DynamicAnalysisofFour-BarBeating-upMechanismwithJointClearanceXUEWen-liang()1*,CHENGuo-zhen(S)2,CHENGe()3,ZHUZhang-chen(c7)1,CHENGLong-di(H)11KeyLaboratoryofTextileScience&Technology,MinistryofEducation,DonghuaUniversity,Shanghai201620,China2ShanghaiShenAnTextileCo.,Ltd.,Shanghai200020,China3CollegeofMechanicalEngineering,DonghuaUniversity,Shanghai201620,ChinaAbstract:Forthefour-barbeating-upmechanismofair-jetloom,theplainbearingoflinkageisthebearingwithdynamicload,andisimmersedinthelubricant-box.Ifthejointclearanceisconsidered,theresearchonlinkagemovementcouldbeverycomplicated.Inthispaper,thekinematiccharacteristicsoffour-barbeating-upmechanismwithjointclearancewerestudiedbyanalyzingthetraceofjournalcenterandthebalanceofradial,tangentialforces,andbearingload.Theregionofprincipalvibrationanditsformingcauseswerediscussed.Andtheresultscouldinterpretthemeasuringcurvesoffour-barbeating-upmechanismcompletely.Keywords:dynamicanalysis；four-barlinkage；beating-upmechanism；jointclearanceCLCnumber:TS193.3Documentcode:AArticleID:1672-5220(2010)04-0559-07IntroductionForthefour-barbeating-upmechanism,thecrankshaftbearingandrockshaftbearingaretheballbearing,andthecouplejournalbearingandcrankjournalbearingarethejournalbearing.Thecrank,coupler,rocker,andtwojournalbearingsareallimmergedinthelubricant,andthereistheradialclearancebetweentheringandpinofjournalbearing.Theclearanceishelpfultotherelativemotionoflinksbyprovidingthespaceofmovingandlubricating,butitalsoleadstothediscontinuousmotionofkinematicpair,whichisthemainreasontoaffectthemechanismdynamiccharacteristics1-3.Forthemechanismstransferringtheforceandmomentappliedintheindustrymanufacturing,asthejointclearanceenlargingthedynamiccharacteristicswillbedestructiveundertheconditionofhighspeedandhighload.Thejointclearanceoffour-barbeating-upmechanismiswithintherangeoftolerance.Ifrunningsmoothlysomeclearanceinthejointofmechanismisalwaysnecessary.Buttheclearanceisoftenincreasedbywearing,thentheimpactforcescouldcausethevibration,noise,bearingdeterioration,andthewearcouldalsobeincreased.Therefore,thevibrationsbecomeonebasicstudycontentaboutmechanismkinetics.Xietal.studiedtherelationbetweenthedynamicbalanceandthevibration4,andSoongetal.studiedthedynamiccharacteristicsofcrank-sliderwithjointclearance5.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,andthecoordinateofrockershaftbearingDcenterarexD=8mmandyD=159.8mm.Theotherparametersare559JournalofDonghuaUniversity(Eng.Ed.)Vol.27,No.4(2010)Receiveddate:2009-01-15*CorrespondenceshouldbeaddressedtoXUEWen-liang,E-mail:showninTable1.Fig.1Four-barlinkageusedforbeatingweftupintoclothTable1Mainparametersoffour-barmechanismLinkageLength/mmMass/kgMomentofinertial/(kg#cm2)CrankAB3535.80155CouplerBC752.27114RockerCD14510.42528SleyandsleyswordDE)64.953728GroundlinkAD160)ThesleyandsleyswordDEistheworkinglinkoffour-barmechanism,whichisintegratedwiththerocker.Whenthesleyreciprocates,thereedpushestheweftintothefellofclothfortheinertiaofsleyandsleysworddrivenbytherockerandelbowpositionofmechanism.Forthelinksoffour-barbeating-upmechanism,themassofsleyandsleyswordincludingtherockerismuchheavierthanotherlinks.Themainbodyofrockingshaftisthesteeltubeoflargediameter.Themotionofrockerisstableanditspropertyofant-ijammingiswell,sothesleyswordischosenasthemeasuringobjectiveofbeating-upmechanismaccelerationcurve.Apiezoelectricaccelerometerisadsorbedonthesleysworddirectlybythemagneticseat,whichisshowninFig.2.Thesleyswordisshortandstrong,whichoutputsignalcouldreflectsensitivelythedynamiccharacteristicsoffour-barlinkage.ThemeasuringaccelerationcurveofsleyswordisshowninFig.3,whichaccordswiththetheoreticalaccelerationcurve,andcharacterizedin.(1)Thecurveisnotsmooth,whichmeansthatthetheoreticalsmoothcurvehasbeenaddedbytheoscillationswithdifferentfrequenciesandamplitudes(seeFig.4).Fig.2SketchofmeasuringpositionFig.3MeasuringcurveFig.4Contrastbetweenmeasuringcurveandtheoreticalsmoothcurve(2)Theoscillationswithdifferentfrequenciesexpressstrictperiodical,andthedifferenceisonlytheamplitudes(seeFig.3).Forthefour-barbeating-upmechanismwithfixedgeometricalandkinematicparameters,inthefirsttwoor560JournalofDonghuaUniversity(Eng.Ed.)Vol.27,No.4(2010)threeyearstheoutputaccelerationsignalofmechanismwillappearagaincorrectlyinthenextperiod,andthevibrationpulsewithfixedfrequencyandamplitudewillalsoappearagaineveryperiodofcrankangle.Sotheoutputaccelerationsignaloffour-barbeating-upmechanismwithjointclearanceisnottherandomsignal,butthemainbodyofsignalisthesignalwiththestrictperiodicity.Theoutputcurveofmechanismismainlymadeupofsignalswiththestrictperiodicity,andalsoincludessomerandomcomponent.(3)Therandomcomponentofvibrationwillincreaseastheworkingtimeofloom.Thatistosayastheworkingtimeofmechanismincreases,therandomcomponentofoutputcurvewillbegraduallyimproved.ShowninFig.5,Bistheincludedangleofcoupleroritsextendedlineandcrank.WhenB=0bor180b,thecrankandthecouplerareinthesameline,andwhentheaccelerationofcrankiszero,themechanismisinthepositionofelbowlink.WhenB=90bor270b,thecrankandthecouplerareverticaleachother,andtheaccelerationofcrankislarge.Accordingtothefourspecialpositionsabove,theswingprocessofsleycouldbedividedintofourregions.Fig.5Bangleoffour-barmechanism2RelativeTraceofCouplerPinCenterwithJointClearanceatStaticBalancePositionAccordingtothemeasuringcurve,thereistheimpactoflinksinthejointclearance.Bymeasuringtheclearanceofcrankbearingis2Lm,andtheclearanceofcouplerpinjournalis42Lm.Soitcouldbeconcludedthattheimpactinthejointclearancewillhappenmainlyinthecouplerpinjournal.2.1CouplerpinjournalwithclearanceTherearetwocylindersofpinholeandjournalshowninFig.6.TheradiusofjournalbearingholeisR,theradiusofjournalisr,andtheradiusclearanceisc=R-r.Thedistancebetweentwocentrallinesofcylindersistheeccentricitye=C1C2.Thecouplerandtherockerconnectedbythecouplerjournalbearingarebothmovableparts,sothebearingandthejournalarealsobothturning.Thereistheoilbetweentwocylinders,andthethicknesshofextrusionfilmish=c+esinH=c(1+EsinH),(1)whereE=e/cistheeccentricity；HistheangleincludedbetweenhandC1C2intheverticaldirection.Fig.6GeometricdimensionofjournalforradialloadFisthetotalloadofjournalbearing,Ubcisthelinearvelocityofpinalongthepinsurface,andUcdisthelinearvelocityofjournalalongtheringsurface(seeTable2).Table2MainparametersofcouplerpinbearingNominaldimensionofjournalbearingholeandjournal2R/mmWidthofplainjournalbearingL/mmViscositycoefficientoflubricantG/(N#s#m-1)Radiusclearancec=R-r/mm40420.01750.0212.2JournalcentertraceofstaticbalancepositionThecrankandthecouplerarebothimmersedinthelubricant-box.Thelubricantinthejointclearanceofjournalandbearingwillturnwiththem.Thereisthehigherhydrodynamicpressureintheregionoflessclearance,andthelowerhydrodynamicpressureintheregionoflargerclearance,whichleadstothedeliveryhead.Thebearingloadisenduredbythehydrodynamicpressureoflubricantfortheeffectofoilwedge.Thestaticbalancepositionofjournalcenteristhebalancepositionofoilfilmforceandbearingforce.Thereisthedifferencebetweencouplerpinjournalandordinaryradialbearing.(1)Thedirectionandintensityofloadonthecouplerpinjournalalternateasthetime.(2)Theswingvelocityofjournalandbearingchangesasthetime.TherelationbetweenbearingloadFanddimensionlessoilfilmforceisshowninEq.(2)6.5=F#(c/R)2G#(Ubc+Ucd)#L,(2)561JournalofDonghuaUniversity(Eng.Ed.)Vol.27,No.4(2010)whereFisthebearingload,Gisthedynamicviscosity,andUbcandUcdareshowninFig.6.AccordingtothedatainTable3,thebalanceposition7=N(F,C1C2)couldbesolvedbytheinterpolation.Table3Bearingparametersofcircularcylinder(ratioofwidthandradiusL/2R=1.0)EccentricityE00.400.500.600.70Eccentricangle7/(b)75.1163.5955.5550.0845.3240.5436.02OilfilmforceX0.1970.4150.6801.0291.5242.2963.654Thejournalcentertracecouldbedrawnaccordingtotheeccentricangleandtheeccentricity.Thejournalcentertraceofbearingwiththestaticloadusuallyissemicircle.Buttheloadofcouplerpinjournalwillvaryinthesizeanddirectionastheturningofcrank,sothejournalcenterwillmovealongthetraceofstaticbalanceposition.TherelativetraceofjournalcenterstaticbalancerelativetothecouplerpinjournalholeshowninFig.7is8-shaped.ThepolarangleshowninFig.7isthedirectionangleofhole,andthepolarradiusistheeccentricity.Accordingtothefigure,therearethreetimesforthejournalcentercomingintothecircleofE=0.1.Whenthecrankangleisat72b-114b,itisthefirsttimeforthejournalcentercomingintothecircle,andtheleasteccentricityis0.001.Lesseccentricity,Fig.7Relativetraceofjournalcenterstaticbalancerelativetohole(themargentangleisthecrankangle)thesystemstabilityisworseandworse.Whenthecrankangleisat178b-192b,itisthesecondtimeforthejournalcentercomingintothecircle,andtheleasteccentricityis0.098.Whenthecrankangleisat302b-338b,itisthethirdtimeforthejournalcentercomingintothecircle,andtheleasteccentricityis0.001.AndtherearetwotimesforthecentertouchingtheoutercircleofE=1,wheretheangularvelocitiesofcouplerandrockerrelativetothebearingloadFarethesame,buttheirdirectionsarereverse,andtheimpactwillhappenbetweentwolinks.2.3BalancebetweenoilfilmforceandbearingloadFnisthereactionforcecomponentinthedirectionoflinkBClength,andFtisthereactionforcecomponentintheverticaldirectionoflinkBC.Between80band150b,Ftisclosetozero,andat92bFnistheleast.Thebearingreactionforceisenduredmainlybytheoilfilmthic