vibration of aircraft

8/14/2019 vibration of aircraft

1/18

1

New Techniques for Vibration Qualification of VibratingEquipment on Aircraft

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

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

2

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,testedandcertifiedtosurvivethesevibrationlevelsovertheirentire

servicelife.DesignstandardssuchasMILSTD810F(1)andRTCADO160E(2)areoftenusedtoobtainthevibrationsign

off test; butwhat is the safetymargin on these tests?Howmany hours do they represent on real aircraft? Can the

equipmentlifebeextendedforaircraftwithlessdamagingusageprofiles?Canreadacrossevidencefromoneaircraftbe

usedtoqualifyacomponentonanotherwithoutfurthertesting?Thispaperdiscussesthelatestapproachestotheanalysis

ofshockandvibrationandshowshowvibrationtestscanbetailoredbasedonmeasuredflightspectra,howdifferenttests

canbecompared,andhowthelifeofequipmentcanbeadjustedbasedonoperationalexperience.

1 Introduction

Thispaperdescribeshowthevibrationenvironmentofanaircraftcanbecharacterized intermsofaFatigueDamageSpectrum (FDS)andShockResponseSpectrum (SRS). Itdescribeshow these spectraare calculated

from both measured flight load data and directly from vibration test specifications. Vibration tests can be

tailoredtoensurethattestspectraexceedflightspectrawithanadequatesafetymargin.

These techniques provide a means of comparing shock and vibrationinduced damage across different

vibrationtestsanddifferentaircraftplatforms.Thisenablesustouse testandserviceevidenceobtainedon

oneaircraftplatformtoqualifyequipmentonanother.Thisreadacrossevidencehasbeensuccessfullyused

toqualifyequipmentwithouttheneedforanyadditionalvibrationtesting. Itoffersconsiderablecostsavings

andalsoenablesarapidpathforthedeploymentofmissioncriticalequipmentinmilitaryoperations.

Techniques are discussed which derive tailored vibration tests based on measured flight load data.

Accelerometers record thevibration levelsatanumberofpositionson theaircraftwhile flyingaprescribed

sequenceofmaneuvers.ThefatiguedamagedosageforeachmaneuveriscalculatedusingaFatigueDamage

Spectrum (FDS),whicheffectivelyplotsdamagevs. frequency.Thedamage fromeachmaneuver issummed

over the usage profile of the aircraft to determine the wholelife damage dosage. From this profile we

determineastatisticallyrepresentativevibrationtestwhichcontainsatleastthesamedamagecontentasthe

wholelife,butoveramuchshortertestperiod.ThisfacilitatestheprovisionforTestTailoring,asspecifiedin

AnnexAofMILSTD810F(1),aswellasRTCADO160E(2)andGAMEG13(3).

CasestudiesarepresentedtodescribehowtheanalysiswasusedbyAgustaWestlandfortailoringvibration

tests for its latestaircraft.Studiesalsodescribehowthetechniqueshavebeenusedtoprovide readacross

evidence to support flight clearance for urgently needed equipment in military operations. These include


2/18

Aircraft Airworthiness & Sustainment 2010

2

clearance forhelicopteravionicsandoptoelectricalequipment.Studiesalsodescribehow cases for limited

type approval (i.e. restricted flight envelope or service life), or experimental flight approval are assessed

quantitativelyusing these techniques.Thepaperconcludesbydescribinghow the techniquecanbeused to

providequantitativeevidence to supportequipment lifeextensionsbasedonOperationalLoadsMonitoring(OLM)andHealthandUsageMonitoringSystem(HUMS)data.

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

ThebasisofthetheoryusedinthispaperoriginatesfromtheworkofAmericanengineerBiotin1934.Further

developmentonthisapproachwasconductedbyLalanneandtheFrenchMinistryofDefenseinpreparationof

the military design standard GAM EG13 (3) in the 1980s. In this section we introduce the two principal

componentsoftheapproach:theShockResponseSpectrum(SRS)andtheFatigueDamageSpectrum(FDS).

TheSRSisusedtodeterminethemaximumpeakamplitudeofloadingwhichtypicallyresultsfromextreme

shockeventssuchassevere landing, impact,weaponsdischargeornearbyexplosions.Theseextremeevents

cangiverisetocatastrophicfailureascomponentstressesexceedthedesignstrength.TheFDS,ontheother

hand,isusedtoaccumulatethedamagecausedbylongtermexposuretofatiguedamagingvibrationswhich,

althoughmodest inamplitude,give rise tomicroscopiccracks thatsteadilypropagateover timeand lead to

eventualfatiguefailure.

2.1 TheShockResponseSpectrum(SRS)

TheSRSisusedtodeterminethepeakamplitudeofloadingseenduringaflighteventoravibrationtest.The

safetymarginofthetestcanbedeterminedbycomparingthetestSRSwiththeflightSRS.Itisinsufficientto

simply record the highest static acceleration level because this does not account for the frequency of the

vibration.Dynamicsystemsaremoresensitivetocertainfrequenciesthanothers,thesocalledresonant(ornatural) frequencies. Structural failure isalsoattributable toexcessive strainenergy,and strainenergy ina

vibratingcomponentisproportionaltodisplacementratherthanacceleration.Thereforethedamagingeffect

ofacceleration isseen to reducewith thesquareof the frequency.High frequenciesbecome lessdamaging

thanlowerfrequencies.Itisthereforeimportanttoconsiderbothaccelerationamplitudeandfrequencyduring

thevibrationassessment.

The SRS essentially represents a plot of the peak amplitude vs. frequency. A typical SRS plot showing

helicopterflightdatacomparedwithaMILSTD810FvibrationqualificationtestisillustratedinFigure1.Inthis

casethequalification testexceeds thepeak inflight levelsbyat leasta factorof2so the test isconsidered

conservative.

TheSRSwasdevelopedbyBiotin1932(4).TocomputeBiotsShockSpectrum,themeasuredacceleration

signal is firstofall filteredbya SingleDegreeof Freedom (SDOF) transfer function centeredona specifiednaturalfrequency(fn)asillustratedinFigure2.Themaximumvalueofthefilteredresponseisthencalculated

and this representsasinglepoint in theSRSplot.Thiscalculation is repeatedoverawholerangeofnatural

frequenciestocreatetheentireSRS.In1934,Biot(5)publishedapaperonearthquakeanalysisandusedthe

termShockSpectrumforthefirsttime.

Biot used the SDOF response function as a frequency filter because of its ability to select a specific

frequency inamannerconsistentwiththephysicalresponseofastructuralsystem. It isalsomathematically

stableandisideallysuitedtorapidtimedomainconvolution.Otherspectrahavebeendocumentedwhichuse

differentfilters.Ruppetal(6),forexample,describeananalogousapproachbasedonabandpass filterand


3/18


3

this is used by some automotive companies in Europe; however, the SDOF approach is the most popular

approach.

Figure1Comparisonbetweeninflightshockexposureandatypicalvibrationtestprofile

Figure2SchematicflowchartillustratingtheSRSandFDScalculationprocess

Frequency

Gain

Frequency

LogDam

age

Acceleration

on airframe

Frequency

filter (SDOF)

Rainflow count

filtered signal

Plot damage Vs

frequency

Increment filter

by f

f

Frequency

Peakvalue

Peak amplitude of

filtered signal

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


4/18


4

TheSDOFresponsefunction(Figure2)isdominatedbyasinglespikelocatedatthenaturalfrequencyfn.At

frequenciesbelowthenaturalfrequency,thecomponentbehavesquasistatically [Gain(f>fn ) 0].

Aroundthenaturalfrequencythecomponentwillresponddynamicallyandwillbecomegreatlyamplifiedwithitsmaximumresponsebeinglimitedonlybythedampinginthesystem[Gain(f=fn)=Q].Theformulaforthe

SDOFfilterfunctionisgiveninEquation1.ThisfilterwillreturnaSRSintermsofaccelerationvs.frequencyfn.

11

1

Equation1

Gain(f)istheSDOFfilterwithrespecttofrequency f,andfnisthenaturalfrequency;bothareexpressedin

Hz.TheratioofthemaximumdynamicresponsetothestaticresponseisknownastheDynamicAmplification

(Q)factor.For5%structuraldamping,thishasthevalueofQ=10as illustrated inFigure2.Therelationship

betweendamping ratio andQ isgiven inEquation2. It ispossible to fit theamplification factorQ to the

particularcomponentbeingtested;however,establishedprocedureassumesavalueofQ=10forcomparative

analysis.ThisassumesthatweusethesameQvaluewhencalculatingtheSRS inflightandtheSRSfromthe

qualificationtest.Qisessentiallyusedtotunethefiltertothedesiredfrequencyrange,itdoesnotimplyany

mechanicalsignificanceintheanalysis.

12 Equation2

TheShockResponseSpectrum (SRS)canbeexpressed in termsofaccelerationordisplacement response

dependingon the frequency response functionused. For fatiguepurposes,wearemostly interested in the

displacement response. The SDOF filter function relating to displacement response is given in Equation 3.

Fatiguecracks initiateandgrow through thecyclicreleaseofstrainenergyand,therefore, thedisplacement

responseprovidesaproportional relationshipwith theenergydriving the failure.Accelerationmightbe the

origin of the load but it is the resulting strain (displacement) that drives the structural failure. The SRS of

displacementcan thereforebeused toquantify thedamagingeffectof the inputacceleration foranySDOF

systemoverarangeofnaturalfrequencies.

121

1

Equation3

Biotproposedusing theSDOFassumption forall componentsunderexcitation regardlessof theiractualfrequency response. Over the past years many have contested the conservatism of this assumption when

appliedtocomponentswithamultimodalresponse.Lalanne(7)documentsanumberofthesestudieswhich

allconcludethat theSDOF response,used inconjunctionwitha frequencysweep, isasuitablyconservative

assumptionforallpracticalcases.

ThearrivalofdigitalcomputershasmadeitpossibletocalculatetheSRSforlongtimesignalsveryrapidly.

UsingtheZtransform,Irvine(8)derivestheequationsforaveryefficientInfiniteImpulseResponse(IIR)filter.

Halfpenny(9)describesaveryefficientprocesswhichisabletocalculatetheSRSandFDSfrommeasuredflight

datawithexceptionalspeed,andHalfpenny(10)describesanalgorithmforrealtimeanalysisofvibrationdata

whichissuitableforConditionBasedMaintenance(CBM)analysisofvibratingequipmentonaircraft.


5/18


6/18


6

Figure

4

Typical

fatigue

SN

curve

for

aluminum

alloy

6082

in

the

T6

condition

When random (variableamplitude) loadsareencountered, rainflowcyclecounting isused todecompose

thesignalintoequivalentsinusoidalstresscycles.Thetotaldamageinthetimesignalisobtainedbysumming

thedamage fromeachstresscycleusingMiners (12) lineardamageaccumulation rule.The totaldamage is

thereforeobtainedfromEquation5.

1 Equation5

TheBasquincoefficientCisusuallytakenasunityforcomparativeFDSanalysis.Thisimpliesthatthesame

value of C is used when calculating the FDS inflight and the FDS from the qualification test. The Basquin

exponent bhasasignificanteffecton theFDSanalysis.For traditional fatigueanalysis b isobtained from

fatigue tests on the material (as per Figure 4) and is then modified to account for geometrical stressconcentrations,etc.ForFDStypeanalysisweareprincipallyinterestedinthefirstfailuresiteandthisusually

coincideswithageometricalstressconcentrationorthelocationofbolted,riveted,weldedorsolderedjoints.

Inthesecasesthevalueofbtendstolieintherange4


7/18


7

calculatedusingthetimedomaintechniquedescribed inFigure2.Thisapproach involvescalculatingtheSRS

and FDS from a derive time signal based on the vibration test specification. The process is quite straight

forward but does require a very long time signal at a very high sampling frequency. The computational

requirementsand riskofhumanerror in thisapproachare significantandmeans thatadirectapproach forobtainingtheSRSandFDSdirectlyfromthetestspecification isoftenpreferred. Inthissectionwe introduce

methodsforcalculatingtheSRSandFDSdirectlyfromPSDandsinesweeptestsratherthantimesignals.

2.3.1 Milesequation

In 1953, Miles (15) presented an equation that is similar in nature to the SRS. Using the simple formula

expressed inEquation6hederiveda spectrumof theRMS (RootMeanSquare)acceleration response toa

randomPSDappliedtoaSDOFsystemofnaturalfrequencyfnanddynamicamplificationQ.

RMSaccelerationspectrum, ( ) ( )2

accel n n nRMS f f Q G f

= Equation6

G(fn) isthePSDofaccelerationing2/Hzatfrequencyfn,andQisthedynamicamplificationfactor

2.3.2 ApproximateequationforobtainingSRSdirectlyfromaPSDtest

MilesequationisusedtodeterminetheRMSaccelerationresponseforaparticularnaturalfrequency.Inorder

todeterminethemaximumlikelyresponse(i.e.theSRS),MilessuggestedmultiplyingtheRMSspectrumbya

factorof3(i.e.the3sigmacurve).However, in1978Lalanne(16)proposedarefinementtoMilesequation.

Fornarrowbandfrequencyresponse,typicalofaSDOFsystem,theamplitudedistributionwasfoundbyRice

(17) to be Rayleigh and not Gaussian as proposed by Miles. Lalanne therefore rederived Miles equation

substituting

the

Rayleigh

probability

function.

The

resulting

equation

is

known

as

the

Maximax

Response

Spectrum (MRS)or theExtremeResponseSpectrum (ERS). It represents themost likelyextremeamplitude

response witnessed during a vibration test of duration T seconds driven by random PSD excitation. The

responsecanalsobeexpressedintermsofrelativedisplacementinmetersusingEquation8.

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

ERSdisplacementspectrum, ( ) ( )

( )2

9.81

2

accel n

disp n

n

ERS fERS f

f=

Equation8

Tisthetestexposuredurationinseconds,andG(fn)isthePSDofappliedaccelerationing2/Hz.

TheERSisanalogoustothetimedomainSRS.However,whereastheSRSisusuallyusedtodeterminethemaximumresponsetoahighlydamagingtransientshock,theERSisusedtorepresentthemaximumexpected

responsewitnessedduringavibrationtest.InthispaperweusethetermSRSlooselytoencompassbothSRS

andERStoavoidunnecessarycomplication.

Theapproximateequationsgivenabovearebasedonseveralassumptions.Themainassumptionsare:

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

containsnosignificantpeaks)

2. theresponseisnarrowbandedthisassumptionisusuallyassuredbyhavingaQvalueof10


8/18


8

Figure 5b shows a comparison between the accurate and approximate ERS derived for a typical PSD

vibrationtestgiveninFigure5a.ThisanalysisassumesQ=10andT=16hours.

2.3.3 ApproximateequationforobtainingFDSdirectlyfromaPSDtest

FollowinginitialworkbyRice(17)andBendat(18)todeterminefatiguedamagedirectlyfromaPSDofstress,

Lalanne(11)wasabletoutilizethistechnologytocreateaclosedformcalculationtoestimatetheFDSdirectly

fromtheaccelerationPSD,thisisgiveninEquation9.Anexplanationofvibrationfatiguetheoryisbeyondthe

scopeofthispaperandyouarereferredtoHalfpenny(19)andBishopetal.(20)formoredetails.

( ) ( )

( ) ( )

22

3

9.811

22 2

b

n

n n

n

Q G fbFDS f f T

f

+

Equation9

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

Gammafunctiondefinedas ( ) ( )10g xg x e dx

=

Theapproximateequationgivenaboveisbasedonthesameassumptionsdescribedinsection2.3.2.Figure

5c showsa comparisonbetween theaccurateandapproximate FDS derived for a typical PSD test given in

Figure5a.ThisanalysisassumesQ=10,b=4andT=16hours.

Figure5ComparisonbetweenapproximateandaccurateSRSandFDSforaPSDvibrationtest

2.3.4 ApproximateequationforobtainingSRSdirectlyfromasinesweeptest

TheSRScanbeestimateddirectlyfromasinesweeptestspecification.Equation10givestheSRSintermsof

accelerationing,whereasEquation11givestheSRSintermsofdisplacementinmeters. Equation109.81 2 Equation11

Accuratemethod

Approximatemethod

Accuratemethod

Approximatemethod

Acceleratio

ng2/Hz

a b c


9/18


9

A(fn)istheamplitudeofthesinesweepingatfrequencyfnHz

Theapproximateequationsgivenabovearebasedonthesameassumptionsdescribedinsection2.3.2and

arevalidover the frequency rangeof the sweep.Figure6bshowsa comparisonbetween theaccurateand

approximateSRSderivedforatypicalsweptsinetestgiveninFigure6a.ThisanalysisassumesQ=10.

2.3.5 ApproximateequationforobtainingFDSdirectlyfromasinesweeptest

TheFDScanbeestimateddirectlyfromasinesweeptestspecificationusingEquation12.InthiscasetheFDS

represents fatigue damage from a single sine sweep and should be multiplied by the number of sweeps

performedduringthetest.

60 2 9.812 2

Equation12

isthelogarithmicsweeprateexpressedinoctavesperminuteandA(fn)istheaccelerationamplitudeing

atfrequencyfnHz

Theapproximateequationgivenaboveisbasedonthesameassumptionsdescribedinsection2.3.2andis

valid over the frequency range of the sweep. Figure 6c shows a comparison between the accurate and

approximateFDSderivedforatypicalsweptsinetestgiveninFigure6a.ThisanalysisassumesQ=10,b=4,=1

octavepersecond,over8completesweeps.

Figure6ComparisonbetweenapproximateandaccurateSRSandFDSforasinesweepvibrationtest

2.3.6 Advanced(accurate)methodsforderivingSRSandFDSfromstandardvibrationtests

The approximate equations given above are adequate for general comparative analyses provided the

assumptionsin2.3.2arevalid.TheyaresuitableformanyofthetestsproposedinMILSTD810F(1)andRTCA

DO160E(2).Lalanne(11)andHalfpenny(9)havefurtherdevelopedtheseapproachesandpresentnumerical

solutionalgorithmsofferingmuchgreateraccuracywithoutthelimitationsinherentintheaboveassumptions.

Thesealsoofferamuchwider rangeofvibration testingoptions includingdifferentsweep typesandmixed

testssuchassinesweepanddwell.Moreadvancedtestssuchassineonrandomarealsosupportedwhichdo

notfulfilltheassumptionsmadein2.3.2.Discussiononthesetechniquesisbeyondthescopeofthispaperand

thereaderisreferredtoHalfpenny(9)formoreinformation.

Accelerationamplitudeg

a b c


10/18


10

3 VibrationEnvironmentonanaircraft

3.1 Sourcesofhelicoptervibration

Thissection introduces thevibrationenvironmentonahelicopteranddescribeshow this ismodeledby thevibrationtest.Theinformationdiscussedhereisalsoapplicabletofixedwingaircraft;however,thediscussion

inthispaperhasfocusedprincipallyonhelicoptersbecausethecasestudiespertaintothese.

Thevibrationspectrumofahelicoptercanbedescribedasaseriesofsinusoidaltonessuperimposedona

backgroundofrandomnoise(sineonrandom).Anexamplerecordedinthefuselageofahelicopterisshownin

Figure7.Themainsourceofthesesinusoidaltones isattributabletoharmonicsofthemainrotor.Themain

rotorfrequencyofahelicopterisrelativelylow(typically38Hz)andinaccuraciesintherotortrack,balanceor

bladepitchwillresultinsinusoidaltonesatthisfrequency.Themainrotorfrequencyisoftendenotedbythe

term1Rwhile the tail rotor frequency isdenotedby the term1T.The tail rotor frequencyofahelicopter is

typicallywithintherange1550Hz.

Whenthehelicopterisinflightthepitchofeachbladevariescyclicallywithrespecttoitsazimuthangle(i.e.

angleofthebladerelativetotheaxisoftheaircraft).Furthermore,thebladeswillslicethroughmanyeddieswhicharisefromturbulence,aerodynamiceffectsoftheaircraft,groundeffects,bladeinducedwakeeffects,

etc.Thesecyclicallyperiodiceffectsgiverisetopeaksatharmonicsofthebladepassingfrequencyasshownin

Figure7.Thebladepassing frequency isdenotedby the term nRwhere n is thenumberofblades in the

rotor.Mosthelicoptershavebetween2and6bladesinthemainandtailrotors.Theprincipalharmonicsare

denotedasnR,2nR,3nR,etc..Theeffectbecomeslessobviousforthehigherorderharmonicsinexcessof3nR

astheseamplitudesaretypicallylowerthanthebackgroundrandomnoise.ThehelicopterusedinFigure7has

4bladesinboththemainandtailrotors.

Figure7FDSrecordedonthemainfuselageofahelicopter

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

GearboxmeshingFrequencyHz


11/18


11

Allcomponentswillwitnesssignificantvibrationfromthemainrotorandthisdominatesthelowfrequency

spectrum for positions throughout the aircraft. Components sited towards the tail of the aircraft will also

witnessprincipalharmonicsofthetailrotor.Componentsthataresitedadjacenttotheenginesandgearboxes

will see additionalharmonics of theengine, shaft,and gearboxmeshing frequencies. It isusual practice tosegregate the aircraft into regions and assume that the vibration amplitudes are similar for all equipment

positionedinthatregion.Themostcommonlydefinedregionsare:

Fuselagevibrationisdominatedbyharmonicsofthebladepassingfrequencyofthemainrotor

Avionicsbay (similar to fuselagebutvibration isolatedmountsaredesigned to reduce rotorinducedvibrationamplitudes)

Onornearenginesadditionalsinusoidalharmonicsinducedthroughengineandgearboxharmonicsandmeshingfrequencies

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

External stores and sponsonsadditional aerodynamic loads inducedbydownwash from themainrotorandaerodynamicsoftheaircraft

Inmostcasestheverticalandlateralaccelerationsdominatetheloadingenvironmentandthefore/aftaxis

isrelativelybenign.

3.2 Typesofvibrationqualificationtest

Vibration qualification tests are typically performed in accordance with the aircraft manufacturers

specificationor tooneof thecommonlyusedmilitarydesignstandardssuchas;USDepartmentofDefense

standardMILSTD810F(1),andRTCADO160E(2).Thequalificationtestisperformedinthefollowingstages:

1. Initial resonancesearchsweptsine test todetermine the resonant frequenciesof thecomponent.

Ideally,resonantfrequenciesshouldnotcoincidewithanyoftheprincipalharmonicsoftheaircraft.A

componentwillusuallyfailqualificationiflowdampedresonancesareencounteredwithinavoidbands

ofaprincipalharmonicunless the supplier canproveadequatedurabilityand theaircraftOEM can

prove that the resonant issues will not adversely affect the durability of the airframe or mounting

structure.

2. Endurance test consisting of either a multiple sineonrandom vibration test or a swept sine and

dwelltest(asdiscussedinthenextparagraph)

3. Finalresonancesearchsweptsinetestasperstep1toensurenochanges inresonant frequencies

whichcouldindicatethepresenceofanemergingfatiguecrack

Mostmodernvibration testsareperformedusinguniaxialelectrodynamicvibration rigs.Theendurance

portionofthetestcommonlyusesamultiplesineonrandomvibrationprofile.Atestdurationof16hoursperaxis(repeatedoverx,yandzaxessequentially)istypicallyequivalentto10,000hoursofoperationalexposure.

Analternativeapproach is to specifya swept sineanddwellvibrationprofile.Thisapproach involvesan

extendedsweptsinetest(typically1hour)followedbyasequenceofstaticsinusoidaltestsdesignedtoexcite

theprincipalharmonicsoftheaircraft(typically1millioncyclesateachharmonic).Thetestisrepeatedforall

axessequentially(oneaftertheother).

The swept sine and dwell test profile is less efficient than the sineonrandom because each principal

harmonic (sine tone) must be tested separately for 1 million cycles and this leads to a very lengthy and

expensivetest.Thisisparticularlyproblematicforhelicopterswherethemainrotorharmonicsoccurata low


12/18


12

frequency.Thesineonrandomtestprofileexcitesallharmonicssimultaneouslywhichismorerepresentative

oftheactualaircraft loadingprofile.Sineonrandomtestshave largelysupersededthesweptsineanddwell

test.Thetechniquesdiscussedinthispaperhavebeensuccessfullyemployedasameansofconvertingexisting

sweptsineanddwelltestprofilestothemorerepresentativeandefficientsineonrandom.

Afinalimpact(hammer)testisperformedontheequipmentasmountedontheaircrafttoensurethatany

additionallyflexibilityinthemountingdoesnotgiverisetoresonanceswithintheavoidbandsoftheprincipal

harmonics.

3.3 Estimationofaccelerationlevelsusedinthevibrationtest

While the aircraft is at the design stage we can obtain estimates of test acceleration levels for use in

preliminary qualification. Suitable estimates are provided by both MILSTD810F and RTCA DO160E.

Accelerationlevelsareprovidedintheformofequationswherethevibrationamplitudeisgivenasafunction

of theprincipalharmonic frequency.Differentequationsareprovided foreachpositionon thehelicopterto

accountforvariationsinvibrationseverity.

As measured flightdata becomes available then thesepreliminary design estimates should be reviewed

againstmeasureddata.Thetestaircraftisinstrumentedwithaccelerometerswhichrecordthevibrationlevels

atanumberofpositionswhileflyingaprescribedsequenceofmaneuvers.Maneuversareflownundervarious

weight conditions so we can obtain a series of measured flight events that are representative of the real

conditions seen inservice. The fatigue damage dosage for each maneuver is calculated using a FDS. The

damagefromeacheventissummedovertheusageprofileoftheaircrafttodeterminethewholelifedamage

dosage.AnequivalentFDScanbecalculated for theproposedqualification testand the testspecification is

iteratedsothetestFDSexceedstheflightFDSbyanacceptablesafetymargin.Theapproach is illustrated in

Figure8.

Theobjectiveoftesttailoringistoderiveaqualificationtestthatcontainsatleastthesamefatiguedamage

contentastherealaircraftenvironmentbut inashortertesttime.Asthedamage isfixedthenthevibrationamplitudeusedinthetestmustvarywiththedurationofthetest.Ashortertestwillrequiregreatervibration

amplitudesinordertoachievethesamedegreeofdamageinashorterperiod.TheShockResponseSpectrum

(SRS)isusedtocomparetheworstamplitudeusedinthetestagainsttheworstamplitudeseenduringflight.In

most cases the worst shock load seen in flight will only occur for very short periods of time at infrequent

intervals; whereas most of the fatigue damage will be attributed to long periods of flight at very modest

vibrationlevels.Testtailoringusesthiseffecttoderivetheoptimumtestduration.Theoptimumtestduration

isachievedwhentheSRSofthetestcoincideswiththeSRSobtainedfortheworstflightcondition.Thisallows

thetesttooperateattheoptimumaccelerationlevelsodamageisaccumulatedatthemaximumratewithout

exceedingtheworstloadsseeninflight.

Most traditional helicopter and fixedwing tests are overaccelerated. This means that the loading

amplitudeexceedstheworst flight loadsbyasignificantmargin.Thisapproach isjustifiedonaccountofthehigh safety margins implicit in the design of aircraft components. However, care is required when over

acceleratingavibrationtesttoensurethattheexcessiveloadsdonotintroduceplasticityintothecomponent

whichcouldaltertheloadpathsandchangethefailuremode.


13/18


13

Figure8Testtailoringforhelicoptervibrationqualification

4 CaseStudies

4.1 Case Study 1: Vibration qualification based on read-across evidence from otheraircraft

Equipmentwasurgentlyrequiredfordeploymentonamilitaryhelicopter.Novibrationqualificationhadbeen

performedforthisaircraft;however,previousclearancehadbeenawardedforadifferenthelicoptertype.The

objectiveofthisanalysis istocomparethedamagecontentoftheoriginalaircrafttestwiththatrequiredfor

thenewhelicopterandassesswhethertheexistingqualificationevidenceissufficientforflightapprovalonthe

newhelicoptertype.

The original sineonrandom qualification test was performed in accordance with MILSTD810E for

equipmentmounted to the fuselage.Theprincipal rotorharmonicsaredifferenton thishelicopterand the

vibrationlevelsarelower.Themanufacturersvibrationrequirementsforthenewhelicopterareexpressedin

termsofaswept 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 helicopter

specificationsignificantlyexceedsthatprovidedintheexistingqualificationevidence.However,aconsiderable

overload is acknowledged in the new helicopter specification in order to accelerate the vibration test. A

comparison was therefore made against measured flight data and this clearly shows an acceptable safety

margin.

Step 1Damage Transformation

Calculate

SRS

Calculate

FDSEvent

FDS

Event

SRS

Step 3

Test Synthesis

Step 2

Mission ProfilingSum FDS

Mission

FDSEnvelope

SRS

Mission

SRS

Compare

SRS

Input data

for eachflight event

Aircraft

usage

profile

Accelerated

vibration test

profile

Calculate

FDS

CalculateSRS

Compare

FDS

Iterate (Tailor)

test specification


14/18


14

Figure9Comparisonofavailablequalifationevidencewithaircraftrequirementspecification

Figure9bshowsacomparisonoftheFDSforbothtests.Thefrequenciesoftheprincipalharmonicsareseen

to varyand cumulativedamageofferedby theexistingqualificationevidence is considerably less than that

requiredbythenewhelicopterspecification.Thereisinsufficientevidencetoconsiderfulltypeapprovalofthe

equipmentatthisstage!

Figure9cshowstheeffectofreducingthesafeoperationallifefrom10,000hoursto100hours.Duetothe

urgentrequirementofthisequipment,limitedflightapprovalwasawardedfor100operationalhoursandthe

equipmentwasfittedtoserviceaircraft.Duringthefirstyearofoperationtheequipmentwasretestedtothe

newspecificationandwaseventuallyawardedfulltypeapproval.However,ithadbeendeployedstraightaway

andusedsuccessfullyintheatreoverthisentireperiod.

Limitedflightapproval isalsopossiblethrougharestrictionoftheflightenvelope; i.e.byrestrictingsome

flight conditions and maneuvers. For this type of analysis it is preferable touse measured flight load data

directly in the comparison rather than using the manufacturer specification. This approach is called Test

TailoringandiscoveredinCaseStudy2.

Inmanycasestheexistingqualificationevidenceprovessufficientforthenewaircraftandfulltypeapproval

canbeawardedwithoutrecoursetoadditionaltesting.Thisoffershugecostsavingsbecausevibrationtestsare

a)ShockResponseSpectrumshowsthatthesuppliers

qualificationevidenceislowerthanthat requiredbythe

aircraftspecificationbut isstillgreaterthanmeasuredflight

databyanacceptablemargin

Originalaircraft

specification

Suppliersqualificationevidence

Measuredflight loaddata

b)Fatigue DamageSpectrumshowsthatthesuppliers

qualificationevidenceisinadequateforthisaircrafton

accountofthedifferenceinrotorharmonicfrequencies

c)Theequipmentcanbeprovisionallydelifed to100

operationalhourspendingfurthervibrationtests

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

Fatigue Damage Spectrum (FDS)

Originalaircraftspecification


Delifed damagespectrum(100hours)



15/18


15

oftenveryexpensiveonaccountofthedirecttestingcostsandthecostofthetestcomponentwhich is life

expiredattheendofthetest.

This approach to qualification has also proveduseful for assessing experimental flight approval for new

equipment. Qualification evidence based on fixed wing installations, shipping or transportinduced damage

qualification, or slosh and vibration qualification tests often prove sufficient for limited flight clearance for

experimentalpurposes.

4.2 CaseStudy2:Testtailoringofcontrolrodvibrationtest

Newyawcontrol rodsandmountingswererequiredonahelicopter.Thecontrol rodsrunthroughthemain

fuselageandtailconeandaresubjectedtoadditionalvibrationfromthetailrotor,thetailrotorgearboxand

theintermediategearbox.Thesecomponentsareflightsafetycriticalandageneralvibrationspecificationwas

considered inadequate in this case.The existing swept sine anddwell testwasalsounacceptably longand

expensive (98hours peraxis), and the safetymarginwasuncertain.A test tailoringexercisewas therefore

authorized to determine a more appropriate sineonrandom qualification test along with a completeassessmentoftheinherentsafetymargin.

Accelerationmeasurementsweretakenoveranumberofflighteventsusingtriaxialaccelerometerslocated

at several positions on the helicopter. The SRS and FDS were calculated for each accelerometer and an

envelopetakentorepresenttheworstloadingcondition.TheFDSwasscaledovertheaircraftusageprofileas

describedpreviouslytodetermine thewholelifedamage.TheSRSandFDSwerecalculatedoverarange5

2000Hz.AcomparisonofthemeasuredspectrawiththestandardtestspecificationisillustratedinFigure10.

Figure10Comparisonofflightvibrationexposuretocertifiedtestlimits

FromFigure10,the inflightshockresponse iswellrepresentedbytheexistingtestspecificationoverthefirstfewrotorharmonics;however,itdoesnotaddressthehighfrequencygearboxinducedpeak.Theinflight

damageresponseisalsowellrepresentedoverthefirstfewrotorharmonicsbuthasanegligiblesafetymargin.

Theexistingtestspecificationdoesnotaddressanyofthehigh frequencygearboxinducedvibrationsor the

peaksat1Rand2Rwhicharesignificantonthisaircraft.

4.2.1 Testtailoringprocess

Thenewtestisbasedonasineonrandomprofilecomprisingthefollowingsteps:

Flightloaddata

Standardqualificationtest


16/18


16

1. Initialresonancesearchatasweepratenotexceeding1octave/mininaccordancewithmanufacturers

existingspecifications

2. 16hoursineonrandomtestinaccordancewithFigure11

3. Finalresonancesearchasperstep1

4. Repeatallabovestepsforeachaxis(x,y,z)

Thistestisdesignedtoofferclearanceforupto10,000operationalhoursandtesttailoringwasperformed

usingtheGlyphWorksAcceleratedTestingpackagefromHBMnCode(21).AcomparisonoftheSRSandFDS

areillustratedinFigure12.ThetestwasderivedusingMILSTD810Fasabasis.ThebackgroundrandomPSD

and the amplitude of the sine tones were then tailored to achieve an adequate safety margin over the

proposedusagespectrum.Furtherconstraintswereappliedsuch thatnovibration levelshouldbe less than

those recommended inMILSTD810F,and the finalFDSshouldnotbe lessthantheexistingsweptsineand

dwelltestspecification.

Figure11

Tailored

vibration

test

based

on

MIL

STD

810F

From Figure12we see that thenew test specificationoffers anacceptable safetymarginonbothpeak

shockandfatiguedamage.Thesineonrandomtesttakesonly16hoursperaxisasopposedto98hoursforthe

previoussweptsineanddwelltestandthisoffersasignificantcostsaving.

These techniques provide a tailored test which accounts for the real vibration environment and avoids

potentialunderdesignissuesbyallowingdirectcontrolofthesafetymargin.Inothersituationstesttailoring

hasbeenusedtorelaxtheoriginaltestspecificationwherethemeasuredusageprofileislessdamaging.This

canreducetheinherentcostimplicationsofovertesting,andtheinherentweightimplicationsofoverdesign.

Acceleration

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


17/18


17

Insome cases ithasbeenusedsuccessfully toqualify importantequipment thatwaspreviously considered

inadequateandalsoextendthelifeofequipmentwherethevibrationlevelsorusagespectrumwerefoundto

be lower than theexistingqualificationevidence.Halfpenny (10)describeshow realtimealgorithmscanbe

used to determine the FDS and SRS inflight and provide quantitative support for life extension and CBMassessments.

Figure12Comparisonbetweenflightvibrationexposureandtailoredtest

5 Conclusion

This paper has described how the vibration environment of an aircraft can be characterized in terms of a

Fatigue Damage Spectrum (FDS) and Shock Response Spectrum (SRS). It described how these spectra are

calculated

from

both

measured

flight

load

data

and

directly

from

vibration

test

specifications.

Vibration

tests

aretailoredtoensurethattestspectraexceedflightspectrawithanadequatesafetymargin.Thetechniques

wereusedsuccessfullytotailorstandardMILSTD810Fteststocoverthemoreonerousvibrationconditions

seenoncertainflightsafetycriticalcomponentsonahelicopter.Theyhavealsobeenusedtocompareexisting

qualificationevidenceforequipmentononetypeofaircraftsoitcouldbeusedonanotherwithouttheneed

for retesting.This enabled urgent equipment tobe provisionally cleared for limited flightapproval without

riskingcrewandaircraftsafetyorperformance.

6 Bibliography

1.USDepartmentofDefense.MILSTD810Fsection514:DepartmentofDefenseTestMethodStandardfor

EnvironmentalEngineeringConsiderationsandLaboratoryTests.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 Essaisgnrauxen

environementdesmatrials.Paris:MinistredelaDfense,France,1986.

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

Technology,AeronauticsDepartment.,1932.

Flightloaddata

Standardqualificationtest

Tailoredqualification

test


18/18


18

5.Biot,M.A.Theoryofelasticsystemsvibratingundertransient impulse,withanapplicationtoearthquake

proofbuildings.ProceedingsoftheNationalAcademyofScience.s.l.:NationalAcademyofScience,1933.Vols.

19No2,pp.262268.

6. RuppA,

Masiere

A,

Dornbusch

T.Durability transfer conceptfor themonitoring of the load and stress

conditionsonvehicles.s.l.:InovativeAutomotiveTechnology IAT'05,Bled,2122April2005,2005.

7.C,Lalanne.MechanicalVibration&Shock,volume2.London:HermesPentonLtd.,2002.

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

9. Halfpenny, A. Accelerated Testing Theory and User Manual. HBMnCode GlyphWorks Product

Documentation.s.l.:HBMnCode,2008.

10.AHalfpenny,TWalton.CBMforvibratingequipmentonrotorcraft.AmericanHelicopterSociety,Technical

Specialists'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.

13.A,Halfpenny.Apracticaldiscussiononfatigue.NewTechnology2001.Warwickshire,UK:MIRA,2001.

14.DowningS.D.,SocieD.F.Simplerainflowcountingalgorithms.Int.JFatiguepp3140.Jan,1982.

15.Miles,JW.Onstructuralfatigueunderrandomloading.JAeronauticalSciencespp.753.1954.

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 and

catastrophicfailures.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: Recent

development.Environmentalengineering.1989.Vols.2,Nos.1and2,pp510.

21.HBMnCode.GlyphWorksAcceleratedTestingPackage.

22.D,QianSandChen.JointTimeFrequencyAnalysis methodsandapplications.London:PrenticeHallPTR,

1996.ISBN0132543842.

7 Definitions,Acronyms,Abbreviations

EFA: Experimental Flight ApprovalFDS: Fatigue Damage Spectrum

FFT: Fast Fourier TransformFTA: Full Type [flight] Approval

IIR filter: Infinite Impulse Response filter

LTA: Limited Type [flight] Approval

RMS: Root Mean SquareSDOF: Single Degree of Freedom System

SRS: Shock Response Spectrum

ERS: Extreme Response Spectrum

MRM: Maximax Response Spectrum

vibration of aircraft

Documents

Transcript of vibration of aircraft