Topics in Modal Analysis & Testing, Volume 10: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics 2017

186 Pages·2017·12.4 MB·English

by  Michael Mains

Conference Proceedings of the Society for Experimental Mechanics Series
Michael Mains · J.R. Blough Editors
Topics in Modal
Analysis & Testing,
Volume 10
Proceedings of the 35th IMAC, A Conference and Exposition
on Structural Dynamics 2017
Conference Proceedings of the Society for Experimental Mechanics Series
SeriesEditor
KristinB.Zimmerman,Ph.D.
SocietyforExperimentalMechanics,Inc.,
Bethel,CT,USA
Moreinformationaboutthisseriesathttp://www.springer.com/series/8922
Michael Mains • J.R. Blough
Editors
Topics in Modal Analysis & Testing,
Volume 10
Proceedings of the 35th IMAC, A Conference and Exposition
on Structural Dynamics 2017
123
Editors
MichaelMains J.R.Blough
ApplicationSolutions-StructuralAnalysis MichiganTechnologicalUniversity
Brüel&Kjær Houghton,MI,USA
Cincinnati,OH,USA
ISSN2191-5644 ISSN2191-5652 (electronic)
ConferenceProceedingsoftheSocietyforExperimentalMechanicsSeries
ISBN978-3-319-54809-8 ISBN978-3-319-54810-4 (eBook)
DOI10.1007/978-3-319-54810-4
LibraryofCongressControlNumber:2017935404
©TheSocietyforExperimentalMechanics,Inc.2017
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Preface
Topics in Modal Analysis & Testing represents one of ten volumes of technical papers presented at the 35th IMAC, A
Conference and Exposition on Structural Dynamics, organized by the Society for Experimental Mechanics, and held in
GardenGrove,California,January30–February2,2017.ThefullproceedingsalsoincludevolumesonNonlinearDynamics;
DynamicsofCivilStructures;ModelValidationandUncertaintyQuantification;DynamicsofCoupledStructures;Sensors
andInstrumentation;SpecialTopicsinStructuralDynamics;StructuralHealthMonitoring&DamageDetection;Rotating
Machinery, Hybrid Test Methods, Vibro-Acoustics and Laser Vibrometry; and Shock & Vibration, Aircraft/Aerospace and
EnergyHarvesting.
Eachcollectionpresentsearlyfindingsfromexperimentalandcomputationalinvestigationsonanimportantareawithin
Structural Dynamics. Topics in Modal Analysis & Testing represents papers on enabling technologies for Modal Analysis
measurementsandapplicationsofModalAnalysisinspecificapplicationareas.
Theorganizerswouldliketothanktheauthors,presenters,sessionorganizers,andsessionchairsfortheirparticipationin
thistrack.
Cincinnati,OH,USA M.Mains
Houghton,MI,USA J.R.Blough
v
Contents
1 Fluid-StructureInteractioninaLabyrinthGasSealCoupledtoaFlexibleStator.............................. 1
A.Dairien,F.Thouverez,L.Blanc,P.Héliès,andJ.Dehouve
2 ModalAnalysisofTowerCranewithCracksbytheDynamicStiffnessMethod ................................ 11
DangXuanTrongandNguyenTienKhiem
3 High-NoiseHigh-SpeedFootageDatainExperimentalModalAnalysis.......................................... 23
JakaJavh,JankoSlavicˇ,andMihaBoltežar
4 Morlet-WaveDampingIdentification:ApplicationtoHigh-SpeedVideo......................................... 27
JankoSlavicˇ,MarkoMihalec,JakaJavh,andMihaBoltežar
5 Fluid-CoupledVibrationControlInspiredbyDragonflyWings................................................... 31
YunjieWang,YajunYin,andGangtieZheng
6 ImprovingModalParameterEstimationbyComplementaryOutput–OutputRelations....................... 37
OscarOlarteandPatrickGuillaume
7 OperationalModalAnalysisinFrequencyDomainUsingGaussianMixtureModels........................... 47
AnkitChiplunkarandJosephMorlier
8 UnderstandingModalVectors ......................................................................................... 55
GeorgeFoxLang
9 BestPracticesforUsingOrder-BasedModalAnalysisforIndustrialApplications.............................. 69
EmilioDiLorenzo,SimoneManzato,BartPeeters,FrancescoMarulo,andWimDesmet
10 CouldtheVeeringPhenomenonbeaMechanicalDesignInstrument? ........................................... 85
CarloRosso,ElvioBonisoli,andFabioBruzzone
11 ImpulseExcitationofPiezoelectricPatchActuatorsforModalAnalysis......................................... 97
V.Ruffini,T.Nauman,andC.W.Schwingshackl
12 ModalParameterEstimationinMulti-PatchOperationalModalAnalysis:PerspectivesandApproaches .. 107
D.MironovsandS.Chauhan
13 ModelingandNonlinearParameterIdentificationofanElectric-PowerSteeringSystem...................... 127
CassioT.Faria,GiorgioPulvirenti,andTheoGeluk
14 AFrameworkforAdditiveManufacturingProcessMonitoring&Control...................................... 137
IanT.Cummings,MeganE.Bax,IvanJ.Fuller,AdamJ.Wachtor,andJohnD.Bernardin
15 ReliabilityofUsingStereoPhotogrammetrytoEstimateModalParameters.................................... 147
DaniloDamascenoSabino,PeymanPoozesh,JoaoAntonioPereira,andChristopherNiezrecki
16 ConstantMassMetastructurewithVibrationAbsorbersofLinearlyVaryingNaturalFrequencies.......... 153
KatherineK.ReichlandDanielJ.Inman
vii
viii Contents
17 StudyonRandomDecrementSignatureUnderDifferentTriggeringLevelandLengthofTimeHistory.... 159
JinzhiWu,XiujuanZheng,JieHu,YigangZhang,andFuh-GwoYuan
18 Experimental Study on the Rotor Dynamics Influence Upon the Modal Characteristics
ofanInductionMachine................................................................................................ 167
F.Chauvicourt,M.Ballweg,W.Desmet,H.VanderAuweraer,andC.T. Faria
19 OptimalModalParameterEstimationforHighlyChallengingIndustrialCases................................ 173
MahmoudEl-Kafafy,BartPeeters,andPatrickGuillaume
Chapter 1
Fluid-Structure Interaction in a Labyrinth Gas Seal Coupled
to a Flexible Stator
A.Dairien,F.Thouverez,L.Blanc,P.Héliès,andJ.Dehouve
Abstract Thispaperdealswiththepredictionofaeroelasticinstabilitiesoccuringinlabyrinthgassealofturbomachinery
components. The purpose of this work is to carry out a numerical investigation on an advanced labyrinth gas seal model
comprising a non-deformable rotor, and a flexible stator. The flexibility of the static part induces pressure and velocity
fluctuationswithintheleakageflow.Themodelretainsseveralcavitiesformedbytheteethlocatedontheshaftandastrong
couplingbetweenthefluidandthestructureisassumed.
Aqualitativeanalysisisperformedtoidentifythevariouscausesofaeroelasticinstabilityoccurence.Then,acomparison
withtheliteratureiscarriedoutinordertoproposeabetterapproachtopredictsuchinstabilities.
Keywords Fluid-structurecoupling (cid:129) Labyrinthgasseal (cid:129) Turbomachinery (cid:129) Aeroelasticinstability (cid:129) Nonlinearity
Nomenclature
t Timevariable
n NumberofharmonicsoftheFourierseries
i Cavitynumber
(cid:2) Orderparameter
(cid:3) Angularposition
R Shaftradius
s
R Statorradius
c
y Linearfunction
i
y1i Periodicfunction
xc Timecoefficientassociatedtocosinefunction
n;i
xs Timecoefficientassociatedtosinefunction
n;i
M Massmatrixofthelinearsystem
C Viscousdampingmatrixoflinearsystem
K Linearstiffnessmatrixofthelinearsystem
XR Coefficientsvectordifferentiatedtwicewithrespecttotime
A.Dairien((cid:2))
ÉcoleCentraledeLyon,LaboratoiredeTribologieetDynamiquedesSystémes,UMR-CNRS5513,36avenueGuydeCollongue,
69134ÉcullyCedex,France
AirbusSafranLaunchers,ForêtdeVernon,BP802,27208VernonCedex,France
e-mail:[email protected]
F.Thouverez(cid:129)L.Blanc
ÉcoleCentraledeLyon,LaboratoiredeTribologieetDynamiquedesSystémes,UMR-CNRS5513,36avenueGuydeCollongue,
69134ÉcullyCedex,France
P.Héliès
AirbusSafranLaunchers,ForêtdeVernon,BP802,27208VernonCedex,France
J.Dehouve
CentreNationald’ÉtudesSpatiales,DirectiondesLanceurs,52,rueJacquesHillairet,75612ParisCedex,France
©TheSocietyforExperimentalMechanics,Inc.2017 1
M.Mains,J.R.Blough(eds.),TopicsinModalAnalysis&Testing,Volume10,ConferenceProceedings
oftheSocietyforExperimentalMechanicsSeries,DOI10.1007/978-3-319-54810-4_1
2 A.Dairienetal.
XP Coefficientsvectordifferentiatedoncewithrespecttotime
X Coefficientsvectorinthetimedomain
f Acousticfrequency
ac
c Soundvelocity
1.1 Introduction
Aerospaceturbopumpsusuallyuselabyrinthgassealstopreventthegasdrivingtheturbinetoleakinthegapbetweenthe
rotorandthestatorparts.Currenttrendsinturbopumpsdesignfocusontheminimizationoftheclearances,soastooptimise
theefficiency,andonthereductionofthestatorweight.However,thesetrendsmayleadtoaeroelasticinstabilityissueswhich
candamagethestructuressurroundingthelabyrinthgasseal,mainlystaticpartsaccordingtopost-mortemobservations.
Sincethe1960s,studieshavebeencarriedouttobetterunderstandandpreventsuchinstabilities.Alford[2]wasthefirst
to show that the side support location of the seal has an importance in preventing self-excited vibrations. Alford discloses
alsoastabilitycriterionwhichcorrelatespressuredropinthesealtonaturalfrequency,weight,andlength.Asecondcriterion
islatersuggestedbyAbbot[1],involvingthelocationofsidesupport.Hisworkrevealsthatifthesupportislocatedonthe
highpressureside,thesealisstableaslongasthemechanicalfrequencyislowerthantheacousticone.Thephenomenonis
reversedwhensupportislocatedonthelowpressureside.
Totacklethesenewchallenges,morepredictivemodelsmustbedevelopedinordertotakethestatorflexibilityandthe
leakages reduction issues into account. The purpose of this work is to carry out a numerical investigation on an advanced
labyrinth gas seal model involving a non-deformable rotor, and a flexible stator. The flexibility of the static part induces
pressureandvelocityfluctuationswithintheleakageflow.Themodelretainsseveralcavitiesdefinedbytheteethlocatedon
theshaftandastrongcouplingbetweenthefluidandthestructureisassumed.
1.2 StrongFluid-Structure Coupling
The model governing the behaviour of the flow within a cavity is inspired by Childs analytical model and Navier-Stokes
equations [3]. The model describing the flow is then coupled to a mechanical system corresponding to a flexible stator
(cf. Fig. 1.1b). A cylinder model, which takes into account the diameter modes in the plane orthogonal to the flow and a
normalizedlongitudinaldisplacementfollowingthefirstbendingmode,isused(cf.Fig.1.1c).Thenormalizedlongitudinal
displacement is assumed to be proportional to the square of the distance from the bearing location. Assuming a strong
couplingimpliesthattheactionofthefluidtothestructureistakenintoaccountandconversely.Itisespeciallyinteresting
toworkwithastrongcouplingforasuchconfinedenvironment.
y
y
x x
2Rs 2Rs
2Rc mean2Rc
(a) (b) (c)
Fig.1.1 (a)Childs’smodel:ellipticmovementoftherotor,non-deformablerotor,non-deformablestator.(b)Flexiblecylindermodel:fixedand
non-deformablerotor,fixedandflexiblestator.(c)Flexiblecylindermodel:visualisationofnormalizedlongitudinaldisplacementfollowingthe
firstbendingmode
1 Fluid-StructureInteractioninaLabyrinthGasSealCoupledtoaFlexibleStator 3
Thestructurecanbesupportedonthelowpressuresideaswellasonthehighpressureside.Takingintoaccount these
boundaryconditionsallowsacomparisonwiththeresultsgivenbyAbbott[1].
Thecoupledsystemobtainedismadeofnonlineardifferentialequations.Toovercomethesenonlinearities,aperturbation
methodisused.Itconsistindeterminingapproximatesolutionsofthenonlinearequationsbyapowerseriesofascalefactor
parameter((cid:2))associatedtothenonlineartermsandtruncatedatthefirstorder.Thismethodallowstoturnanonlinearsystem
intoasetoflinearproblems.Thesolutioncanbewrittenasfollow:
yi.N;t;(cid:3)/Dy0iC(cid:2)y1i.N;t;(cid:3)/ (1.1)
wheretheperiodicfunctiony1i issoughtintheform:
XN (cid:2) (cid:3)
y1i.N;t;(cid:3)/D xnc;i.t/cos.n(cid:3)/Cxns;i.t/sin.n(cid:3)/ (1.2)
nD1
withn,correspondingtothenumberofharmonicsoftheFourierseries,ithecavitynumber,(cid:3) theangularposition.Atzeroth
order ((cid:2) D 0), the nonlinear differential equations become state equations describing the mean leakage flow, pressure and
circumferentialvelocitywithintheseal(withoutanystatordisplacement).Theflowbecomessonicjustaftergoingthrough
thelasttooth.Then,atfirstorder,thesystemissolvedbyreplacingthevariabley1ibyitsexpression(1.2),andsearchingfor
the values fxn;i;xn;ig. These coefficients are related to three variables : radial displacement, circumferential velocities, and
pressureswithincavities.
Tosolvethistwo-dimensionalproblem,aGalerkinapproachwithaFouriertransformwithrespecttothespacevariables,
isused.Thesystemcanbedescribedbythesecondorderhomogeneousdifferentialequation:
MXR CCXP CKX D0 (1.3)
whereXisthecoefficientsvectorfxc ;xs gwithnD1;:::;NcorrespondingtothetrigonometricfunctionsinEq.(1.2).
n;i n;i
The model comprises a pre-rotating flow which can be combined with the axial leakage flow, in addition to the shaft
rotation.Becauseofthecircumferentialvelocitywithineachsealcavity,shearstressincircumferentialdirectionareacting
onbothstatorandrotorwalls.Inthiswork,themodelisextendedtoseveralcavities.Theupstreamanddownstreamcavities
modalparticipationsareconsideredwithinthenthcavityequations
1.3 ValidationoftheZeroth Order
Thetablebelow(cf.Table1.1)givesanaxialmassflowratecomparisonbetweencurrentworkandcalculationsfoundinthe
literatureforvalidationpurposes(Fig.1.2).
Table1.1 Comparativeaxialmassflowrateandpressuresdistributionswithinthelabyrinth
seal
Currentwork Dursen[4] Rosen[6] Experimental[4]
Massflowrate(kgs(cid:2)1) 0:02036 0:02072 0:02117 0:02
Pressurewithincavity(kPa) 225:447 224:592 222:781 222:5
Seal operating conditions Seal geometry
Inlet pressure 241.3 kPa No. of teeth 2
Outlet pressure 206.8 kPa Shaft radius 101.60 mm
Inlet temperature 298.2 K Clearance 0.16 mm
Inlet swirl velocity 16.8 m/s Tooth pitch 12.91 mm
Shaft rotational speed 1800 rpm Tooth height 5.03 mm
Tooth tip width 0.20 mm
Fig.1.2 Sealgeometryandstudyconditions[4]