外文翻译通过优化节点位置减小反旋转引擎的动态响应Word格式文档下载.docx
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外文翻译通过优化节点位置减小反旋转引擎的动态响应Word格式文档下载.docx
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MINIMIZINGDYNAMICRESPONSEOFCOUNTER-ROTATINGENGINESTHROUGHOPTIMIZEDNODEPLACEMENT
PeterD.Hylton
PurdueSchoolofEngineering&
Technology
IndianaUniversityPurdueUniversityIndianapolis
ABSTRACT
Ithasbeenpreviouslyproposedthatalow-speedrotorbalancingprocedurecanbesuitableforsupercriticalshafting(GT2008-50077).Thatpaperdocumentedthenecessityoftakingintoaccountnodallocationsinthebendingmodeshapesofasupercriticalrotorwhendesigninganoptimumbalanceprocessforsucharotor.Thisisduetothefactthatbalancecorrectionforces(orforthatmatter,anyforces)havetheleastimpactwhenappliednearthenodesofaparticularmode.
Thisresultledtoconsiderationthatnodelocationoptimizationcouldhelpwithanotherissue,i.e.theexcitationofbackwardexcitedwhirlmodesinacounter-rotatingsystem.Whendesigningatworotorgasturbine,therearedistinctadvantagestohavingthetworotorsturninoppositedirections.Amongthesearetheabilitytoshortenandlightentheenginebyreducingthelengthoftheenginesincearowofstaticturningvanescanbeeliminated.Theenginecanbefurtherlightenedbyinclusionofaninter-shaftbearingwhicheliminatesstaticbearingsupportstructure.Additionalreductioningyroscopicmaneuverloadsanddeflectionscanalsobeachieved,thusresultinginmultiplebenefitstoacounter-rotatingsystemwithaninter-shaftbearing.
Unfortunately,theexcitationofbackwardwhirlmodesofonerotor,whichwouldnormallynotbeamajorconcerninaco-rotatingengine,canbeasignificantissuewhenexcitedinsuchacounter-rotatingenginethroughtheinter-shaftbearing,whichservesasaconduitforforcesfromtheotherrotor.However,thelogicoftheearlierstatementregardingtheeffectivenessofforcesappliedat,ornear,anodalpointledtothehypothesisthatoptimizingthenodallocationsrelativetotheinterfacepointsbetweentherotorscouldminimizetheresponsivenessofthesystem.Thisledtothehypothesisthatbyoptimizingthenodeplacementrelativetotheinter-shaftbearing,itshouldbepossibletominimizetheexcitationofthebackwardmodes.Thispaperexaminesthatpropositionanddemonstratesthatconsideringthisaspectduringthedesignofsuchanenginecouldleadtosignificantbenefitintermsofminimizeddynamicresponses.
Keywords:
Balancing,Counter-Rotating,BackwardWhirl
INTRODUCTION
Inanefforttodesignandbuildsmaller,lightweightengines,thatarestillcapableofsignificantpoweroutput,gasturbinedesignershavemadeattemptstoeliminatestaticstructuresthroughdevelopmentofinnovativetwo-spoolengineconfigurations.AnumberofsuchresearchactivitieshavebeenfundedthroughadvancedtechnologyprogramssuchastheAirForce’sIntegratedHighPerformanceTurbineEngineTechnology(IHPTET)[1,2]andtheNationalAeronauticsandSpaceAdministration’s(NASA)HighSpeedRotorCraft(HSRC)[3]programs.Counter-rotationsystemshavebeenevaluatedinbothprograms[4,5]andfoundtoofferadvantages.Iftworotorsaredesignedtorotateinoppositedirections,thenitispossibletoeliminatetherowofturningvanesbetweenthelastrowofturbinebladesgoinginonedirectionandthefollowingrowofturbinebladesturningintheoppositedirection[6,7].Eliminationofthesevanesallowstheenginetobeshorterandthereforelighter.Freedman[8]haspointedoutthat,inadditiontothesavingsinlength,andthusweight,thereisalsoasavingsinrequiredcoolingairthatwouldhavebeenusedfortheremovedvanesandadditionallythereisagaininefficiencyduetoimprovedswirloftheairtravelingthroughthestages.AssummarizedbyZhaoandWang,“Thevanelesscounter-rotatingturbine,whichiscomposedofahighlyloadedsinglestagehighpressureturbinecoupledwithavanelesscounter-rotatinglowpressureturbine,isusedtosignificantlyincreasethethrust-to-weightratioofthepropulsionsystem.”[9]
Thesecondwaytoeliminatestaticstructure,andthuslengthandweight,istomovefromtwoseparatebearingssupportingthetworotorsthroughtwobearingsupportstructures,asshowninFigure1,andgotoaninter-shaftbearingandasinglebearingsupportstructure,asshowninFigure2.AsGambleexplains,“Advancedengineconfigurationstudieshaveshownlargelifecyclecostadvantagesforanenginewithcounter-rotatingspoolsandarotorsupportsysteminwhichthehigh-speedrotorisstraddlemounted(bearingsoneachend)withaninter-shaftbearingsupportatthehighpressureturbine.”[10]
Figure1.Sampleturbineconfigurationshowingtwoseparatebearingsupportstructuresforthetwoenginerotors.
Figure2.Sampleturbineconfigurationshowinganinter-shaftbearingandasinglebearingsupportstructure.
Additionaladvantagestocounter-rotatingthespoolsoftheengineoccurwhenmaneuverconditionsoftheaircraftareconsidered.AsexplainedbyCohen,[11]“duringthenormalmaneuveringofairplanesandmissiles,gyroscopicloadsareappliedtotherotatingparts.”Hegoesontoexplainthatthisproblemisofconcerntoenginedesignersbecauseoftheinducedvibratorybendingstressesbetweentherotatingandstationaryparts.Undermaneuverconditions,thegyroscopicforcesappliedbytherotorstothestaticstructures,andthustotheairframemounts,canbetheprimaryloadsfortheengine,exceedingtherotationalloads.[12]Howevertheseloadscanbereducedbyutilizingcounter-rotatingdesigns.Thisallowsweighttobestrategicallyremovedfromboththeenginecaseandthenacellestructure.Thesourceofthisloadreductionisthatgyroscopicloadsoccurorthogonaltoboththerotationalvectorassociatedwiththeturningaxisoftheairplaneandtherotationalvectorassociatedwiththerotationoftheenginerotor.Sincethecounter-rotatingspoolshaveoppositerotationalvectors,theresultingloadsfromthetwospools,whencombinedthroughtheinter-shaftbearing,tendtocanceleachotherattheenginecaseandmounts.Itshouldbenoted,however,thatthisdoesnotreducetheloadattheindividualbearings,sothesemuststillbeaccommodatedinbearingselectionanddesign.
Thiscanbeshownmathematicallyasfollows.Considerarotatinginertia,withanangularvelocityaboutthexaxisoftheengine,x.Thiscorrespondstotherotationalspeedoftheengine.Nowapplytothissameinertia,anangularrotationabouttheyaxisofy,correspondingtotheeffectcreatedwhenthevehicleinwhichtheengineresidesexperiencesaturningmaneuverabouttheyaxis(i.e.ayawmotioniftheyaxisisintheverticaldirectionrelativetothevehicle’scenterofgravityconsistentwiththestandardorientationofaircraftaxes).Usingstandardgyroscopictheory,acouple(i.e.torque)willbecreated,whichisgivenbyTz=IPxy.WhereIPisthepolarmomentofinertiaoftherotatingmassandthedirectionofapplicationofthisresultingtorqueisshowninFigure3.Theforcesnecessarytoreactthistorqueontherotorsystemmustbesuppliedtotherotorbytheenginecaseatthebearingsandmustultimatelybereactedbytheairframestructurewhichsupportstheenginecase.
Figure3.Applicationofgyroscopictorquecausedbymaneuverloads.
Ifasecondrotorexistsintheengine,rotatinginthesamedirection,onseparatesupports,additionalforcesfromthesecondrotorwillhavetobereactedbytheenginecaseandmounts.Nowsupposethesecondrotorisinsteadsupportedbythefirstrotor,andisrotatinginthesamedirectionasthefirstrotor,butwithanangularvelocityofx’.Asecondgyroscopictorquewouldbeappliedtothisrotor,givenbyTz’=IPx’y,asrepresentedinFigure4.Theforcesnecessarytoreactthismomentwouldhavetobesuppliedbythefirstrotorandthereforeultimatelybytheaforementionedbearingsandcase.However,ifthesecondrotoriscounter-rotatingrelativetothefirstrotor,thenx’hastheoppositesignasx,andTz’isinanoppositedirectiontoTz(oppositethistimetowhatisshowninFigure4).Ifthisisthecase,thenitcanbeeasilyseenthattheforceswhichmustbereactedbytheenginecaseandmounts,arebasedontheresultanttorqueTz–Tz’,andarethereforelessthanwouldhavetobereactedineitherofthepreviousscenarios.
Figure4.Applicationofgyroscopictorquetoaco-rotatingdualrotorsystemcausedbymaneuverloads.
Therearedown-sideeffectstosuchadesign.Withanormal,singlespoolgasturbine,thestaticnaturalfrequencyoftherotorincreasesduetothegyroscopicstiffeningeffectsthatoccurastherotorturnsfaster,asshowninFigure5.However,whentherearetwocounter-rotatingrotors,whichcanpotentiallyexciteeachotherthroughtheinter-shaftbearing,thegyroscopiceffectscreatebothanincreasinganddecreasingnaturalfrequency,[13]suchthattherearebothforwardexcitedandbackwardexcitedcriticalspeeds,asshowninFigure6.
Thiscanbeshownmathematicallyasfollows.Thedynamicequationofmotionforadiskrotatingonshaftisusuallywrittenasfollows:
Representingtheresultantharmonicmotionasafunctionoftheformeitandrearrangingasaneigenvalueproblem,wegetthefollowingdeterminantform:
Figure5.Gyroscopicstiffeningcausesthenaturalfrequencytoincreaseasafunctionofrpm.
Figure6.Gyroscopiceffectsforacounter-rotatingrotorsystemcanleadtotwocriticalspeeds,onebackwardexcitedandforwardexcited.
Theresultantdeterminant,whensolvedasaneigenvalueproblem,willyieldoneresultfortheeigenvalues(i.e.naturalfrequencies)basedonpositivevaluesoftherotationalspeedparameter,,anddifferent,lower,eigenvaluesbasedonnegat
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