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DynamicAnalysisofFour-BarBeating-upMechanismwithJointClearanceXUEWen-liang1*,CHENGuo-zhenS2,CHENGe3,ZHUZhang-chen c71,CHENGLong-diH11KeyLaboratoryofTextileScienceTechnology,MinistryofEducation,DonghuaUniversity,Shanghai201620,China2ShanghaiShenAnTextileCo.,Ltd.,Shanghai200020,China3CollegeofMechanicalEngineering,DonghuaUniversity,Shanghai201620,ChinaAbstractForthefour-barbeating-upmechanismofair-jetloom,theplainbearingoflinkageisthebearingwithdynamicload,andisimmersedinthelubricant-box.Ifthejointclearanceisconsidered,theresearchonlinkagemovementcouldbeverycomplicated.Inthispaper,thekinematiccharacteristicsoffour-barbeating-upmechanismwithjointclearancewerestudiedbyanalyzingthetraceofjournalcenterandthebalanceofradial,tangentialforces,andbearingload.Theregionofprincipalvibrationanditsingcauseswerediscussed.Andtheresultscouldinterpretthemeasuringcurvesoffour-barbeating-upmechanismcompletely.Keywordsdynamicanalysis；four-barlinkage；beating-upmechanism；jointclearanceCLCnumberTS193.3DocumentcodeAArticleID1672-5220201004-0559-07IntroductionForthefour-barbeating-upmechanism,thecrankshaftbearingandrockshaftbearingaretheballbearing,andthecouplejournalbearingandcrankjournalbearingarethejournalbearing.Thecrank,coupler,rocker,andtwojournalbearingsareallimmergedinthelubricant,andthereistheradialclearancebetweentheringandpinofjournalbearing.Theclearanceishelpfultotherelativemotionoflinksbyprovidingthespaceofmovingandlubricating,butitalsoleadstothediscontinuousmotionofkinematicpair,whichisthemainreasontoaffectthemechanismdynamiccharacteristics[1-3].Forthemechanismstransferringtheforceandmomentappliedintheindustrymanufacturing,asthejointclearanceenlargingthedynamiccharacteristicswillbedestructiveundertheconditionofhighspeedandhighload.Thejointclearanceoffour-barbeating-upmechanismiswithintherangeoftolerance.Ifrunningsmoothlysomeclearanceinthejointofmechanismisalwaysnecessary.Buttheclearanceisoftenincreasedbywearing,thentheimpactforcescouldcausethevibration,noise,bearingdeterioration,andthewearcouldalsobeincreased.Therefore,thevibrationsbecomeonebasicstudycontentaboutmechanismkinetics.Xietal.studiedtherelationbetweenthedynamicbalanceandthevibration[4],andSoongetal.studiedthedynamiccharacteristicsofcrank-sliderwithjointclearance[5].Thedynamicalternatingloadisenduredbythejournalbearingoffour-barbeating-upmechanism.Theforcesoflinksaretransferredbytheoilfilm,andthepincenterofcouplejournalmovesonthetrace.Whentheeccentricityislittle,themotionofrockerisunstable,whichshouldleadtotheinstantaneousimpactbetweentheringandthepinandmoreseriouswear,sothestrongvibrationwillhappenmorefrequently.1Four-BarLinkagewithJointClearanceIfthejointclearanceofmechanismiszero,thecentersofbearingandjournalareinthesameposition.Butiftheclearanceappears,twocenterswillbeseparated,whichcanresultintheeccentricity,andthereistheextradegreeoffreedomforthemechanism.Thebeating-upmechanismwithjointclearanceisshowninFig.1,whichisthecrank-rockerinversion.ThebearingBismadeupofcrankandcoupler,thebearingCismadeupofcouplerandrocker,therockershaftbearingDismadeupofrockerandgroundlink,andthecrankshaftbearingAismadeupofgroundlinkandcrank.Forthebeating-upmechanism,theconnectingarmpinbearingCiseasiesttobeworn,soitisassumedthatthereisonlytheclearancebetweenthecouplerpinandring,andnoclearanceinotherthreebearings.Inthispaper,themeasuringloomistheZA203air-jetloomanditsspeedis450r/min.XYreferencecoordinateframeofmechanismshowninFig.1issetaccordingtothepracticalworkingposition.TheoriginisthebearingcenterofcrankshaftA,andthecoordinateofrockershaftbearingDcenterarexD8mmandyD159.8mm.Theotherparametersare559JournalofDonghuaUniversityEng.Ed.Vol.27,No.42010Receiveddate2009-01-15*CorrespondenceshouldbeaddressedtoXUEWen-liang,E-mailxwldhu.edu.cnshowninTable1.Fig.1Four-barlinkageusedforbeatingweftupintoclothTable1Mainparametersoffour-barmechanismLinkageLength/mmMass/kgMomentofinertial/kgcm2CrankAB3535.80155CouplerBC752.27114RockerCD14510.42528SleyandsleyswordDE64.953728GroundlinkAD160ThesleyandsleyswordDEistheworkinglinkoffour-barmechanism,whichisintegratedwiththerocker.Whenthesleyreciprocates,thereedpushestheweftintothefellofclothfortheinertiaofsleyandsleysworddrivenbytherockerandelbowpositionofmechanism.Forthelinksoffour-barbeating-upmechanism,themassofsleyandsleyswordincludingtherockerismuchheavierthanotherlinks.Themainbodyofrockingshaftisthesteeltubeoflargediameter.Themotionofrockerisstableanditspropertyofant-ijammingiswell,sothesleyswordischosenasthemeasuringobjectiveofbeating-upmechanismaccelerationcurve.Apiezoelectricaccelerometerisadsorbedonthesleysworddirectlybythemagneticseat,whichisshowninFig.2.Thesleyswordisshortandstrong,whichoutputsignalcouldreflectsensitivelythedynamiccharacteristicsoffour-barlinkage.ThemeasuringaccelerationcurveofsleyswordisshowninFig.3,whichaccordswiththetheoreticalaccelerationcurve,andcharacterizedin.1Thecurveisnotsmooth,whichmeansthatthetheoreticalsmoothcurvehasbeenaddedbytheoscillationswithdifferentfrequenciesandamplitudesseeFig.4.Fig.2SketchofmeasuringpositionFig.3MeasuringcurveFig.4Contrastbetweenmeasuringcurveandtheoreticalsmoothcurve2Theoscillationswithdifferentfrequenciesexpressstrictperiodical,andthedifferenceisonlytheamplitudesseeFig.3.Forthefour-barbeating-upmechanismwithfixedgeometricalandkinematicparameters,inthefirsttwoor560JournalofDonghuaUniversityEng.Ed.Vol.27,No.42010threeyearstheoutputaccelerationsignalofmechanismwillappearagaincorrectlyinthenextperiod,andthevibrationpulsewithfixedfrequencyandamplitudewillalsoappearagaineveryperiodofcrankangle.Sotheoutputaccelerationsignaloffour-barbeating-upmechanismwithjointclearanceisnottherandomsignal,butthemainbodyofsignalisthesignalwiththestrictperiodicity.Theoutputcurveofmechanismismainlymadeupofsignalswiththestrictperiodicity,andalsoincludessomerandomcomponent.3Therandomcomponentofvibrationwillincreaseastheworkingtimeofloom.Thatistosayastheworkingtimeofmechanismincreases,therandomcomponentofoutputcurvewillbegraduallyimproved.ShowninFig.5,Bistheincludedangleofcoupleroritsextendedlineandcrank.WhenB0bor180b,thecrankandthecouplerareinthesameline,andwhentheaccelerationofcrankiszero,themechanismisinthepositionofelbowlink.WhenB90bor270b,thecrankandthecouplerareverticaleachother,andtheaccelerationofcrankislarge.Accordingtothefourspecialpositionsabove,theswingprocessofsleycouldbedividedintofourregions.Fig.5Bangleoffour-barmechanism2RelativeTraceofCouplerPinCenterwithJointClearanceatStaticBalancePositionAccordingtothemeasuringcurve,thereistheimpactoflinksinthejointclearance.Bymeasuringtheclearanceofcrankbearingis2Lm,andtheclearanceofcouplerpinjournalis42Lm.Soitcouldbeconcludedthattheimpactinthejointclearancewillhappenmainlyinthecouplerpinjournal.2.1CouplerpinjournalwithclearanceTherearetwocylindersofpinholeandjournalshowninFig.6.TheradiusofjournalbearingholeisR,theradiusofjournalisr,andtheradiusclearanceiscR-r.ThedistancebetweentwocentrallinesofcylindersistheeccentricityeC1C2.Thecouplerandtherockerconnectedbythecouplerjournalbearingarebothmovableparts,sothebearingandthejournalarealsobothturning.Thereistheoilbetweentwocylinders,andthethicknesshofextrusionfilmishcesinHc1EsinH,1whereEe/cistheeccentricity；HistheangleincludedbetweenhandC1C2intheverticaldirection.Fig.6GeometricdimensionofjournalforradialloadFisthetotalloadofjournalbearing,Ubcisthelinearvelocityofpinalongthepinsurface,andUcdisthelinearvelocityofjournalalongtheringsurfaceseeTable2.Table2MainparametersofcouplerpinbearingNominaldimensionofjournalbearingholeandjournal2R/mmWidthofplainjournalbearingL/mmViscositycoefficientoflubricantG/Nsm-1RadiusclearancecR-r/mm40420.01750.0212.2JournalcentertraceofstaticbalancepositionThecrankandthecouplerarebothimmersedinthelubricant-box.Thelubricantinthejointclearanceofjournalandbearingwillturnwiththem.Thereisthehigherhydrodynamicpressureintheregionoflessclearance,andthelowerhydrodynamicpressureintheregionoflargerclearance,whichleadstothedeliveryhead.Thebearingloadisenduredbythehydrodynamicpressureoflubricantfortheeffectofoilwedge.Thestaticbalancepositionofjournalcenteristhebalancepositionofoilfilmforceandbearingforce.Thereisthedifferencebetweencouplerpinjournalandordinaryradialbearing.1Thedirectionandintensityofloadonthecouplerpinjournalalternateasthetime.2Theswingvelocityofjournalandbearingchangesasthetime.TherelationbetweenbearingloadFanddimensionlessoilfilmforceisshowninEq.2[6].5Fc/R2GUbcUcdL,2561JournalofDonghuaUniversityEng.Ed.Vol.27,No.42010whereFisthebearingload,Gisthedynamicviscosity,andUbcandUcdareshowninFig.6.AccordingtothedatainTable3,thebalanceposition7NF,C1C2couldbesolvedbytheinterpolation.Table3BearingparametersofcircularcylinderratioofwidthandradiusL/2R1.0EccentricityE0.100.200.300.400.500.600.70Eccentricangle7/b75.1163.5955.5550.0845.3240.5436.02OilfilmforceX0.1970.4150.6801.0291.5242.2963.654Thejournalcentertracecouldbedrawnaccordingtotheeccentricangleandtheeccentricity.Thejournalcentertraceofbearingwiththestaticloadusuallyissemicircle.Buttheloadofcouplerpinjournalwillvaryinthesizeanddirectionastheturningofcrank,sothejournalcenterwillmovealongthetraceofstaticbalanceposition.TherelativetraceofjournalcenterstaticbalancerelativetothecouplerpinjournalholeshowninFig.7is8-shaped.ThepolarangleshowninFig.7isthedirectionangleofhole,andthepolarradiusistheeccentricity.Accordingtothefigure,therearethreetimesforthejournalcentercomingintothecircleofE0.1.Whenthecrankangleisat72b-114b,itisthefirsttimeforthejournalcentercomingintothecircle,andtheleasteccentricityis0.001.Lesseccentricity,Fig.7Relativetraceofjournalcenterstaticbalancerelativetoholethemargentangleisthecrankanglethesystemstabilityisworseandworse.Whenthecrankangleisat178b-192b,itisthesecondtimeforthejournalcentercomingintothecircle,andtheleasteccentricityis0.098.Whenthecrankangleisat302b-338b,itisthethirdtimeforthejournalcentercomingintothecircle,andtheleasteccentricityis0.001.AndtherearetwotimesforthecentertouchingtheoutercircleofE1,wheretheangularvelocitiesofcouplerandrockerrelativetothebearingloadFarethesame,buttheirdirectionsarereverse,andtheimpactwillhappenbetweentwolinks.2.3BalancebetweenoilfilmforceandbearingloadFnisthereactionforcecomponentinthedirectionoflinkBClength,andFtisthereactionforcecomponentintheverticaldirectionoflinkBC.Between80band150b,Ftisclosetozero,andat92bFnistheleast.Thebearingreactionforceisenduredmainlybytheoilfilmthicknessh,andifaverticalloadwasplacedonthejournal,theoilwouldsqueezeandthereisthesufficientpressuretosupporttheload.ThepressurecouldbedividedintotheradialforceF0ninthedirectionoftielineandthetangentialforceF0tintheverticaldirectionoftieline.F0nGUbcUcdL5c2E21-E22,MC1C2F0t14GUbcUcdL5c2PE1-E25/2,LC1C23whereUbcistherelativelinearvelocityofholesurface,Ucdistherelativelinearvelocityofjournalsurface.Thereactionforceofjournalfortheoilfilmwillchangeastheturningofcrank.Thebearingloadistheconcentratedforce,andthereactionforceisthedistributionforce.ThefunctionofradialforceF0nistosupportthejournal.Inthedirectionofturning,thejournalcenterwillmovefortheactionoftangentialforceF0t,andtheeccentricitywillincrease.Thetangentialforcewilldestroythebalanceofjournal.Whenthemainbearingloadisinthedirectionofcouplerlength,thecomponentofforceFtintheverticaldirectionisverylittle.ThepressurecurvesofF0ninthedirectionofcoupleandF0tintheverticaldirectionareshowninFig.8.BecausetheoilfilmforceF0tisnotlikethebearingforceFtwhichisaroundzero,inthisconditionF0tiseasytodestroythestabilityofjournalmotion.562JournalofDonghuaUniversityEng.Ed.Vol.27,No.42010