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Receiveddate:2010-01-19Foundationitems:NationalNaturalScienceFoundationofChina(No50875243);ZhejiangTechniqueInnovationGroupofModernTextileMachinery,China(No2009R50018);FoundationofEducationDepartmentofZhejiangProvince,China(NoY201019088);FoundationofNewTextileRDEmphasisedLaboratoryofZhejiangProvince,China(No2009FZD004)*CorrespondenceshouldbeaddressedtoCHENJian-neng,E-mail:jiannengchenzstueducnKinematicAnalysisandTestStudyofElliptic-GearandCrank-RockerBeating-UpMechanismZHAOXiong(赵雄),RENGen-yong(任根勇),CHENJian-neng(陈建能)*CollegeofMechanicalEngineeringandAutomation,ZhejiangSci-TechUniversity,Hangzhou310018,ChinaAbstract:Inordertoanalyzethekinematicperformancesofelliptic-gearandcrank-rocker(EGCR)beating-upmechanism,kinematicmathematicmodelsofthemechanismwereestablished,andanaidedanalysisandsimulationsoftwarewerecompiledThissoftwarecandisplaythekinematiccharacteristicsandsimulationmotionofthemechanismaccordingtodifferentparametersItalsosuppliesaplatformforhuman-computerinteractionAgroupofsatisfactoryparameterswereselectedbythesoftwareAtestbedofEGCRbeating-upmechanismwasdevelopedaccordingtotheseparametersThekinematicperformancesofthemechanismwereverifiedbyhigh-speedvideotaperecorderKeywords:beating-upmechanism;elliptic-gear;crank-rocker;kinematicsCLCnumber:TS103135Documentcode:AArticleID:1672-5220(2011)02-0222-04IntroductionBeating-upmechanismisoneofthekeymechanismsofaloomItbeatstheweftwhichisinsertedbyweft-insertionmechanismtoformthefabricItsfunctionistotransformtheconstantspeedrotationoftheloomsspindletothenon-constantspeedreciprocatingswingofthesleyInordertoallowtheweft-insertionmechanismtofinishinsertingthewefts,thesleyofthebeating-upmechanismshouldhaveadequatedwelltimeorrelativedwelltimeinthefrontpositionTheperformancesofbeating-upmechanismdeterminethefabricsquality,andalsodecidethequalityandcompetitivenessofaloom1Nowadays,therearethreegeneralkindsofbeating-upmechanisms:four-barlinkagebeating-upmechanism,six-barlinkagebeating-upmechanism,andconjugatedcambeating-upmechanismGenerally,four-barlinkagebeating-upmechanismisthesimplestmechanismwith65-75relativedwelltimeSix-barlinkagebeating-upmechanismhasabout120relativedwelltimeIthasmorehingeswhichproducelargercumulativeerrorsThedwelltimeofconjugatedcammechanismis220-240,buttheconjugatedcammechanismneedsveryhighprecisionmachiningIftherearesomeprocessingerrorsitwillcausecertainvibration2-4Inthispaper,anewtypeofbeating-upmechanismbasedonelliptic-gearandcrank-rocker(EGCR)wasproduced5,anditskinematicmathematicmodelswereestablishedAtestbedwasdevelopedandthekinematicperformancesofthemechanismwereverifiedbyhigh-speedvideotaperecorder,whichdemonstratedthatthisnewmechanismcouldmeettherequirementsofweftbeating-up1EGCRBeating-UpMechanismFigure1showstheEGCRbeating-upmechanisminitsinitialpositionOisoneofthefocusesoftheactiveelliptic-gear1andtherotationcentreoftheloomsspindleAisoneofthefocusesandtherotationcentreofthedrivenelliptic-gear2CrankAB(l1)isfixedonthedrivenelliptic-gearRockerCD(l3)isdrivenbyBC(l2)andswingsreciprocallySleyDE(l5)isfixedwithCDbyaxisDandswingsreciprocallytogetherwithCDByoptimizingtheeccentricityk(theratiooftheelliptic-gearsminorradius(b)tomajorradius(a),theangle(theincludedanglebetweenAD(l4)andcrankABwhencrankABandlinkageBCarecollinear,thatisthesleyDEwillbeinthefrontposition),(theincludedanglebetweenthemajoraxisoftheactiveelliptic-gearandAO),(theincludedanglebetweenADandx-axis),andthelengthsoflinkagesincrank-rockermechanism,thekinematicperformancesofthisnovelbeating-upmechanismbecomeexcellent,whicharesimilartothoseoftheconjugatedcambeating-upmechanism1Activeelliptic-gear;2Drivenelliptic-gear;DESleyFig1EGCRbeating-upmechanismwithitsinitialposition2KinematicMathematicModelsofEGCRBeating-UpMechanism21Mathematicalmodelsofthedrivenelliptic-gearInFig1,whentheactivegear1rotatesanticlockwiseataconstantspeed,gear2willrotateclockwiseatanon-constantspeedGiventheangulardisplacementsoftheactivegear11anddrivengear22,thedistancefrommeshpointPtoaxisOisr1andPAisr2Withcalculation,thenr1=b2/(a+ccos1),(1)r2=b2/(a+ccos2),(2)where,cisthedistancebetweentheelliptic-gearcenterandthefocus;1rangesfrom0to2,and2from0to26Accordingtothetransmissionprinciplesofelliptic-gearsr1=2ar2,(3)222JournalofDonghuaUniversity(EngEd)Vol28,No2(2011)thatis,cos2=(a+ccos1)b2(2a2+2accos1b2)cac(4)FromEq(4),therelationshipbetween2and1canbeobtainedAccordingtotheprinciplesofgeartransmission2=1r1r2(5)Giventhatthevelocityofactivegearisconstant,2=1r1r2r1r2r22=2ar2r221(6)TakingthederivativeofEqs(1)and(3),r1=b2csin1(a+ccos1)21andr2=r1,soinEq(6)r2=b2csin1(a+ccos1)21(7)22KinematicalmodelsofrockerCDSincethecrankisfixedonthedrivenelliptic-gear,itsangularvelocityandangularaccelerationarethesameasthoseofthedrivenelliptic-gearThatistosay,j1=2,j1=2,andj1=+2FromFig2,thefollowingequationscanbededuced7Fig2Crank-rockermechanismj2=arctanyCyBxCxB(8)j4=arctan(yByDxBxD)(9)j3=arccos(l32+(xDxB)2+(yDyB)2l222l3(xDxB)2+(yDyB)槡2)+j4(10)j2=VxBcosj3+VyBsinj3l2sin(j2j3)(11)j3=VxBcosj2+VyBsinj2l3sin(j2j3)(12)j2=c1cosj3+c2sinj3l2sin(j2j3)(13)j3=c1cosj2+c2sinj2l3sin(j2j3)(14)InEqs(13)and(14),c1=axB+l3j23cosj3l2j22cosj2,(15)c2=ayB+l3j23sinj3l2j22sinj2(16)23KinematicmodelsofEinx-axisdirectiononthesleyDEDisplacementequation:sxE=xD+lDEcos(j3)(17)Velocityequation:VxE=lDEj3cos(j3/2)(18)Accelerationequation:axE=lDEj32cosj3+lDEj3jcos(j3/2)(19)3AidedAnalysisandSimulationSoftwareofMechanismandParameterOptimization31AidedanalyticalsoftwareThevisualizationofthemechanismisanalyzingandoptimizingprocessthatcandisplaymoreinformationoftheprocesstousersUserscanobservethewholeprocessandfindouttheessentialparametersofthemechanismHuman-computerinteractionanalysisandoptimizationcombinethevirtuesofbothhumanandcomputersHumanspossessthecapabilitiesofillegibleillation,judgmentandinnovation,whichcanhelptodisposerandomeventsaswellMeanwhile,computersaregoodataccuratecalculationandrepeativeworkHumanandcomputercanfullydisplaytheirrespectiveadvantagesinhuman-computerinteractionoptimizationThussatisfactoryparameterscanbeeasilyachieved8-10BasedontheabovekinematicmodelsofEGCRbeating-upmechanism,anaidedanalysisandsimulationsoftwarearecompiledwhichisshowninFig3ItcanbeusedtoanalyzetheinfluencesofdifferentmechanismparametersandverifywhetherthereexistinterferencesamongthecomponentsofthemechanismFig3AidedanalysisandsimulationsoftwareofmechanismWiththissoftware,userscaninputmechanismparameterssuchasa,k,l1,l2,l3,l4,androtaryspeedoftheloomsspindleThemechanismmotionsimulationwillbeshownontheleftoftheinterface;thedisplacement,velocity,andaccelerationcurvesofpointEwillbeshownrespectivelyontherightoftheinterface;theoptimalvalueofwillbeshownontheleft-bottomoftheinterfaceThedisplacementcurveshowsthatdwelltimeintherearpositiondecreasesaskincreases;322JournalofDonghuaUniversity(EngEd)Vol28,No2(2011)meanwhiletheaccelerationcurveshowsthatthemaximalaccelerationalsodecreasesaskincreasesForkinematicperformancesofthemechanism,kneedstobeoptimizedaccordingtotherequirementsofthebeating-upweft;l1,l2,l3,andl4alsoneedtobemodifiedbytheuserincompanywithk,soastoachieveidealkinematicperformances32OptimizationresultsanalysisOneofthemostimportantperformancesofbeating-upmechanismisthedwelltimeofsleyIncreasingmechanismparameterkcanprolongdwelltime,meantimethemaximalaccelerationincreasesremarkably,andtheoversizefluctuationofaccelerationwilldegrademechanismdynamicperformanceDesignermustthereforemakeabalancebetweenprolongingdwelltimeandcontrollingaccelerationfluctuationWiththeaboveaidedanalysisandsimulationsoftware,agroupofparameterswasobtained:=4,k=085,=135,a=71233mm,l1=40mm,l2=100mm,l3=180mm,l4=199mm,andlDE=1895mmBasedontheseparameters,whentheloomhasaspeedof300r/min,thekinematicalcurveofthebeatingpointEisshowninFig4Whenthebeating-upmechanismisontherearposition,thedisplacementcurveisalmostflatThedwelltimeofsleyiscloseto200(rangingfrom92to285),whichwillnotleadtointerferenceofthebeating-upmechanismandweft-insertionmechanismInaddition,duringthisperiod,thecurvesofthevelocityandaccelerationofthesleyarealmostcloseto0Thereforeitwillnotcausevibration,whichwillbenefittheweftsenteryandexitfromshedAttheendofthebeating-up,themaximaldisplacementis85mmandthemaximalaccelerationis6158434m/s2,whichbothcanmeettherequirementsofthebeating-upweftFig4ThekinematiccurvesofEGCRbeating-upmechanism4TestStudyBasedontheaboveparameters,atestbedofEGCRbeating-upmechanismisdeveloped(Fig5)Usingthehigh-speedvideotaperecorderandvideoanalysissoftwareBlastersMAS,thedisplacementandvelocityareobtainedwithloomspindlesrotaryspeedat100r/minTheoreticalandexperimentaldisplacementsofbeatingpointEareshowninFig6,andtheoreticalandexperimentalvelocitiesofbeatingpointEareshowninFig7Theactualmeasureddisplacementcurveisconsistentwiththetheoreticalone,buttheactualmeasuredvelocitycurveshowssomefluctuationTherearetworeasonsforthisfinding:thegapamongthecomponentsofthemechanismcausesvibration;thevideoanalysiscontainserrors422JournalofDonghuaUniversity(EngEd)Vol28,No2(2011)5Conclusions(1)Inthispaper,theEGCRbeating-upmechanismhadbeenproducedItskinematicmathematicmodelshadbeenestablishedandanaidedanalysisandsimulationsoftwarehadbeencompiledbyvisualbasicAgroupofsatisfactoryparametershadbeengotbythissoftware(2)AtestbedoftheEGCRbeating-upmechanismwasdevelopedWiththevideotaperecorder,itskinematicperformanceswereverifiedThisdemonstratedthevalidityofthemodelsandthefeasibilityofthemechanismReferences1ZhuSK,GaoWDWeavingMachineM2ndedBeijing:ChinaTextileApparelPress,2004:267-268(inChinese)2LiangHS,HuQE,WangGC,etalTheFuzzyOptimizationDesignoftheFour-LinkWeftBeat-UpMechanismJMachineDesignandResearch,2005,21(2):72-75(inChinese)3MaSPOptimalDesignandSimulationon6-LinkB

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