起落架噪声预测的统计模型【中文15000字】
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上传时间：2018-04-12
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起落架
噪声
预测
统计
模型
中文
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起落架噪声预测的统计模型【中文15000字】,起落架,噪声,预测,统计,模型,中文
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JOURNALOFSOUNDANDVIBRATIONJOURNALOFSOUNDANDVIBRATION28220056187WWWELSEVIERCOM/LOCATE/JSVIASTATISTICALMODELFORLANDINGGEARNOISEPREDICTIONYUEPINGGUO丰THEBOEINGCOMPANY,MAILCODEH013B308,5301BOLSAAVENUE,HUNTINGTONBEACH,CA92647,USARECEIVED8AUGUST2003ACCEPTED14FEBRUARY2004AVAILABLEONLINE22SEPTEMBER2004ABSTRACTTHISPAPERPRESENTSTHEDEVELOPMENTOFAFRAMEWORKFORAIRCRAFTLANDINGGEARNOISEPREDICTIONAPREDICTIONMODELISDERIVEDTHATDECOMPOSESTHELANDINGGEARNOISEINTOTHREESPECTRALCOMPONENTS,FORTHELOW,MIDANDHIGHFREQUENCIES,RESPECTIVELYTHISCORRESPONDSTOCATALOGUINGTHEPARTSINTHELANDINGGEARASSEMBLYINTOTHREEGROUPS,NAMELY,THEWHEELSFORLOWFREQUENCIES,THEMAINSTRUTSFORMIDFREQUENCIESANDTHESMALLDETAILSFORHIGHFREQUENCIESTHESPECTRALDECOMPOSITIONISDEMONSTRATEDBYEXPERIMENTALDATAFROMAFULLSCALEBOEING737LANDINGGEARTEST,WHICHSHOWDIFFERENTSPECTRALCHARACTERISTICSOFTHENOISEINTHETHREEDIFFERENTFREQUENCYDOMAINSINEACHFREQUENCYDOMAIN,ASYMPTOTICRESULTSAREDERIVEDFORTHEFARELDNOISE,BYMAKINGUSEOFDIFFERENTLENGTHSCALESTOSIMPLIFYTHEPHASEBEHAVIOROFTHESOURCESTHEDERIVEDRESULTSREQUIREASINPUTONLYSOMESTATISTICALDESCRIPTIONSOFTHESURFACEPRESSUREUCTUATIONSANDTHEGEOMETRYOFTHELANDINGGEARASSEMBLYSOMESIMPLEEXAMPLESAREGIVENTODEMONSTRATETHEFEATURESOFTHEPREDICTEDNOISE,WHICHSHOWTRENDSCONSISTENTWITHEXPERIMENTALDATATHEFREQUENCYDOMAINDECOMPOSITIONALSOPOINTSTOSIMPLEWAYSOFOBTAININGTHESURFACEPRESSUREPROPERTIESREQUIREDFORNOISEPREDICTION,WHICHISALSODISCUSSEDINTHISPAPERR2004ELSEVIERLTDALLRIGHTSRESERVED1INTRODUCTIONLANDINGGEARNOISEHASBEENATTRACTINGALOTOFATTENTIONINRECENTYEARSBECAUSEITISNOWRECOGNIZEDASONEOFTHEMAJORCOMPONENTSOFAIRFRAMENOISEFORCOMMERCIALAIRCRAFTITISALSO丰TEL7148961527FAX17148961559EMAILADDRESSYUEPINGGUOBOEINGCOMYGUO0022460X/SEEFRONTMATTERR2004ELSEVIERLTDALLRIGHTSRESERVEDDOI101016/JJSV20040202162YGUO/JOURNALOFSOUNDANDVIBRATION28220056187NOMENCLATUREATYPICALDIMENSIONOFCROSSSECTIONATRANSFORMATIONMATRIXFROMGLOBALTOLOCALCOORDINATESBLONGITUDINALCORRELATIONFUNCTIONOFSURFACEPRESSURESCCONSTANTSOUNDSPEEDCJCROSSSECTIONCONTOUROFJTHCOMPONENTDMAINSTRUTDIAMETERDWHEELDIAMETERFITOTALFORCEONLANDINGGEARINITHDIRECTIONFIJSECTIONALFORCEONJTHCOMPONENTINITHDIRECTIONKACOUSTICWAVENUMBERLJLENGTHOFJTHCOMPONENTMOWMACHNUMBERQDYNAMICHEADSARCLENGTHCOORDINATES0ARCLENGTHCOORDINATEATSTATIONARYPOINTSTOTALSURFACEAREASJSURFACEAREAOFJTHCOMPONENTSTSTROUHALNUMBERSTDDOPPLERSHIFTEDSTROUHALNUMBERTSURFACETANGENTVECTORTTIMEUMEANOWVELOCITYUCCONVECTIONVELOCITYNORMALTOLENGTHDIRECTIONVCCONVECTIONVELOCITYINLENGTHDIRECTIONXICOORDINATESXEDONGROUNDYISOURCECOORDINATESZILOCALCOORDINATESDDOPPLERFACTORJAUTOCOHERENCEOFSECTIONALFORCESNFUNITVECTOROFSECTIONALFORCENISURFACENORMALINITHDIRECTIONNTOTALNUMBEROFCOMPONENTSPACOUSTICPRESSUREPCCIRCUMFERENTIALLYAVERAGEDSURFACEPRESSUREPSSURFACEPRESSUREONGEARCOMPONENTFPNOISESPECTRUMZMOVINGCOORDINATESRCONSTANTMEANDENSITYTSOURCETIMEOANGULARFREQUENCYCPHASEFUNCTIONONEOFTHEMOSTDIFCULTNOISECOMPONENTSTOUNDERSTAND,PREDICTANDSUPPRESSTHISISBECAUSETHEMECHANISMSRESPONSIBLEFORTHENOISERADIATIONINVOLVECOMPLEXOWSINACOMPLEXGEOMETRYSETTING,WHICHMAKESDETAILEDSTUDIES,EXPERIMENTALAND/ORNUMERICAL,VERYDIFCULTCONSEQUENTLY,ITCANBEEXPECTEDTHATINTHEFORESEEABLEFUTURE,PRACTICALNOISEPREDICTIONFORLANDINGGEARSWILLEITHERHEAVILYRELYONEMPIRICISMORINVOLVEACCEPTABLEAPPROXIMATIONSTOSIMPLIFYTHEPROBLEMINTHISPAPER,WEFOLLOWTHELATTERAPPROACHTODEVELOPASTATISTICALFRAMEWORKFORLANDINGGEARNOISEPREDICTIONINESSENCE,OURMETHODOLOGYDECOMPOSESTHELANDINGGEARNOISESPECTRUMINTOTHREEFREQUENCYDOMAINS,WHICHAREDENOTEDASTHELOW,THEMIDANDTHEHIGHFREQUENCYDOMAIN,RESPECTIVELYTHECOMPONENTSINTHELANDINGGEARASSEMBLYAREGROUPEDACCORDINGTOTHEIRMAINNOISECONTRIBUTIONSINTHESETHREEFREQUENCYDOMAINSNOISEPREDICTIONFOREACHFREQUENCYCOMPONENTISDERIVEDASYMPTOTICALLYBYMAKINGUSEOFSTATISTICALDESCRIPTIONSOFTHEOWPROPERTIES,SUCHASTHEIRENSEMBLEAVERAGEDCROSSANDAUTOSPECTRA,TOAVOIDDETAILEDDETERMINISTICCOMPUTATIONOFTHENEARELDOWTHEENTIREFREQUENCYDOMAINOFPRACTICALINTERESTCANBECOVEREDBYEMPIRICALLYMATCHINGTHESEASYMPTOTICRESULTSANDTHETOTALNOISEISPREDICTEDBYSTATISTICALENERGYADDITIONOFTHENOISECONTRIBUTIONSFROMINDIVIDUALPARTSOFTHELANDINGGEARASSEMBLY63YGUO/JOURNALOFSOUNDANDVIBRATION28220056187THEFREQUENCYDOMAINDECOMPOSITIONENABLESUSTODERIVEANALYTICALSOLUTIONSBECAUSETHENOISESOURCESBEHAVEQUITEDIFFERENTLYINTHESEDIFFERENTFREQUENCYDOMAINSTHEAGGREGATEEFFECTSOFTHEDISTRIBUTEDSOURCESONTHEFARELDRADIATIONCRITICALLYDEPENDONTHERELATIVEPHASESOFTHESOURCESFORLOWFREQUENCIES,THETYPICALSOUNDWAVELENGTHISLONGERTHANTHEDIMENSIONSOFTHELANDINGGEARCOMPONENTSSOTHATTHEPHASEVARIATIONOFTHESOURCESISSMALLACROSSTHELANDINGGEARASSEMBLYINTHISCASE,THEFARELDSEESALLSOURCESINPHASEANDTHESOURCEDISTRIBUTIONISEQUIVALENTTOACONCENTRATEDSOURCETHISISINFACTTHEEXTENSIVELYSTUDIEDCASEOFSOUNDFROMCOMPACTBODIESWHERETHECOMPACTNESSISMEASUREDBYTHEACOUSTICWAVELENGTH14INTHISCASE,NOISEPREDICTIONONLYREQUIRESINFORMATIONONTHETOTALFORCESONTHELANDINGGEARASSEMBLYINTHEMUCHLESSSTUDIEDCASEOFHIGHFREQUENCIES,THEPHASESOFTHESOURCESVARYSIGNICANTLYACROSSTHESOURCEDISTRIBUTIONTHISRAPIDPHASEVARIATIONLEADSTOSOMEMUTUALCANCELLATIONOFTHERADIATEDSOUNDASARESULT,THEFARELDNOISEISDOMINANTLYGENERATEDBYSOURCESATLOCATIONSWHERETHEIRPHASEVARIATIONVANISHESINTHISCASE,NOISEPREDICTIONONLYREQUIRESINFORMATIONATAFEWLOCATIONSINTHESOURCEDISTRIBUTIONWHETHERTHESOURCESARECOMPACTORNONCOMPACTDEPENDSONTHERATIOOFAPHYSICALDIMENSIONTOTHEACOUSTICWAVELENGTHFORATYPICALELONGATEDLANDINGGEARCOMPONENTSUCHASASTRUT,ITSLENGTHMAYBELONGERTHANTHEACOUSTICWAVELENGTHBUTITSCROSSSECTIONDIMENSIONMAYBECOMPACTTHISISWHATWECALLTHELOWFREQUENCYDOMAIN,INWHICHDIFFERENTAPPROXIMATIONSAPPLYINTHETWODIFFERENTLENGTHSCALESTHESEDIFFERENTKINDSOFSOURCEBEHAVIORINDIFFERENTFREQUENCYDOMAINSAREREPRESENTEDBYAPHASEFUNCTIONOFTHESOURCESINTHEFREQUENCYDOMAINVERSIONOFTHEFFOWCSWILLIAMS/HAWKINGSEQUATION5,WHICHHASBEENAPPLIEDTOVARIOUSAEROACOUSTICSPROBLEMS68WEWILLSHOWTHATINEACHFREQUENCYDOMAIN,DIFFERENTAPPROXIMATIONSCANBEAPPLIEDTOTHISPHASEFUNCTION,WHICHENABLESTHEDERIVATIONOFANALYTICALSOLUTIONSFORTHEFARELDSOUNDWECHOOSETOWORKWITHFREQUENCYDOMAINDECOMPOSITION,NOTONLYBECAUSETHISAPPROACHENABLESUSTODERIVESIMPLEANALYTICRESULTSFOREACHSPECTRALCOMPONENT,BUTALSOBECAUSETHESESPECTRALCOMPONENTSCORRESPONDTONOISEGENERATEDBYDIFFERENTGROUPSOFLANDINGGEARPARTSTODEMONSTRATETHIS,WEWILLDISCUSSSOMEEXPERIMENTALDATA,OBTAINEDINANACOUSTICTESTFORAFULLSCALEBOEING737LANDINGGEAR9THEEXPERIMENTWASDONEINSUCHAWAYTHATCONTRIBUTIONSFROMTHEWHEELS,THEMAINSTRUTSANDTHEDETAILEDDRESSINGSSUCHASHOSESANDWIRESCANBEEASILYSEPARATEDFROMEACHOTHERITWILLBESHOWNTHATTHETHREEGROUPSOFLANDINGGEARCOMPONENTSGENERATENOISEWITHQUITEDIFFERENTSPECTRALCHARACTERISTICS,MOSTLYCONTROLLEDBYTHEIRRESPECTIVELENGTHSCALESWHILENOISEFROMTHEWHEELSANDMAINSTRUTSHAVEBEENSTUDIEDINTHEPAST4,10,11,THESMALLERCOMPONENTSSUCHASTHEHOSESANDWIRESASSOCIATEDWITHTHEHYDRAULICSYSTEMANDTHESMALLCUTOUTSANDSTEPSHAVENOTRECEIVEDASMUCHATTENTIONITISONLYINRECENTYEARSTHATTHESESMALLPARTSWERERECOGNIZEDASVERYIMPORTANTCONTRIBUTORSTOTHEHIGHFREQUENCYNOISE12,13,WHICHISTHEMOSTIMPORTANTCOMPONENTINAIRCRAFTNOISECERTICATIONBECAUSEOFTHIS,EXISTINGPREDICTIONTOOLS,MOSTLYBASEDONSTUDIESONWHEELANDSTRUTNOISE,USUALLYUNDERPREDICTTHETOTALLANDINGGEARNOISE,ESPECIALLYFORPRACTICALNOISEMETRICSSUCHASTHEEFFECTIVEPERCEIVEDNOISELEVELEPNL,ASTANDARDMEASUREFORAIRCRAFTNOISETHISISBECAUSEHIGHFREQUENCYNOISEISHEAVILYWEIGHTEDINCALCULATINGTHISNOISEMETRIC,BUTISMISSINGINPREDICTIONSBASEDONWHEELANDSTRUTNOISETODEMONSTRATETHIS,WEWILLUSETHEBOEING737LANDINGGEARASANEXAMPLEANDSHOWTHATPREDICTIONTOOLSCURRENTLYINUSE11UNDERPREDICTLANDINGGEARNOISEBYASMUCHAS7EPNLDBWEWILLALSOSHOWTHATTHISLARGEAMOUNTOFUNDERPREDICTIONISMOSTLYFROMTHEHIGHFREQUENCYDOMAINTHIS64YGUO/JOURNALOFSOUNDANDVIBRATION28220056187CLEARLYPOINTSTOTHENEEDFORPREDICTIONTOOLSWITHHIGHFREQUENCYCAPABILITYUNFORTUNATELY,HIGHFREQUENCYNOISEISALSOAVERYDIFCULTCOMPONENTTOWORKWITHBECAUSEOFTHESMALLLENGTHSCALESASSOCIATEDWITHTHEHIGHFREQUENCYSOURCESTHISISWHYWECHOOSETOWORKWITHANAPPROXIMATEAPPROACHBASEDONASYMPTOTICANALYSISTHERESULTSOFTHISAPPROACH,WHILEADMITTEDLYNOTPRECISEINDETAILSCANBEUSEFULINMANYASPECTSTHERSTISITSPREDICTIONCAPABILITYFORPRACTICALAPPLICATIONSWEWILLDERIVEFORMULASTHATONLYREQUIRESTATISTICALDESCRIPTIONSOFTHEOWELD,SUCHASTHECROSSANDAUTOCOHERENCEOFTHESURFACEPRESSURES,ANDTHEGEOMETRYOFTHELANDINGGEARASSEMBLYTHECOMPUTATIONALREQUIREMENTFORCOMPUTINGTHENOISEISQUITETRIVIALTHESECONDUSEFULASPECTOFTHISAPPROACHISTHEREVELATIONOFFUNCTIONALDEPENDENCIESOFLANDINGGEARNOISEONOWANDGEOMETRYPARAMETERSTHESEFUNCTIONALDEPENDENCIESARECONTROLLEDBYTHEPHYSICALMECHANISMSTHATARERESPONSIBLEFORTHENOISEGENERATION,ANDHENCE,POINTTODIRECTIONSFORPOTENTIALTECHNOLOGYDEVELOPMENTFORNOISEREDUCTIONBECAUSEOURAPPROACHINVOLVESMAKINGASERIESOFAPPROXIMATIONSTOTHEEXACT,COMPLETEPROBLEM,THEPROCEDUREPROVIDESAHIERARCHYOFPREDICTIONTOOLSWITHVARIOUSDEGREESOFACCURACYTHEINTERMEDIATERESULTSINTHEDERIVATIONCANALLBEREGARDEDASPREDICTIONTOOLSWHOSEUSEFULNESSDEPENDSONTHEDEGREEOFACCURACYREQUIREDANDTHECOMPLETENESSOFTHEAVAILABLEOWINFORMATIONTHETHEORETICALLYMOSTACCURATECASEISWHEREALLTHEOWINFORMATIONISKNOWNEXACTLYINSUCHATHEORETICALCASE,THECOMPLETEFFOWCSWILLIAMS/HAWKINGSEQUATION5PROVIDESPRECISEPREDICTIONSFORTHENOISEAPPARENTLY,SUCHPRECISEPREDICTIONSARENOTAVAILABLEATTHEPRESENTTIMEFORPRACTICALAPPLICATIONSATTHEOTHERENDOFTHISHIERARCHY,THEFORMULASTHATREQUIRETHELEASTINPUTINFORMATIONARETHOSEUSINGEMPIRICALDATAFORTHEOWSTATISTICSITISCONCEIVABLETHATINTHEFUTURETHISKINDOFOWSTATISTICSCANBEDERIVEDFROMMOREDETAILEDSIMULATION,INSTEADOFPUREEMPIRICALCURVETTINGTHEAPPROACHFOLLOWEDHERETODERIVETHENOISEPREDICTIONFORMULASISPRECISELYINTHESPIRITOFTHELIGHTHILLACOUSTICANALOGY14,NAMELY,BYASSUMINGTHATTHENEARELDOWINFORMATIONISOBTAINABLEINDEPENDENTOFTHEACOUSTICELDTHISCANBEJUSTIEDBYTHELOWOWMACHNUMBERTYPICALOFLANDINGGEARNOISEAPPLICATIONS,WHERETHEOWGENERATEDNOISESIMPLYPROPAGATESAWAYFROMTHEGEARWITHOUTMUCHBACKREACTIONONTHEOWTHEASYMPTOTICANALYSISINTHETHREEFREQUENCYDOMAINSNOTONLYLEADSTOEXPLICITANALYTICALFORMULASFORNOISEPREDICTION,WHICHISVERYDESIRABLEFORENGINEERINGAPPLICATIONS,BUTALSOPOINTSTOSIMPLEWAYSTOOBTAINTHENEARELDINFORMATIONREQUIREDFORNOISEPREDICTIONTHISISBECAUSETHENOISEFROMDIFFERENTFREQUENCYDOMAINSISGENERATEDBYDIFFERENTGROUPSOFLANDINGGEARPARTSTHIS,TOGETHERWITHSOMEASSUMPTIONSCONCERNINGTHEMUTUALINTERACTIONSBETWEENTHEPARTS,MAKESITQUITEFEASIBLETOOBTAINTHEREQUIREDNEARELDOWPROPERTIESWITHOUTFULLBLOWNNUMERICALSIMULATIONSFORREALISTICLANDINGGEARSORLARGESCALEDETAILEDHIGHDELITYLANDINGGEARTESTSTHISWILLBEDISCUSSEDINTHISPAPER2SOMEEXPERIMENTALOBSERVATIONSTODEMONSTRATEHOWTHECOMPONENTSINTHELANDINGGEARASSEMBLYGENERATENOISEINDIFFERENTFREQUENCYDOMAINSANDTOSHOWTHECHARACTERISTICSOFTHEGENERATEDNOISEINTHESERESPECTIVEFREQUENCYDOMAINS,WEDISCUSSSOMEEXPERIMENTALDATAINTHISSECTIONTHEDATAWEREOBTAINEDFROMANACOUSTICTESTINTHEBOEINGLOWSPEEDAEROACOUSTICSFACILITYLSAFTHETESTWASDONE65YGUO/JOURNALOFSOUNDANDVIBRATION28220056187FORAFULLSCALEMODELOFABOEING737LANDINGGEARWITHFARELDNOISEMEASUREMENTSMADEBYBOTHFREEELDMICROPHONESANDBYAPHASEDMICROPHONEARRAYTHEFREEELDMICROPHONEMEASUREMENTS,WHICHARETHEDATADISCUSSEDINTHISPAPER,COVERTHEEMISSIONANGLERANGEFROM651TO1501,THEDIRECTIVITYANGLEBEINGMEASUREDFROMTHEUPSTREAMDIRECTIONDETAILSOFTHISTESTHAVEBEENPREVIOUSLYREPORTED9SOTHATONLYRELEVANTDATAAREDISCUSSEDHERETHELANDINGGEARWASTESTEDINVARIOUSCONGURATIONSANDOWCONDITIONSFLOWCONDITIONSVARYWITHMACHNUMBERRANGINGFROM018TO024FORTHEGEARCONGURATIONS,THREEAREOFPARTICULARINTERESTTOUS,NAMELY,THEDIRTY,THECLEANANDTHENOWHEELCONGURATIONTHEDIRTYCONGURATIONISAFULLYDRESSEDLANDINGGEARWITHALLTHESMALLPARTSSUCHASTHEHOSESANDWIRESFROMTHEHYDRAULICSYSTEMTHUS,ITSNOISEISTHETOTALNOISEFORTHISLANDINGGEARTHECLEANCONGURATIONISASIMPLIEDGEARCONSISTINGOFONLYTHEWHEELSANDTHEMAINSTRUTSTHISISTYPICALOFTHECONGURATIONSSTUDIEDINSMALLSCALEEXPERIMENTSINTHEPASTTHENOWHEELCONGURATIONCONSISTSOFONLYTHESTRUTSTHESETHREECONGURATIONSAREINTERESTINGBECAUSETHEDIFFERENCEBETWEENANYTWOOFTHEMYIELDSNOISEFROMAPARTICULARGROUPOFCOMPONENTSINTHELANDINGGEARASSEMBLYWEWILLTAKETHECLEANCONGURATIONASOURBASELINE,WHICHMAINLYRADIATESLOWANDMIDFREQUENCYNOISEBECAUSETHEWHEELSANDMAINSTRUTSHAVERELATIVELYLARGELENGTHSCALESWHENTAKINGTHEDIFFERENCEBETWEENTHEDIRTYANDTHECLEANCONGURATION,THERESULTSARETHENOISEFROMTHESMALLCOMPONENTSSUCHASHOSESANDWIRES,WHICHISMAINLYINTHEHIGHFREQUENCYDOMAINSIMILARLY,LOWFREQUENCYNOISEFROMTHEWHEELSCANBEFOUNDBYTAKINGTHEDIFFERENCEBETWEENTHECLEANANDTHENOWHEELCONGURATIONTHISSOURCESEPARATIONISILLUSTRATEDINFIG1,WHICHSHOWSATYPICALNOISESPECTRUMFORTHEBOEING737LANDINGGEAR,PLOTTEDASSOUNDPRESSURELEVELINONETHIRDOCTAVEBANDSTHETOPCURVEWITHOUTANYSYMBOLSISTHETOTALNOISEANDTHEDIFFERENTCOMPONENTSINDIFFERENTFREQUENCYFIG1ILLUSTRATIONOFATYPICALNOISESPECTRUMOFTHEBOEING737LANDINGGEARANDITSDECOMPOSITIONINTODIFFERENTCOMPONENTS,FROMWHEELSMMM,FROMMAINSTRUTS,FROMSMALLDETAILS,FROMANUNKNOWNSOURCEANDTHESOLIDCURVEREPRESENTSTHETOTALNOISE66YGUO/JOURNALOFSOUNDANDVIBRATION28220056187DOMAINSAREPLOTTEDANDIDENTIEDBYTHESYMBOLSTHECURVEFORTHEBASELINE,CLEANCONGURATIONNOISELOWANDMIDFREQUENCY,ISIDENTIEDBYTHEUPPOINTINGTRIANGLESTHISISUSEDASTHEBASELINETODERIVEOTHERCOMPONENTS,THEHIGHFREQUENCYCOMPONENTSQUARESFROMTHEDIFFERENCEBETWEENTHEDIRTYANDCLEANCONGURATIONANDTHEVERYLOWFREQUENCYCOMPONENTCIRCLESFROMTHEDIFFERENCEBETWEENTHECLEANANDTHENOWHEELCONGURATIONTHELOWFREQUENCYNOISECOMPONENTISSEENTOBEDOMINANTAROUNDANDBELOWABOUT100HZANDDECREASESVERYRAPIDLYWITHINCREASINGFREQUENCYITCANBESEENFROMFIG1THATTHEMIDFREQUENCYCOMPONENTALSODECREASESWITHFREQUENCY,BUTATAMUCHMOREGRADUALRATETHUS,INTHEFREQUENCYRANGEBETWEENABOUT100AND600HZ,ITISTHEDOMINANTNOISESOURCEINTHEFREQUENCYBANDBETWEENABOUT600AND1000HZ,THEREISASPECTRALHUMPSHOWNINFIG1,WHICHWEHAVEMARKEDBYTHEDOWNPOINTINGTRIANGLESTHISHUMP,HOWEVER,DOESNOTAPPEARINANYCONSISTENTWAYINTHETESTFURTHERMORE,BYSTUDYINGTHEFUNCTIONALDEPENDENCIESOFTHENOISEONOWCONDITIONSANDCONGURATIONS,WEHAVENOTNOTICEDANYCONSISTENTTRENDASSOCIATEDWITHTHISHUMPTHUS,WEHAVENOTBEENABLETOCONCLUDEWHETHERITISFROMANYREALLANDINGGEARNOISESOURCEFORTHEDISCUSSIONSINTHISPAPER,WEWILLIGNORETHISHUMPASARESULT,THEMIDFREQUENCYCOMPONENTCANBEREGARDEDASDOMINANTINTHEFREQUENCYRANGEBETWEEN100AND1000HZITISCLEARFROMFIG1THATTHEDOMINANTNOISEFORFREQUENCIESABOVE1000HZISMAINLYFROMTHESMALLPARTSINTHELANDINGGEARASSEMBLYFORTHESEFREQUENCIES,THEDIRTYCONGURATIONISMUCHNOISIERTHANTHECLEANCONGURATIONTHISLEADSTOTWOIMPORTANTCONCLUSIONSONEISTHATPREDICTIONTOOLSFORLANDINGGEARNOISEMUSTHAVEHIGHFREQUENCYCAPABILITYBECAUSEITISTHEMOSTIMPORTANTFREQUENCYDOMAINFORAIRCRAFTNOISECERTICATIONUNFORTUNATELY,ALMOSTALLTHEPREDICTIONTOOLSCURRENTLYINUSEDONOTHAVETHISCAPABILITYINTHEPAST,MOSTEMPIRICALPREDICTIONSHAVEBEENBASEDONMODELGEARTESTSTHATONLYINVOLVEDLANDINGGEARWHEELSANDTHEMAINSTRUTSCONNECTINGTHEM4,10,11THISISBASICALLYTHECLEANCONGURATIONWEARECONSIDERINGANDONLYGIVESTHELOWANDMIDFREQUENCYNOISECLEARLY,THESMALLPARTSSUCHASTHEHOSES,WIRES,CUTOUTSANDSTEPSAREDIFCULTTOIMPLEMENTINSMALLSCALEMODELSTHUS,ACCURATEEMPIRICALPREDICTIONSOFLANDINGGEARNOISEFORPRACTICALAPPLICATIONSSHOULDRELYONFULLSCALETESTSORHIGHDELITYLARGESCALEMODELTESTS,SUCHASTHOSEDONEINRECENTYEARS12,13FORNUMERICALANDANALYTICALPREDICTION,THEHIGHFREQUENCYDOMAINCLEARLYPOSESANEXTREMELYDIFCULTTASK,BECAUSEOFTHECOMPLEXITYOFTHESMALLPARTSINTHEGEAR,THEIRSMALLLENGTHSCALESANDTHESMALLTIMESCALESOFTHESOUNDWAVESTHEYGENERATETHOUGHMUCHPROGRESSHASBEENMADEINRECENTYEARSINCOMPUTATIONALFLUIDDYNAMICSCFDANDCOMPUTATIONALAEROACOUSTICSCAA,NUMERICALPREDICTIONOFLANDINGGEARNOISEINTHEHIGHFREQUENCYDOMAINFORPRACTICALAPPLICATIONSISPROBABLYSTILLMANYYEARSAWAYTHESECONDIMPORTANTCONCLUSIONWECANDRAWFROMFIG1ISTHATTHEREISMUCHTOGAININTERMSOFNOISEREDUCTIONBYSIMPLYCLEANINGUPTHESMALLPARTSINTHEGEARASSEMBLYTHISMAYSIMPLYINVOLVESMOOTHINGOUTABRUPTGEOMETRYCHANGES,LLINGUPCUTOUTSANDCAVITIESANDIFPOSSIBLE,GROUPINGANDSTREAMLININGTHESMALLPARTSTHESESMALLMODICATIONSDONOTSIGNICANTLYCHANGETHELANDINGGEARDESIGN,BUTHAVETHEPOTENTIALTOREDUCETHEMOSTOFFENDINGNOISECOMPONENT,NAMELY,THEHIGHFREQUENCYNOISETODEMONSTRATETHEIMPORTANCEOFTHEHIGHFREQUENCYCOMPONENT,THEBOEING737LANDINGGEARNOISEDATAAREUSEDTOCALCULATETHEEPNLTHERESULTSARESHOWNINFIG2FORTHECASEOFIGHTMACHNUMBEROF024,WHICHPLOTSTHEPERCEIVEDNOISELEVELSASAFUNCTIONOFTHENOISEEMISSIONANGLEWITHTHETOTALEPNLSHOWNINTHEBOXINTHISGURE,THEPREDICTIONCIRCLESISMADEBYUSINGFINKSMETHOD11,WHICHISBASICALLYANEMPIRICALMETHODDERIVEDFROMSMALLSCALETEST67YGUO/JOURNALOFSOUNDANDVIBRATION28220056187FIG2COMPARISONOFTESTDATAWITHPREDICTIONBYFINKSEMPIRICALMODELFORTHEBOEING737LANDINGGEAR,SHOWINGTHEUNDERPREDICTIONINALLDIRECTIONS,FROMTESTDATA,AND,FROMPREDICTIONFIG3COMPARISONOFTESTDATAWITHFINKSPREDICTIONFORBOEING737LANDINGGEARNOISEINTHEOVERHEADDIRECTION,SHOWINGTHELARGEDISCREPANCYBETWEENTHETWOATHIGHFREQUENCIES,FROMTESTDATA,AND,FROMPREDICTIONDATAITCANBESEENTHATTHEPREDICTIONUNDERESTIMATESTHENOISELEVELSINALLDIRECTIONSANDTHEPREDICTEDEPNLIS78DBLOWERTHANTHETESTDATATHISHUGEDISCREPANCYISDUETOTHEFACTTHATFINKSPREDICTIONONLYCAPTURESTHELOWANDMIDFREQUENCYNOISETHISISFURTHERDEMONSTRATEDINFIG3BYTHESPECTRALCOMPARISONBETWEENDATAANDPREDICTIONINTHEOVERHEADLOCATIONCLEARLY,68YGUO/JOURNALOFSOUNDANDVIBRATION28220056187FINKSPREDICTIONAGREESWELLWITHDATAATLOWFREQUENCIESBUTISSIGNICANTLYLOWERTHANDATAATHIGHFREQUENCIESWHENTHESOURCEDECOMPOSITIONILLUSTRATEDINFIG1ISAPPLIEDTOALLTHETESTDATA,THESPECTRALCHARACTERISTICSOFTHENOISEINDIFFERENTFREQUENCYDOMAINSCANBECLEARLYREVEALEDTHISISSHOWNINFIGS46INALLTHESEGURES,THEDATAAREPLOTTEDINNONDIMENSIONALFORMSWITHTHESOUNDPRESSURELEVELSPLNORMALIZEDBYTHEOVERALLSOUNDPRESSURELEVELOASPLTHENORMALIZEDFIG4NORMALIZEDNOISESPECTRAFROMLANDINGGEARWHEELSFORVARIOUSOWCONDITIONSWHERETHEFREQUENCYISNORMALIZEDBYTHEOWVELOCITYUANDTHEWHEELDIAMETERD,ANDTHESPLISNORMALIZEDBYTHEOASPLFIG5NORMALIZEDNOISESPECTRAFROMLANDINGGEARWHEELSANDMAINSTRUTSFORVARIOUSOWCONDITIONSWHERETHEFREQUENCYISNORMALIZEDBYTHEOWVELOCITYUANDTHESTRUTDIAMETERD,ANDTHESPLISNORMALIZEDBYTHEOASPL69YGUO/JOURNALOFSOUNDANDVIBRATION28220056187FIG6NORMALIZEDNOISESPECTRAFROMSMALLPARTSOFTHELANDINGGEARASSEMBLYFORVARIOUSOWCONDITIONSWHERETHEFREQUENCYISNORMALIZEDBYTHEOWVELOCITYUANDTHETYPICALSIZEOFTHESMALLPARTSL,ANDTHESPLISNORMALIZEDBYTHEOASPLSPECTRAAREPLOTTEDASAFUNCTIONOFTHESTROUHALNUMBER,DENEDBYTHEMEANOWVELOCITYUFORALLTHREECASES,BUTWITHDIFFERENTLENGTHSCALESFORTHEVERYLOWFREQUENCYNOISE,THEDIAMETERDOFTHEWHEELSISUSEDASTHELENGTHSCALETHEDIAMETERDOFTHEMAINST
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