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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