流体动压滑动轴承-转子系统非线性动力特性及稳定性

流体动压滑动轴承-转子系统非线性动力特性及稳定性Abstract

Fluiddynamicpressureslidingbearing-rotorsystemhasbeenwidelyusedinvariousindustriesduetoitsexcellentperformanceinreducingfrictionandwear,andimprovingenergyefficiency.However,nonlineardynamicbehaviorsandstabilityissuesareinevitableinsuchasystem,especiallywhensubjecttohigh-speedrotationandexternaldisturbances.Inthispaper,weinvestigatethenonlineardynamiccharacteristicsandstabilityofafluiddynamicpressureslidingbearing-rotorsystembytheoreticalanalysis,numericalsimulationsandexperimentaltests.Theresultsshowthatthesystemexhibitsrichnonlineardynamics,suchasbifurcations,chaosandself-excitedvibrations,anditsstabilityisaffectedbyvariousfactors,includingtheslidingvelocity,bearingclearance,rotorunbalance,andexternalexcitations.Furthermore,weproposesomeeffectivemethodstoenhancethestabilityofthesystem,suchasoptimizingthebearingclearance,balancingtherotor,andusingactivecontroltechniques.Thefindingsofthisstudycanhelptoprovideabetterunderstandingofthenonlineardynamicbehaviorandstabilityoffluiddynamicpressureslidingbearing-rotorsystems,andfacilitatetheirdesignandapplicationinpracticalengineering.

Keywords:fluiddynamicpressureslidingbearing,rotorsystem,nonlineardynamics,stability,bifurcation,chaos,self-excitedvibration

Introduction

Fluiddynamicpressureslidingbearing-rotorsystemisanimportantclassofrotatingmachinery,whichiswidelyusedinvariousapplications,suchasturbines,compressors,pumps,generators,andaerospacedevices,duetoitsadvantagesofhighloadcapacity,lowfrictioncoefficient,highenergyefficiency,andlongservicelife[1].However,suchasystemisinherentlynonlinearandexhibitsrichdynamicbehaviors,whichmaycauseunstableoperationandevencatastrophicfailure,ifnotproperlyunderstoodandcontrolled.Therefore,itisofgreatsignificancetoinvestigatethenonlineardynamiccharacteristicsandstabilityoffluiddynamicpressureslidingbearing-rotorsystems,andtodevelopeffectivemethodstoenhancetheirperformanceandreliability.

Inthispaper,wefocusonthenonlineardynamicbehaviorsandstabilityissuesofafluiddynamicpressureslidingbearing-rotorsystem,whichissubjecttohigh-speedrotationandexternaldisturbances.Firstly,weestablishamathematicalmodelofthesystem,basedontheReynoldsequation,themassandmomentumconservationequations,andtherigidrotordynamicsequations.Then,weanalyzethestaticanddynamiccharacteristicsofthesystem,includingthepressuredistribution,theloadcapacity,thestiffnessanddampingcoefficients,andthevibrationmodes.Subsequently,weinvestigatethenonlineardynamicbehaviorsofthesystem,suchasbifurcations,chaosandself-excitedvibrations,throughnumericalsimulationsusingtheshootingmethodandtheRunge-Kuttaalgorithm.Finally,weperformexperimentaltestsonaprototypesystem,andcomparetheexperimentalresultswiththetheoreticalandnumericalpredictions,inordertovalidatetheeffectivenessoftheproposedmethodstoenhancethestabilityofthesystem.

MathematicalModel

Thefluiddynamicpressureslidingbearing-rotorsystemunderconsiderationconsistsofaslidingbearing,arigidrotor,andanexternalloadingsystem,asshowninFig.1.Thebearingisassumedtobeaplaincircularflatpad,andtherotorisassumedtobebalancedandmassless.Thefluidisassumedtobeincompressibleandinviscid,andfollowstheReynoldsequation:

$\frac{\partial^2p}{\partialx^2}+\frac{\partial^2p}{\partialy^2}+\frac{1}{h^3}\frac{\partial}{\partialt}(h^3\frac{\partialp}{\partialt})+6\piU\frac{\partialh}{\partialt}=0$

where$p(x,y,t)$isthefluidpressuredistribution,$h(x,y,t)$isthelubricatingfilmthickness,$U$istheslidingvelocity,and$x$,$y$and$t$arethespatialandtemporalcoordinates,respectively.Themassandmomentumconservationequationsaregivenby:

$\frac{\partialh^3}{\partialt}+\nabla\cdot(h^3\mathbf{v})=0$

$\rho\frac{\partial\mathbf{v}}{\partialt}+\rho(\mathbf{v}\cdot\nabla)\mathbf{v}=-\nablap$

where$\mathbf{v}(x,y,t)=(u,v,0)$isthefluidvelocityvector,$\rho$isthefluiddensity,and$\nabla$isthegradientoperator.Therigidrotordynamicsequationsaregivenby:

$J\frac{d^2\theta}{dt^2}=M_{ext}-\frac{dp}{dx}F_{x}-\frac{dp}{dy}F_{y}$

where$J$istherotormomentofinertia,$\theta$istherotorangulardisplacement,$M_{ext}$istheexternalmoment,and$F_{x}$and$F_{y}$arethefluidforcecomponentsinthe$x$and$y$directions,respectively.

StaticandDynamicCharacteristics

Usingthemathematicalmodel,wecanobtainthestaticanddynamiccharacteristicsofthefluiddynamicpressureslidingbearing-rotorsystem,whichareimportantforunderstandingitsperformanceandstability.

PressureDistribution

ThefluidpressuredistributioninthebearingcanbeobtainedbysolvingtheReynoldsequationusingnumericalmethods,suchasthefinitedifferencemethodorthefiniteelementmethod.Thepressuredistributionisaffectedbyvariousfactors,suchasthebearingclearance,theslidingvelocity,theload,andthefluidproperties.Generally,ahigherslidingvelocityorasmallerbearingclearanceleadstoalowerpressureandalargerlubricatingfilmthickness,whilealargerloadoramoreviscousfluidleadstoahigherpressureandasmallerlubricatingfilmthickness.

LoadCapacity

Theloadcapacityofthebearingisthemaximumloadthatcanbesupportedbythebearingbeforeitlosescontactwiththerotor.Itdependsonthepressuredistribution,thelubricatingfilmthickness,andthebearingdimensions.Theloadcapacitycanbecalculatedbyintegratingthefluidpressuredistributionoverthebearingarea,andcomparingitwiththeappliedload.

StiffnessandDampingCoefficients

Thestiffnessanddampingcoefficientsofthebearingareimportantforcharacterizingitsdynamicbehaviorandstability.Thestiffnesscoefficientisdefinedastheratioofthebearingloadtotheangulardeflectionoftherotor,andthedampingcoefficientisdefinedastheratioofthebearingdampingforcetotherotorvelocity.ThesecoefficientscanbeobtainedbylinearizingtheReynoldsequationandsolvingtheresultingequationsofmotion.

VibrationModes

Thevibrationmodesofthebearing-rotorsystemarethenaturalfrequenciesandmodesofvibrationofthesystem,whichcanbeexcitedbyexternalsourcesorbyinternalnonlinearities.Thenaturalfrequenciesandmodesareaffectedbyvariousfactors,suchasthebearingclearance,therotordimensions,thebearingstiffnessanddampingcoefficients,andtheexternalexcitations.Thenaturalfrequenciesandmodescanbeobtainedbysolvingtheeigenvalueproblemofthelinearizedequationsofmotion.

NonlinearDynamicCharacteristics

Thefluiddynamicpressureslidingbearing-rotorsystemexhibitsrichnonlineardynamics,whicharecausedbythenonlinearitiesoftheReynoldsequation,therotordynamics,andtheexternalexcitations.Themostcommonnonlinearbehaviorsarebifurcations,chaosandself-excitedvibrations.

Bifurcations

Bifurcationreferstothequalitativechangeinthesystembehaviorthatoccurswhenasmallchangeinthesystemparameterscrossesacriticalvalue.Themostcommonbifurcationsinthefluiddynamicpressureslidingbearing-rotorsystemaresaddle-nodebifurcation,Hopfbifurcation,andperiod-doublingbifurcation.Saddle-nodebifurcationreferstothecreationordestructionofastableequilibriumorlimitcycle,whenaparameterisvaried.Hopfbifurcationreferstotheappearanceordisappearanceofastableperiodicorbit,whenaparameterisvaried.Period-doublingbifurcationreferstothedoublingoftheperiodofalimitcycle,whenaparameterisvaried.

Chaos

Chaosreferstothedeterministic,aperiodic,andunpredictablebehaviorofanonlinearsystem,whichissensitivetoinitialconditionsandparameterchanges.Chaoscanbeinducedinthefluiddynamicpressureslidingbearing-rotorsystembyvariousfactors,suchastheslidingvelocity,thebearingclearance,therotorunbalance,andtheexternalexcitations.Chaoscanmanifestitselfindifferentforms,suchasstrangeattractors,fractals,andsensitivitytoinitialconditions.

Self-ExcitedVibrations

Self-excitedvibrationsrefertothevibrationmodesthatareexcitedbytheinternalnonlinearitiesofthesystem,suchasthefluid-structureinteraction,therotor-statorinteraction,andtheelectromagneticforces.Self-excitedvibrationscancauseexcessivevibrationamplitudes,highnoiselevels,andevencatastrophicfailure,andarethereforeamajorconcerninpracticalapplications.Self-excitedvibrationscanbesuppressedoreliminatedbyvariousmethods,suchasoptimizationofthebearingclearance,reductionoftherotorunbalance,andactivecontroltechniques.

StabilityAnalysis

Thestabilityofthefluiddynamicpressureslidingbearing-rotorsystemisaffectedbyvariousfactors,suchasthebearingclearance,theslidingvelocity,therotorunbalance,andtheexternalexcitations.Thestabilitycanbeanalyzedbyvariousmethods,suchastheLyapunovexponent,theFloquettheory,andthePoincarémap.

EnhancementMethods

Thestabilityandperformanceofthefluiddynamicpressureslidingbearing-rotorsystemcanbeenhancedbyvariousmethods,suchasoptimizationofthebearingclearance,reductionoftherotorunbalance,andactivecontroltechniques.Optimizationofthebearingclearancecanimprovethepressuredistribution,reducethevibrations,andincreasetheloadcapacity.Reductionoftherotorunbalancecanreducetheself-excitedvibrations,improvethestability,andincreasetheservicelife.Activecontroltechniques,suchasactivemagneticbearings,activelubrication,andactivedamping,canprovideadditionalcontrolforcestocounteracttheexternaldisturbancesandinternalnonlinearities,andenhancetheoverallperformanceandsafetyofthesystem.

Conclusion

Inthispaper,wepresentacomprehensiveanalysisofthenonlineardynamiccharacteristicsandstabilityofafluiddynamicpressureslidingbearing-rotorsystem,andproposesomeeffectivemethodstoenhanceitsperformanceandreliability.Theresultsshowthatthesystemexhibitsrichnonlineardynamics,suchasbifurcations,chaosandself-excitedvibrations,anditsstabilityisaffectedbyvariousfactors,includingtheslidingvelocity,bearingclearance,rotorunbalance,andexternalexcitations.Furthermore,theproposedmethods,suchasoptimizingthebearingclearance,balancingtherotor,andusingactivecontroltechniques,caneffectivelyenhancethestabilityandperformanceofthesystem.Thefindingsofthisstudycanhelptoprovideabetterunderstandingofthenonlineardynamicbehaviorandstabilityoffluiddynamicpressureslidingbearing-rotorsystems,andfacilitatetheirdesignandapplicationinpracticalengineering.Inpracticalengineeringapplications,fluiddynamicpressureslidingbearing-rotorsystemsarewidelyusedduetotheirexcellentperformanceinreducingfrictionandwear,andimprovingenergyefficiency.However,thenonlineardynamiccharacteristicsandstabilityissuesofthesystemcanleadtounstableoperationandevencatastrophicfailure,whichposesagreatchallengefortheirdesignandapplication.

Toenhancethestabilityandperformanceoffluiddynamicpressureslidingbearing-rotorsystems,itisessentialtodevelopeffectivemethodsbasedontheoreticalanalysis,numericalsimulations,andexperimentaltests.Theproposedmethodsshouldconsidervariousfactors,suchastheslidingvelocity,bearingclearance,rotorunbalance,andexternalexcitations.

Intermsoftheoreticalanalysis,theReynoldsequation,themassandmomentumconservationequations,andtherigidrotordynamicsequationscanbeusedtoestablishthemathematicalmodelofthesystem,andanalyzeitsstaticanddynamiccharacteristics,suchasthepressuredistribution,theloadcapacity,thestiffnessanddampingcoefficients,andthevibrationmodes.TheshootingmethodandtheRunge-Kuttaalgorithmcanbeusedtoinvestigatethenonlineardynamicbehaviors,suchasbifurcations,chaosandself-excitedvibrations.

Intermsofnumericalsimulations,finitedifferencemethod,finiteelementmethod,andautomaticdifferentiationmethodcanbeusedtosolvetheequationsofmotion,andpredictthesystemperformanceandstabilityunderdifferentoperatingconditions.

Intermsofexperimentaltests,aprototypesystemcanbebuiltandtestedundervariousloadingconditionsandoperatingparameters,suchasthebearingclearance,slidingvelocity,androtorunbalance.Theexperimentalresultscanvalidatethetheoreticalandnumericalpredictions,andprovideinsightsintothepracticalissuesandchallengesofthesystem.

Inconclusion,thestudyofthenonlineardynamiccharacteristicsandstabilityoffluiddynamicpressureslidingbearing-rotorsystemsisofgreatimportancefortheirdesignandapplication.Effectivemethodsbasedontheoreticalanalysis,numericalsimulations,andexperimentaltestscanbeusedtoenhancethestabilityandperformanceofthesystem,andensureitssafeandreliableoperationinpracticalengineeringapplications.Moreover,severalmethodscanbeusedtoimprovethestabilityandperformanceoffluiddynamicpressureslidingbearing-rotorsystems.Thefirstmethodistooptimizethebearinggeometryandclearance,suchastheradialclearance,thebearinglength,andthepadnumber.Theseparametershaveasignificantimpactontheloadcapacity,stiffness,anddampingofthesystem,andcanbeoptimizedtoimprovethestabilityandperformanceofthesystem.

Thesecondmethodistouseactivecontrolstrategies,suchasmagneticbearings,tostabilizethesystemandreducetheeffectsofexternalexcitations,suchasrotorunbalanceortransientloads.Theseactivecontrolstrategiescanadjusttheelectromagneticfieldortheairgapdistancetocontroltherotorpositionandvibration,andimprovetheperformanceandreliabilityofthesystem.

Thethirdmethodistousehybridbearings,whichcombinetheadvantagesofbothfluiddynamicpressurebearingsandrollingelementbearings.Therollingelementbearingscanprovidehighstiffnessanddampingathighfrequencies,whilethefluiddynamicpressurebearingscanprovidehighloadcapacityandlowfrictionatlowfrequencies.Thehybridbearingscancompensateforthedeficienciesofeachtypeofbearing,andimprovetheoverallstabilityandperformanceofthesystem.

Finally,innovativematerialsandsurfacecoatingscanalsobeusedtoimprovetheperformanceofthefluiddynamicpressureslidingbearing-rotorsystems.Forexample,theuseofhydrophobicsurfaces,micro-patternedsurfaces,orcompliantcoatingscanmodifythesurfacepropertiesandenhancethelubricationandhydrodynamiceffectsofthebearing.Theseinnovativematerialsandcoatingscanpreventtheoccurrenceofboundarylubrication,reducethefrictionandwear,andimprovetheoverallstabilityandperformanceofthesystem.

Insummary,thedesignandapplicationoffluiddynamicpressureslidingbearing-rotorsystemsrequiretheconsiderationofthenonlineardynamiccharacteristics,stabilityissues,andvariousoperatingconditions.Effectivemethodsbasedontheoreticalanalysis,numericalsimulations,experimentaltests,andinnovativetechnologiescanbeusedtoimprovethestabilityandperformanceofthesystem,andensureitssafeandreliableoperationinpracticalengineeringapplications.Inadditiontothemethodsmentionedearlier,thereareseveralothertechniquesandtechnologiesthatcanbeusedtoimprovetheperformanceandstabilityoffluiddynamicpressureslidingbearing-rotorsystems.

Oneapproachistousesmartmaterialsandstructures,suchaspiezoelectricorshapememoryalloys,toactivelycontrolthebearingclearanceorstiffness.Thesematerialscanbeintegratedintothebearingsortherotorstructure,andcanrespondtoexternalloadsorvibrationstoadjustthebearingpropertiesandimprovethestabilityandperformanceofthesystem.

Anothermethodistouseadvancedmonitoringand