproportionaltotllesqllareofthecoilcurrentandlheproblelns arisehomironcoresaturation,thesystemmeasurementcharacteristicsarenotsatisfactory・

nleEMisreplacedbyvoicecoilmotordevicewheretllefbrceisproportionaltothecoil culrentandthesourceofthefluxispennanentmagnets(ＰＭ，s)hlordertokeepunifbnn fluxdensitymsidetlleyokegapfbrcertainrangealongtllecenter,sonlepennalloyfilnls areattachedtothesurfaceofthePM，s;thishemfbrdecreasingthecmremhsteresisBy lllesamewaytlleexpemnentsarecarriedoutontllesystenlandsamplesofeqUalmasses areaddedglHduallyandremoved・Thecontrolcurentvs、samplemasscharacteristicsis showninFig､１５(a).Itisfbundtllatthesystemsensitivityismcreasedtomoretllantwo times;tllellystersisisdecreasedtolOl』gandthenonlmearityerrortoabout１％・A1sothe readabilityoftlleSystemwasabout751LgasillustratedmFigl5(b)．

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Inordertomcreasethesystemreadabilityandsensitivitywllichistllemainobjectivefbr proposedsystemtheeqUalbrassbeambrassbeamiSreplacedbyunequalambeammade 丘omDuralun血wllichisliglltandstiffmateriaLＴｈｅａｎｎｌｅｎｇｔｌｌｔｏｔｈｅｈoldersideis becon血gdoubletheamlengtllattheactuatorside,andtlleflatmassholderisreplacedby aknife-edgeone・Aftertllismodification,thesystemsensitivityisdoUbledasshownmfIg andtllenonlmearityerrorisdecreasedto0.2％asshowninFig､１６(a)Wheretllereadability rcached3OILgasshownmFigl6(b).AnotllereXperilnentiscaneiedOutontllesystemto evaluateitsaccuracyandprecisionWherethereadingofthesystemiscomparedbytlle readingofaMattlerToledobalanceAB204-s(2209×0.1ｍｇ).Intllisexpelimentsome samplCofdifferentmassesintllerange金omO-100mgarepreparedandmeasure,firstby MettlerTolcdobalanceandthenbytlleproposedsystenl・AsshownmFig､１７(a),the maxnnumdifferencemthereadiｎｇｂｅｔｗｅｅｎｔｈｅｔｗｏｓｙｓｔｅｌｎｓｗａｓ0.2ｍｇ、hanother experimenteachsampleismeasuledbytheproposedsystemlnanytinlesandtllestandard deviationiscalculated・Itisfbundthatthemaxinmndeviationwasabout0.1mgasgiven

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１８(b)．

9.Conclusi皿

T11erepulsivetypemagneticbearingisriglltsuitedfbrmanufacturingsuchsystenlbecause ofitsnon-contactoperationW11ichmakestllesystelnmoresensitivethantlleconventional bearingbalances､Moreover,ｉｔｉｓｓｍｇｌｅａｘｉｓｃｏｎｔｒｏｌｌｅｄａｎｄａｓｒｅsult,asimplifiedcontrol schemeisneededfbrcompletelystablelevitation､Thedesignprincipledependsonusmga balancebeamwitlltwoendsfbrtllemeasunng,ｗｈｅｒｅａｔｏｎｅｅｎｄ,themassholderis locatedandanactuatorislocatedontheother・Ihisenablestheusertoclinmnatetheeffect

ofgravityandasaresult,measuresthelnassoftllesanlple・Thebalancebeamisdesigned sotllattllesampleholderandtheactuatoraredistant;sotllissystemcanbeusedtodetect tllechangemtllelnassofasampleasafimctionofacontrolledtemperatureand/ortinle wllichisknownastllerlnogravimetericanalysis（TGA)．Theexperimentalresults confirlnedtllatthesystemcanmeasuretllemassofthesanlpleswitllsatisfactory

measurementperfbnnances．

hfilture,tlleplanofworkwillconcernwitllusinganothercontroldesignteclmiqUesuch asH-oocontrolWhichconsiderstllemodeluncertaintysuchasumnodeledhigh丘eqUency dynanmcs，neglectednon-1inearties，andplantparameterperturbationsdueto environmentalfactors・Usingsuchcontro1teclmiqUewillincreasetllesystelnlDbustness

andinlprovetllesystelnperfbrmancesandasaresulttllemeasurementerrordecreases．

References

[1］Ａ・Hussien,Ｔ,Okada,TOhji，Ｓ・Yamada,ａｎｄＭ､Iawhara,“Arepulsive-type magneticbearingnncro-massmeasurelnentsystemandmeasurementofresolution"，

Ｔｍ"Ｍがo"q/・伽MZgMjcSbcjel1WMW",voL4,no､２，pｐ51-55,2004

[2]AlaaA・Hussien,TomotadaOkada,TakallisaOllji,SotoshiYamadaandMasayoshi IWallara,“Investigationoftheconfigurationandcontrolofarepulsive-typemagnetic levitationsystemusedfbrlnicro-massmeasurement"Ｐ'wee伽ｇＱかＡＢＩ砂ＳＥ4,.,

ＪUne2004,Kyushu,Japan

[3]Ｔ､Okada,A1aaA・Hussien,Ｔ・Ohji,Ｓ・Yamada,andlnasayoshilwallara"APennanent Ma印etRepulsiveTypeMagneticbearingBalanceSystem，，ProceedingsqMbe3〃

・ﾉZIPα〃AzJMJﾉﾒα,jVbwZba伽肌ﾉb〃比〃"〃ｏ'MZ2pﾉｊｃａがo"ｓｑ/Ｅﾉｃｃ加川cJgMic Pﾉbe"o〃e"αｊ〃Ｅﾉecmcaﾉα"αMCCA〃jcaﾉ＆〕入y花川.pp53-57,January2004,Auckland，

NewZealand．

[4]Ａ,Hussien,Ｔ・Okada,Ｔ・Ollji,Ｍ,Iawhara,ａｎｄＳ,Yamada"Improvelnentoftlle meamenlentcharacteristicsofaInagneticbearingbalancesystenf，,Ｚ７ｗｚＭｃがo〃q/､伽 MJg7zeZjcSbcjel【Ｗ/〔ﾉﾋZpα",vol､５，no､２，pp.，7-100,ZOO5．

[5]A1aaA・Hussien,Ｓ､Ｙamada,andMIawhara,Ｔ,Okada,andT､O11ji"Applicationof tllerepulsive-typemagneticbearingfbrmanufactulingmcromassmeasurement balanceequipment，，,｣EEE伽"Ｍｃがo〃Ｑ/MJg7ze伽,vol41,ｎｏｌＯ，pp3802-3804

０ct2005.

－２９－

学位論文審査結果の要旨

－．当該髪f之諭Ｘに対上Ｚ,_妥成11.霊Z且.qL且に第.廻諭文審査委壜会迄關催L`-2-回窪.１日.1旦腫 行われた口頭発表後に第２回論文審査委員会をＦＭｉＬ討識した結果，以下の通り判定した。

●●●●●●●一口ＰＣ●ＣＣＣ●■ＣＤ●■■－･●ロロ●●■●･￣￣■￣●●●￣●●●￣●●●●の●･●･ＤＰＣの●●●●●●●●●●●の●ロ゛●●●●●●●●■●い●｡●●●●･￣･ＤＣＣ●●の●●●●●●●●･￣⑰゛■ローロロ■￣●ＰＣ●￣●●･の●●･ＣＤＣ●･●⑤■●￣￣ロー￣｡●●●･●●

本研究は，1111''1不安定特性をもつ永久磁石反発磁気lIilll受をデジタル制御により安定させた非接ｌｉＩＩｌ

ＣＣ－Ｃ●ＤＣ－●ＤＣＣＣＣ￣■●□￣●￣■･￣￣●●￣￣￣｡￣●￣￣■●●●￣●●●￣￣￣●●ロ゛●●●●･の●￣句一●●■●●￣■の゛・Ｐ｡￣■●￣ｃｃ●￣￣●￣￣●￣･￣●￣■●￣●￣･●￣ロ゛ＣＤ●●の●･￣●￣●の●●の￣●■￣￣。｡￣￣￣●￣￣ＣＤＣ●●●●●●ＤＣＣ●￣●￣●●￣￣￣･●つつ●一・ｍ￣●

磁j気Il11ll鷺と完全雑腱蹴P)徹ＩｌＩＬ鴦肌)進積蜜蝋4蝋城jMji三Ｍ)応用!篶闇式畳班寵で重量２．ｌ脇化の訂 能な本磁気''1111受機柵による精密微小質1,1【測定器の研究開発は,磁気Ili1Il受の特徴をibliも発揮できるも

ＣＣＤ●●□●－．－ＣＣＣ･●●●●●●■●ｃ－ＤＤＣＣ●●●●ＣＣＣ●●･●￣■●･￣￣■￣●■ＤＣ■■●￣￣●■ロ゛ｃ●●●●￣●ＣＯ￣ＣＤＣＣＣ●￣●●●●●●●￣●●･●●･･●ロ●●●●●●●●ＰＣＣ・ＣＣＣＣＣ￣￣■￣￣￣￣￣●●●●●●￣●●●●のＣＣＣの￣●￣￣￣￣ロローロロ･ＣＣＣ･の－■●●｡●⑤

のとして工学的|ご重要であり，以下にその研究成果を列記する。

－ロ・・・・・－．－．・ロの・・・・・・・○・・・・・・・の。■－．●・・・・・・・・－－－｡。●●－－○・－－●ｃ－－ＣＣ●●－－－｡●ローーウ゛●￣■ロ゛⑤￣。￣⑤●ＣＤＣ●●￣●●･●●●●●ＣＣＣ●●■￣

（１）永久磁石反発磁気llilll受の磁気回路椛成の設計

。●・－．．－■ロロー・ＣＤ・－･●ＣＯ●･ロ・・ロ・ロロロ－－．。●●しＤＣＣＣＣＣＤＣｃ●・￣●●●●●●●･●■￣●●･●￣￣￣￣￣￣ＣｐＣ●ロロ￣￣￣●｡●

？Ｍ礎ｴｺﾞ!Z壷磁気』IMI鷺９２磁気厚1鴎と反発力猿惟②閣侭に豆！)工:､磁気Ｚ：ｖＬＺｆ回路を提案LL鉱元 ｉｌ:9,11塁1iYj1tによ・１２錆性L9q賑１１１１量行kLJZ発力:_遡り性1-縫麗朧在.ど査制jmM菖雄p雄護itと迄２－

（２）質１１(測定用のパランサビーム系の検討

一・・・ｃ・－．．－－・・・●●・・・・・・の●・・・・・・・・・・●●－－．－－－－●・・一一・・■－－●Ｃ－ｐ゛－●－●●ＣＯ●●●●－￣

測定質:１１t用のバランサビーム系にボイスコイルモータを適用し,バランサビームの非接lIlllでの安定

・・．－一・一ｃ・・・・・・・一口・・・・□・ロ・・・・口・・・・－－ローーローロー■－■■●■。。■●－つ●。●－●●ＤＣ･￣●●･●□●･●･●●●●･●￣￣￣●￣●●￣￣。ｐ￣￣●●｡■ＤＣロ゛●●・●￣￣￣￣●●￣ロロ￣■●￣●￣●￣●￣￣●￣￣●●￣￣●ｃ￣￣●●･●･●●●●－●－－－●●■・・－－・・・

化，ならびに測定質:爪変化によるバランサ位|if移動から生ずる誤差発生を抑制することを実現した。

の－．－－・・ｃ一・・■－．－．．－・・・ＣＤ。。●･の●・ロ一一・・・・・●・一・・・一･●●・●●●●ＣＣＤ●●｡□ＣＣＤ■□●●￣■￣●●ロ゛●￣ロ゛￣●･口｡●●￣●￣●●●･●●ＣＯ□●●●￣●ロー￣￣￣￣￣・●●￣ＤＣ●●･●ＣｃＣ￣●￣￣￣￣｡●●●￣●■,●●￣￣￣●●｡●￣●●●●･●－ローＣＣＣ●ゥ①一・・

（３）システムモデリングとデジタル制1卸

Ｃｓ－－．．．ローロー・・・・・ロ・・・・・・・・・のロ・ロロ・・・・●。。－■－－つ・・・■・●●－●、■－．ｂ￣■■●■の□●●

/Liズヱ辻の磁気|M1量の制御奮旦αに質邸M定〃i重ヱﾅｺﾞ:ビームQzkjFP:制御1二粒し<x1-磁気系在三 LKl二機撞系Ｑ玉:壬.リヱ・互産行い王乏互｣脂量H1騨堕主負制ｊｌＷＺＸ壬△塗議ｉＬ噂．

（４）磁気I1ilI1受付質1,t測定器の性能の測定

・・・－口ｃ・・－●・一・・●・・・－．－－－．－ＰＣＣ一・○●・・の。－．□－－－－－－－－｡――ワー－－－－●－￣－－￣●ロー■

同室１云ﾑ量実｣験腫より量の蝋睦証伍し:左結果』…謎冠鷺瓜l:LLg-(雄大)..}二封LL工.,L…計111誤差』｣ｑ

蝋.騒止謎雄値、鵬２値塗侵迄具一

」》A上里ljlI究畦:．提塞Fr量永久磁石反発li臓ll1l11受囚撒'111塗熱)LL迄砿'i蜜興Ｍ１１定器を強試し《た噸

^{討した内容}

であり，i1j士（工学）iiiii文に値するものと判定した。

●●□●⑤ＣＤ●･･●●●●●●･･●｡－●●●●●￣●ＣＣＣ●ＣｏＣｏ･￣の●●￣･￣￣￣の●●●･ＣＯｃＣＣ￣￣□の●●●■■｡●●●●●●●●￣■･の●￣●●●●□●●●

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