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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
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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
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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)
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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.
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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
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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
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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
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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
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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
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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
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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.
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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
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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
Suppliersqualificationevidence
Delifed damagespectrum(100hours)
Suppliersqualificationevidence
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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
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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
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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
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Technology,AeronauticsDepartment.,1932.
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Standardqualificationtest
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test
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Masiere
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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