Optimization design of main parameters for double spiral grooves face seal.pdf

SCIENCEINCHINASERIESETECHNOLOGICALSCIENCES2007SCIENCEINCHINAPRESSRECEIVEDJANUARY5,2005ACCEPTEDFEBRUARY26,2007DOI101007/S1143100700585CORRESPONDINGAUTHOREMAILLIUYINGMAILTSINGHUAEDUCNWWWSCICHINACOMSCICHINASERETECHSCI|AUG2007|VOL50|NO4|448453OPTIMIZATIONDESIGNOFMAINPARAMETERSFORDOUBLESPIRALGROOVESFACESEALLIUZHONG,LIUYINGBASSEMBLYOFSTATICRINGMODULE2THEORETICALMODELS21OPTIMIZATIONMODELTHEOPTIMIZATIONMODELINCLUDESTHREEELEMENTSOPTIMIZATIONTARGETS,OPTIMIZATIONVARIABLESANDCONSTRAINTCONDITIONSMUCHLESSLEAKISTHEFIRSTREQUIREMENTFORTHESEALANDNEXT,THESTIFFNESSOFTHEFLUIDFILMBETWEENTHESEALINGRINGSMUSTBELARGEENOUGHTOREDUCETHEPOSSIBLEFILMPERTURBATIONANDGUARANTEETHESEALINGSTABILITYSOOPTIMIZATIONTARGETSSHOULDBETHATTHEFLUIDFILMAXIALSTIFFNESSSKREACHESITSMAXIMUMWHENTHEFLOWLEAKAGEQISTHELEASTTHEOPTIMIZATIONFUNCTIONCANBEEXPRESSEDASMAX/SSPFKDFDHAND3MIN,12HPFQRWHEREHISTHEFILMTHICKNESSBETWEENTHESTATICANDROTATIONALRINGS,ANDSPFISTHEOPENINGFORCEPRODUCEDBYTHEFLUIDFILMBETWEENTHESEALINGGAPTOOPENTHESEALOPTIMIZATIONVARIABLESINCLUDETHEOPERATINGCONDITIONSROTATINGSPEED,SEALINGPRESSURE,FLUIDVISCOSITYANDTHESTRUCTURALPARAMETERSOUTERANDINNERRADIUSOFTHESEALINGRINGS,RATIOOFTHEGROOVEWIDTHTOTHELANDWIDTH,RATIOOFTHESEALINGDAMWIDTHTOTHEFACEWIDTH,GROOVEDEPTH,GROOVENUMBER,SPIRALANGLE,ETCTHEPOSSIBLERANGEOFTHEOPTIMIZATIONVARIABLESISLIMITEDANDSUCHLIMITATIONSAREREGARDEDASTHECONSTRAINTCONDITIONSOFTHEOPTIMIZATIONTHEMAINCONSTRAINTCONDITIONSARE2MHAND090ATPRESENT,THEGENERALIDEAOFTHEOPTIMIZATIONMETHODFORTHESINGLESPIRALGROOVEFACESEALISASFOLLOWSSELECTAFIXEDANDSMALLVALUEOFTHEGAP,ANDKEEPONEOFTHEPARAMETERSOFGROOVEDEPTH,GROOVENUMBER,RATIOOFTHEGROOVEWIDTHTOTHELANDWIDTHANDSPIRALANGLEASVARIABLEANDKEEPOTHERSINVARIABLE,ANDTHENDEDUCETHEVARIATIONTRENDOFTHESEALINGPERFORMANCE4USINGSUCHMETHOD,ONLYTHEINDIVIDUALEFFECTOFEVERYELEMENTISCONSIDERED,ANDMUTUALACTIONTOSEALINGPERFORMANCEBETWEENALLELEMENTSISNEGLECTEDDOINGBYTHISWAYCAUSEERRORS,ANDDOESNOTREFLECTTHEREALRUNNINGCONDITIONUNDERWHICHTHECLOSINGFORCEOFTHEFACESEALSISUSUALLYAFIXEDVALUEPARAMETERSOPTIMIZATIONWITHAFIXEDCLOSINGFORCESHOULDBECONSISTENTWITHPRACTICALCONDITIONSINADDITION,THEFILMTHICKNESSVARIESWITHTHEOPTIMIZATIONVARIABLES,SOMUTUALEFFECTSOFSYNCHRONOUSVARIATIONSOFTHEOPTIMIZATIONVARIABLESANDTHEFILMTHICKNESSSHOULDBETAKENINTO450LIUZHONGETALSCICHINASERETECHSCI|AUG2007|VOL50|NO4|448453CONSIDERATIONTHEOPTIMIZATIONPROCESSISSHOWNINFIGURE2FIGURE2DESIGNFRAMEFORPARAMETERSOPTIMIZATION22FUNDAMENTALEQUATIONSINCALCULATIONOFSEALINGPERFORMANCETHEGOVERNINGEQUATIONFORTHEFORCEBALANCEISGIVENASFOLLOWSFIGURE3222222221144SPMPFFFDDPDDP,1WHERED1ISTHEINNERRADIUSOFTHESTATOR,D2THEOUTERRADIUSOFTHESTATOR,D1,D2THEINNERANDOUTERRADIUSOFTHECORRUGATEDPIPE,FMTHECLOSINGFORCEPRODUCEDBYCOMPRESSEDCORRUGATEDPIPE,FPTHEAXIALFORCECAUSEDBYTHEFLUIDPRESSUREPASSINGTHROUGHTHECORRUGATEDPIPE,P1THEPRESSUREOFTHELEAKAGESPACEANDP2THEPRESSUREOFTHESEALSPACEFIGURE3SKETCHMAPOFTHEFORCEBALANCEINSTEADYSTATETHEOPENINGFORCEISCOMPOSEDOFTHESTATICPRESSUREANDDYNAMICPRESSUREOFTHESEALINGFLUIDTHEGOVERNINGEQUATIONFORTHEFLUIDDYNAMICSISATWODIMENSIONSTEADYSTATETURBULENTREYNOLDSEQUATION3310,2RHPRHPRHRKRKR2LIUZHONGETALSCICHINASERETECHSCI|AUG2007|VOL50|NO4|448453451ANDITSDIMENSIONLESSFORMIS3310/12/12RHPRHPHRKRRRKR,3WHERERISTHERADIUS,THEFLUIDDENSITY,HTHEFILMTHICKNESS,THEFLUIDVISCOSITY,THERADIAN,P0THEPRESSUREATOUTERRADIUSOFTHESEALINGRING,PTHEDYNAMICPRESSURE,THEROTATINGSPEED,R1THEINNERRADIUSOFTHESEALINGRING,AND0HTHESEALINGGAPDIMENSIONLESSRADIUS1,RRRDIMENSIONLESSPRESSURE0,PPPDIMENSIONLESSGAP0HHHKANDRKTHETURBULENTCOEFFICIENTS,AND22106/ORPHTHECOMPRESSINGCOEFFICIENTTHECALCULATIONREGIONOFEQ3ISACIRQUEBETWEENTHEINNERRADIUSANDTHEOUTERRADIUSOFTHESEALINGRING,WHICHCANBEDIVIDEDINTOTHREEPARTSINNERCIRQUE,OUTERCIRQUEANDMIDDLEDEEPGROOVEINWHICHTHEFLUIDPRESSUREISSUPPOSEDTOBEEQUALEVERYWHEREACCORDINGTOTHECONDENSABILITYOFTHEINVOLVEDFLUID,THEFLUIDDENSITYANDVISCOSITYINATINYCELLARESUPPOSEDTOBECONSISTENT,BUTDIFFERENTAMONGBORDERINGCELLSPERIODICITYOFTHESPIRALGROOVESINTHESEALINGFACECAUSESPERIODICDISTRIBUTIONOFTHEFLUIDPRESSURESOTHEPRESSUREOFTHEWHOLECALCULATIONREGIONMAYBEGAINEDBYONLYCONSIDERINGONESPIRALGROOVE,ONELANDANDITSADJACENTSEALINGDAMACOORDINATESWITCH,LN,URISADOPTED,WHICHTRANSFORMSTHEQUADRANGLEWITHSPIRALANDARCBORDERSUNDERRCOORDINATETOPARALLELOGRAMUNDERUCOORDINATETHEFINITEELEMENTANALYSISMETHODWITHQUADRANGLEEQUIVALENCECELLISADOPTEDTOCALCULATEFLUIDPRESSUREINTHESEALINGGAPTWOBOUNDARYCONDITIONSAREASFOLLOWS1INRADIALDIRECTION,ATINNERANDOUTERRADIUS,THEPRESSUREBOUNDARYCONDITIONIS1101/1,PPPPRR00011/PPRRRR2INCIRCUMFERENTIALDIRECTION,THEPERIODICPRESSUREBOUNDARYCONDITIONIS2/,PZRPRNEWTONRAPHSONMETHODWITHRELAXATIONTECHNIQUEISUSEDTOSOLVEDISCRETEEQ3INORDERTOGAINTHEPRESSUREDISTRIBUTIONINTHESEALINGGAPTHENTHEFOLLOWINGSTEADYSTATESEALINGPERFORMANCESCOULDBEOBTAINED1OPENINGFORCE,SPAFPDRD4WHEREASTANDSFORTHEWHOLEREGIONOFTHESEALINGFACE,ANDPTHEDYNAMICPRESSURE2FLOWLEAKAGE312HPQR53THEPRESSURELOSSTHROUGHFEEDINGHOLES4128,QLPD6WHEREQDENOTESTHEFLOWLEAKAGEINVOLUME,LTHELENGTHOFFEEDINGHOLES,ANDDTHEDIAMETEROFFEEDINGHOLES4STEADYSTATEAXIALSTIFFNESSOFFILM452LIUZHONGETALSCICHINASERETECHSCI|AUG2007|VOL50|NO4|448453SP/SKDFDH723OPTIMIZATIONRESULTFORTHESTRUCTURALPARAMETERSOFDOUBLESPIRALGROOVESFACESEALTHEINFLUENCESOFTHESTRUCTURALPARAMETERSONTHESEALINGPERFORMANCE,SUCHASGROOVEDEPTH,GROOVENUMBER,RATIOOFGROOVEWIDTHTOLANDWIDTH,SPIRALANGLE,ARESHOWNINFIGURE4INWHICH0/KKKISDIMENSIONLESSAXIALSTIFFNESSOFTHEFILM,AND0KISTHEAXIALSTIFFNESSOFABENCHMARKSEALTHEPARAMETRICOPTIMIZATIONISCONDUCTEDUNDERASPECIFICOPERATINGSTATE,20000NR/MIN,018PMPA,THEFLUIDVISCOSITYANDCLOSINGFORCEFORSEALAREFIXEDFIGURE4THEINFLUENCEOFMAINSTRUCTURALPARAMETERSONSEALINGPERFORMANCEATHEINFLUENCEOFGROOVEDEPTHBTHEINFLUENCEOFGROOVENUMBERCTHEINFLUENCEOFRATIOOFGROOVEWIDTHTOLANDWIDTHDTHEINFLUENCEOFSPIRALANGLE,SEALINGGAPM,DIMENSIONLESSFILMSTIFFNESS,K,DIMENSIONLESSLEAKAGE,Q,RATIOOFFILMSTIFFNESSTOLEAKAGE,K/QFIGURE4ASHOWSTHATBOTHTHESEALINGGAPANDLEAKAGEINCREASE,BUTTHESTIFFNESSOFTHEFLUIDFILMDECREASESASTHEGROOVEDEPTHGROWSUNDERTHECONDITIONOFFIXEDCLOSINGFORCETHEDYNAMICEFFECTISSTRONGERWITHLARGERGROOVEDEPTH,BUTLARGERGROOVEDEPTHABOVE20MTENDSTOINFINITYWITHOUTDYNAMICEFFECTANDCANONLYBETREATEDASBOUNDARYCONDITIONONLYWITHSMALLERGROOVEDEPTHBELOW20M,SEALINGPERFORMANCE,EGFILMSTIFFNESS,FLOWLEAKAGE,ISBETTERFIGURE4BINDICATESTHATTHEEFFECTOFTHEGROOVENUMBERONTHEFILMSTIFFNESSISLITTLEINAWIDERANGE820ADDITIONALLY,OTHEROPTIMIZATIONRESULTSSHOWTHATTHECURVEOFTHEFILMSTIFFNESSTOTHEGROOVENUMBERVARIESWITHDIFFERENTFLUIDVISCOSITY5FIGURE4CDESCRIBESTHECHANGINGTRENDOFTHESEALINGGAP,FLOWLEAKAGEANDFILMSTIFFNESSWITHTHEINCREASEOFTHERATIOOFTHEGROOVEWIDTHTOTHELANDWIDTHTHEDYNAMICEFFECTALONGTHELIUZHONGETALSCICHINASERETECHSCI|AUG2007|VOL50|NO4|448453453CIRCUMFERENTIALDIRECTIONOFTHESEALRINGGROWSUPWITHANINCREASEINTHERATIOOFTHEGROOVEWIDTHTOTHELANDWIDTH,WHICHINTRODUCESLARGESEALINGGAPSANDFLOWLEAKAGEONTHECONTRARY,THEFILMSTIFFNESSDECREASESSMOOTHLYDURINGTHISPROCESSLARGERFILMSTIFFNESSISOBTAINEDWHENTHERATIOOFTHEGROOVEWIDTHTOTHELANDWIDTHISBETWEEN0205THECIRCULARVELOCITYOFTHESEALRINGCANBEDECOMPOSEDINTOSHEARANDNORMALVELOCITYLETUSCONSIDERASINGLECALCULATIONCELLTHELARGERTHESPIRALANGLEISANDTHESMALLERTHEINTERSECTIONANGLEBETWEENSHEARVELOCITYANDCIRCLEVELOCITYIS,THESTRONGERTHEEFFECTOFTHESPIRALANGLEISBUTWHENTHESPIRALANGLEBECOMESMUCHLARGER,THEAREAOFTHECALCULATIONCELLWILLBENARROWER,ANDTHEINTERFERENCEOFTHEFLOWBETWEENADJACENTCELLSWILLALSOBECOMEMORESERIOUSWHICHWILLWEAKENTHEDYNAMICPRESSUREEFFECTUNDERSOMECONDITIONONTHECONTRARYTHISWILLOBVIOUSLYAPPEARUNDERTHEWORKINGCONDITIONSWITHHIGHROTATINGSPEEDANDHIGHVISCOSITYANYWAY,THESPIRALANGLEANDTHESEALGAPINFLUENCETHEPERFORMANCEOFTHEFACESEALUNDERTHEFIXEDCLOSUREFORCECONDITIONTHEREFORE,FIGURE4DSHOWSTHATTHESMALLERTHESPIRALANGLEBELOW50DEGREE,THEHIGHERTHEFILMAXIALSTIFFNESSANDTHELARGERTHERATIOOFTHEFILMSTIFFNESSTOTHEFLOWLEAKAGEONTHEOTHERHAND,WHENTHESPIRALANGLEISABOVE60DEGREES,THESEALINGGAPISWIDERTHESERESULTSSUGGESTTHATTHESEALINGGAPISTHEMAINFACTOREXERTINGTHEDYNAMICEFFECTSTHEBUMPINGEFFECTOFTHESPIRALREACHESTHEMAXIMUMWHENTHESPIRALANGLEISAPPROACHING90DEGREESATTHESAMETIME,THESEALINGGAPANDTHEFLOWLEAKAGEAUGMENTRAPIDLYWITHTHEGROWINGDYNAMICEFFECTTHEFILMAXIALSTIFFNESSANDTHERATIOOFTHEFILMSTIFFNESSTOTHEFLOWLEAKAGEARRIVEATTHEIRMAXIMAWITHTHESPIRALANGLEBETWEEN7580DEGREES4CONCLUSIONS1THEINTERACTIONOFMAINSTRUCTURALPARAMETERSANDTHEINFLUENCEOFTHESEALGAPONTHEPERFORMANCEOFTHEDOUBLESPIRALGROOVESFACESEALAREINVESTIGATEDSIMULTANEOUSLYWITHTHEFIXEDCLOSUREFORCETHEOPTIMIZATIONRESULTSOFTHEGROOVEDEPTH,GROOVENUMBER,RATIOOFTHEGROOVEWIDTHTOTHELANDWIDTHANDSPIRALANGLEAREOBTAINEDUNDERTHEWORKINGCONDITIONOFHIGHSPEED,HIGHPRESSUREANDULTRALOWTEMPERATURETHESERESULTSAREDIFFERENTFROMTHOSEOFSINGLESPIRALGROOVEGASFACESEALTHETRENDOFOPTIMIZATIONCURVESWITHFIXEDCLOSUREFORCEISALSODISSIMILARWITHTHATASSUMINGFIXEDSEALGAP2THEOPTIMIZATIONRESULTSSHOWTHATMUCHBETTERSEALINGPERFORMANCECANBEOBTAINEDWHENTHERATIOOFTHEGROOVEWIDTHTOTHELANDWIDTHIS05ANDTHESPIRALANGLEISABOUT75DEGREESBUTTHEINFLUENCEOFTHEGROOVENUMBERONTHESEALINGPERFORMANCEISNOTOBVIOUS3ASMALLERRORISCAUSEDBYTHEASSUMPTIONOFPARALLELSEALINGGAP,WHICHIGNORESTHEEFFECTOFCONINGFILMDUETOHEATANDELASTICDISTORTIONBUTITDOESNOTAFFECTTHERELIABILITYOFPARAMETRICOPTIMIZATIONRESULTS1PENGXD,JIAOYR,YEZW,ETALTHEHOTSPOTSINMECHANICALFACESEALSGENERMECHINCHINESE,2003,354572LIUZ,LIUY,LIUXFSTATICPERFORMANCEANALYSISOFANEWDOUBLESPIRALGROOVEFACESEALSLUBRICENGININCHINESE,2005,16763653ZHENGXQ,BERARDGLARGEDIAMETERSPIRALGROOVEFACESEALDEVELOPMENT,PERKINELMERFLUIDSCIENCESCENTURIONMECHANICALSEALS,2000,1071344HUDM,HAOMM,PENGXD,ETALGEOMETRYOPTIMIZATIONOFSPIRALGROOVEUPSTREAMPUMPINGMECHANICALSEALSLUBRICENGININCHINESE,2003,135415LIUZ,LIUY,LIUXFEFFECTOFLOWTEMPERATUREFLUIDVISCOSITYONGEOMETRYOPTIMIZATIONOFDOUBLESPIRALGROOVEMECHANICALSEALSLUBRICENGININCHINESE,2006,1827981免费论文查重HTTP/FREEPAPERYYCOM3亿免费文献下载HTTP/WWWIXUESHUCOM超值论文自动降重HTTP/WWWPAPERYYCOM/REDUCE_REPETITIONPPT免费模版下载HTTP/PPTIXUESHUCOM阅读此文的还阅读了1LOCATORSOPTIMIZATIONFORMEASURINGFIXTUREDESIGN2MAINTECHNICALPARAMETERSFORINDOORLED3THEDESIGNANDOPTIMIZATIONSPECTROMETERWITHDOUBLEDIAGNOSTICSOFANEUTRONTIMEOFFLIGHTSCINTILLATORSFORNEUTRONONEAST4OPTIMIZATIONDESIGNOFRESISTANCESPOTWELDINGPARAMETERSOFMAGNESIUMALL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