机械毕业设计英文外文翻译342评价为微型工厂设计的微型机床的尺度效应.docx

机械毕业设计英文外文翻译342评价为微型工厂设计的微型机床的尺度效应.docx

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机械毕业设计英文外文翻译342评价为微型工厂设计的微型机床的尺度效应

英文资料

EvaluationofSizeEffectonMicro-machine-toolsDesignforMicrofactory

M.Yamanaka1,S.Hirotomi2andK.Inoue3

1TohokuUniversity,6-6-01,Aramaki-Aoba,Sendai980-8579,Japan,yamanaka@elm.mech.tohoku.ac.jp

2ShimanoInc,Japan

3TohokuUniversity,Japan

Abstract.Amicrolathewithamachinebasesizeof150×100mm（postcardsize）wasdevelopedbytheauthors.Ithasagoodcuttingperformanceforbrasstestworkpieces.Toknowthedevelopedmachineismostsuitablesizeformachiningthegivenworkpiecesize,theerrorfunctions,whichaffectthecuttingperformance,areexaminedhowtochangetothemachinetoolsize.Thecalculationmethodandasimplesizeeffectoferrorfunctionsareproposedandtheirusefulnessisexaminedbysomecalculationresults.

Keywords:

Microfactory,Machinetools,Lathe,Machinedesign,Sizeeffect

1.Introduction

Ordinaryproductionsystemsuseenlargedmachinetoolsaimingathighrigidityregardlessofthesizeofthepartsproduced.Theconceptofmicrofactoryistousesmallmachinetoolscorrespondingtotheminiaturizationofworkpieces.Thisisusefulforsavingresources,space,andenergy.Someprototypesweredevelopedtorealizethisconcept[1].OkazakidevelopedanNCmicrolathewhichis32×28×30mminsize[1].Parkdevelopedaminiaturized3-axismillingmachineof200×300×200mm[2].Theauthorsaredevelopingmicrolathesaimingatthepracticaluseinmassproductionsystemsofsmall/micropartsforoptics,ITandelectronics,untilnow[3].Themachinewithabasesizeof150×100mm（postcardsize）hasbeendevelopedandtherelationbetweenmachinecharacteristicsandcuttingperformanceareevaluatedtoclarifyadvantage/disadvantageofthedevelopedlathe[4].

Todesignmicromachinetools,itisimportanttoproperlyunderstandthemeritsanddemeritsofdownsizing.Mishimaproposedadesigntools[5]combinedwiththeform-shapingtheoryofmachinetools[6]andTaguchimethod[7].Itoffersasimplifiedmethodtoconsiderthedeformationofmachinetoolstructuresandthecomponenterrors.Thedevelopedmicrolathehasagoodcuttingperformanceforthetestworkpiece.However,itisobscurethatthedevelopedmachineismostsuitablesizeformachiningthegivenworkpiecesize.Itisimpossibletomakemanysizesofmachinetoolsandevaluatetheirperformances.

Inthispaper,theoutlineofdevelopedmicrolatheisintroduced,andtheinfluenceofaccuraciesaccordingtothemachinesizetothecuttingperformanceisexaminedinasimulation.Thecalculationmethodconsideringthesizeeffectonmicromachinetoolsdesignisdiscussedwiththecalculationresults.

2.MicroLathe

Themaximumsizeoftargetworkpiecewasassumedtobeφ5×10mmandthelathewasdesigned.ThesizeofthemachinebasewasdecidedtobeofA6size（150×100mm）foritsfootprintareaconsideringthedegreeofminiaturization,itspracticality,assemblyand,inparticular,asufficientrigidity.Eachdeviceofthemachinewasdesignedwiththisrestriction.ThedevelopedmicrolatheMTS2（productofNanoCorporation,Japan）isshowninFig.1.1.XandZ-axistables,whichusethesamemodules,areguidedbycross-rollerways,anddrivenbyaφ2-trianglescrewthreadandanAC15-mminsquareservomotor.Thesizeofthetableisabout50×80mm（excludingmotor）.Theweightincludingthemotoris585g.TheheadstockisfixedontheX-axistableandthetoolpostismountedontheZ-axistable.

Figure1.1.AppearanceofdevelopedmicrolatheMTS2（NanoCorporation,Japan,basesize:

150x100mm）

Amicromotorof16mmdiameterisusedtodrivetheworkspindleintheheadstockfromthebalancewiththetable.Arotaryspeedofmorethan10000min-1isnecessarytoobtainacuttingspeedofabout150m/minforsmall-diameterworkpieces.Becauseofthis,adirectdriveispreferred,butareducerisrequiredtodrivetheworkpiecebecausethemotortorqueofaφ16mmclassmotorisextremelysmall（onlyafewmNm）,whichisgenerallynotenoughtoobtainasufficientcuttingpower.Therotaryspeedissecuredasmuchaspossiblebyselectingahigh-speedmotor.Theplanetaryrollerreducerusingtractiondrivesisadoptedforthisworkspindle.Thereductionratiois4.Thesizeandweightoftheheadstockis75×40×30mm,itsweightis230g（includemotor）.

3.CalculationofErrorinConsiderationofSizeEffect

Therearemanyerrorfunctions,whichaffectthecuttingperformance.Here,onlyfourerrorfunctions,namelytheassemblyerror,themotionerror,thedeformationbycuttingforceandthethermaldeformation,areconsidered,andhowtheychangetothemachinetoolsizeisexamined.Thenweproposethecalculationmethodoferrorinconsiderationofsizeeffect.Themodelwithdimensionsofabove-mentionedmicrolatheandthoseofenlarged/reducedareusedtocalculatebyusingtheformshapingtheory.Thedeviationfromthetargetpositionofthetoolpointisobtainedandtheproposedmethodisevaluated.

3.1Calculationmethod

Theabove-mentionedmicrolatheismodeledasshowninFig.1.2.Themodelconsistsofeightelements.Thenumbersfrom0to7aregiventothereferencepointincoordinatetransformationoneachelement.Thoughthebedisactuallyonesolidcomponent,itisdividedintotwopartsvirtuallytoconsidertheinfluenceofthebed’srigidity.Thetargetpositioninthetoolpointisapartfromthepoint0tohinZ-directionandRinX-direction,respectively.

AnorthogonalcoordinatesystemSicorrespondingtoanelementiisdefined.ThetransformationfromSitoSi+1isrepresentedbythecoordinatetransformation,whichisrepresentedbythehomogeneoustransformationmatricesAi.Vectorrwrepresentstherelativedisplacementbetweentheworkpieceandthetool,andvectorrTrepresentsthepositionofthetoolpoint.TherelationbetweenrwandrTisgivenbyEq.

（1）,andrwisdefinedastheform-shapingfunction.

Theerrorbetweenelementiandi+1isrepresentedbyanotherhomogeneoustransformationmatrixεiasfollows.

Theform-shapingfunctionconsideringtheerrorisdefinedasr’wexpressedby

Theform-shapingerrorfunctionre,whichexpressestheerrorasaquantitativedeviationfromthetargetposition,isdefinedasEq.（4）.

Theerrorbetweenelementsofthemicrolatheisrepresentedby6components,whicharetranslationalandrotationalmotionsalongtheX,YandZaxes,asδx,δy,δz,α,β,andγ,respectively.

ThelimitedfourerrorfunctionsmayaffectbetweenelementsshowninFig.1.3.Theassemblyerrorappearsbetweenallelementsexceptbetweenthebed1andthebed2,whicharedividedintotwoparts.Themotionerrorappearsbetweentheelementsthatmoverelativelyduringcutting.Becauseforceandheatpropagatethroughanelement,thedeformationsbycuttingforceandheatappearbetweenallelements.Moreover,asshowninTable1,itwasanalyzedandclassifiedwhicherrorcomponentsareaffectedbyabove-mentionedfourerrorfunctions.Forexample,themotionerrorbetweentheworkpieceandtheworkspindledependsontherunoutoftheworkspindle.BecausetheworkpiecerotatesaroundtheZ-axis,thetranslationalerrorinXandYexceptZ-axesareconsidered.Theassemblyerrorcannotdefinethedirectiontoappear,andisassumedtoappearinall6components.Thedeformationsbycuttingforceandheatareassumedtoappearin3componentsoftranslationalerror.

3.2Sizeeffectoferror

Table2showstowhatextenttheamountoferrorofeachiteminTable1

changeswhenthesizeofthemachinetoolischangedntimes,whichisexaminedbyotherreports[8,9]andthecalculation.Itisthoughtthatthedifficultyofassemblyisconstantregardlessofthemachinesize.Therefore,thesizeeffectoftheassemblyerroris1.Themotionerrordependsontheaccuraciesofguidesinaslidetableorbearingsinaworkspindle.Here,itisconsideredthatthemachineelementofsameabsoluteaccuracycanbeselectedregardlessofthesize,andthesizeeffectofthemotionerrorisassumedtobe1aswellastheassemblyerror.Thecuttingforceisdividedin3directions,namelyprinciple,thethrustandthefeedforce.Asimplebendandcompressionofbeamaccordingtothedirectionofappliedforceoneachelementisconsidered,thesizeeffectofdeformationbycuttingforceisassumedtobe1/nand1/n2,respectively.Ifthetemperatureincreases,generallyamaterialexpands.Thedeformationδtofamemberhavingalengthℓcanbecalculatedusingtheformula

where,αtisthelinearcoefficientofthermalexpansionandΔTisthetemperatureriseofthemember.Therefore,thesizeeffectofthermaldeformationisconsideredasn.

ThedimensionsofeachelementofthemodelinFig.1.2arerequiredtocalculatetheerror.TherealdimensionsofthedevelopedmicrolatheshowninFig.1.1,andtheseareusedasthatofamodelforn=1.ThenthemodelisenlargedntimesandtheerrorinEq.（4）iscalculatedbythemethodmentionedaboveusingthesizeeffectoferrorsshowninTable1.2.Andhowtheerrorchangesaccordingtonisexaminedchangingnfrom0.5to10.However,thedimensionsofworkpieceandtoolareassumedtobeconstantregardlessofn,whereRis2.5mm,his10mmandtis8mm.Inthismethod,actualvaluesoferrorarerequiredforthecalculation.Hence,themagnitudeofeacherrorforn=1isdecidedasshowninTable1.1.Theassemblyandthemotionerrorsweredecidedinconsiderationofactualmicrolathe.Botherrorscantakeapositiveornegativevalue,andareexpressedwiththesignof+or-.ThedeformationsbycuttingforceandheatareobtainedbyFEM.Thedeformationofworkpieceandtoolwerenotconsidered.Theelement7isfixedandthemagnitudeofdeformationofe