New Techniques for Vibration Qualification of Vibrating Equipment on Aircraft

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New Techniques for Vibration Qualification of Vibrating Equipment on Aircraft

Dr. Andrew Halfpenny, Chief Technologist, HBM-nCode Products1

Mr. T. C. Walton, Principal Dynamicist, AgustaWestland2

1HBM-nCode Products. Travelers Tower 1, 26555 Evergreen Road, Suite 700, Southfield, MI 48076. www.ncode.com

2AgustaWestland, Yeovil, Lysander road, Somerset, BA20 2YB. UK

www.agustawestland.com

AbstractAllaircraftvibrateandallcomponentsaredesigned,testedandcertifiedtosurvivethesevibrationlevelsovertheirentireservicelife.DesignstandardssuchasMILSTD810F(1)andRTCADO160E(2)areoftenusedtoobtainthevibrationsignoff test; butwhat is the safetymargin on these tests?Howmany hours do they represent on real aircraft? Can theequipmentlifebeextendedforaircraftwithlessdamagingusageprofiles?Canreadacrossevidencefromoneaircraftbeusedtoqualifyacomponentonanotherwithoutfurthertesting?Thispaperdiscussesthelatestapproachestotheanalysisofshockandvibrationandshowshowvibrationtestscanbetailoredbasedonmeasuredflightspectra,howdifferenttestscanbecompared,andhowthelifeofequipmentcanbeadjustedbasedonoperationalexperience.

1 IntroductionThispaperdescribeshowthevibrationenvironmentofanaircraftcanbecharacterized intermsofaFatigueDamageSpectrum (FDS)andShockResponseSpectrum (SRS). Itdescribeshow these spectraare calculatedfrom bothmeasured flight load data and directly from vibration test specifications. Vibration tests can betailoredtoensurethattestspectraexceedflightspectrawithanadequatesafetymargin.

These techniques provide a means of comparing shock and vibrationinduced damage across differentvibrationtestsanddifferentaircraftplatforms.Thisenablesustousetestandserviceevidenceobtainedononeaircraftplatformtoqualifyequipmentonanother.Thisreadacrossevidencehasbeensuccessfullyusedtoqualifyequipmentwithouttheneedforanyadditionalvibrationtesting. Itoffersconsiderablecostsavingsandalsoenablesarapidpathforthedeploymentofmissioncriticalequipmentinmilitaryoperations.

Techniques are discussed which derive tailored vibration tests based on measured flight load data.Accelerometers record thevibration levelsatanumberofpositionson theaircraftwhile flyingaprescribedsequenceofmaneuvers.ThefatiguedamagedosageforeachmaneuveriscalculatedusingaFatigueDamageSpectrum (FDS),whicheffectivelyplotsdamagevs. frequency.Thedamage fromeachmaneuver issummedover the usage profile of the aircraft to determine the wholelife damage dosage. From this profile wedetermineastatisticallyrepresentativevibrationtestwhichcontainsatleastthesamedamagecontentasthewholelife,butoveramuchshortertestperiod.ThisfacilitatestheprovisionforTestTailoring,asspecifiedinAnnexAofMILSTD810F(1),aswellasRTCADO160E(2)andGAMEG13(3).

CasestudiesarepresentedtodescribehowtheanalysiswasusedbyAgustaWestlandfortailoringvibrationtests for its latestaircraft.Studiesalsodescribehowthetechniqueshavebeenusedtoprovide readacrossevidence to support flight clearance for urgently needed equipment inmilitary operations. These include

Aircraft Airworthiness & Sustainment 2010

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clearance forhelicopteravionicsandoptoelectricalequipment.Studiesalsodescribehow cases for limitedtype approval (i.e. restricted flight envelope or service life), or experimental flight approval are assessedquantitativelyusing these techniques.Thepaperconcludesbydescribinghow the techniquecanbeused toprovidequantitativeevidence to supportequipment lifeextensionsbasedonOperational LoadsMonitoring(OLM)andHealthandUsageMonitoringSystem(HUMS)data.

2 Review of background theory Fatigue Damage Spectrum (FDS) andShockResponseSpectrum(SRS)

ThebasisofthetheoryusedinthispaperoriginatesfromtheworkofAmericanengineerBiotin1934.FurtherdevelopmentonthisapproachwasconductedbyLalanneandtheFrenchMinistryofDefenseinpreparationofthemilitary design standard GAM EG13 (3) in the 1980s. In this sectionwe introduce the two principalcomponentsoftheapproach:theShockResponseSpectrum(SRS)andtheFatigueDamageSpectrum(FDS).

TheSRSisusedtodeterminethemaximumpeakamplitudeofloadingwhichtypicallyresultsfromextremeshockeventssuchassevere landing, impact,weaponsdischargeornearbyexplosions.Theseextremeeventscangiverisetocatastrophicfailureascomponentstressesexceedthedesignstrength.TheFDS,ontheotherhand,isusedtoaccumulatethedamagecausedbylongtermexposuretofatiguedamagingvibrationswhich,althoughmodest inamplitude,give rise tomicroscopiccracks thatsteadilypropagateover timeand lead toeventualfatiguefailure.

2.1 TheShockResponseSpectrum(SRS)TheSRSisusedtodeterminethepeakamplitudeofloadingseenduringaflighteventoravibrationtest.ThesafetymarginofthetestcanbedeterminedbycomparingthetestSRSwiththeflightSRS.Itisinsufficienttosimply record the highest static acceleration level because this does not account for the frequency of thevibration.Dynamicsystemsaremoresensitivetocertainfrequenciesthanothers,thesocalledresonant(ornatural) frequencies. Structural failure isalsoattributable toexcessive strainenergy, and strainenergy inavibratingcomponent isproportionaltodisplacementratherthanacceleration.Thereforethedamagingeffectofacceleration isseen to reducewith thesquareof the frequency.High frequenciesbecome lessdamagingthanlowerfrequencies.Itisthereforeimportanttoconsiderbothaccelerationamplitudeandfrequencyduringthevibrationassessment.

The SRS essentially represents a plot of the peak amplitude vs. frequency. A typical SRS plot showinghelicopterflightdatacomparedwithaMILSTD810FvibrationqualificationtestisillustratedinFigure1.Inthiscase thequalification testexceeds thepeak inflight levelsbyat leasta factorof2so the test isconsideredconservative.

TheSRSwasdevelopedbyBiotin1932(4).TocomputeBiotsShockSpectrum,themeasuredaccelerationsignal is firstofall filteredbyaSingleDegreeof Freedom (SDOF) transfer function centeredona specifiednaturalfrequency(fn)asillustratedinFigure2.Themaximumvalueofthefilteredresponseisthencalculatedand this representsasinglepoint in theSRSplot.Thiscalculation is repeatedoverawhole rangeofnaturalfrequenciestocreatetheentireSRS.In1934,Biot(5)publishedapaperonearthquakeanalysisandusedthetermShockSpectrumforthefirsttime.

Biot used the SDOF response function as a frequency filter because of its ability to select a specificfrequency inamannerconsistentwiththephysicalresponseofastructuralsystem. It isalsomathematicallystableandisideallysuitedtorapidtimedomainconvolution.Otherspectrahavebeendocumentedwhichusedifferentfilters.Ruppetal(6),forexample,describeananalogousapproachbasedonabandpassfilterand


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this is used by some automotive companies in Europe; however, the SDOF approach is themost popularapproach.

Figure1Comparisonbetweeninflightshockexposureandatypicalvibrationtestprofile

Figure2SchematicflowchartillustratingtheSRSandFDScalculationprocess

Frequency

Gai

n

Frequency

Log

Dam

age

Accelerationon airframe

Frequencyfilter (SDOF)

Rainflow countfiltered signal

Plot damage Vsfrequency

Increment filterby f

f

Frequency

Peak

val

ue

Peak amplitude offiltered signal

Shock Response Spectrum (SRS) Fatigue Damage Spectrum (FDS)


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TheSDOFresponsefunction(Figure2)isdominatedbyasinglespikelocatedatthenaturalfrequencyfn.Atfrequenciesbelowthenaturalfrequency,thecomponentbehavesquasistatically [Gain(f>fn ) 0].Aroundthenaturalfrequencythecomponentwillresponddynamicallyandwillbecomegreatlyamplifiedwithitsmaximumresponsebeinglimitedonlybythedampinginthesystem[Gain(f=fn)=Q].TheformulafortheSDOFfilterfunctionisgiveninEquation1.ThisfilterwillreturnaSRSintermsofaccelerationvs.frequencyfn.

1

1

1

Equation1

Gain(f)istheSDOFfilterwithrespecttofrequencyf,andfnisthenaturalfrequency;bothareexpressedinHz.TheratioofthemaximumdynamicresponsetothestaticresponseisknownastheDynamicAmplification(Q)factor.For5%structuraldamping,thishasthevalueofQ=10as illustrated inFigure2.Therelationshipbetweendamping ratio andQ isgiven inEquation2. It ispossible to fit theamplification factorQ to theparticularcomponentbeingtested;however,establishedprocedureassumesavalueofQ=10forcomparativeanalysis.ThisassumesthatweusethesameQvaluewhencalculatingtheSRS inflightandtheSRSfromthequalificationtest.Qisessentiallyusedtotunethefiltertothedesiredfrequencyrange,itdoesnotimplyanymechanicalsignificanceintheanalysis.

1

2

Equation2

TheShockResponseSpectrum (SRS)canbeexpressed in termsofaccelerationordisplacement responsedependingon the frequency response functionused. For fatiguepurposes,wearemostly interested in thedisplacement response. The SDOF filter function relating to displacement response is given in Equation 3.Fatiguecracks initiateandgrow throughthecyclic releaseofstrainenergyand,therefore, thedisplacementresponseprovidesaproportional relationshipwith theenergydriving the failure.Accelerationmightbe theorigin of the load but it is the resulting strain (displacement) that drives the structural failure. The SRS ofdisplacementcan thereforebeused toquantify thedamagingeffectof the inputacceleration foranySDOFsystemoverarangeofnaturalfrequencies.

1

2 1

1

Equation3

Biotproposedusing theSDOFassumption forall componentsunderexcitation regardlessof theiractualfrequency response.Over the past yearsmany have contested the conservatism of this assumptionwhenappliedtocomponentswithamultimodalresponse.Lalanne(7)documentsanumberofthesestudieswhichallconcludethat theSDOF response,used inconjunctionwitha frequencysweep, isasuitablyconservativeassumptionforallpracticalcases.

ThearrivalofdigitalcomputershasmadeitpossibletocalculatetheSRSforlongtimesignalsveryrapidly.UsingtheZtransform,Irvine(8)derivestheequationsforaveryefficientInfiniteImpulseResponse(IIR)filter.Halfpenny(9)describesaveryefficientprocesswhichisabletocalculatetheSRSandFDSfrommeasuredflightdatawithexceptionalspeed,andHalfpenny(10)describesanalgorithmforrealtimeanalysisofvibrationdatawhichissuitableforConditionBasedMaintenance(CBM)analysisofvibratingequipmentonaircraft.


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2.2 TheFatigueDamageSpectrum(FDS)Lalanne(11),workingonthehypothesisoftheShockResponseSpectrum(SRS),proposedananalogousFatigueDamage Spectrum (FDS). This provides a relationship between fatigue damage and frequency. The FDS iscalculatedinthesamewayastheSRSbutratherthansimplyfindingthemaximumdisplacementresponse,thefiltereddisplacementresponseisnowrainflowcyclecountedandthefatiguedamageobtainedusingaWhlercalculation. The approach is illustrated in Figure 2. Figure 3 shows a comparisonbetween inflightdamageexposureandatypicalMILSTD810Fqualificationtest.Inthiscasethetestoffersareasonablesafetymarginoveroperationalexposure.

Fatiguedamagevariesexponentiallywithrespecttostress(andrelativedisplacement)asshownFigure4.This represents the familiar SN (orWhler) curvewhich relates stress range S to thenumberof cycles tofailureNf.ThecurvefollowsastraightlinewhenplottedonlogaxesandwasdescribedbyBasquinusingthepowerlawrelationshipgiveninEquation4.

Figure3Comparisonbetweeninflightdamageexposureandatypicaltestprofile

Equation4

C is theBasquin coefficient (interceptof the SN curvewith the yaxis), S is the stress range (twice theamplitudeofthesinusoidalstress),bistheBasquinexponent(gradientoftheSNcurveinlogspace)andNfisthenumberofsinusoidalcyclestofailure


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Figure4TypicalfatigueSNcurveforaluminumalloy6082intheT6condition

When random (variableamplitude) loadsareencountered, rainflowcyclecounting isused todecomposethesignalintoequivalentsinusoidalstresscycles.Thetotaldamageinthetimesignalisobtainedbysummingthedamage fromeachstresscycleusingMiners (12) lineardamageaccumulation rule.The totaldamage isthereforeobtainedfromEquation5.

1

Equation5

TheBasquincoefficientCisusuallytakenasunityforcomparativeFDSanalysis.Thisimpliesthatthesamevalue of C is usedwhen calculating the FDS inflight and the FDS from the qualification test. The Basquinexponent bhasasignificanteffecton theFDSanalysis.For traditional fatigueanalysis b isobtained fromfatigue tests on the material (as per Figure 4) and is then modified to account for geometrical stressconcentrations,etc.ForFDStypeanalysisweareprincipally interested inthefirstfailuresiteandthisusuallycoincideswithageometricalstressconcentrationorthelocationofbolted,riveted,weldedorsolderedjoints.Inthesecasesthevalueofbtendstolieintherange4


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calculatedusingthetimedomaintechniquedescribed inFigure2.Thisapproach involvescalculatingtheSRSand FDS from a derive time signal based on the vibration test specification. The process is quite straightforward but does require a very long time signal at a very high sampling frequency. The computationalrequirementsand riskofhumanerror in thisapproachare significantandmeans thatadirectapproach forobtainingtheSRSandFDSdirectlyfromthetestspecification isoftenpreferred. Inthissectionwe introducemethodsforcalculatingtheSRSandFDSdirectlyfromPSDandsinesweeptestsratherthantimesignals.

2.3.1 MilesequationIn 1953, Miles (15) presented an equation that is similar in nature to the SRS. Using the simple formulaexpressed inEquation6hederiveda spectrumof theRMS (RootMeanSquare)acceleration response toarandomPSDappliedtoaSDOFsystemofnaturalfrequencyfnanddynamicamplificationQ.

RMSaccelerationspectrum, ( ) ( )2accel n n n

RMS f f Q G f=

Equation6

G(fn)isthePSDofaccelerationing2/Hzatfrequencyfn,andQisthedynamicamplificationfactor

2.3.2 ApproximateequationforobtainingSRSdirectlyfromaPSDtestMilesequationisusedtodeterminetheRMSaccelerationresponseforaparticularnaturalfrequency.Inordertodeterminethemaximum likelyresponse(i.e.theSRS),MilessuggestedmultiplyingtheRMSspectrumbyafactorof3(i.e.the3sigmacurve).However, in1978Lalanne(16)proposedarefinementtoMilesequation.Fornarrowbandfrequencyresponse,typicalofaSDOFsystem,theamplitudedistributionwasfoundbyRice(17) to be Rayleigh and not Gaussian as proposed byMiles. Lalanne therefore rederivedMiles equationsubstituting the Rayleigh probability function. The resulting equation is known as the Maximax ResponseSpectrum (MRS)or theExtremeResponse Spectrum (ERS). It represents themost likelyextremeamplituderesponse witnessed during a vibration test of duration T seconds driven by random PSD excitation. TheresponsecanalsobeexpressedintermsofrelativedisplacementinmetersusingEquation8.

ERSaccelerationspectrum, ( ) ( ) ( )lnaccel n n n nERS f f Q G f f T Equation7

ERSdisplacementspectrum, ( ) ( )( )29.81

2accel n

disp nn

ERS fERS f

f= Equation8

Tisthetestexposuredurationinseconds,andG(fn)isthePSDofappliedaccelerationing2/Hz.

TheERSisanalogoustothetimedomainSRS.However,whereastheSRS isusuallyusedtodeterminethemaximumresponsetoahighlydamagingtransientshock,theERSisusedtorepresentthemaximumexpectedresponsewitnessedduringavibrationtest.InthispaperweusethetermSRSlooselytoencompassbothSRSandERStoavoidunnecessarycomplication.

Theapproximateequationsgivenabovearebasedonseveralassumptions.Themainassumptionsare:

1. the inputPSD isbroadbanded tending towhitenoise (i.e. thePSDhasa fairly flatprofileandcontainsnosignificantpeaks)

2. theresponseisnarrowbandedthisassumptionisusuallyassuredbyhavingaQvalueof10


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Figure 5b shows a comparison between the accurate and approximate ERS derived for a typical PSDvibrationtestgiveninFigure5a.ThisanalysisassumesQ=10andT=16hours.

2.3.3 ApproximateequationforobtainingFDSdirectlyfromaPSDtestFollowinginitialworkbyRice(17)andBendat(18)todeterminefatiguedamagedirectlyfromaPSDofstress,Lalanne(11)wasabletoutilizethistechnologytocreateaclosedformcalculationtoestimatetheFDSdirectlyfromtheaccelerationPSD,thisisgiveninEquation9.AnexplanationofvibrationfatiguetheoryisbeyondthescopeofthispaperandyouarereferredtoHalfpenny(19)andBishopetal.(20)formoredetails.

( ) ( )( ) ( )22

3

9.811 22 2

b

nn n

n

Q G f bFDS f f Tf

+

Equation9

Tisthetestexposuredurationinseconds,G(fn) isthePSDofappliedaccelerationing2/Hz,and() isthe

Gammafunctiondefinedas ( ) ( )10

g xg x e dx =

Theapproximateequationgivenaboveisbasedonthesameassumptionsdescribedinsection2.3.2.Figure5c shows a comparisonbetween the accurate and approximate FDSderived for a typicalPSD test given inFigure5a.ThisanalysisassumesQ=10,b=4andT=16hours.

Figure5ComparisonbetweenapproximateandaccurateSRSandFDSforaPSDvibrationtest

2.3.4 ApproximateequationforobtainingSRSdirectlyfromasinesweeptestTheSRScanbeestimateddirectlyfromasinesweeptestspecification.Equation10givestheSRSintermsofaccelerationing,whereasEquation11givestheSRSintermsofdisplacementinmeters.

Equation10

9.81

2

Equation11

AccuratemethodApproximatemethod

AccuratemethodApproximatemethod

Accelerationg2/Hz

a b c


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A(fn)istheamplitudeofthesinesweepingatfrequencyfnHz

Theapproximateequationsgivenabovearebasedonthesameassumptionsdescribedinsection2.3.2andarevalidover the frequency rangeof the sweep.Figure6b showsa comparisonbetween theaccurateandapproximateSRSderivedforatypicalsweptsinetestgiveninFigure6a.ThisanalysisassumesQ=10.

2.3.5 ApproximateequationforobtainingFDSdirectlyfromasinesweeptestTheFDScanbeestimateddirectlyfromasinesweeptestspecificationusingEquation12.InthiscasetheFDSrepresents fatigue damage from a single sine sweep and should be multiplied by the number of sweepsperformedduringthetest.

60

29.81 2

2

Equation12

isthelogarithmicsweeprateexpressedinoctavesperminuteandA(fn)istheaccelerationamplitudeingatfrequencyfnHz

Theapproximateequationgivenaboveisbasedonthesameassumptionsdescribedinsection2.3.2andisvalid over the frequency range of the sweep. Figure 6c shows a comparison between the accurate andapproximateFDSderivedforatypicalsweptsinetestgiveninFigure6a.ThisanalysisassumesQ=10,b=4,=1octavepersecond,over8completesweeps.

Figure6ComparisonbetweenapproximateandaccurateSRSandFDSforasinesweepvibrationtest

2.3.6 Advanced(accurate)methodsforderivingSRSandFDSfromstandardvibrationtestsThe approximate equations given above are adequate for general comparative analyses provided theassumptionsin2.3.2arevalid.TheyaresuitableformanyofthetestsproposedinMILSTD810F(1)andRTCADO160E(2).Lalanne(11)andHalfpenny(9)havefurtherdevelopedtheseapproachesandpresentnumericalsolutionalgorithmsofferingmuchgreateraccuracywithoutthelimitationsinherentintheaboveassumptions.Thesealsoofferamuchwider rangeofvibration testingoptions includingdifferentsweep typesandmixedtestssuchassinesweepanddwell.Moreadvancedtestssuchassineonrandomarealsosupportedwhichdonotfulfilltheassumptionsmadein2.3.2.DiscussiononthesetechniquesisbeyondthescopeofthispaperandthereaderisreferredtoHalfpenny(9)formoreinformation.

Accelerationam

plitu

deg

a b c


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3 VibrationEnvironmentonanaircraft3.1 SourcesofhelicoptervibrationThissection introduces thevibrationenvironmentonahelicopteranddescribeshow this ismodeledby thevibrationtest.Theinformationdiscussedhereisalsoapplicabletofixedwingaircraft;however,thediscussioninthispaperhasfocusedprincipallyonhelicoptersbecausethecasestudiespertaintothese.

Thevibrationspectrumofahelicoptercanbedescribedasaseriesofsinusoidaltonessuperimposedonabackgroundofrandomnoise(sineonrandom).AnexamplerecordedinthefuselageofahelicopterisshowninFigure7.Themainsourceofthesesinusoidaltones isattributabletoharmonicsofthemainrotor.Themainrotorfrequencyofahelicopterisrelativelylow(typically38Hz)andinaccuraciesintherotortrack,balanceorbladepitchwillresult insinusoidaltonesatthisfrequency.Themainrotorfrequency isoftendenotedbytheterm1Rwhile thetail rotor frequency isdenotedby the term1T.The tail rotor frequencyofahelicopter istypicallywithintherange1550Hz.

Whenthehelicopterisinflightthepitchofeachbladevariescyclicallywithrespecttoitsazimuthangle(i.e.angleofthebladerelativetotheaxisoftheaircraft).Furthermore,thebladeswillslicethroughmanyeddieswhicharisefromturbulence,aerodynamiceffectsoftheaircraft,groundeffects,bladeinducedwakeeffects,etc.ThesecyclicallyperiodiceffectsgiverisetopeaksatharmonicsofthebladepassingfrequencyasshowninFigure7.Thebladepassing frequency isdenotedby the term nRwhere n is thenumberofblades in therotor.Mosthelicoptershavebetween2and6bladesinthemainandtailrotors.TheprincipalharmonicsaredenotedasnR,2nR,3nR,etc..Theeffectbecomeslessobviousforthehigherorderharmonicsinexcessof3nRastheseamplitudesaretypicallylowerthanthebackgroundrandomnoise.ThehelicopterusedinFigure7has4bladesinboththemainandtailrotors.

Figure7FDSrecordedonthemainfuselageofahelicopter

1R 2R 4R 8R 12R 4T

GearboxmeshingFrequencyHz


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Allcomponentswillwitnesssignificantvibrationfromthemainrotorandthisdominatesthelowfrequencyspectrum for positions throughout the aircraft. Components sited towards the tail of the aircraftwill alsowitnessprincipalharmonicsofthetailrotor.Componentsthataresitedadjacenttotheenginesandgearboxeswill see additionalharmonicsof the engine, shaft, and gearboxmeshing frequencies. It isusualpractice tosegregate the aircraft into regions and assume that the vibration amplitudes are similar for all equipmentpositionedinthatregion.Themostcommonlydefinedregionsare:

Fuselagevibrationisdominatedbyharmonicsofthebladepassingfrequencyofthemainrotor Avionicsbay (similar to fuselagebutvibration isolatedmountsaredesigned to reduce rotorinduced

vibrationamplitudes)

Onornearenginesadditionalsinusoidalharmonicsinducedthroughengineandgearboxharmonicsandmeshingfrequencies

On or near tail rotor additional sinusoidal harmonics induced through tail rotor and gearboxharmonics

External stores and sponsons additional aerodynamic loads inducedbydownwash from themainrotorandaerodynamicsoftheaircraft

Inmostcasestheverticalandlateralaccelerationsdominatetheloadingenvironmentandthefore/aftaxisisrelativelybenign.

3.2 TypesofvibrationqualificationtestVibration qualification tests are typically performed in accordance with the aircraft manufacturersspecificationor tooneof thecommonlyusedmilitarydesignstandardssuchas;USDepartmentofDefensestandardMILSTD810F(1),andRTCADO160E(2).Thequalificationtestisperformedinthefollowingstages:

1. Initial resonancesearchsweptsine test todetermine the resonant frequenciesof thecomponent.Ideally,resonantfrequenciesshouldnotcoincidewithanyoftheprincipalharmonicsoftheaircraft.Acomponentwillusuallyfailqualificationiflowdampedresonancesareencounteredwithinavoidbandsofaprincipalharmonicunless the supplier canproveadequatedurabilityand theaircraftOEM canprove that the resonant issueswill not adversely affect the durability of the airframe ormountingstructure.

2. Endurance test consisting of either amultiple sineonrandom vibration test or a swept sine anddwelltest(asdiscussedinthenextparagraph)

3. Finalresonancesearchsweptsinetestasperstep1toensurenochanges inresonant frequencieswhichcouldindicatethepresenceofanemergingfatiguecrack

Mostmodernvibration testsareperformedusinguniaxialelectrodynamic vibration rigs.Theenduranceportionofthetestcommonlyusesamultiplesineonrandomvibrationprofile.Atestdurationof16hoursperaxis(repeatedoverx,yandzaxessequentially)istypicallyequivalentto10,000hoursofoperationalexposure.

Analternativeapproach is to specifya swept sineanddwellvibrationprofile.Thisapproach involvesanextendedsweptsinetest(typically1hour)followedbyasequenceofstaticsinusoidaltestsdesignedtoexcitetheprincipalharmonicsoftheaircraft(typically1millioncyclesateachharmonic).Thetestisrepeatedforallaxessequentially(oneaftertheother).

The swept sine and dwell test profile is less efficient than the sineonrandom because each principalharmonic (sine tone) must be tested separately for 1 million cycles and this leads to a very lengthy andexpensivetest.Thisisparticularlyproblematicforhelicopterswherethemainrotorharmonicsoccurata low


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frequency.Thesineonrandomtestprofileexcitesallharmonicssimultaneouslywhichismorerepresentativeoftheactualaircraft loadingprofile.Sineonrandomtestshave largelysupersededthesweptsineanddwelltest.Thetechniquesdiscussedinthispaperhavebeensuccessfullyemployedasameansofconvertingexistingsweptsineanddwelltestprofilestothemorerepresentativeandefficientsineonrandom.

Afinalimpact(hammer)testisperformedontheequipmentasmountedontheaircrafttoensurethatanyadditionallyflexibilityinthemountingdoesnotgiverisetoresonanceswithintheavoidbandsoftheprincipalharmonics.

3.3 EstimationofaccelerationlevelsusedinthevibrationtestWhile the aircraft is at the design stage we can obtain estimates of test acceleration levels for use inpreliminary qualification. Suitable estimates are provided by both MILSTD810F and RTCA DO160E.Accelerationlevelsareprovidedintheformofequationswherethevibrationamplitudeisgivenasafunctionof theprincipalharmonic frequency.Differentequationsareprovided foreachpositiononthehelicoptertoaccountforvariationsinvibrationseverity.

Asmeasured flightdatabecomes available then thesepreliminarydesign estimates shouldbe reviewedagainstmeasureddata.Thetestaircraftisinstrumentedwithaccelerometerswhichrecordthevibrationlevelsatanumberofpositionswhileflyingaprescribedsequenceofmaneuvers.Maneuversareflownundervariousweight conditions sowe can obtain a series ofmeasured flight events that are representative of the realconditions seen inservice. The fatigue damage dosage for each maneuver is calculated using a FDS. Thedamagefromeacheventissummedovertheusageprofileoftheaircrafttodeterminethewholelifedamagedosage.AnequivalentFDScanbecalculated for theproposedqualification testand the testspecification isiteratedsothetestFDSexceedstheflightFDSbyanacceptablesafetymargin.Theapproach is illustrated inFigure8.

Theobjectiveoftesttailoringistoderiveaqualificationtestthatcontainsatleastthesamefatiguedamagecontentastherealaircraftenvironmentbut inashortertesttime.Asthedamage isfixedthenthevibrationamplitudeusedinthetestmustvarywiththedurationofthetest.Ashortertestwillrequiregreatervibrationamplitudesinordertoachievethesamedegreeofdamageinashorterperiod.TheShockResponseSpectrum(SRS)isusedtocomparetheworstamplitudeusedinthetestagainsttheworstamplitudeseenduringflight.Inmost cases theworst shock load seen in flightwillonly occur for very shortperiodsof time at infrequentintervals;whereasmost of the fatigue damagewill be attributed to long periods of flight at verymodestvibrationlevels.Testtailoringusesthiseffecttoderivetheoptimumtestduration.TheoptimumtestdurationisachievedwhentheSRSofthetestcoincideswiththeSRSobtainedfortheworstflightcondition.Thisallowsthetesttooperateattheoptimumaccelerationlevelsodamageisaccumulatedatthemaximumratewithoutexceedingtheworstloadsseeninflight.

Most traditional helicopter and fixedwing tests are overaccelerated. This means that the loadingamplitudeexceedstheworst flight loadsbyasignificantmargin.Thisapproach is justifiedonaccountofthehigh safety margins implicit in the design of aircraft components. However, care is required when overacceleratingavibrationtesttoensurethattheexcessiveloadsdonotintroduceplasticityintothecomponentwhichcouldaltertheloadpathsandchangethefailuremode.


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Figure8Testtailoringforhelicoptervibrationqualification

4 CaseStudies4.1 Case Study 1: Vibration qualification based on readacross evidence from other

aircraftEquipmentwasurgentlyrequiredfordeploymentonamilitaryhelicopter.Novibrationqualificationhadbeenperformedforthisaircraft;however,previousclearancehadbeenawardedforadifferenthelicoptertype.Theobjectiveofthisanalysis istocomparethedamagecontentoftheoriginalaircrafttestwiththatrequiredforthenewhelicopterandassesswhethertheexistingqualificationevidenceissufficientforflightapprovalonthenewhelicoptertype.

The original sineonrandom qualification test was performed in accordance with MILSTD810E forequipmentmounted to the fuselage.Theprincipal rotorharmonicsaredifferenton thishelicopterand thevibrationlevelsarelower.Themanufacturersvibrationrequirementsforthenewhelicopterareexpressedintermsofa swept sineanddwell test.Adirect comparisonbetween the two testswasperformedusing theSRS/FDSapproachandtheresultsareshowninFigure9.

A comparison of the SRS for both tests is shown in Figure 9a. The SRS required by the new helicopterspecificationsignificantlyexceedsthatprovidedintheexistingqualificationevidence.However,aconsiderableoverload is acknowledged in the new helicopter specification in order to accelerate the vibration test. Acomparisonwas thereforemade againstmeasured flight data and this clearly shows an acceptable safetymargin.

Step 1Damage Transformation

Calculate SRS

Calculate FDS

EventFDS

EventSRS

Step 3Test Synthesis

Step 2Mission Profiling

Sum FDSMission

FDSEnvelope

SRSMission

SRS

CompareSRS

Input data for each

flight event

Aircraft usage profile

Accelerated vibration test

profile

Calculate FDS

Calculate SRS

CompareFDS

Iterate (Tailor)test specification


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Figure9Comparisonofavailablequalifationevidencewithaircraftrequirementspecification

Figure9bshowsacomparisonoftheFDSforbothtests.Thefrequenciesoftheprincipalharmonicsareseento vary and cumulativedamageofferedby theexistingqualificationevidence is considerably less than thatrequiredbythenewhelicopterspecification.Thereisinsufficientevidencetoconsiderfulltypeapprovaloftheequipmentatthisstage!

Figure9cshowstheeffectofreducingthesafeoperationallifefrom10,000hoursto100hours.Duetotheurgentrequirementofthisequipment,limitedflightapprovalwasawardedfor100operationalhoursandtheequipmentwasfittedtoserviceaircraft.Duringthefirstyearofoperationtheequipmentwasretestedtothenewspecificationandwaseventuallyawardedfulltypeapproval.However,ithadbeendeployedstraightawayandusedsuccessfullyintheatreoverthisentireperiod.

Limitedflightapproval isalsopossiblethrougharestrictionoftheflightenvelope; i.e.byrestrictingsomeflight conditions andmaneuvers. For this type of analysis it is preferable tousemeasured flight loaddatadirectly in the comparison rather than using the manufacturer specification. This approach is called TestTailoringandiscoveredinCaseStudy2.

Inmanycasestheexistingqualificationevidenceprovessufficientforthenewaircraftandfulltypeapprovalcanbeawardedwithoutrecoursetoadditionaltesting.Thisoffershugecostsavingsbecausevibrationtestsare

a)ShockResponseSpectrumshowsthatthesuppliersqualificationevidenceislowerthanthat requiredbytheaircraftspecificationbut isstillgreaterthanmeasuredflightdatabyanacceptablemargin

OriginalaircraftspecificationSuppliersqualificationevidenceMeasuredflight loaddata

b)FatigueDamageSpectrumshowsthatthesuppliersqualificationevidenceisinadequateforthisaircraftonaccountofthedifferenceinrotorharmonicfrequencies

c)Theequipmentcanbeprovisionallydelifed to100operationalhourspendingfurthervibrationtests

Shock Response Spectrum (SRS) Fatigue Damage Spectrum (FDS)

Fatigue Damage Spectrum (FDS)

OriginalaircraftspecificationSuppliersqualificationevidence

Delifed damagespectrum(100hours)Suppliersqualificationevidence


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oftenveryexpensiveonaccountofthedirecttestingcostsandthecostofthetestcomponentwhich is lifeexpiredattheendofthetest.

This approach toqualificationhas alsoproveduseful for assessing experimental flight approval fornewequipment.Qualification evidence based on fixedwing installations, shipping or transportinduced damagequalification, or slosh and vibration qualification tests often prove sufficient for limited flight clearance forexperimentalpurposes.

4.2 CaseStudy2:TesttailoringofcontrolrodvibrationtestNewyawcontrolrodsandmountingswererequiredonahelicopter.Thecontrolrodsrunthroughthemainfuselageandtailconeandaresubjectedtoadditionalvibrationfromthetailrotor,thetailrotorgearboxandtheintermediategearbox.Thesecomponentsareflightsafetycriticalandageneralvibrationspecificationwasconsidered inadequate in this case. The existing swept sine anddwell testwas alsounacceptably long andexpensive (98hoursperaxis), and the safetymarginwasuncertain.A test tailoring exercisewas thereforeauthorized to determine a more appropriate sineonrandom qualification test along with a completeassessmentoftheinherentsafetymargin.

Accelerationmeasurementsweretakenoveranumberofflighteventsusingtriaxialaccelerometerslocatedat several positions on the helicopter. The SRS and FDS were calculated for each accelerometer and anenvelopetakentorepresenttheworstloadingcondition.TheFDSwasscaledovertheaircraftusageprofileasdescribedpreviously todetermine thewholelifedamage.TheSRSandFDSwerecalculatedoverarange52000Hz.AcomparisonofthemeasuredspectrawiththestandardtestspecificationisillustratedinFigure10.

Figure10Comparisonofflightvibrationexposuretocertifiedtestlimits

FromFigure10,the inflightshockresponse iswellrepresentedbytheexistingtestspecificationoverthefirstfewrotorharmonics;however,itdoesnotaddressthehighfrequencygearboxinducedpeak.Theinflightdamageresponseisalsowellrepresentedoverthefirstfewrotorharmonicsbuthasanegligiblesafetymargin.Theexistingtestspecificationdoesnotaddressanyofthehigh frequencygearboxinducedvibrationsorthepeaksat1Rand2Rwhicharesignificantonthisaircraft.

4.2.1 TesttailoringprocessThenewtestisbasedonasineonrandomprofilecomprisingthefollowingsteps:

FlightloaddataStandardqualificationtest


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1. Initialresonancesearchatasweepratenotexceeding1octave/mininaccordancewithmanufacturersexistingspecifications

2. 16hoursineonrandomtestinaccordancewithFigure113. Finalresonancesearchasperstep14. Repeatallabovestepsforeachaxis(x,y,z)Thistestisdesignedtoofferclearanceforupto10,000operationalhoursandtesttailoringwasperformed

usingtheGlyphWorksAcceleratedTestingpackagefromHBMnCode(21).AcomparisonoftheSRSandFDSare illustrated inFigure12.ThetestwasderivedusingMILSTD810Fasabasis.ThebackgroundrandomPSDand the amplitude of the sine tones were then tailored to achieve an adequate safety margin over theproposedusagespectrum.Furtherconstraintswereappliedsuch thatnovibration levelshouldbe less thanthoserecommended inMILSTD810F,and the finalFDSshouldnotbe lessthantheexistingsweptsineanddwelltestspecification.

Figure11TailoredvibrationtestbasedonMILSTD810F

From Figure12we see that thenew test specificationoffers an acceptable safetymarginonbothpeakshockandfatiguedamage.Thesineonrandomtesttakesonly16hoursperaxisasopposedto98hoursfortheprevioussweptsineanddwelltestandthisoffersasignificantcostsaving.

These techniques provide a tailored testwhich accounts for the real vibration environment and avoidspotentialunderdesign issuesbyallowingdirectcontrolofthesafetymargin. Inothersituationstesttailoringhasbeenusedtorelaxtheoriginaltestspecificationwherethemeasuredusageprofileis lessdamaging.Thiscanreducetheinherentcostimplicationsofovertesting,andtheinherentweightimplicationsofoverdesign.

Acc

eler

atio

n

Log frequency Hz

10 300

2000

22 44

2.2g 2.2g

0.001

0.01

120

1.0g

Random PSD (g2/Hz)

Sinusoidal tones (g)

11

1.1g

Freq. PSDg2/Hz

10 0.01

300 0.01

2000 0.001

Freq. Amp.g

2R=11Hz 1.1g

4R =22Hz 2.2g

8R=44Hz 2.2g

4T=120Hz 1.0g

PSDrandom

Sinetones


17

In some cases ithasbeenused successfully toqualify importantequipment thatwaspreviously consideredinadequateandalsoextendthelifeofequipmentwherethevibrationlevelsorusagespectrumwerefoundtobe lower than theexistingqualificationevidence.Halfpenny (10)describeshow realtimealgorithmscanbeused to determine the FDS and SRS inflight and provide quantitative support for life extension and CBMassessments.

Figure12Comparisonbetweenflightvibrationexposureandtailoredtest

5 ConclusionThis paper has described how the vibration environment of an aircraft can be characterized in terms of aFatigue Damage Spectrum (FDS) and Shock Response Spectrum (SRS). It described how these spectra arecalculatedfrombothmeasuredflight loaddataanddirectlyfromvibrationtestspecifications.Vibrationtestsaretailoredtoensurethattestspectraexceedflightspectrawithanadequatesafetymargin.ThetechniqueswereusedsuccessfullytotailorstandardMILSTD810Fteststocoverthemoreonerousvibrationconditionsseenoncertainflightsafetycriticalcomponentsonahelicopter.Theyhavealsobeenusedtocompareexistingqualificationevidenceforequipmentononetypeofaircraftsoitcouldbeusedonanotherwithouttheneedfor retesting. This enabledurgent equipment tobeprovisionally cleared for limited flight approvalwithoutriskingcrewandaircraftsafetyorperformance.

6 Bibliography1.USDepartmentofDefense.MILSTD810F section514:DepartmentofDefenseTestMethodStandard forEnvironmentalEngineeringConsiderationsandLaboratoryTests.2003.

2. RTCA Inc. RTCA DO160E: . Environmental conditions and test procedures for airborne equipment.WashingtonDC:s.n.,2004.

3.Ministrede laDfense,DlgationGnralepour l'ArmementFrance.GAMEG13 Essaisgnrauxenenvironementdesmatrials.Paris:MinistredelaDfense,France,1986.

4. M.A., Biot. Transient oscillations in elastic systems. Thesis No. 259. Pasadena: California Institute ofTechnology,AeronauticsDepartment.,1932.

FlightloaddataStandardqualificationtestTailoredqualificationtest


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5.Biot,M.A.Theoryofelasticsystemsvibratingundertransient impulse,withanapplicationtoearthquakeproofbuildings.ProceedingsoftheNationalAcademyofScience.s.l.:NationalAcademyofScience,1933.Vols.19No2,pp.262268.

6. RuppA,MasiereA,Dornbusch T.Durability transfer concept for themonitoring of the load and stressconditionsonvehicles.s.l.:InovativeAutomotiveTechnologyIAT'05,Bled,2122April2005,2005.

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8.T.,Irvine.AnIntroductiontotheShockResponseFunction.[Online]2002.www.vibrationdata.com.

9. Halfpenny, A. Accelerated Testing Theory and User Manual. HBMnCode GlyphWorks ProductDocumentation.s.l.:HBMnCode,2008.

10.AHalfpenny,TWalton.CBMforvibratingequipmentonrotorcraft.AmericanHelicopterSociety,TechnicalSpecialists'MeetingonConditionBasedMaintenance.Huntsville,AL:s.n.,2009.

11.C,Lalanne.MechanicalVibration&Shock,volume5.London:HermesPentonLtd.,2002.

12.Miner,MA.Cumulativedamageinfatigue.J.AppliedMechanics.1945.Vols.67pp.A159A164.

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16.Lalanne,C.Lesvibrationsaleatoires.CoursADERA.1978.

17.Rice,SO.Mathematicalanalysisofnoise.Selectedpapersonnoiseand stochasticprocesses.NewYork:Dover,1954.

18. Bendat, JS. Probability functions for random responses: prediction of peaks, fatigue damage andcatastrophicfailures.NASAreportoncontractNAS54590.1964.

19.Halfpenny,A.RainflowcyclecountingandfatigueanalysisfromPSD.ProceedingsofASTELAB.France:s.n.,2007.

20. F,BishopNWM and Sherratt. Fatigue life prediction from power spectral density data. Part 2: Recentdevelopment.Environmentalengineering.1989.Vols.2,Nos.1and2,pp510.

21.HBMnCode.GlyphWorksAcceleratedTestingPackage.

22.D,QianSandChen.JointTimeFrequencyAnalysismethodsandapplications.London:PrenticeHallPTR,1996.ISBN0132543842.

7 Definitions,Acronyms,AbbreviationsEFA: Experimental Flight Approval FDS: Fatigue Damage Spectrum FFT: Fast Fourier Transform FTA: Full Type [flight] Approval IIR filter: Infinite Impulse Response filter LTA: Limited Type [flight] Approval RMS: Root Mean Square SDOF: Single Degree of Freedom System SRS: Shock Response Spectrum ERS: Extreme Response Spectrum MRM: Maximax Response Spectrum

New Techniques for Vibration Qualification of Vibrating Equipment on Aircraft

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