Non-linear dynamic analysis of rub-impact rotor su

InternationalJournalofMechanicalSciences50(2008)1090–1113Non-lineardynamicanalysisofrub-impactrotorsupportedbyturbulentjournalbearingswithnon-linearsuspensionCai-WanChang-Jiana,Chao-KuangChenb,aDepartmentofMechanicalandAutomationEngineering,I-ShouUniversity,KaohsiungCounty,TaiwanbDepartmentofMechanicalEngineering,NationalChengKungUniversity,Tainan,TaiwanReceived5June2006;receivedinrevisedform7January2008;accepted1February2008Availableonline15February2008AbstractThisstudypresentsadynamicanalysisofarub-impactrotorsupportedbytwoturbulentmodeljournalbearingswithnon-linearsuspension.Thedynamicsoftherotorcenterandbearingcenterarestudied.Theanalysisoftherotor-bearingsystemisinvestigatedundertheassumptionsofturbulentlubricantflowandashortbearingapproximation.Thespatialdisplacementsinthehorizontalandverticaldirectionsareconsideredforvariousnon-dimensionalspeedratiosanddimensionlessunbalanceparameter.Thenumericalresultsshowthatthestabilityofthesystemvarieswiththenon-dimensionalspeedratiosandthenon-dimensionalunbalanceparameters.Thecontributionofthisstudyistoprovideafurtherunderstandingofthecharacteristicsanddynamicbehaviorsoftherotor-bearingsystem.r2008ElsevierLtd.Allrightsreserved.Keywords:Turbulentjournalbearing;Non-linearsuspension;Rub-impact1.IntroductionMostoftheflowoflubricantisassumedtobethelaminarflow,butthehigh-speedjournalbearingslubri-catedwithunconventionallubricantsoflowviscositygiverisetolarge-filmReynoldsnumbers.Asaresult,theflowofthebearingbecomesturbulent.Togetthemostaccuratesolutionsofthedynamicanalysisoftherotor-bearingsystem,theanalysisoftheflowoflubricantmustbesimulatedasturbulentflow.Constantinescu[1]firstpresentedamodifiedReynoldsequationtodescribetheturbulentlubricationbasedonthemixinglengthconceptofPrandtl.ElroldandNg[2]proposedanapplicationtothecombinedlubricantflowofbothpressureandshearflows.Hirs[3]developedanewmethod,basedonthebulkflowconcept,byrelyingontherelationshipsbetweenwallshearstressandmeanvelocityrelativetothewall.Hashimotoetal.[4,5]examinedtheeffectsofwearonsteady-stateanddynamiccharacteristicsofthetheoreticalandexperimentalmethodsunderoperatingconditionsincludingturbulence.Capone[6]predicteddynamiccharacteristicsandstabilityofajournalbearinginanon-laminarlubricationregime.KumarandMishra[7]analyzedthestabilityoftherigidrotorinturbulenthydrodynamicwornjournalbearingsandalsoconcludedthatlowerL/Dratiosaremorestableforwornbearings.Lin[8]investigatedtheturbulenthydrodynamiclubricationassociatedwiththelubricationofthree-dimensionalsurfaceirregularity.Lahmar[9]proposedanoptimizedshortbearingtheoryfornon-lineardynamicanalysisofturbulentjournalbearings.Theyalsoprovedthattheturbulenteffectsonthedynamicbehaviorofrotor-bearingsystemsbecomemoresignificantasthejournalrotationalspeedincreases.Theaboveresearchesallemphasizedthattheusageofturbulentflowanalysiswillmaketheanalysisofhydrodynamiclubricationmoreapproximateintherealsituations.Manyaspectsshouldbeconcernedintheoperationofturbo-machineries,suchasrub-impactbetweentherotorandstator.Manyturbo-machinerieswithhighrotationalARTICLEINPRESS:10.1016/j.ijmecsci.2008.02.003Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddress:[e-mail](C.-K.Chen).speedoftenmeettherub-impactbetweentherotorandthestator.Ignoringtheoccurrenceofrubbingmayleadtocatastrophicbreakdownoftherotatingmachinery.Thecontinuousrubbingoftherotorandthestatorcouldresultintheshutdownofamotor,andtherubbingbetweenabladeanditssealscouldalsoresultinbrokenblade.Thustheconsiderationofrub-impactofthedynamicanalysisofrotor-bearingsystemhasbecomemoreandmoreimpor-tant.Muszynska[10]analyzedthephysicalphenomenarelatedtopartiallateralrotor-to-statorrub.Theinfluenceofclearancevariationwasobtainedoverawiderangeofoperatingparameters.Muszynska[11]alsoproposed,inhisrotatingmachinery-literaturesurvey,therotor-to-station-aryelementinrub-relatedvibrationphenomena.Beatty[12]inducedamathematicalmodelforrubbingforces,whichisstillwidelyusednowadays,andalsodevelopedseveralsolutionsfordiagnosingthisfaultbytheoreticalsimulationandlaboratoryverification.GoldmanandMuszynska[13]foundthechaoticbehaviorofrotor/statorsystemswithrubs.ChuandZhang[14]investigatedthenon-linearvibrationcharacteristicsofarub-impactJeffcottrotor.Theyalsofoundthatwhentherotatingspeedincrease,thegrazingbifurcation,thequasi-periodicmotionandchaoticmotionoccuraftertherub-impact.Yuetal.[15]presentedtheresultsofexperimentalandanalyticalstudiesaswellassomeconclusionsonrotor/sealfullannularrub.Theaboveresearchesallemphasizedtheimportanceoftherub-impactforcebetweentherotorandthestatorinarotor-bearingsystem.Therefore,itindeedneedstheconsiderationofrub-impactforceofthestudyoftherotor-bearingsystem.Inarotor-bearingsystem,thehydrodynamicpressureisgeneratedentirelybythemotionofthejournalanddependsontheviscosityofthelubricatingfluid.However,thehydrodynamicpressurearoundthebearingisnon-linearandhencethefluidfilmrotor-bearingsystemhasastrongnon-linearit