Modern flexible multi-body dynamics modeling methodology for flapping wing vehicles

183 Pages·2018·3.499 MB·English

by  Altenbuchner, Cornelia, Hubbard, James Edward

MODERN FLEXIBLE
MULTI-BODY
DYNAMICS MODELING
METHODOLOGY FOR
FLAPPING WING
VEHICLES
CORNELIA ALTENBUCHNER
NASA Jet Propulsion Laboratory, Pasadena, CA, USA
JAMES E. HUBBARD JR.
University of Maryland, Way Hampton, VA, USA
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and grace of nature.
PREFACE
During the past decade the Nation has seen a surge of interest in small un
mannedvehicles.Therehasbeenaparticularfocusonbio inspiredflightasa
design paradigm for these platforms. The application of biomimetic princi
plestothedevelopmentofsmallunmannedvehiclesspansthescaleofflight
from insects to avian flyers. Biomimetics is defined as the imitation of the
models,systems,andelementsofnatureforthepurposeofsolvingcomplex
problems. Researchers, engineers, hobbyist, and aircraft designers all over
the world now use nature to inspire and inform the design of modern un
manned platforms. There is no doubt that animal flight has played such a
role for centuries, but recent times have seen an increased interest.
Avian inspired birdlike robotic designs have given rise to modern orni
thopters whose aerodynamic and kinematic properties are marginally pre
dictable and can produce nonlinear behaviors, which are time varying and
involve multiple dynamic scales. The goal of the work presented herein is
to develop canonical modeling techniques that can drive the engineering
design of avian scale flapping wing ornithopters.
Our approach to the modeling of such a complex vehicle is an energy
based Lagrangian approach that includes the flexible multi body dynamics
characteristic of this class of platforms. We are particularly interested in
developing a model form and function suitable for feedback control. This
will allow the work here to form the basis of algorithms, which can be
implemented for improved agility, stability, lift, and thrust.
In developing the approach presented here the authors worked closely
withNASAengineers,dronepilots,academicscholars,anddesignerstoun
derstandthesubtletiesoflowReynoldsnumberflightanditsassociateddy
namics and aerodynamics. We are particularly grateful for the insights and
assistance of Dr. Marty Wazak of the NASA Langley Research Center,
Dr. Jared Grauer and Dr. Aimy Wissa formerly of the University of Mary
landMorpheusLaboratory,andtheauthorshipandeditingassistanceofMs.
Debbie McFee. Finally, we are also grateful for the support of the NASA
Langley Research Center, theNationalInstitute of Aerospace,theUniver
sity of Maryland, the Air Force Office of Scientific Research, and the
Morpheus Laboratory.
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ix
LIST OF FIGURES
Figure1.1 Flightcapabilityofflappingwingflyers. 2
Figure1.2 Missionapplicationsforunmannedairvehicles.(A)Civilianand
(B)Military. 3
Figure1.3 (A)Naturalflyersdemonstrateglide,hover,dive,andperch.(B)
Exampleofmaneuverabilityperformanceofnaturalflyers. 4
Figure1.4 Conceptvehicleexhibitadjustablestiffnessacrossthewing. 5
Figure1.5 Fuselagebodyaccelerationsinstate-of-the-artflappingwing
robotic. 6
Figure1.6 Positionstateoffuselageofornithoptertestplatform. 7
Figure1.7 Liftandthrustgeneratingmechanismsofflappingwingflight(A)
downstrokeand(B)upstroke. 9
Figure1.8 Wingtippathasindicatorordominantwingmotionshownon
naturalflyers(A)albatrossinfast-forwardflightmode,(B)pigeon
in slow flight mode, (C) horseshoe bat in fast-forward flight
mode,and(D)horseshoebatinslowflightmode. 11
Figure1.9 Passivewingmorphing.(A)Bioinspiredtestplatformwing
morphing though thrust flap region and (B) radical shape
morphingwing. 16
Figure1.10 Activewingmorphingbioinspiredtestplatform.(A)Ornithopter
platform. (B) Extended half wingspan versus retracted half
wingspan. 16
Figure1.11 Firstornithoptervehicledesigns.(A)DaVincis1490and(B)
Lilienthal1894. 17
Figure2.1 Ornithopterschematic:rigidmulti-bodysystem. 24
Figure2.2 Ornithopterschematic:linearelasticmulti-bodysystems. 24
Figure2.3 Ornithopterschematic:nonlinearelasticmulti-bodysystems. 25
Figure2.4 SimXpert:flexiblemulti-bodydynamicsmodelimplementation. 31
Figure2.5 SimXpert:Imageoffullyintegratedflexiblemulti-bodydynamics
modelofornithopter. 32
Figure2.6 Ornithoptervehicledynamicsmodels.(A)Singlerigidbody,(B)
rigidmulti-bodydynamics,and(C)flexiblemulti-bodydynamics
model. 33
Figure2.7 Quasi-steadybladeelementmodel. 38
Figure2.8 CFDanalysisshowing(A)vorticitycontoursontheflexible
deformed wing and (B) deformed grid at 50% span location
duringupstrokeofthewingatstartofupstroke. 42
Figure2.9 Rigid-bodyornithopterfitinflighttestdataforaerodynamic
modelstructuredetermination. 43
Figure2.10 Modelingmethodology:workflowstage1. 44
Figure2.11 Modelingmethodology:workflowstep2. 45
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xi
xii ListofFigures
Figure2.12 Modelingmethodology:workflowstep3. 45
Figure2.13 Modelingmethodology:workflowstage4. 45
Figure2.14 Modelingmethodology:workflowstage5. 46
Figure2.15 Modelingmethodology:workflowstage6. 46
Figure2.16 Modelingmethodology:workflowstage7. 46
Figure3.1 PrimarytestplatformMorpheusLabcustom-buildtest
ornithopter(ML101). 51
Figure3.2 SecondarytestplatformmodifiedornithopterShawnKinkade
(MSK004). 52
Figure3.3 Wingstructurebioinspiredornithoptertestplatform(ML101). 52
Figure3.4 Designfeaturewingspars(ML101);(A)leadingedgespar,(B)
diagonalspar,(C)fingerspar(ML101). 52
Figure3.5 Schematicandnomenclaturestiffeningcarbonfiberspar
configuration. 52
Figure3.6 Abat(Cynopterusbrachyotis)inflight. 53
Figure3.7 Lowerwingsurfaceofanaturalavianflyerphoto. 54
Figure3.8 Designfeaturetail(ML101). 54
Figure3.9 Designfeaturefuselage(ML101). 54
Figure3.10 Definitionflappingangleandupstrokeanddownstrokeon
shoulderjoint/barlinkage(ML101). 56
Figure3.11 Upstrokeanddownstrokesequenceornithopter(ML101)scale. 56
Figure3.12 MSK004wingswithtrackingmarkers. 57
Figure3.13 MSK004andViconcamerasystemforthemeasurementof
ornithopterwingandconfigurationmotions. 58
Figure3.14 Harmonaerodynamicmodelresultsandbenchtestresults
measured integrated forces ML101 at 5 Hz flapping frequency,
over a flapping cycle t/T, (A) vertical propulsive force (VPF), (B)
horizontalpropulsiveforce(HPF),(C)normalizedFA. 59
Figure3.15 HarmonbenchtestresultsmeasuredintegratedforcesML101at
5 Hz flapping frequency, over a flapping cycle t/T, (A) vertical
propulsive force (VPF), (B) horizontal propulsive force (HPF)
versusnormalizedflappingangle(FA). 59
Figure3.16 Harmonaerodynamicmodelresultsandbenchtestresults
measuredintegratedforcesML101at6.17Hzflappingfrequency,
over a flapping cycle t/T, (A) vertical propulsive force (VPF), (B)
horizontalpropulsiveforce(HPF),(C)normalizedflappingangle
(FA). 60
Figure3.17 HarmonbenchtestresultsmeasuredintegratedforcesML101at
6.17Hzflappingfrequency,overaflappingcyclet/T,(A)vertical
propulsive force (VPF), (B) horizontal propulsive force versus
normalizedflappingangle(FA). 60
Figure3.18 ResultsandbenchtestresultsmeasuredintegratedforcesML101
versus flapping frequency, over a flapping cycle t/T, (A) mean
absolute value vertical propulsive force (MAVPF), (B) mean
horizontalpropulsiveforce(MHPF)versusflappingangle. 61
ListofFigures xiii
Figure3.19 ViconVisionwingkinematicsequencedthreepositionstate
trackingmarkersi¼1e110,(A)isometricview,(B)sideviewina
fuselagefixedreferenceframeCB0. 62
Figure3.20 Viconcamerasystemforthemeasurementofornithopterwing
andconfigurationmotions. 62
Figure3.21 AerodynamicforcesonthewingsdresultssystemIDmodelby
Grauer.FA,flappingangle;HPF,horizontalpropulsiveforce;VPF,
verticalpropulsiveforce. 63
Figure3.22 Asymmetricretroreflectivemarkersonthewing(seenaswhite
dots)andwingtiplocation(markedinred). 64
Figure3.23 RetroreflectivemarkerpositiononthewingmeasuredwithVicon
Visionsystemmarkersi¼1e53.Markersi¼1e5weremountedon
thefuselage. 65
Figure3.24 ImagesmallUnmannedAerialSystemflighttestfacilitydVicon
Visionsystemcameras. 65
Figure3.25 Testsetupschematicdtestchamberdimensions:700(W)(cid:2)350(D)
(cid:2)350(H). 66
Figure3.26 Schematicornithopterandreferenceframesusedforthe
processingoffree-flighttestdata. 67
Figure3.27 Datasetmarkerpositionduringfreeflightintheinertiareference
frameCI0. 68
Figure3.28 Datasetmarkerpositioni¼1e53duringfreeflightintheinertia
referenceframeCI0dviewZI0/ZI0. 68
Figure3.29 Datasetmarkerpositioni¼1e53duringfreeflightintheinertia
referenceframeCI0dviewYI0/XI0. 69
Figure3.30 Positionstatesalltrackingmarkersonthewing/volumeshows
testdatausedformodeldevelopmentd3.5flappingcycles. 69
Figure3.31 Singlepositionstateonornithoptershowsalltrackingmarkers
i¼1to53inthefuselagefixedreferenceframeCB0. 70
Figure3.32 Verticalpropulsiveforcesactingonthefuselagecenterof
massdobtained from experiment. VF, vertical force; HF,
horizontalforce;FA,flappingangle. 70
Figure3.33 VacuumchamberatNASALangleyResearchCenter.(Left)Test
platform mounted on six degrees of freedom load cell, (Right)
vacuumchamber. 71
Figure3.34 ResultsofvacuumchambertestML101testplatformversus
flapping frequency, (A) inertial horizontal propulsive force IHPF
(B) inertial horizontal propulsive force (C) inertial pitching
moment(IPM)versusmagnitude. 72
Figure4.1 Schematicfive-bodydynamicssystem. 80
Figure4.2 Schematicinertialandfuselagebodyfixedreferenceframes. 81
Figure4.3 Schematicwingfixedreferenceframes. 81
Figure4.4 Articulatedmulti-bodysystemrepresentationoftheornithopter. 82
xiv ListofFigures
Figure4.5 Positionvectorofrigidmulti-bodymodelofornithopter. 89
Figure4.6 Positionvectorofflexiblemulti-bodymodelofornithopter. 90
Figure4.7 Schematicnotationdefinitionforgeneralizedcoordinatesofthe
flexiblemulti-bodysystem. 92
Figure4.8 Positionvectorofflexiblemulti-bodymodelofornithopter,luff
region[blue(darkergrayinprintversions)andred(lightgrayin
print versions)], thrust flap region [orange (dark gray in print
versions)andred(lightergrayinprintversions)]. 94
Figure4.9 Schematicfiniteelementmodelwingstructurecarbonfiberspars
andwing. 103
Figure4.10 Thrustflapregionmeshnodes¼352,elements¼860. 105
Figure4.11 Thrustflapregionmodeshapescontourplot. 105
Figure4.12 Modelimageflexiblewingcomponentconnections. 106
Figure5.1 Bladeelementgridschematicaero-modelA. 111
Figure5.2 (A)Bladeelementgridschematicaero-modelB.(B)Blade
element(BE)gridschematicaero-modelC. 111
Figure5.3 Variablesforcalculationofaerodynamicforces. 115
Figure5.4 ML101ornithopterconfigurationbladeelement(BE)selection. 119
Figure5.5 Bladeelement(BE)selectionthrustflapregionML101
ornithopterconfiguration. 119
Figure5.6 Aerodynamicloadsmodeldworkflow.FMBD,flexiblemulti-body
dynamics. 120
Figure5.7 AerodynamicloadsmodeldworkflowAeroLoadInitialized
ExperimentalCoupled.FMBD,flexiblemulti-bodydynamics. 122
Figure6.1 IsometricviewofthepositionstatespathofallViconmarkers
overoneflappingcycleat6.06Hz. 129
Figure6.2 SideviewofthepositionstatespathofallViconmarkersoverone
flappingcycleat6.06Hz. 130
Figure6.3 TopviewofthepositionstatespathofallViconmarkersoverone
flappingcycleat6.06Hz. 130
Figure6.4 Topviewoftheornithoptermarkerspositionstate0deflection
plane. 131
Figure6.5 TopviewoftheYcoordinateflexibilityinthewingfixed
referenceplaneCW. 132
Figure6.6 TopviewoftheXcoordinateflexibilityinthewingfixed
referenceplaneCW. 132
Figure6.7 Bioinspiredornithoptertestplatforminfreeflight:three
experimental orientations during a wing beat: viewed in the
fuselagebodyfixedreferenceframeCB0. 133
Figure6.8 WingfixedreferenceframeCW. 134
Figure6.9 Bioinspiredornithoptertestplatformwinginfreeflight:maximal
elasticdeflectionsofthewinginthewingfixedreferenceframe
during a wing beat; viewed in the fuselage fixed reference
frameCB0. 135
ListofFigures xv
Figure6.10 Bioinspiredornithoptertestplatformwinginfreeflight:maximal
occurringelasticdeformationinthethrustflapregionofthewing
inthewingfixedreferenceframeCW. 135
Figure6.11 BioinspiredornithoptertestplatformML101winginfreeflight:
maximaloccurringelasticdeflectionsluffregioninthewingfixed
referenceframeCW. 136
Figure6.12 Bioinspiredornithoptertestplatformwinginfreeflight:maximal
occurring elastic deflections of the wing fixed reference frame
duringawingbeat;viewedinthefuselagereferenceframeCB0. 136
Figure6.13 SchematiclocationthrustflapregionreferenceframeCBT. 137
Figure6.14 Bioinspiredornithoptertestplatformwinginfreeflight:X-axisof
modeledthrustflapregionreferenceframein34positionstates
viewedinthefuselagefixedreferenceframeCB0. 137
Figure6.15 Bioinspiredornithoptertestplatformwinginfree-flightmarker
location: XBT-axis location on experimental test platform
resulting in minimal deformation of a reference YBT/ZBT
referenceplaneusinga1degreeoffreedomflappingmotion. 138
Figure6.16 Flappinganglezetaandbetalocationonshowninexperimental
wing test data (maximal deformation of CW,0 reference plane,
andXBTpositionstates). 139
Figure6.17 Modeledflappingangle(FA)timehistorybasedonflighttest
dataversusFAinflighttestdataE-2. 139
Figure6.18 Experimentalthrustflapreferencemotionin34positionstatesin
thefuselagefixedreferenceplaneCB0. 140
Figure6.19 Modeledthrustflapreferencemotionin34positionstatesinthe
fuselage fixed reference plane CB0 versus wing at zero
deformation(PS0). 141
Figure6.20 Experimentalelasticdeflectionsinthefuselagefixedreference
frameCB0duringawingbeat. 142
Figure6.21 Experimentalelasticdeformationinthewingfixedreference
frameCWduringawingbeat. 142
Figure6.22 ModelimageSimXpertdML101five-bodyflexiblemulti-body
dynamicsmodel(fuselagereferenceframeCBishighlighted). 143
Figure6.23 Verificationbenchtestdmodel3AdscaleML101(6.17Hz).
FMBD,flexiblemulti-bodydynamics;HFI,horizontalforceinertia;
HPF,horizontalpropulsiveforce;VPF,verticalpropulsiveforce. 145
Figure6.24 Wingtiplocationdviewedatoneexperimentalpositionstate
(mid-downstroke). 146
Figure6.25 Resultswingkinematicsmodel5experiment:flighttest:(left)
backviewand(right)sideview. 147
Figure6.26 Propulsiveforcesactingonthefuselagecenterof
massdobtained from experiment (E-2) and five-body vehicle
dynamicsmodelusingaerodynamicmodelC. 148
Figure6.27 SimulatedinertiaforcesonfuselagecenterofmassCBinfree
flight (inertial vertical propulsive force)dupstrokeedownstroke
transition. 149
xvi ListofFigures
Figure6.28 Resultsinertiaforces(E3)witherrorbarsversussimulationresults
withSTD,(A)inertialhorizontalpropulsiveforce(IHPF),(B)inertial
verticalpropulsiveforce(IVPF),(C)inertialpitchingmoment(IPM)
versusmagnitude. 150
Figure6.29 Results:bodyforcemagnitudesystemIDmodel(MSK004E1-I)d
bodyforcemagnitudedaero-modelC. 152