行星齿轮传动电动滚筒设计（全套含CAD图纸）
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11OptimalDesignofCompliantTrailingEdgeforShapeChangingAbstract:AdaptivewingshavelongusedsmoothmorphingtechniqueofcompliantleadingandtrailingedgetoimprovetheiraerodynamiccharacteristicsThispaperintroducesasystematicapproachtodesigncompliantstructurestocarryoutrequiredshapechangesunderdistributedpressureloadsInordertominimizethedeviationofthedeformedshapefromthetargetshape，thismethodusesMATLABandANSYStooptimizethedistributedcompliantmechanismsbywayofthegroundapproachandgeneticalgorithm(GA)toremovetheelementspossessiveofverylowstressesIntheoptimizationprocess，manyfactorsshouldbeconsideredsuchasairloads，inputdisplacements，andgeometricnonlinearities。DirectsearchmethodisusedtolocallyoptimizethedimensionandinputdisplacementaftertheGAoptimization。Theresultantstructurecouldmakeitsshapechangefrom0to93degreesTheexperimentaldataofthemodelconfirmsthefeasibilityofthisapproachKeywords：adaptivewing；compliantmechanism；geneticalgorithm；topologyoptimization；distributedpressureload；geometricnonlinearity1Introduction：AsconventionalairfoilcontoursareusuallydesignedwithspecificliftcoefficientsandMachnumbers，theycouldnotchangeinaccordancewiththeenvironmentchangingSiclariandAustinindicatedthatthevariablecambertrailingedgewouldproducethedragaboutsixtypercentlessthantheconventionalfixedcamberairfoilTherearethreemethodsusedtodesignablecamberwingsOfthemoneisconventionalhingedmechanism，which，however,willcreatediscontinuitiesoverthewingssurfaceleadingtoearlierairflowseparationanddragincreaseTheothersaresmartmaterialandthecompliantmechanism，ofwhichbothcouldrealizesmoothshapechangingNevertheless，comparedtothecompliantmechanism，thesmartmaterialmadeactuatorshavemanydisadvantages，suchasdeficientinenergy,slowinresponse，stronginhysteresis，limitedbytemperature，anddifficulttocontroltoomanyactuatorsMusolfffromIndustryUniversityofBerlin12usedNiTishapememoryalloywiretomakeanadaptivevariablecamberwing，whichcouldquicklychangeitsshape，butcouldnotperformhighlyfrequentalterationbecauseofitsresiliencedependentontheheatexchangewiththeoutsideenvironment。Compliantmechanismisakindofone-pieceflexiblestructure，whichcantransfermotionandpowerthroughitsownelasticdeformationItisnotonlyflexibleenoughtodeform，butalsohasenoughstiffnesstowithstandexternalloadsThankstoitsjointfreenature，itdoesnothavethetroublesomeproblemsconfrontedbyconventionalmechanismsuchasfriction，lubrication，noiseandrecoiling，therebyachievingsmoothshapechanging.In1994，Kota，aprofessorfromUniversityofMichigan，firstlypointedoutthatcompliantmechanismcouldbeusedtocontrolstaticshapechangingunderthesponsorshipoftheAirForceOficeofScientificResearchinUSASaggereandKotasuggestedanewmethodtodesigncompliantadaptivestructures，whichmadetheleastsquareerrorsbetweentheshapechangedcurveandthetargetcurveastheobjectivefunctionforoptimizationBasedontheirwork，LuputforwardaloadpathrepresentationmethodHowever,herworkwaslimitedtoonlylinearanalysisunderconsiderationofnodalloadsGoodfromVirginiaPolytechnicInstituteofStateUniversityusedthecompliantmechanismandtheMovingAsymptotesmethodtodesignthefuselagetailwithintheallowablerangeofitstipmaximaldeflectionKotaandHetrickin2004designedacomplianttrailingedgeonthebaseoftheF16sdata，whichcanchangefrom0。to15。andobtainedapatentCampanilefromGermanAerospaceCenterpresentedamodalproceduretodesignsyntheticflexiblemechanismsforairfoilshapecontrol，andpointedoutthatthefutureresearchshouldtakeintoaccounttheairloadandthegeometricnonlinearityBuhlfromRisoNationalLaboratoryoftheWindEnergyDepartmentinDenmarkusedtheSIMPmethodandgeometricallynonlinearfiniteelementmethodtodesigncomplianttrailingedgeflapsFlxSysIncin2006producedanadaptivecompliantwing，whichstoodthetestontheWhiteKnightairplaneTheresults13indicatedthatthecomplianttrailingedgecouldchange+10InChina，theresearchofadaptivewinghasbeenconcentratedonsmartmaterialandconventionalmechanismFewpeople，itseems，haveworkedondesigningadaptivewingswiththecompliantmechanismYangisanexceptionHeanalyzedtheactiveaeroelasticwingsbasedontheaeroservoelasticitytechnologyChenandHuangseparatelyinvestigatedthemorphingofthecompliantleadingedgefromtheviewpointsofdiscretenessandcontinuity.ThispaperpresentsamethodtodesigntheshapechangeablestructurebyMATLABandANSYSassociatedwithdistributedcompliantmechanismonthebaseofthegroundstructureapproachandgeneticalgorithm(GA)takingintoaccounttheexternaldistributedloadsandgeometricnonlinearity.2OptimizationProcess:21DefiningthetrailingedgemodelandobjectivefunctionAsshowninFig1，bothcurvesrepresenttwoidealshapesofthetrailingedgeinthedifferentflyingstatesOnesidepoint)ofthestructureissupposedtobefixed，andtheothersidepoint)tobeslidinghorizontally.Firstly,thedesigndomainshouldbedefinedbytheinitialcurveshapetheinputlocationandtheboundaryconditionsThenitisdividedwithabeamelementnetworksimulatingthebirdsfeatherasshowninFig2Thisistermedthepartialgroundstructuremethod.Fig1InitialshapeandtargetshapeFig2DiscretizationofthedesigndomainThesimplestandmosteffectivewaytomanufacturetheplanarcompliantmechanismistousewirecuttingtechnologyIntheoptimizationprogram，alltheelementsareofrectangularbeamswiththesamewidthequaltothethicknessofthematerial，everybeamsheightbeingadesignvariable14Inordertomakethestructuresdeformationcomeclosetothetargetshapecurve，theleastsquareerror(LSE)betweenthedeformedcurveandthetargetcurveisdefinedastheobjectivefunctionLSEisthesumofsquaresofpositiondifferencesofvariouspointsalongthecurvesItsexpressioniswhereI(=1，2，P)isthenumberofthepointsalongthecurves，PisthetotalnumberofpointsandarethecoordinatesofithnodeonthetargetanddeformedboundarycurverespectivelyTheconstraintsareWhereJ(=1，2，)isthenumberofelements，missthetota1numberofelements，hithedimensionvariable，hminandhmaxarethelowerandupperboundsoftheelementbeamheightforallelementswiththevaluedependentonmanufacturing，hbtheheightoftheboundaryelements，themaximumnoda1deformationofthenodesonthecurveboundarywhentheinputpointisinactive，andshouldbesmallerthandtoensurestructurestiffness，dtheallowablemaximumdisplacementwhentheinputpointisinactive，Omaxthemaximumstressofal1theelementswhichmustbesmallerthanTjtopreventyielding，Tjthetopologyvariableequalto1，orelse0whentheelementiseliminated22GAoptimizationGAisanoptimizationmethodwhichsimulatestheheuristicselectionruleinnature，wherethefittestlivingthingshavethemostchancetosurvive，buttheinferioronesalsohavetheopportunitytoexistDifferentfromthecontinuousoptimizationmethod，itdoesnotrequirethegradient-basedinformationoftheobjectivefunction.15EveryelementcouldbeexpressedasatopologyvariableandadimensionvariableTherefore，eachindividua1couldbecodedasfollowswhere，2isthenumberofelementsexcepttheboundaryonesWiththesameheights，theboundaryelementsthroughouttheoptimizingprocessarerepresentedbyonlyonevariable，hb.ThefitnessisthecriterionoftheGAoptimizationItcouldbetransformedfromtheobjectivefunctionintowhereisacoefficientdecidingthecompulsiveselectionofthebetterindividua1Thesmallerthevalue，themoredifferentwouldbebetweenthetwoindividualsfitnessthusincreasingthecompulsivenessofchoosingtheindividualofhigherfitnessTheselectionofcontrolparametersplaysanimportantroleintheconvergenceoftheGAGenerallyspeakingthecrossprobabilityranges040099；themutationprobabilityis000001-001andthenumberofindividuals10200Thevariablewouldbeupdatedthroughthecrossoverandmutation，sothepossibledesigncouldgenerateintheGAprocess23Finiteelementanalysis(FEA)Becauseofthelimiteddesignvariablesandthetargetfunction，theoptimizationmoduleofFEAsoftwarecouldnotbeusedtodesignthecompliantmorphingmechanismTherefore，thispaperprogrammedtheGAinMATLABandtheFEAinANSYSIntheFEA，takingonlyaccountofgeometricnonlinearitiesandthematerialbeingoflinearelasticity,ANSYScouldsolvethenodedisplacementsandtheelementstressesThenbydeletingtheelementswithlowstress，thefitnesscouldbecalculatedFig3showsthedetailedprocess16Fig3Flowchartofthestructuraloptimizationprogram24SecondoptimizationAlthoughtheGAcouldoptimizethetopologyanddimensionsimultaneouslyinalargesolutionspace，thedimensionusuallycouldnotdirectlyconvergetotheoptimizationInordertosolvethisproblem，aftertheGA，theDirectSearchmethodshouldbeusedtofindthebestvaluesoftheinputdisplacementandthedimensionsoftheelementswhichremainintheresultsaftertheGAFormorphingofcompliantmechanism，Fig3describesthewholeoptimizationprocessItmainlycontainsinitializationofthedesigndomain，FEA，GAoptimizationandsecondoptimization.3PresentationofResults:AdoptedfromRef，thesizesoftheinitialandthetargettrailingedgearereducedbysixtypercent，I1ab1e1liststhedesignparameters.Becausethedisplacementisusedastheinput，thenonlinearanalysiscouldhardlyconvergeandthestressoftheinitia1solutionsisverylargeWhichshouldbeconsideredafterthirtiethgeneration.17Table1DesignparametersFig4andFig5illustratetheresultsfromtheGAoptimizationandthesecondoptimizationrespectivelyFig4ResultsaftertheGAoptimizationFig5ResultsafterthesecondoptimizationFormTable2，itcouldbefoundthatthroughthesecondoptimizationoftheinputdisplacementandthedimension，theLSEisreducedby13528mmandimprovedby313Thealteredangleisincreasedby10493Table2Resultsafterthetwooptimization18Fig6StabilityoffinaloptimalstructureFig6showstheinfluencesoftheparameterswhentheoutsidedistributedpressureloadchangesfrom0to10Nmmandtheinputdisplacementremains113897mmontheoptimalstructureItcouldbeseenthattheoptimalstructurehasagoodstabilityiftheloadiskeptintherangeOf05NmmAstheexternalloadexceeds5Nmm，themaxstressislikelytoexceedtheyieldstress19BecausethisoptimizationprogramisbasedontheMATLABandANSYSinordertoverifytheresultsanattemptismadetointroducetheanalyticalresultsoftheoptimizedstructureintoANSYSandPATRANrespectively,andthenacomparisonismadebetweenthemAsshowninFig7andFig8，thetwoalteredshapesareingoodagreement：forinANSYSthetipdisplacementis5497mmandinPATRRAN5450mmTheminordifferencebetweenthemisfromthesoftwareFig7ResultsofFEAinANSYSFig8ResultsofFEAinPATRANOntheotherhand，amodelismadebywirecuttingtechnologytoverifytheanalyticalresultsThematerialofthemode1identicalwiththatofthedesign，is5mmthickIntheexperiment，thedistrib
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