On the Mechanics, Computational Modeling, and Design Implementation of Piezoelectric Actuators on Micro Air Vehicles

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Title:
On the Mechanics, Computational Modeling, and Design Implementation of Piezoelectric Actuators on Micro Air Vehicles
Physical Description:
1 online resource (236 p.)
Language:
english
Creator:
Lacroix, Bradley W
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering, Mechanical and Aerospace Engineering
Committee Chair:
IFJU,PETER G
Committee Co-Chair:
SANKAR,BHAVANI V
Committee Members:
HAFTKA,RAPHAEL TUVIA
MYERS,MICHELE V

Subjects

Subjects / Keywords:
composite -- fiber -- flying -- macro -- materials -- mav -- mfc -- morphing -- optimization -- piezoelectric -- smart -- uav -- wing
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre:
Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
This document details the research performed on applying piezoelectric macro fiber composite actuators on micro air vehicles. The research objective was to apply the minimum number of macro fiber composites to the aircraft in an optimized manner in order to obtain complete control authority. To do this, a local-global approach was taken. Numerical predictions, experiments, and finite element models were used to model the macro fiber composites in a local manner, approximating the curvature of the actuator when bonded to a substrate. The substrate was selected to maximize the curvature when submitted to expected loads. In a global manner, the design of the aircraft was optimized, using a computational model, to provide the largest control authority under expected flight conditions. A variety of experimental tests were conducted to create an accurate aeroelastic computer model, including tests to determine material properties, static loading tests, and wind tunnel testing. Two of the optimized designs were tested in the wind tunnel to verify the predicted improvement, which confirmed the accuracy of the computer model. Other experimental results are also included, including experiments examining the unimorph fabrication technique, rigid assumptions used for the aerodynamic model, and high frequency dynamics of the macro fiber composite unimorph.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Bradley W Lacroix.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: IFJU,PETER G.
Local:
Co-adviser: SANKAR,BHAVANI V.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0046212:00001


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ON THEMECHANICS,COMPUTATIONALMODELING,ANDDESIGN IMPLEMENTATIONOFPIEZOELECTRICACTUATORSONMICROAIRVEHICLES By BRADLEYW.LACROIX ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2013

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c r 2013 BradleyW.LaCroix 2

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I dedicatethisdocumenttoMikayla,mypartnerinlife,whohasenduredtheeraticand taxingschedulethatcomeswithcompletingaPhD.Ialsodedicateittomyparents,who haveunrelentlesslyencouragedandsupportedmethrougheverystepofmyeducation. 3

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A CKNOWLEDGMENTS ThankyoutoDr.PeterIfjuforguidingmethroughtheoftenlargeandambiguous worldofuniversityresearchandkeepingmefocusedonmyendgoal.Inaddition,thank youtomycommitteemembers,Dr.RaphaelHaftka,Dr.BhavaniSankar,andMichele Manuelforyourextensivehelpthroughthisprocess. ThankyoutoKevinShortelle,KyuhoLee,andBillGrahamofSystemDynamics Internationalforyourendlesssupportandpatienceinthenumerousexperimentsand ighttestsranthroughouttheprocessofthisresearch. ThankyoutoMikeSytsmaforhismanyhourshelpingmeattheREEFwindtunnel. Withoutyourhelp,Iwouldhavebeenspendingalotmoretimeatthewindtunneland accomplishingalotless. Also,abigthankstoJasonCantrellforsteppinguptohelpwheneverIneededa hand.Thisincludesthenumeroushoursintheon-campuswindtunneltryingtosalvage theoutdatedwindtunnelsystem. AspecialthankstoKelseyDyalandChrisGardiner,whohavehelpedme immeasurablybyputtinginnumeroushoursinthedesign,fabrication,andtestingof MAVsandtestxtures. Finally,thankyoutoAnirbanChaudhuriwhoprovidedmesignicantadviceand insightintotheapplicationofoptimizationtothisresearch. ThisresearchhasbeenfundedinpartbyAirForceResearchLaboratories(AFRL)DistributionA.Approvedforpublicrelease,distributionunlimited.(96ABW-2013-0381) 4

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T ABLEOFCONTENTS page A CKNOWLEDGMENTS ..................................4 LISTOFTABLES ......................................9 LISTOFFIGURES .....................................10 ABSTRACT .........................................18 CHAPTER 1INTRODUCTION ..................................19 1.1HistoricalBackgroundandApplications ..................19 1.2MacroFiberCompositesinDetail .....................20 1.3Motivation ..................................24 2PRIORAPPLICATIONSOFMFCSONUAVS ..................28 2.1ApplicationofMFCsonUAVs .......................28 2.2AlternativeMorphingTechnologies ....................37 2.3Discussion ..................................39 3PRELIMINARYANALYSIS .............................41 3.1Overview ..................................41 3.2BimetallicBeamNumericalApproximation ................42 3.3ClassicalLaminatePlateTheory(CLPT) .................44 3.4DiscussionandFurtherComparison ...................47 4COMPOSITEMATERIALSTESTING .......................49 4.1TensileTests ................................50 4.1.1Setup .................................50 4.1.2Results ................................50 4.2CantileverTests ...............................53 4.2.1Experiments .............................55 4.2.2FiniteElementModel ........................57 4.2.3Results ................................58 5MFCFREESTRAINEXPERIMENTALTESTS .................60 5.1Setup ....................................60 5.2ProcedureandResults ...........................61 5.3ElectricalSetup ...............................63 5

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6 UNIMORPHMODEL,EXPERIMENTALVALIDATION,ANDDESIGN SPACEEXPLORATION ..............................66 6.1AdhesionMethod ..............................66 6.2ExperimentalComparisonofMFCs ....................70 6.3SubstrateComparison ...........................71 6.4ComparisonBetweenExperimentalandFiniteElementResults ....73 6.4.1FiniteElementModel ........................73 6.4.2ExperimentalProcedure ......................73 6.4.3Results ................................74 6.5DesignSpaceExploration .........................75 6.6AlternativeDesigns .............................77 6.6.1BimorphConguration .......................78 6.6.2PrecompressedActuators .....................81 6.6.3LIPCAActuators ..........................83 7FOURPOINTBENDTESTS ...........................85 7.1Setup ....................................85 7.2Procedure ..................................86 7.3Results ....................................87 8INITIALMAVDESIGN,LESSONSLEARNED,ANDVALIDATIONOF AERODYNAMICMODELASSUMPTION ....................90 8.1Manufacturing ................................90 8.2DICTesting .................................92 8.3FlightTesting ................................94 8.4DiscussionandLessonsLearned .....................94 8.5AerodynamicAssumptionValidation ...................95 8.5.1BackgroundandConceptOutline .................96 8.5.2InitialExperiments .........................98 8.5.2.1Manufacturing ........................98 8.5.2.2TestingProcedure ......................100 8.5.2.3DigitalImageCorrelationPostProcessing .........101 8.5.3RigidWingManufacturing .....................104 8.5.3.1ExtrapolationandConversionofDICDatatoCNCFormat 104 8.5.3.2Fabrication ..........................105 8.5.4ValidationExperiments .......................107 8.5.5Discussion ..............................109 9FORWARDSWEPTMAV .............................110 9.1ConceptEvaluation .............................110 9.2Motivation ..................................113 9.3PrototypesandFlightTesting .......................114 9.3.1FirstPrototype-Testingtheforwardsweptwingdesign .....114 6

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9.3.2 SecondPrototype-Testingelevoncontrol ............116 9.3.3ThirdPrototype(MFC1)-ImplementingMFCs ..........117 9.3.4FourthPrototype(MFC2)-Anattempttoimproverollcontrol ..119 9.4WorkbenchTesting .............................121 9.4.1MFC1Tests .............................121 9.4.2MFC2Tests .............................122 9.5FiniteElementModel ............................122 9.5.1ModelSetup .............................122 9.5.2ConvergenceAnalysis .......................123 9.6ModelValidation ..............................125 9.6.1MFC1 ................................125 9.6.2MFC2 ................................131 9.6.3Discussion ..............................132 10AEROELASTICMODEL ..............................133 10.1ComputationalModel ............................133 10.1.1ABAQUS ...............................133 10.1.2AthenaVortexLattice(AVL) ....................135 10.1.3CouplingABAQUSandAVL ....................137 10.2WindTunnelTests .............................138 10.2.1Facilities ...............................138 10.2.2Setup .................................140 10.2.3Procedure ..............................140 10.3Results ....................................142 10.3.1DICResults .............................142 10.3.2AerodynamicResults ........................145 10.4Discussion ..................................149 11OPTIMIZATIONROUTINE .............................152 11.1ImplementationofOptimizationScheme .................156 11.1.1LatinHypercubeSampling(LHS)ofDesignSpace .......156 11.1.2EGOOptimization ..........................159 11.1.3Fmincon ...............................166 11.1.4ResultsandDiscussion .......................169 11.2ApplicationtoaRearSweptWingDesign ................171 11.2.1MaintaininganAnalogousComparison ..............171 11.2.2LatinHypercubeSampling(LHS)ofDesignSpace .......173 11.2.3EGOOptimization ..........................175 11.2.4Fmincon ...............................175 11.2.5ManualTestCase ..........................179 11.2.6Discussion ..............................180 7

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12 CONCLUDINGTESTS ...............................182 12.1Manufacturing ................................182 12.2Procedure ..................................182 12.3Results ....................................184 12.3.1DICResults .............................184 12.3.2EffectsofSpeed ...........................188 12.3.3AerodynamicResults ........................188 12.4Conclusion .................................195 APPENDIX ADIGITALIMAGECORRELATION(DIC) .....................197 BUSINGDICDISPLACEMENTSTOCALCULATESTRAIN ...........202 CUNIMORPHBANDWIDTHMEASUREMENT ..................204 C.1HighSpeedCameraSetup ........................204 C.2Analysis ...................................205 C.3Results ....................................205 DMFC1ANDMFC2WORKBENCHCOMPARISONS ...............208 D.1MFC1 ....................................208 D.2MFC2 ....................................210 D.2.1Noactuation .............................210 D.2.2Noload ................................212 D.2.3LV1500RV1500 ...........................215 D.2.4LV-500RV-500 ...........................218 D.2.5Miscellaneous ............................221 EMFC1AEROELASTICCOMPARISONS .....................222 FSMARTMATERIALSCORPORATION'SMFCENGINEERING PROPERTIES ...................................225 REFERENCES .......................................227 BIOGRAPHICALSKETCH ................................236 8

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LIST OFTABLES T able page 1-1 ThethreeMFCsexaminedduringtheinitialphaseofthisresearch ......23 4-1Summaryoftensiontestsamplesandtheirrespectiveelasticmoduli .....54 4-2Dimensionsforthebendingsamples .......................57 4-3Finiteelementpropertiesforunidirectionalandbidirectionalcarbonber ...58 5-1FreestrainvaluesusedintheFEAmodel ....................64 8-1Resultsofrigidandexiblewingcomparison ..................109 10-1MFC2qualityoftforeachcongurationtested .................143 11-1Boundsforforwardsweptoptimizationdesignregion ..............160 11-2BestcasesfromEGOandfmincon(Table1/2) .................167 11-3BestcasesfromEGOandfmincon(Table2/2) .................167 11-4Boundsforrearsweptoptimizationdesignregion ................174 11-5BestcasesfromEGOandfminconforrearsweptwing(Table1/2) ......179 11-6BestcasesfromEGOandfminconforrearsweptwing(Table2/2) ......179 12-1MFC13qualityoftforeachcongurationtested ................185 12-2MFC14qualityoftforeachcongurationtested ................188 E-1MFC1qualityoftforeachcongurationtested .................222 9

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LIST OFFIGURES Figure page 1-1 M8528-P1MFCactuatormanufacturedbySmartMaterialsCorp .......20 1-2ApplicationofpiezoelectricsonthetailofamodelF/A-18toreducebuffeting 21 1-3Expandedviewofthemateriallay-upoftheSmartMaterialsCorpMFC ...22 1-4ThethreeMFCsthatwereconsideredduringtheinitialphaseofresearch ..23 1-5OneoftherstMAVsmanufacturedwithMFCs .................25 2-1ThinairfoilMFCresearchconductedbyBilgen .................29 2-2ThickairfoilMFCresearchconductedbyBilgen .................29 2-3MFCactuatedthick-airfoilliftanddragcoefcientsbyBilgen ..........30 2-4MAVwithMFCactuatedrollcontrolbuiltandtestedbyBilgen .........31 2-5OptimizedMFCwingbyParadies .........................32 2-6EAPskindesignresearchbyWickramasinghe .................32 2-7Post-buckledprecompressedwinggeometrybyVos ..............34 2-8Post-buckledprecompressedwingactuationbyVos ..............34 2-9MFCactuatedwingdesignbyOhanian ......................35 2-10MFChysteresismeasurementsandlinearizationconductedbyOhanian ...36 2-11Lifttodragresultsandpowerconsumptionofthehighvoltageelectronics ..37 3-1Illustrationofbendinginaunimorph .......................42 3-2CurvatureaspredictedbyBimetallicBeamTheory ...............44 3-3CurvatureaspredictedbyClassicalLaminatePlateTheory(CLPT) ......47 3-4PercentdifferencebetweenCLPTandBimetallicBeamTheory ........48 4-1ThetwotypesofcarbonberusedintheMAVmanufacturingprocess ....49 4-2Tensiontestsamples ................................51 4-3Tensiontestsetup .................................51 4-4Stress-straincurvesfortensiletestsamples ...................52 4-5ResultingstrainfortheSample2btensiletest ..................53 10

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4-6 Acloserlookatwovencarbonber ........................54 4-7Testsamplesusedforthecantileverbendingtests ...............55 4-8Cantileverbendingtestsetup ...........................56 4-9Bidirectionalcompositeapproximationforniteelementmodel ........58 4-10Resultsfromthecantileverbendingtests ....................59 5-1Experimentalsetupusedtomeasurefreestrain .................60 5-2ExperimentallydeterminedfreestrainfortheM8528-P1MFC .........62 5-3FreestrainapproximationforFEAmodel .....................63 5-4WiringsetupforMFCactuation ..........................64 5-5Measurementerrorinvoltagereadingbasedonresistorselection .......65 6-1CantileveredunimorphDICsetup .........................67 6-2Unimorphspreparedforcantileverloadingexperiments ............67 6-3ExampleofbondinganMFCtounidirectionalcarbonberpre-preg ......68 6-4Comparisonofthreeadhesiontechniques ....................69 6-5Steelsubstratepartiallypreparedforbonding ..................70 6-6SteelsubstrateandMFCpreparedandreadytovacuumbag .........70 6-7Experimentalcantileverresultsforthethreeunimorphs .............71 6-8Cantileversubstratecomparison .........................72 6-9ExampleofFEAcantilevermodel .........................73 6-10FEAandDICevaluationofaunidirectionalcarbonberunimorph .......74 6-11Evaluationofthe0.05mmsteelunimorph ....................75 6-12Evaluationofthe0.10mmsteelunimorph ....................75 6-13FEAunimorphcomparisonbetweenthreethicknessesofsteelsubstrate ...76 6-14FEAunimorphcomparisonbetweentwoepoxythicknesses ..........76 6-15FEAunimorphtipdisplacementforvarioussubstrates(1500V) ........77 6-16FEAunimorphtipdisplacementforvarioussubstrates(-500V) ........77 6-17Illustrationofbimorphactuation ..........................78 11

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6-18 PredictedcurvatureofabimorphusingCLPT ..................79 6-19Comparisonbetweenunimorphsandbimorphs .................79 6-20FEAbimorphtipdisplacementvssubstratemoduliandthickness .......81 6-21FEAbimorphtipdisplacementvssubstratemoduliandthickness .......81 6-22Predictedbehaviorofprecompressedbimorphs(PBP) .............82 6-23ThedesignsmodeledinFEAsimilartotheLIPCAlayups ...........83 6-24TheresultsoftheLIPCAFEAmodelsvsastandardunimorphsample ....84 7-1Fourpointbendtestsetup .............................86 7-2Fourpointbendtestprocedure ..........................88 7-3Fourpointbendexperimentalresults .......................89 8-1ImagesoftherstMFCactuatedMAV ......................91 8-2ManufacturingoftherstMFCactuatedMAVwing ...............91 8-3DICsetupforrstMFCactuatedMAVwing ...................92 8-4DigitalimagecorrelationresultsfortherstMFCactuatedMAV ........93 8-5Conceptualillustrationofrigidvs.exiblewingloading .............97 8-6Flipsideviewofsiliconemembranewings ....................97 8-7Isometricviewofsiliconemembranewings ...................99 8-8FlexiblewingwindtunnelsetupwithDIC .....................100 8-9Flexiblemembranewinginthewindtunnel ...................101 8-10IllustrationofDICpostprocessingprocedure ..................103 8-11DICresultsforbattenreinforcedexiblemembranewing ............103 8-12DICresultsforperimeterreinforcedexiblemembranewing ..........103 8-13GeometricedgetruncationofDIC ........................104 8-14ExtrapolationofDICdatatorestoreuncorrelatedgeometry ..........105 8-15Smoothingtechniqueforextrapolateddata ....................106 8-16Illustratedrigidwingmanufacturingprocess ...................106 8-17Rigidwingcounterparts ..............................107 12

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8-18 Comparisonofexibleandrigidbattenreinforcedwings ............108 8-19Comparisonofexibleandrigidperimeterreinforcedwings ..........108 9-1DesignconsiderationsforMFCplanform .....................111 9-2Illustrationofanisotropicwingvsabend-twistcoupledwing ..........112 9-3Firstprototypeoftheforwardsweptwing .....................115 9-4Therevisedversionoftherstprototype .....................115 9-5Thesecondprototype ...............................116 9-6Initialforwardsweptwingdesignconcept ....................117 9-7TherstMFCprototype,MFC1 ..........................118 9-8Steelsubstratetestsection ............................120 9-9ThesecondMFCprototype,MFC2 ........................120 9-10Diagramoftheloadingpointsfortheworkbenchtests .............121 9-11LoadingpointsfortheMFC1andMFC2 .....................122 9-12TheworkbenchsetupforMFC1 ..........................123 9-13TheworkbenchsetupfortheMFC2 ........................124 9-14FEAlayoutoftheMFC1andMFC2wings ....................124 9-15Pointsexaminedfortheconvergenceanalysis ..................126 9-16Meshesconsideredintheconvergenceanalysis ................127 9-17Seedspacingvsnumberofelementsandcomputationaltime .........128 9-18Seedspacingvsresultingdisplacements ....................128 9-19MFC1workbenchcomparisonLV-500RV-500 ..................129 9-20MFC1workbenchcomparisonLV0000RV1500 .................129 9-21MFC1workbenchcomparisonLV0000RV0000RLE100 ............130 9-22MFC1workbenchcomparisonLV0000RV1500RTE20 .............130 9-23MFC2LV0000RV0000LLE-100gRLE-100g ..................131 9-24MFC2LV1500RV-500 ...............................131 9-25MFC2LV-500RV-500LTE-20gRTE-20g .....................132 13

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10-1 ExampleoftheAthenaVortexLattice(AVL)interface ..............136 10-2Overviewoftheprogrammingarchitecturefortheaeroelasticmodel .....137 10-3TheREEFwindtunnel ...............................139 10-4Close-upofwindtunnelsetup ...........................139 10-5Theoverallwindtunnelsetup ...........................141 10-6Illustrationoftheout-of-planetare ........................143 10-7ComparisonofMFC2niteelementmodeltoexperimentalresults(nowind) .144 10-8ComparisonofMFC2niteelementmodeltoexperimentalresults(15m/s) .146 10-9MFC1pitchandrollcomparison .........................147 10-10MFC1pitchcomparison(fullvshalfactuation) ..................148 10-11MFC1rollcomparison(fullvshalfactuation) ...................148 10-12MFC2pitchrangecomparison ..........................149 10-13MFC2rollrangecomparison ...........................150 10-14MFC2comparisonbetweenrst&secondsetofmeasurements(pitch) ...151 10-15MFC2comparisonbetweenrst&secondsetofmeasurements(roll) ....151 11-1Variablesensitivity(Page1of2) .........................154 11-2Variablesensitivity(Page2of2) .........................155 11-3LHSdesignmethodology .............................158 11-4LHSdesignregion .................................159 11-5ExamplesofthreeLHSdesigns ..........................159 11-6ConceptualillustrationofEGOmethodology ...................161 11-7LHSDesignandEGOresults ...........................163 11-8LHSandEGOdesignpoints ...........................163 11-9EGOpresentbestsolutionduringoptimizationcycles .............164 11-10TopveEGOdesigns ...............................165 11-11Exampleofanunsymmetriclayupexhibitingwarping ..............166 11-12Localfminconoptimizationforthefmincon13design ..............168 14

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11-13 Localfminconoptimizationforthefmincon14design ..............169 11-14Paretofrontfortheforwardsweptoptimization ..................170 11-15ComparisonbetweentheoriginalMFCprototypesandoptimizeddesigns ..171 11-16Centerofgravitydeterminationfortherearsweptwing .............172 11-17Forwardandrearsweptboundaryconditions ..................173 11-18ExamplesofthreerearsweptLHSdesigns ...................174 11-19LHSdesignandEGOresultsfortherearsweptwing ..............176 11-20EGOpresentbestsolutionduringoptimizationcycles .............176 11-21TopveEGOresultsfortherearsweptwing ...................177 11-22Localfminconoptimizationfortherearsweptdesign ..............178 11-23Side-by-sidecomparisonofoptimizedforwardsweptandrearsweptdesigns 178 11-24Paretofrontfortherearsweptoptimization ...................180 11-25Rearsweptuser-speciedtestcase .......................181 12-1Windtunnelsetupforsecondseriesoftests ...................183 12-2ManufacturingoftheMFC13wing ........................183 12-3RepairmadetotheMFConMFC13 .......................184 12-4ComparisonofMFC13FEAmodelandexperimentalresults(nowind) ....186 12-5ComparisonofMFC13FEAmodelandexperimentalresults(15m/s) .....187 12-6ComparisonofMFC14FEAmodelandexperimentalresults(nowind) ....189 12-7ComparisonofMFC14FEAmodelandexperimentalresults(15m/s) .....190 12-8MFC13deformationundervariousvelocities ...................191 12-9MFC14deformationundervariousvelocities ...................191 12-10MFC13pitchcomparison .............................192 12-11MFC13rollcomparison ..............................193 12-12MFC14pitchcomparison .............................194 12-13MFC14rollcomparison ..............................195 A-1DICconceptualillustration .............................197 15

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A-2 DICexamplepattern ................................198 A-3DICsetup ......................................199 A-4DICsetupinthewindtunnel ............................200 A-5DICofarotatingUAVpropeller ..........................201 B-1Calculationofstraincomponents .........................202 C-1Highspeedcamerasetupfordynamictesting ..................204 C-2Unimorphdynamicspost-processing .......................205 C-3M8528-P1unimorphdynamicsat1Hz ......................206 C-4M8528-P1unimorphdynamicsfrom5-40Hz ..................207 D-1MFC1workbenchcomparisonLV0000RV0000RPZ20 .............208 D-2MFC1workbenchcomparisonLV0000RV0000RTE20 .............208 D-3MFC1workbenchcomparisonLV0000RV1500RLE100 ............209 D-4MFC1workbenchcomparisonLV0000RV1500RPZ20 .............209 D-5MFC2LV0000RV0000LLE100gRLE100g ...................210 D-6MFC2LV0000RV0000LTE20gRTE20g .....................210 D-7MFC2LV0000RV0000LTE-20gRTE-20g ....................211 D-8MFC2LV0000RV0000LPZ20gRPZ20g .....................211 D-9MFC2LV0000RV0000LPZ-20gRPZ-20g ....................212 D-10MFC2LV0000RV1500 ...............................212 D-11MFC2LV1500RV0000 ...............................213 D-12MFC2LV1500RV1500 ...............................213 D-13MFC2LV-500RV1500 ...............................214 D-14MFC2LV-500RV-500 ...............................214 D-15MFC2LV1500RV1500LLE100gRLE100g ...................215 D-16MFC2LV1500RV1500LLE-100gRLE-100g ..................215 D-17MFC2LV1500RV1500LTE20gRTE20g .....................216 D-18MFC2LV1500RV1500LTE-20gRTE-20g ....................216 16

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D-19 MFC2LV1500RV1500LPZ20gRPZ20g .....................217 D-20MFC2LV1500RV1500LPZ-20gRPZ-20g ....................217 D-21MFC2LV-500RV-500LLE100gRLE100g ....................218 D-22MFC2LV-500RV-500LLE-100gRLE-100g ...................218 D-23MFC2LV-500RV-500LTE20gRTE20g ......................219 D-24MFC2LV-500RV-500LPZ20gRPZ20g .....................219 D-25MFC2LV-500RV-500LPZ-20gRPZ-20g .....................220 D-26MFC2LV-500RV-500LPZ-20gRPZ-20gLLE-100gRLE-100g ........221 D-27MFC2LV1500RV0000LLE-100gRLE-100g ..................221 E-1ComparisonofMFC1FEAmodeltoexperimentalresults(nowind) ......223 E-2ComparisonofMFC1FEAmodeltoexperimentalresults(15m/s) ......224 17

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Abstr actofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy ONTHEMECHANICS,COMPUTATIONALMODELING,ANDDESIGN IMPLEMENTATIONOFPIEZOELECTRICACTUATORSONMICROAIRVEHICLES By BradleyW.LaCroix December2013 Chair:PeterG.Ifju Major:MechanicalEngineering Thisdocumentdetailstheresearchperformedonapplyingpiezoelectricmacro bercompositeactuatorsonmicroairvehicles.Theresearchobjectivewastoapply theminimumnumberofmacrobercompositestotheaircraftinanoptimizedmanner inordertoobtaincompletecontrolauthority.Todothis,alocal-globalapproachwas taken.Numericalpredictions,experiments,andniteelementmodelswereusedto modelthemacrobercompositesinalocalmanner,approximatingthecurvatureof theactuatorwhenbondedtoasubstrate.Thesubstratewasselectedtomaximize thecurvaturewhensubmittedtoexpectedloads.Inaglobalmanner,thedesign oftheaircraftwasoptimized,usingacomputationalmodel,toprovidethelargest controlauthorityunderexpectedightconditions.Avarietyofexperimentaltests wereconductedtocreateanaccurateaeroelasticcomputermodel,includingteststo determinematerialproperties,staticloadingtests,andwindtunneltesting.Twoofthe optimizeddesignsweretestedinthewindtunneltoverifythepredictedimprovement, whichconrmedtheaccuracyofthecomputermodel.Otherexperimentalresultsare alsoincluded,includingexperimentsexaminingtheunimorphfabricationtechnique, rigidassumptionsusedfortheaerodynamicmodel,andhighfrequencydynamicsofthe macrobercompositeunimorph. 18

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CHAPTER 1 INTRODUCTION 1.1HistoricalBackgroundandApplications Thepiezoelectriceffectwasrstdiscoveredin1880byFrenchphysicistsJacques andPierreCurie[ 1].ItisderivedfromtheGreekwordmeaningtopressandcan bedescribedasamechanicalforceresultingfromanelectricalinputorconversely, amechanicalinputresultinginanelectricaloutput.Piezoelectricdeviceswererst implementedintheearly1920sasquartzcrystalstabilizedelectricaloscillatorsand shortlythereafterincorporatedintohighfrequencyradiotransmitters[ 2].WorldWarI broughtgreatattentiontowardspiezoelectrictechnologywiththeinventionofsonar[ 3]. Incrementaladvancementshavetakenplaceduetodiscoveriesofnewpiezoelectric materialssuchasbariumtitanate( BaTiO 3 )andsinglecrystallithiumniobate( LiNbO 3 ). Theseadvancementshaveexpandedtheuseofpiezoelectrics,whichhavebeenutilized indevicesrangingfromphonographstomicrophonestoaccelerationsensorstoink-jet printers. Originally,piezoelectricactuatorswerelimitedtosmalldisplacementapplications, suchaspreciseopticalpositioning[ 4]andpiezoelectricmotors[ 5, 6],butrecent advancementshaveallowedpiezoelectricactuatorstoachievenewlevelsofstrain. MacroFiberComposites(MFCs),whicharedescribedinthenextsection,offera previouslyunseenexibilityandactuatedstrainthathasopenedthedoorforseveral innovationsandresearchareas.OnesuchMFCisshowninFig. 1-1,whichmeasures 112mm(4.4inches)by40mm(1.6inches)andiscapableofproducing1800 InitiallydevelopedbyNASA[ 8 ],MFCshavealsomadetheirwayintosporting applications.Inskiing,theyhavebeenimplementedinskistoactivelydampen vibrations[ 9].Intennis,piezoelectricdeviceshavebeenincorporatedintotheracket toorientthedirectionoftheforcewhilestiffeningtheracketforultimatepower.Theyalso helptoreducevibrationsintheracket,therebyimprovingcomfort[ 10].Piezoelectrics 19

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Figure 1-1.M8528-P1MFCactuatormanufacturedbySmartMaterialsCorp.[7].Photo takenbyBradleyLaCroix. alsoholdalargepresenceinenergyharvesting,especiallyinremote,off-the-gridlow powerdeviceswhichoperateforlongperiodsoftime[ 11].Intheseapplications,the piezoelectricsareabletoharvestenergyfromvibrationsoruidoscillations. Inaerospaceapplications,piezoelectricactuatorshavebeenutilizedinanarray ofaircraft.Theyhavebeenusedonhelicopterrotorsforactivetwistcontrolonthe orderof 1 withoutaddingexcessiveamountofmass[12 ]aswellasvibration dampening[ 13, 14].Researchhasalsobeenconductedinapplyingpiezoelectric actuatorstotheverticaltailofanF/A-18,asseeninFig. 1-2,toreducebuffetloads. Intheseexperiments,rootstrainswerereducedbyupto60%athighanglesof attack[ 15 16 ].AdditionaltestsshowedthattheMFCscouldreduceboththebending andtorsionmodesofthetailnsufcientlydoublingthefatiguelife[ 17]. MFCshavealsobeenusedinstructuralhealthmonitoringofUAVsusingacoustic guidedwaves[ 18 19 ].Intheseapplications,theMFCsystemisabletodetermine delaminationanddamageduetodebondingofjoints.Theresearchrelatestohealth monitoringratherthanactuation,andisthereforebeyondthescopeoftheresearchin thisdocument. 1.2MacroFiberCompositesinDetail Thepiezoelectricactuatorsstudiedwithinthisprojectareofaspecictypetermed MacroFiberComposites(MFCs).TheywererstdevelopedbyNASAin1996and 20

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Figure 1-2.ApplicationofpiezoelectricmaterialsonthetailofamodelF/A-18toreduce buffeting.PhotocourtesyofNASA[ 16]. thenenteredcommercialproductionin2002bySmartMaterialCorporation[ 11 20 ]. Piezoceramicsthemselvesareextremelybrittleandthereforecannotbeeasily conformedtocurvedsurfaces.Theyareverysusceptibletobreakageduringhandling andbondingprocedures.Toresolvetheseissues,thepiezoceramicsareembedded intheirbrousphaseinacompositematerial.Thesecrystallinematerialshavea muchhigherstrengthintheberform,wherethedecreaseinthevolumefractionof awsleadstoanincreaseinspecicstrength.Additionally,theexiblenatureofthe polymermatrixallowsforthematerialtoconformtocurvedsurfaces[ 20].MFCshave anadvantageovertraditionalpiezoelectricsinthattheyareexible,haveimproved reliability,andexhibitrelativelyhighstrainwhenactuated. AnexpandedviewofaSmartMaterialsCorporationMFCisshowninFig. 1-3 (adapted from[ 7 ]).MFCsuseaninterdigitatedelectrodepatterntodelivertheelectriceldalong theentirelengthofthebers.Thisrequiressolidbondingbetweenthematrixandbers totransferactuationloadstotheexternalsurfaceofthedevice.Inmanufacturing,the bersoftheMFCaremachinedfromlow-costpiezoceramicwafersusingacomputer controlleddicingsaw.Thebersarethenplacedinbetweentwoseriesofelectrodes 21

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Figure 1-3.Expandedviewofthemateriallay-upoftheSmartMaterialsCorporation MFC(adaptedfrom[7]). withepoxyandvacuumpressedwithheatedplatens.Afterfabrication,thepiezoceramic materialispoledbyapplying1500Vtotheinterdigitatedelectrodesforapproximately 1minute[ 21 ]. TheMFCsareavailableascommercialoff-the-shelfcomponentsandareofferedin avarietyofsizes.OneMFC,theM8528-P1,isquotedasbeingcapableofastrainrange of1800 .ThethreeMFCsconsideredthusfarinthisresearchareshowninFig. 1-4 withthepropertiesdescribedinTable 1-1.TheMFCsarenamedaccordingtothelength andwidthoftheactiveareaoftheMFCandtheactuationdirection.Forexample,if thepiezoelectricportionoftheMFCis85mmlongand28mmwide,itisgiventhe designation'8528'.The'P1'indicatesthatitisanelongatingMFC,whichutilizesthe d33effectforactuation,whereasthe'P2'and'P3'designationsarereservedforthe contractingMFCswhichutilizethed31effectforactuation.Thereisalsoatwisting actuatorwiththebersorientedat45 designatedby'F1'. Electrically,theMFCsfunctionalmostidenticallytocapacitors.Whenavoltageis applied,theMFCstoresthechargepotentialacrossthepiezoelectric.Whenthevoltage potentialisremoved,thepotentialremains,butitisslowlydissipatedthroughtheslightly less-than-idealelectricalinsulation.Allofthe'P1'typeactuatorsacceptaninputvoltage 22

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Figure 1-4.ThethreeMFCsthatwereconsideredduringtheinitialphaseofresearch. Fromlefttoright:M8528-P1,M8507-P1,andM8503-P1.Phototakenby BradleyLaCroix. Table1-1.ThethreeMFCsexaminedduringtheinitialphaseofthisresearch. MFC OverallOverallStrainBlockBlockForce Length,Width,Range,Force,peractivewidth, mmmm NN/mm M8528-P1 11240180045416.2 M8507-P11011313808712.4 M8503-P1110141050289.3 of -500Vto1500VwhichiseasilyconnectedthroughtheexposedleadsontheMFC (silverincolor),ascanbeseeninFig. 1-4.Whilethisvoltageissubstantiallyhigher thanthatsuppliedbytraditionalpowersystemsonMAVs,itisachievablebytheproper amplicationhardware.Specialtysystems,describedinSection 5.3,allowforthehigh voltagetobeobtainedusingatraditional11.1VLiPobattery.Furthermore,Williams notesthattheMFCscansafelybeactuatedto1700Vwithoutnegativeeffects[ 22], 23

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which couldpotentiallyincreasethestrainrangebeyondtheirquotedvalues.Additional specicationsfortheMFCsareprovidedinAppendix F. 1.3Motivation MAVsareidealplatformsforMFCsbecauseoftheirrelativesize.Duetothe lowReynoldsnumbersthatMAVsyat,airfoilthicknessisnolongerbenecialfor ightperformance.Athinundercamberedairfoilisthepreferredsolution,reducing dragandimprovingstability[ 23 24 ].Inaddition,owseparationoverconventional controlsurfacescancausedrag,whereasasmoothmorphingcontourcanimprove efciency[ 2529].Furthermore,duetothesmallsizeofMAVs,asmallactuationcan producealargeresponse. OnepotentialalternativeinvestigatedearlyonwhenconsideringdesignsforMFCs onMAVswastheoptiontoincorporatemembranematerialwithinasupportingstructure. Utilizingamembranewing,wherecarbonberlaminateisreplacedwithaexible membranesuchassiliconeorripstoppolyestercanreducethewing'sexuralstiffness, therebymakingmorphingmoreeasilyrealized.FlexiblemembraneMAVwingshave beenstudiedattheUniversityofFloridaforoveradecade.Theyprovideanumberof performanceimprovementssuchasadaptivewashoutforgustrejection,ightstability, anddelayedstall[ 30, 31].Figure 1-5 showsanexampleofoneoftherstMAVs manufacturedwithMFCsandaripstoppolyestermembranewing.Chapter 8 detailsthe variousaspectsofthisdesign.Laterworkfocusedonamainlycarbonberwingandis coveredindetailinChapter 9.Flighttestsshowedthatthiswasamorestabledesign andbetterdistributedtheMFCactuationacrossthewingforimprovedcontrolauthority. Servomotors,termedservosforshort,haveconventionallybeenusedinsmall unmannedairvehicles(UAVs).Servosaremotorsconnectedinparallelwithanencoder toprovideconstantfeedbacksotheirpositionisknownatanytime.Theyprovidean economicalandeffectivewayofactuatingcontrolsurfaces.However,theirrateof actuationislimitedtoapproximately1-2Hz.MFCsarecapableofactuatingatmorethan 24

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Figure 1-5.OneoftherstMAVsmanufacturedwithMFCs.Themembraneisripstop polyesterwithaDICspecklepatternapplied.MFCsareappliedtothe undersideofthebattens.PhototakenbyBradleyLaCroix. anorderofmagnitudefasterat25Hzormore[ 29, 32].Independenttestswerealso conductedwithahighspeedcameraandtheresultsexaminedinAppendix C.Theshort reponsetimeopensthepossibilityofactivegustsuppressionandimprovedightcontrol. MFCsarealsosolidstatewhichprovidestwodistinctadvantages.Firstly,theMAV canbeenvironmentallysealed,withthemotorandelectronicsencasedwithinthe fuselage.Thisisolatestheelectronicsfromwaterandcorrosion.TheMFCs,placed ontheexteriorsurfaces,areweatherproofandarenotnegativelyaffectedbysand, dirt,orwaterwhichcandamagegeardrivenservos.Secondly,theMFCsarecapable ofwithstandinghighaccelerationwithoutdegradationofresponse,excludinginertial considerations.Thisopensthepossibilityforhighaccelerationmaneuversandhigh accelerationlaunches,suchasballistics. Moreover,theproleoftheMFCisextremelythinwhichmakesthevolumeofthe actuatornegligible.Flexibilityinpositioningisaffordedsincethehighvoltageelectronics andcontrolscanbeplacedanywhereontheaircraftasopposedtoaservowhich necessitatesamechanicallinkagetothecontrolsurface.Sincethewingcanbemade withouthingesandcontrolrods,thepartcountissignicantlyreduced[ 29 32 ].Instead, 25

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MFCs mountedtothesurfaceofthewingcanactivelymorphthestructuretoachieve ightcontrol.Thewingstructureandtailsurfacescansmoothlymorphintodifferent shapesquicklyandseamlessly. Byconversionofelectricalenergydirectlytomechanicalenergy,MFCseliminate complicateddeviceswithseveralparts,andalsooffersuperiorenergyefciency.In anearlyapplicationofpiezoelectricstoUAVs,asimilarMFCwasmeasuredtohavea powerconsumptionof65mWcomparedtothatofatradtionalservoof2500mW[ 33]. InanotherresearchUAV,powerconsumptionwasdecreasedfrom24Wto100mWand currentdrawwascutfrom5Ato1.4mA[ 32, 34].Amajorityofthepowerconsumption isthroughthethelossofefciencyviathehighvoltageelectronicsratherthantheMFC itself.Inaddition,thelifecycleofanMFCisgreaterthan10billioncycles[ 7, 11 ],so failureduetonormaluseisnotaconcern. InordertooptimizetheoverallperformanceofaMAVttedwithMFCs,nite elementanalysis(FEA)isessential.Furthermore,sincethewingisrelativelyexible, theFEAsimulationmustbeiteratedwithuid-structureinteractiontocreatean aeroelasticsimulation.Thesimulationunlocksthepotentialforexploringnumerous designpossibilitiescomputationallyratherthanexperimentallytestingeachdesign.A combinationofMATLAB,ABAQUS(FEA),andAthenaVortexLattice(AVL)[ 35]were utilizedforthispurpose.Furthermore,withpropervalidation,thismodelcanbeusedto conductafullscaleoptimizationinwhichanumberofvariablesareconsideredduring theoptimizationscheme. Intheend,theworkinthisresearchwasapproachedinalocal-globalmanner.For instance,signicantresearchwasconductedonthelocalbehaviorofMFCstoimprove thedegreeofactuationacheivedbyanindependentunimorphconguration.Thiswork examinedvarioussubstratematerialsandadhesiontechniques.Aglobalapproachwas alsoconductedtooptimizetheoverallwingdesigntoimprovethecontrolauthorityofthe 26

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o verallaircraft.Thisportionoftheresearchexaminedtheplacementandorientationof theMFCaswellasthelayupofthewingstructure. Thedetailsaboutthisresearcharedescribedinthefollowingchaptersofthis document.Butrst,aliteraturereviewispresentedinthenextchapterdetailingprevious MFCresearchandaircraft. 27

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CHAPTER 2 PRIORAPPLICATIONSOFMFCSONUAVS 2.1ApplicationofMFCsonUAVs UnmannedAirVehicles(UAVs)haveproventobeanidealtestplatformforMFCs andothermorphingtechnologyduetothemoremanageablecostrequirements,relative easeofmanufacturing,andfortunateremovalofconcernforthesafetyofahumantest pilot[ 36 37 ].Asaresult,agreaterlevelofriskcanbetakenwithUAVs.Therefore, UAVsmakeidealtestplatformsforemergingtechnologies,includingMFCactuators. Thischapterisdedicatedtothediscussionofvariousmorphingtechnologiesandhow theyrelatetotheresearchinthisdocument. TherstresearchdiscussedwillbetheworkofOnurBilgen,astudentofDaniel J.Inman.AgreatdealofresearchonMFCsandtheirapplicationtoMAVshasbeen performedunderbothDanielJ.InmanandOnurBilgen[ 26 28 3840]. Inoneproject,abimorphcongurationwasimplementedinavariablecamber,thin airfoilintendedforaductedfanaircraft[ 38 ].ThebimorphwasasandwichoftwoMFCs withasheetof25.4 m stainlesssteel.Thevariablecamberairfoil,showninFig. 2-1A, wassimplysupportedattwopoints.Thepinlocationwasoptimizedandthesetuptested atvariousightconditions.Thedisplacementwasmeasuredwithaerodynamicloadsfor asinglesetofpinconditionsandtheresultsareshowninFig. 2-1B.Thetrailingedgetip displacementinthiscaseisapproximately19.5mmforanactuationrangeof-1400V to1400V.Hysteresis,duetothepiezoelectricmaterial,isespeciallynoticeableatthe pointsdesignatedbythecirclesinFig. 2-1B wheretheairfoilissweepingdown(red circles)andsweepingup(blackcircles)stoppingat0Vduringeachsweep. Bilgenalsomadeathickairfoilsectionusingapairofbimorphs,inwhichone bimorphwastheupperairfoilsurfaceandtheotherbimorphwasthelowerairfoil surface[ 39].ThisairfoilwasalsointendedforuseonaductedfanMAVandagainused 25.4 m stainlesssteelasthesubstratematerial.Theairfoil,aswellastheactuated 28

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A B Figure 2-1.ThinairfoilMFCresearchconductedbyBilgen[ 38] c r IOPPublishing. Reproducedwithpermission.Allrightsreserved.A)Athin,bimorphairfoil comprisedoftwoMFCswithasheetof25.4 m stainlesssteelsandwiched inbetween.Theairfoilissimplysupportedattwolocationsbythepins protrudingfromtheedges.B)Displacementresponseoftheairfoilwhen actuatedfrom-1400Vto1400Vandfrom1400Vto-1400Vwiththe calculatedcamberforeachactuationlisted. A B Figure 2-2.ThickairfoilMFCresearchconductedbyBilgen.Photoscourtesyof Bilgen[39 ].A)Unactuatedbimorphairfoil.B)Actuatedbimorphairfoiltothe twoextremepositionsaswellastheunactuatedposition. positions,areshowninFig. 2-2.Atotalliftcoefcientchangeof1.54wasobserved purelythroughtheactuationoftheMFCs.ThisisexempliedinFig. 2-3 wherethelift anddragcoefcientsareplottedversusMFCactuationvoltage. 29

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A B Figure 2-3.MFCactuatedthick-airfoilliftanddragcoefcients.Photoscourtesyof Bilgen[39 ].A)Liftcoefcientvsangleofsupports.B)Dragcoefcientvs angleofsupports. Althoughthereisnomentionoftrailingedgetipdeection,theeffectiveangleof attackandcamberwerecalculatedfortheactuatedpositions.Theeffectiveangleof attackhadarangeof10.7 andthecamberchangewas7.59%forthepeak-to-peak actuationrange.Bilgenalsonotesthatnomeasureabledeformationoccuredfrom aerodynamicloading.Furthermore,thisresearchshowedthatasignicantchangeinlift canbeachievedwitharelativelysmalldragpenaltybywayofvoltageactuation. Buildingonthisresearch,BilgenbuiltaMAVwithawingspanofapproximately 2.5feet(0.76m),asshowninFig. 2-4 [27 28 ].TheMFCsusedwereM8557-P1, whicharedoublethewidthoftheM8528-P1mentionedinSection 1.2 .TheMAVwas successfullytestownforatotalofapproximately15minutes.However,thepilotnoted thattheaircraft'scontrolauthoritywaslimitedwhenusingtheMFCs.Althoughthe authordoesnotexplicitlynoteit,itisprobablethataeroelasticityandcontrolreversal playedalargeroleinthecontrolauthorityoftheaircraft.AnadditionalpairofMFCs wereaddedaftertheinitialighttesting.However,windtunneltestingshowedonlya smallincreaseincontrolauthorityandintheformofmixedresultsduetotheforward positioningofthesecondsetofMFCs. 30

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A B Figure 2-4.MicroairvehiclewithMFCactuatedrollcontrol.Photoscourtesyof Bilgen[39 ].A)CompletedMAVshownwithMFCs.B)ThesameMAVduring ighttesting. Inrelatedresearch,ParadiesoptimizedtheMFCandsubstratesectionlocallyas wellastheoverallwingdesign[ 41 ].Inhiswork,hecoupledtheniteelementsolverof ANSYS c r ,withthecomputationaluiddynamicssolver(CFD)ofANSYS c r toiteratively calculatethedeformedshapeofthewinggeometryandthenoptimizethedesignand placementoftheMFCs.Figure 2-5 showsthenalsandwichdesignandthelocationof theMFCs.Thenalcross-sectionwascomposedofcarbonbercomposite,AIREX c r foamcore,andglassreinforcedcompositelaidupusingawetlay-upmethod.The designwascapableof4.3mmtipdeectionwhichgeneratedarollmomentof0.17N m. WorkbyWickramasingheprovidesyetanotherdesign,asshowninFig. 2-6,which incorporatesanElectroactivePolymer(EAP)skinalongwithabimorphconguration. Thebimorphiscomposedofanaluminumsubstrate,76 m thick,sandwichedin betweentwoMFCsandadheredusingepoxyandvacuumpressure[ 42].EAPsproduce increasedtensionwhenactuated.Therefore,theskincouldaidinthetipdisplacement oftheairfoilbyactuatinginconjunctionwiththebimorph.Inthisdesign,theEAP isimplementedasaskinonthetrailingedgeofthewinginwhichtheribisentirely composedoftheMFCbimorph.Coincidentally,theEAPactuationvoltageisthesame astheMFCs,2000Vpeak-to-peak.Therefore,thissetupbecomesmoreviableasa potentialdesignoption. 31

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Figure 2-5.OptimizedMFCwingdesignbyParadies[ 41] c rIOPPublishing.Reproduced withpermission.Allrightsreserved. A B Figure 2-6.EAPskindesignresearchbyWickramasinghe[ 42] c rIOPPublishing. Reproducedwithpermission.Allrightsreserved.Alsocourtesyofthe NationalResearchCouncil,Canada.A)Illustrationoftheelectroactive polymerdesignforincreasedactuation.B)Smartwinghardwaremodel withouttheEAPskin. Thisresearchshowedpromiseinnumericalmodelsaswellaspreliminary experimentaltests,buttheskincouldnotbeusedduringsubsequenttestingbecauseit couldnotbesufcientlypre-loadedoradheredtothestructure.Specialcarewasalso requiredtoensurethatthecompressiveloadactedexactlyatthelineofsymmetryin ordertoproduceequaldeectioninbothdirections. 32

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Ne vertheless,byutilizinglatexanda40Npre-load,theauthorwasabletoincrease thetrailingedgedeectionfrom8.3 to13.6 .Furthermore,theauthornotesthat deectionsofalmost30 areobtainable.However,thisiswithanassymmetricsetup, sotheresultingcontrolactuationwouldbeapproximately 15 forasymmetricsetup. Convertingthistommdisplacementbyestimatingtheactinglengthresultsinapotential tipdeectionof 2.8cm.Theauthoralsotestedthesetupunderaerodynamicloading andnotedslightaeroelasticdeectionsofthetrailingedgeofabout1 foreachcase tested.Therefore,ifthemanufacturingmethodcouldbeimprovedandmademore reliable,thisdesignwouldbeverypromising. VosandBarretthavedevelopedanoveldesignforMFCactuatorsbyincorporating themintopost-buckledprecompressed(PBP)bimorphs[ 32, 34 43 45 ].PBPbimorphs pre-stressthesubstrateaxiallyinacontrolledmannerbyheatingitupduringthe adhesionprocess.Oncethebimorphcoolstoroomtemperature,itiseffectively pre-stressed.ThePBPbimorphisthenarrangedinasetupwhereacompressive loadisappliedaxially.Theauthorsuseprimarilyaluminumwithathicknessof51 m Withthissetup,Barrettwasabletoachievedeectionsof 6 atratesexceeding 15Hz.Heclaimsthatthisisa4.5foldincreaseinstaticanddynamicdeectionswhen comparedtotraditionalbimorphdesigns.TestingofaVTOLMAVshoweda99.6%drop inpowerconsumption,a7-foldincreaseinbandwidth,87%dropinactuatorweight (excludingnecessaryhighvoltageelectronics),anorderofmagnitudedropinpart count,anda99%cutincontrolsurfaceslop[ 34 ].Furthermore,thePBPbimorphsare designedtoproducesignicantlyhigherforcelevels,therebybeinglesscompliantwhen submittedtoaerodynamicloading[ 43]. FlighttestingforamorphingwingUAV,withcomponentsshowninFig. 2-7, showedanincreaseinrollmomentof38%and3.7timesgreatercontrolderivatives comparedtoconventionalailerons[ 32 ].Inthissetup,benchtestsshowedthataxial compressionofthebimorphsubstrateincreaseddeectionbymorethanafactorof2to 33

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A B Figure 2-7.Post-buckledprecompressedwinggeometry,designedbyVosetal.[ 32] c rIOPPublishing.Reproducedwithpermission.Allrightsreserved A)Illustrationofwingdesign.B)PictureofPBPwingwithlatexskin. Figure 2-8.Post-buckledprecompressedwingactuation.PhotocourtesyofVoset al.[ 32]. 15.25 peak-to-peakandanactuationfrequencyof34Hz.Latexskinwasusedasthe membraneinthisprototype.Theresultingwingandcorrespondingactuateddeectionis showninFig. 2-8. InVos'smostrecentpaper,heclaimedthatthePBPactuatorstrokehada300% largeractuationoverastandardMFCbimorph[ 45 ].Inaddition,hisresearchstudied theendrotationofthePBPasafunctionofaxialforceandexternalmoment.Oncethe loadingincreasesbeyondacertainpoint,thePBPcannolongeractuateagainstthe 34

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moment andcanonlyactuateintheotherdirection.Therefore,forthisdesign,there isatensilefailureboundarythatlimitsthecurvaturepotentialofthebimorph.Asthe curvatureofthebimorphapproachesthislimit,fractureordepolingoftheMFCcan occur. OhanianalsomadeadetailedcomparisonbetweentraditionalservosandMFC actuatedMAVs[ 29].Inhisresearch,hestudiedtheimplementationofMFCsontheAir ForceResearchLaboratory(AFRL)researchMAV,calledGENMAV.Inthiswork,the MFCswereappliedasbimorphsonthetopsurfaceofanairfoilwithapassivewiper surfacefollowingthebimorphpositionthroughoutthefullactuationrangeasseenin Fig. 2-9A.TheimplementeddesignisshowninFig. 2-9B,wheretheMFCbimorphsare locatedontheoutboardportionofthewing. AsseenbyBilgen'sresearch,hysteresisisareoccuringissue.Figure 2-10A shows anexampleofatypicalresponseforanMFCactuatedsurface.Byincorporatinga hysteresisinversionprogramfromareduced-ordermodelofthehystereticbehavior, OhanianwasabletoachieveanearlylinearresponseasseeninFig. 2-10B.Thishas signicantimplicationsregardingtheincorporationofautopilotsystems. Itwasalsoexperimentallyvalidatedthatsmoothcontinuousmorphingsurfaces providehigherlift-to-dragratiosthantraditionalcontrolsurfaces,asseeninFig. 2-11A. A B Figure 2-9.MFCactuatedwingdesignbyOhanian.PhotoscourtesyofAvidLLC[29] A)Illustrationofconcept.B)Resultingwingwithbimorphsimplemented. 35

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A B Figure 2-10.MFChysteresismeasurementsandlinearizationconductedbyOhanian. PhotoscourtesyofAvidLLC[ 29].A)Typicalresponsebythe hysteresis-proneMFCs.B)Linearizedresponseafterimplementinga hysteresisinversionfromareduced-ordermodelofthehystereticbehavior. Inthiscase,thesupportangleisidenticaltotheangleofattack.However,regarding error,thisconclusioncanonlybeimplied,sincetheerrorboundscouldpotentially negateanydifferencebetweenthetwocontrolmethods.Inalaterseriesoftests, Ohanianobservedthatthemorphingaircraftdisplayednegligibledecreasesin velocitywhileexecutingmaneuvers,thereforedemonstratinglowerdragandhigher efciency[ 46]. OhanianvalidatedthattheMFCsarecapableofanorderofmagnitudegreater actuationfrequencythantraditionalservos.Healsoperformedadetailedanalysison thepartcountandweightcomparisonbetweenservosandMFCs.Itwasfoundthat thepartcountwassignicantlyreducedbecausetheconnectingrodsandhinges, transmittingtheloadfromtheservotothecontrolsurface,wereunnecessaryintheMFC aircraft.Inaddition,theweightwasmoderatelyincreased,butstillcomparablebecause ofthehighvoltageelectronics. Contrarytootherresearch,Ohanianexploredthepowerconsumptionoftheentire highvoltagesystem,ratherthanjusttheMFCs.Thehighvoltagepowerboardwas 36

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A B Figure 2-11.Experimentallifttodragmeasurementsandpowerconsumptionofthehigh voltageelectronics.PhotoscourtesyofAvidLLC[29 ].A)Lifttodragratioof thebimorphconguredwingplottedagainstsupportangle.B)Power consumptionofthehighvoltageelectronicsascomparedtoaservo system. designedincollaborationwithAMPowerSystems.Theresults,whichshowthepower consumptionasafunctionofactuationfrequency,areshowninFig. 2-11B.Itcanbe seenthatthepowerconsumptionissimilarbetweentheMFCsystemandthetraditional servosystem,eventhoughthepowerconsumptionoftheMFCsthemselvesaremuch lowerthanservos.Therefore,amajorityofthepowerconsumptioncanbeattributedto thehighvoltageconversion. 2.2AlternativeMorphingTechnologies TheprevioussectiondiscussedrelatedresearchregardingMFCsasmanufactured bySmartMaterialsCorp[ 7].Thissectionintroducesafewsimilarmorphingtechnologies thatutilizeothermodesofactuationtoachievemorphing.Theintentistopresentsimilar morphingplanformsthatcouldhaveapplicabilityintheresearchfoundwithinthis document. Therstitemofinterestisanalternativemacroberpiezoelectricactuatorcalled alightweightpiezo-compositeactuator(LIPCA),whichhasbeenusedinsimilar research[ 47 ].TheLIPCAactuatorutilizesapiezoceramicfoundinanoff-the-shelf 37

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component designatedtheThunder7-R c r .Theoff-the-shelfcomponentincorporates aluminumandstainlesssteeltomaximizebendingactuation,however,toreduce weight,theLIPCAdevicereplacesthemetalcomponentswithberglassandcarbon bercomposites.TheinputvoltageforthispiezoceramicismuchlessthantheSmart MaterialCorp'sMFC,ontheorderof500Vto600Vpeak-to-peak(insteadof2000V peak-to-peak).Assumingthepiezoceramicmaterialbehavesinasimilarmanner,this mayreducetheoverallstrainrangethatcanbeacheivedbytheThunderactuators,and thereforetheoveralldisplacementpotential. Nonetheless,thisresearchintroducesakeynotion:Tomaximizebendingactuation, theneutralaxisofthecross-sectionmustbeoutsideofthepiezoceramicmaterial.In thisresearch,theLIPCA-C1actuatorplacestheneutralaxiswithinthepiezoceramic material,whichtheauthornotescouldpotentiallylimittheoverallactuatordeection. Inlaterresearch,variouslayupswereexploredtoattempttoadjustthepositionofthe neutralaxisaswellastomaximizebendingandreduceweight[ 48].However,outofthe differentlayupstested,thebestdeectionwasonlyontheorderof0.7mm. TheoverallactuationwasincreasedwhentwoLIPCAactuatorswereimplemented onthetopandbottomofanairfoil.Inthissetup,theywereabletoproduceabout1.5cm oftipdeection[ 49].WhilethisdeectionislargerthananindividualLIPCAactuator,itis stillrelativelylimited. Shapememoryalloys(SMAs)haveasimilarbehaviortoMFCsandhaveahigher single-strokeenergydensitywhencomparedtoallcurrentadaptivematerials.However, theysubstantiallylackbandwidth,havesignicanthysteresis,andhavehighpower consumption.SMAactuatedsystemsarealsosignicantlycomplex,thereforemaking themdifculttoimplement.StrelecexaminedtheuseofSMAstomorphanaircraftwing tooptimizeefciencyatdifferentphasesofight[ 50].However,duetothedrawbacks mentioned,SMAswerenotconsideredforthisresearch. 38

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Garcia andAbdulrahimexaminedmorphingintheformofwingtwistonbotha 12inchanda24inchMAV[ 51 52].Theirworkshowedthatwingtwistisaviableand potentiallysuperiormethodforactuatingrollcontrolduringight.TheirMAVwasa similarsizetothelatermodelsconstructedfortheresearchinthisdocument,measuring 24inches.Actuationwascontrolledbyservo-driventorquerodsconnectedtothe membranewingusingkevlarstring.Withthissetup,arollrateof1000 persecondwas achieved.Furthermore,thewingtwistinducedrollsexperiencedalmostnoightpath divergence,implyinganearlypure,uncoupledrollmaneuver. AcoupleofothertwistingwingprototypeswereconstructedbyVosandRicci[53 56].InVos'sdesign,wingtwistwasimposedbyutilizinganinternalscrewanda compliantwingstructure.Preliminarywindtunneltestingshowedthattheliftcoefcient canbeincreasedbyasmuchas0.7foranglesofattackupto12degrees.However, thisdesignwasheavierandhadalargerpartcountthanothermorphingdesigns.In addition,thewingmustbemaderelativelycomplianttoallowforthetwisting,whichmay beanissueathigherowrates. InRicci'sdesign,arotatingribstructureisutilizedtoallowforadaptabilityby adjustingthecamberalongthespan.However,frictionplayedagreaterrolethan expectedwhichcouldlimitactuationperformance.Overall,thismechanismcontains morepartsandissignicantlyheavierthanalternativemorphingstructures.Regardless, itcouldbebetterforscalingupandbettersuitedforlargeraircraft. 2.3Discussion Thischapterintroducedanddiscussednumerousapplicationsofpiezoelectric devicesinavarietyofelds.Eventhoughalloftheresearchisnotdirectlyapplicable totheresearchfoundinthisdocument,theyprovideinsightintopossibledesign considerationsandalternativesthatmaybenettheoveralldesign.Furthermore, theydemonstratedesignsthatdidor,moreimportantly,didnotperformwell. 39

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The mostrelevantresearchitemsincludetheworkwithPBPbimorphsand LIPCAs.Thesetwopotentialdesignsareexaminedusingniteelementmodelingin Sections 6.6.2 and 6.6.3 .Theotherresearch,chieytheworkbyBilgenandOhanian, furtherreinforcetheviabilityofMFCsonMAVs. Beforeproceeding,itisimportanttonotethattheresearchreviewedinthischapter islimitedincertainways.Mostofthedesignsonlyprovidepitchauthorityorroll authority,insteadoffullcontroloftheaircraft.Inaddition,thepiezoelectricdesigns usemultipleactuators,ontheorderof6-8.Thiscanbeaneconomicalconcernsince theactuatorsaccountforthelargestportionofthematerialcosts.Theresearchinthis documentaimstoprovidecompletecontrolauthoritywithonlytwoactuators,therefore reducingthecomplexityofthenecessaryelectronicsandreducingcosts.Thelocal design,implementation,andglobalaircraftoptimizationaretheprimarysubjectofthis research. 40

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CHAPTER 3 PRELIMINARYANALYSIS 3.1Overview Attheinitiationoftheproject,itwasdecidedtoproceedintwodirections.The rst,wasalocalapproachwhichwasintendedtodeterminethebestwaytomount theMFCs,andwhatsubstratematerialtomounttheMFCsto,inordertogeneratethe largestdeection.Itwasexpectedthatvariousmaterialsandsubstratethicknesses wouldgeneratevaryingamountsofdeectionwhenactuated.Theotherplanofattack, wasaglobalapproachtodeterminethebestMAVdesigntoimplementtheMFCson toachievesufcientcontrolauthorityforcontrolledight.Preliminaryresultsshowed thatMFCactuatedsurfacesgeneratedarelativelysmallamountofdeectionwhen comparedtotraditionalservos.ThismeanthatthepositioningoftheMFConthe planformandthedesignoftheplanformisofgreatimportance.Beforerunningany experimentsorcreatingextensivecomputermodels,apreliminarysetofnumerical calculationswereconducted.Thesecalculations,aspartofthelocalapproach,were usedtodeterminetheeffectofthesubstratematerialandthicknessontheresulting curvature. TheMFCitselfproducesverylittlecurvaturewhenitisnotbondedtoasubstrate. ThisisbecausetheMFCisprincipallyalinearstrainactuator,butduetotheslightly asymmetriclayup,asmalldegreeofcurvaturestillresultswhenactuated.Incontrast,a majorityofthecurvatureinaunimorphcongurationisproducedbybondingtheMFC toasubstrate,asshowninFig. 3-1.Curvatureresultswhentwodifferentmaterials arebondedtogetherandstrainofvaryingdegreesisinducedinthematerials.This straincanbeinducedpassivelythroughtemperaturechangesoractively,throughthe applicationofvoltageinaMFCcomposedofpiezoelectricmaterial. WhenthepiezoelectricwithintheMFCisactuated,alinearstrainresultsandthe MFClengthensorshortensbyasmalldegree.WhentheMFCisbondedtoasubstrate, 41

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Figure 3-1.Illustrationofbendinginaunimorph.Out-of-planebendingiscreatedby bondinganMFCtoasubstratematerial. itformsaunimorph,andthesubstrateresiststhestrainoftheMFCtherebycreating curvature.Withnoexternalloadsappliedtotheunimorphcomposite,thecurvatureis relativelypreciseandpredictable. Thischapterpresentsthepreliminarycalculationsforthepredictedcurvature basedonvarioussubstratematerials,suchascarbonbercomposite,steel,and aluminum.Twoapproachesareaddressed,BimetallicBeamNumericalApproximation andClassicalLaminatePlateTheory.TechniquesforbondingtheMFCtothesubstrate arediscussedinSection 6.1. 3.2BimetallicBeamNumericalApproximation Therstequationusedtostudytheimpactofthesubstratematerialonthe unimorphcurvaturewastheBimetallicBeamEquation[ 57 ],showninEq.( 3).This equationisintendedtobeusedfortwometallicmaterialswithdifferingcoefcientsof thermalexpansionanddifferingmechanicalproperties.Furthermore,thisequation assumesthatbothmaterialsareisotropic.ThisisnotnecessarilytruewiththeMFC unimorph,butaswewillseewithClassicalLaminatePlateTheoryinSection 3.3,itstil providesreasonableresults.Thepropertiesaredesignatedwiththefollowingnotation: -coefcientofthermalexpansion, E -ElasticModulus, h -sectionthickness,and T -thechangeintemperaturefromtheinitialtemperature. 42

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= 6 E 1 E 2 (h 1 + h 2 )h 1 h 2 ( 1 )Tj /T1_0 11.955 Tf 11.96 0 Td ( 2 )T E 2 1 h 4 1 + E 2 2 h 4 2 + 4E 1 E 2 h 3 1 h 2 +4 E 1 E 2 h 3 2 h 1 +6E 1 E 2 h 2 1 h 2 2 (3) Thisequationrequiresonlyrelativelyminormodiciationstoachieveaformulation applicabletoMFCs.SincetheMFCistheonlymaterialexhibitingstrain,thethermal expansionportionoftheequation, ( 1 )Tj /T1_0 11.955 Tf 12.49 0 Td ( 2 )T canbereplacedwiththelongitudinal strainoftheMFC, MFC .Next,thenumericalsubscripts,1and2,arereplacedwiththe materialdesignations, MFC and sub ,where MFC designatesthemacrobercomposite and sub designatesthesubstrate.Theresultingequationisshownbelow. = 6 E sub E MFC ( h sub + h MFC )h sub h MFC MFC E 2 sub h 4 sub + E 2 MF C h 4 MFC +4 E sub E MFC h 3 sub h MFC +4 E sub E MFC h 3 MFC h sub +6 E sub E MFC h 2 sub h 2 MFC (3) Thisequationcanberearrangedfurtherbydividingboththenumeratorand denominatorby E sub E MFC and h 2 sub h 2 MFC .ThisresultsinEq.( 3),whichprovides furtherinsightintothecurvatureoftheunimorphasafunctionofthesubstratematerials andtheratiooftheirpropertieswithrespecttotheMFC.Sincethegoalistomaximize curvature,thenumeratormustbemaximizedwhileminimizingthedenominator. BecausetheMFCpropertiesaredeterminedbythemanufacturer,thenumeratorcan onlybeincreasedbydecreasing h sub .Thedenominatorcanbedecreasedbymakingthe ratioofmaterialproperties, E sub E MF C h 2 sub h 2 MF C and h sub h MF C ,ascloseto1aspossible.Inotherwords, increasingthesubstratemoduluswhiledecreasingthesubstratethicknessbyapowerof 2aswellaskeeping h sub and h MFC similarinmagnitude. = 6 1 h sub + 1 h MF C MFC E sub E MF C h 2 sub h 2 MF C + 1 E sub E MF C h 2 sub h 2 MF C +4 h sub h MF C + 1 h sub h MF C +6 (3) Atthispoint,thematerialpropertiesfortheMFCcanbesubstitutedintothe expression.ThepropertiesfortheSmartMaterialsCorporationMFCsare E = 30.3GPa 43

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Figure 3-2.CurvatureaspredictedbyBimetallicBeamTheory. and h = 0.3mm.ThequotedstrainrangefortheM8528-P1MFCis1800 .Withthese valuesincorporated,thereareonlytwovariablesremaining: E sub and h sub .MATLAB wasutilizedtorunthrougharangeofmaterialpropertiesforthesetwovariables. TheresultingplotisshowninFig. 3-2.Thisgureshowsthatastheelasticmodulus increasesandthethicknessdecreases,thecurvatureincreases.Asthethickness approacheszero,thematerialisunabletoresistthestressinducedbythestrain,which drasticallyreducestheresultingcurvature.Variousmaterialsaresuperimposedonthe plottodemonstratetheeffectsofdifferentmaterialsubstrates.Itmustbenotedthat carbonberpre-pregwastheonlymaterialoriginallyconsidered,duetoitseaseofuse inMAVconstructionandavailability.Later,steelandaluminumwerealsoincorporated intotheanalysis. 3.3ClassicalLaminatePlateTheory(CLPT) Analternative,andpossiblymoreaccurate,methodforcalculatingcurvaturecanbe performedbyusingClassicalLaminatePlateTheory(CLPT)[ 58].Thismethodhasbeen 44

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used tomodelMFCsurfacesinotherpiezoelectricresearchaswell[ 26, 44, 48, 59]. Furthermore,CLPTallowsthematerialstobemodeledorthotropically,ratherthan isotropically.SinceMFCsarelinearstrainactuators,theyexhibitthesamemechanical effectsasorthotropicmaterialsundergoingthermalexpansion.Thecurvature, ,canbe predictedusingCLPTwithappliedthermalstresses.InCLPT,thegoverningequationfor thermalstressesinalaminateis: 8 > < > : N M 9 > = > ; 6 x 1 = 2 6 4 AB BD 3 7 5 6 x 6 8 > < > : 0 9 > = > ; 6x 1 )Tj /T1_2 11.955 Tf 11.95 28.1 Td (8 > < > : N T M T 9 > = > ; 6 x 1 (3) Where N and M aretheexternalloadsandmoments,respectively. A represents theextensionalstiffness, B representsthecouplingmatrix,and D representsthe bendingstiffnessesofthelaminate. 0 and arethemid-planestrainsandcurvatures, respectively. N T and M T aretheloadsandmomentscreatedbythethermalstresses. Sincetherearenoexternalloads( N = M =0 ),Eq. 3 canberearrangedasfollows: 8 > < > : 0 9 > = > ; 6x 1 = 2 6 4 AB BD 3 7 5 )Tj /T1_4 7.97 Tf (1 6x 6 8 > < > : N T M T 9 > = > ; 6 x 1 (3) Forlaminateswithdiscretelayers,thestiffnessmatricescanbecalculatedasfollow: [ A ] = n X k =1 Q k h k (3) [ B ] = n X k =1 Q k h k z k (3) [ D ] = n X k =1 h 3 k 12 + h k z 2 k Q k (3) Where Q = T T QT h is thelayerthickness,and z isthedistanceofthemidplane ofeachlayerfromthemidplaneofthelaminate. Q istheinversionofthecompliance 45

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matr ix,usuallydenotedby S ,andisgivenbytheexpression: Q = [ S ] )Tj /T1_4 7.97 Tf (1 = 2 6 6 6 6 4 E 1 1)Tj /T1_7 7.97 Tf 11.02 0 Td ( 12 21 12 E 2 1 )Tj /T1_7 7.97 Tf ( 12 21 0 12 E 2 1)Tj /T1_7 7.97 Tf 11.02 0 Td ( 12 21 E 2 1 )Tj /T1_7 7.97 Tf ( 12 21 0 00 G 12 3 7 7 7 7 5 (3) The straintransformationmatrix,denotedby T ,issimplyanidentitymatrixsince thetwomaterialsareinthesamecoordinatesystem.Therefore, Q = [ Q ] .Thethermal loadsandmoments, N T and M T ,canbecalculatedby: N T = n X k =1 Q k f g k T k h k (3) M T = n X k =1 Q k f g k T k h k z k (3) Thethermalexpansioncoefcent, ,andchangeintemperature, T ,canbe combinedtorepresentthestrainexhibitedintheMFC.SincetheMFCisacommercially available,off-the-shelfcomponent,thepropertiescannotbechanged.Therefore, pluggingintheMFCmaterialproperties( E 1, MFC = 30.3GPa, E 2, MFC = 15.86GPa, G MFC = 5.5GPa, 12 = 0.31, 21 = 0.16,and h MFC = 0.3mm)aswellasthemaximum changeinstrainfrom0V(1350 correspondstothemaximumvoltageof1500V),the curvaturecanbeplottedagainstthesubstratematerialpropertiesforarangeofstiffness andthickness.Note,itwaslaterexperimentallydeterminedthatthestrainrangeofthe MFCwasgreaterthan1800 butthisonlyaffectedthemagnitudeoftheplot,notthe contours. Theshearmodulus, G 12 ,forthesubstratewasapproximatedas5GPaand Poisson'sratio, 12 ,istakentobe0.3.Testingvariousvaluesofsubstrateshear modulus,itwasdeterminedtohavenegligibleeffectontheshapeoftheplot.Figure 3-3 showsthecurvatureplottedagainstthesubstratematerialelasticmodulusand thickness.Itshouldbenotedthat 3 x 1 isactuallythreeterms, x y ,and xy .The 46

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Figure 3-3.CurvatureaspredictedbyClassicalLaminatePlateTheory(CLPT). curvatureplottedisthecurvatureinthelengthdirectionwhichisobtainedbytherst 3x 1 term, x 3.4DiscussionandFurtherComparison Figure 3-3 matchestheoneshowninFig. 3-2 wellintermsofshapeandonlyvaries slightlyinmagnitude.Thisreinforcesthetwosetsofindependentcalculationssince theybothprovideasimilarresult.Toillustratethedifferencebetweenthetwonumerical models,thepercentdifference,withCLPTtakenasthereference,isshowninFig. 3-4. Formostoftheregion,thepercentdifferenceisbetween 1%,indicatingverygood agreement. TheresultsfoundinthischapterarereinforcedbytheworkofBilgen.Bilgen, usingRayleigh-Ritzpredictions,predictedsimilarbehaviorwithvariationsinsubstrates andreinforcedhispredictionswithexperimentalresults[ 26].Chapters 6 and 7 further investigatethesepredictionsbyperformingexperimentsandniteelementanalysis. 47

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Figure 3-4.PercentdifferencebetweenCLPTandBimetallicBeamTheory. AsmentionedinSection 3.2 ,steelwasnotinitiallyconsidered,sincecarbonber wasreadilyavailableandeasytointegratewiththecurrentMAVmanufacturingprocess. However,itwaslaterincludedintestingandshortlythereafterincorporatedintoMAV designs.Theplotsshowninthissectionillustratethepredictedcurvaturewhenno loadingisapplied.Thecurvatureoftheunimorphswhensubmittedtoloadingwillbe investigatedindetailinChapters 6 and 7. 48

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CHAPTER 4 COMPOSITEMATERIALSTESTING Beforeproceedingfurther,itwasnecessarytocharacterizethedifferentmaterials usedinMAVs.Carbonbercompositesaretheprimarymaterialusedforthestructure oftheaircraft.Thisresearchexaminestwoparticularkinds,unidirectional(inwhichall thebersareorientedinonedirection)and5.7ozbidirectionalplainweave(inwhich thestrandsofbersareperpendiculartooneanotherandwovenintoacloth).The bidirectionalfabricwillhereafterbereferredtoassimplybidirectional.Thesetwo compositesareshowninFig. 4-1. Theunidirectionalcarbonberprovidessuperiorstrengthcharacteristicsinthe longitudinaldirection.However,itstransversestrengthandmodulusareextremely lowsincethesepropertiesrelyontherelativelyweakepoxymatrix.Incomparison, thebidirectionalexempliesthesamestrengthandmodulicharacteristicsinboththe 0 directionandinthe90 direction.However,the45 directionexhibitssignicantly reducedmaterialproperties,onthesameorderofmagnitudeastheepoxymatrixalone. A B Figure 4-1.ThetwotypesofcarbonberusedintheMAVmanufacturingprocess. A)Unidirectionalcarbonberpre-preg.B)Bidirectionalcarbonberplain weavepre-preg.PhotostakenbyBradleyLaCroix. Thecompositetestingforthisresearchwasconductedinanefforttoaccurately modelthecompositematerialsintheniteelementanalysis.Twosetsoftestswere conducted,aseriesoftensiletestsandaseriesofbendingtests.Forbothtestsets, 49

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a varietyofberorientationsweretestedtobetterunderstandthematerialproperties sothattheycouldbemodeledaccuratelyintheniteelmentmodel.Thesetestsare describedinthefollowingsections. 4.1TensileTests Inthisseriesoftests,avarietyofunidirectionalsamplesandbidirectionalsamples weretested,asshowninFig. 4-2.Threetypesofunidirectionalweretested.Twoor moreofeachtypewerecreatedtoincreasetheresultcondence.Two0-90samples ofbidirectional(onehalfofthebersorientedwithrespecttotheloadingdirectionand theotherhalforientedperpendiculartotheload)andthree 45bidirectionalsamples (bersoriented 45 withrespecttoloadingdirection)werealsofabricatedand tested.Thetestsampleswerefabricatedwithadditionallayersatthegriplocationsfor reinforcement.Steelsamplesoftwothicknesseswerealsotestedtoprovideabaseline comparison. 4.1.1Setup ThetensiontestsetupwascomposedofaTestResources315R150tension machine,equippedwitha50,000lbloadcell.TestResources'sR-Controllersoftware wasusedtocontrolthemachineandtomeasuretheloads.Thetensiletestswereused incombinationwithDigitalImageCorrelationtomeasurestrainsthroughouteachtest. DigitalImageCorrelation(DIC)isamethodformeasuringfull-elddisplacementsof asurfaceusingacamerasystemandanappliedspecklepattern.ThebasicsofDIC areexplainedinAppendix A.Forthisseriesofexperiments,theloadwasrecorded inincrementsandmanuallysynchronizedwiththeDICimages.Therefore,theload foreachimagewasrecordedduringthetestallowingforthecalculatedstraintobe measuredagainsttheload.ThetensilesetupisshowninFig. 4-3. 4.1.2Results ThedisplacementandloaddataforacouplesamplesobtainedfromtheTest ResourcesequipmentareshowninFig. 4-4.However,thisdisplacementdataisarough 50

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Figure 4-2.Thetensiontestsamplesusedtodeterminetheelasticmodulusofthe availablecompositematerials.PhototakenbyBradleyLaCroix. Figure 4-3.ThetensiontestsetupwiththeDICcamerasshown.PhototakenbyBradley LaCroix. 51

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A B Figure 4-4.Stress-straincurvescreatedusingthedisplacementandloadsdatafromthe TestResourcesmachine.A)Stress-straincurvefortheunidirectionalcarbon berspecimen,sample2b.B)Stress-straincurvefor0.004steel. measurementandisinaccurateduetogripslippage.Therefore,DICdataisusedto calculatethestrainoptically,asdescribednext.Nonetheless,theseplotsgiveageneral indicationofthematerialbehaviorunderloading. ThepositionsanddisplacementsacquiredbytheDICsystemwereconverted tostrainsusingGreen'sEquations,asdescribedinAppendix B.Anexampleofthe computedstrainsforSample2b,usingthismethod,areshowninFig. 4-5A.The calculatedstraincanthenbeusedincombinationwiththeappliedloadtogeneratea stress-straincurvewhichcanbeusedtocalculatetheelasticmodulus,asshownin Fig. 4-5B. TheresultingelasticmoduliaresummarizedinTable 4-1.Thesteelsamples,used toprovideabaseline,providedanelasticmodulusonasimilarorderofmagnitude astextbookvaluesforsteel,whichistypicallyquotedashavingamodulusaround 200GPa.Theexperimentalresultswereslightlyless,indicatingthattheexperimental resultsmaybe,onaverage,lessthanthetruevalues.Regardingthecarbontest samples,theresultsshowthatthecompositematerialshavearelativelylowelastic moduluscomparedtotextbookvalues,butarestillonthesameorderofmagnitude. 52

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A B Figure 4-5.ResultingstrainfortheSample2btensiletest.A)ComputedGreen'sstrain andcorrespondingstraincomponents.B)Stress-strainplotusedtocalculate elasticmodulususing yy Unidirectionalcarbonberwithanepoxymatrixnormallyhasanelasticmodulus closerto110GPa,whichindicatesthatthecarbonberusedinourlabisslightlymore compliantthanaverage. Whiletheseresultsprovideasignicantamountofinsightintothematerial propertiesofthecompositesusedinthelabandcanbearststeptowardsanite elementmodel,theydon'tprovideanentirepicture.Thebendingpropertiesof compositescandeviategrosslyfromthein-planeproperties.Thistopicisexamined inthefollowingsection. 4.2CantileverTests Thepropertiesdeterminedintheprevioussectionareverywellsuitedforin-plane analysisofcarbonbercomposites.However,out-of-planebendingstiffnessesfor wovencompositeswithoneortwopliescanvarybyasmuchas400%[ 60].The reasonforthisbecomesapparentwhenlookingatthewovencompositeonamagnied scale,asshowninFig. 4-6A.Inthe0-90direction,halfofthebersareintransverse directionandonlyhalfofthebersareinthelongitudinaldirectionandarecontributing 53

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T able4-1.Summaryoftensiontestsamplesandtheirrespectiveelasticmoduli. Samplethic kness,width,cross-sectional,calculatedmoduli, mmmmareamm 2 GPa 0.004 steel0.1039.33.9 194.4 (0.1016mm) 0.008steel0.2040.18.0 190.8 (0.2031mm) Bi1(0-90)0.3243.113.8 35.6 Bi2(0-90)0.3237.211.9 37.0 Bi3(+/-45)0.3141.312.6 5.1 Bi4(+/-45)0.3037.611.3 3.7 Bi5(+/-45)0.3136.811.4 4.9 Uni1a 0.2142.38.7 94.0 Uni1c 0.2041.38.4 92.1 Uni1d 0.2243.49.5 83.7 Uni2a 0.1955.210.2 73.0 Uni2b 0.1852.69.5 83.6 Uni3b 0.1945.08.3 92.5 Uni3c 0.1844.28.0 93.2 A B Figure 4-6.Acloserlookatwovencarbonber.A)Magniedillustrationofsingle-ply wovencarbonber.B)Bendingapproximationofsingle-plycarbonber. towardsthebendingstiffness.Thiseffectisdemonstrated,inanexaggeratedmanner, inFig. 4-6B.Furthermore,thebersarenotdistributedhomogeneouslyacrossthe thicknessofthelaminateandepoxyllsinamajorityoftheremainingspace. Inaddition,sincetheloadsonthewingwillbeappliedmainlyinanout-of-plane direction,itisimportanttoaccuratelymodelthebendingstiffnessesofthevarious compositesinvariousorientations.Thefollowingsetoftestsexaminedtheout-of-plane bendingpropertiesofthecompositesusedinourlabbyusingacantileversetup. 54

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A B Figure 4-7.Testsamplesusedforthecantileverbendingtests.A)Bottomview.B)Top view(DICspecklepatternapplied).PhotostakenbyBradleyLaCroix. 4.2.1Experiments Severaltestsamples,showninFig. 4-7 werecreatedforthissetofexperiments. Threepairsofunidirectionalsamplesandthreepairsofbidirectionalsampleswere made.Athirdsetofsampleswerealsocreated.Thesesamplesweremodeled aftertheleadingedgeportionoftheforwardsweptwingprototype,whichwillbe discussedinChapter 9 .Eachoftheseleadingedgelaminateshavethefollowing layup: [Uni49 ,Bi27 ,Uni49 ].Thislayupisintendedtocreatebend-twistcouplingin whichbendingofthesampleinducestwisting,oralternatively,twistinginducesbending. ThisisdescribedindetailinChapter 9. A0 ,45 ,and90 unidirectionalpairofsamplesweremade.Eachoftheunidirectional sampleswerecomposedoftwoplystopreventthesamplesfrombreakingduring testing,sincesingleplyunidirectionalcarbonbersplitseasilyalongtheberdirection. Inaddition,a0-90,22 ,and45 pairofbidirectionalsamplesweremade.Eachofthe bidirectionalsampleswascomposedofonlyonelayer. Thesamplesweretestedinacantilevercongurationinwhichonesideofthe samplewasclampedinaviceandloadswereappliedtothefreetip.Analuminum tubewasadheredtotheedgeofthesampleandthedistancetothecantilevercarefully 55

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A B Figure 4-8.Cantileverbendingtestsetup.A)Uni45 samplewith10gloadapplied. PhototakenbyBradleyLaCroix.B)Illustrationofthecantileversetup. measured.Astringwaspassedthroughthetubeandloopstiedoneachside.To applyloads,masseswereattachedtothestring.Thetubeandstringsetupenabled quick,repeatable,andaccurateloadapplicationwithoutproducingalargelocalized deformation.ThesetupwithaunidirectionalsampleisshowninFig. 4-8A.Thisloading conditiondemonstratestheinterestingpropertiesofabend-twistlaminate,inwhichthe bersareorientedat45 .Theloadisappliedononlyoneside,butduetothelayupof thesample,thetwistisnearlynegligibleandonlybendingoccurs. Allofthesamplesweretestedwithtwosetsofmasses.Themorecompliant samplesweretestedwith5and10grammasses.Thestiffersamplesweretestedwith 10and20grammasses.Priortobeginningeachtest,areferenceimageofthesample wastakenwiththeDICsystem.Thedisplacementforeachappliedloadcouldthen bemeasuredusingtheDICsystem.Masses,ingrams,wereappliedinthefollowing combinations,whereLdesignatestheleftsideandRdesignatestherightside:R00 L05,R05L00,R05L05,R00L10,R10L00,R10L10.Thesamepairingpatternwas executedforthe10and20grammasses.Ultimately,theDICresultswereusedto quantifythedisplacementofeachcornerofthesample,asshowninFig. 4-8B.The dimensionsforeachsamplearesummarizedinTable 4-2. 56

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T able4-2.Dimensionsforthebendingsamples. Sample Length,mmWidth,mmThickness,mmDistancetoload,mm Uni 0a75.828.00.32 65.2 Uni0b 0.32 64.5 Uni90a51.730.70.33 55.0 Uni90b 0.32 54.6 Uni45a65.832.80.34 41.1 Uni45b 0.34 41.4 Bi090a60.032.00.30 50.0 Bi090b 0.31 48.6 Bi45a60.131.80.31 48.9 Bi45b 0.31 49.4 Bi22a60.032.10.31 49.1 Bi22b 0.30 49.3 La79.131.90.57 68.8 Lb 0.57 68.4 4.2.2 FiniteElementModel Themaingoalofthecantileverbendingexperimentswastogenerateadatasetoff whichtobuildaniteelementmodel.Asmentionedpreviously,ifthebidirectionalmodel wascreatedwiththepropertiesofthein-planetests,thebendingstiffnesscouldbe drasticallyincorrect.Toaccountforthis,theniteelementmodelwasmodiedtomatch theexperimentalresults. Itwasfoundthatcenteringthematerialaroundthecenterlineofthethickness,as showninFig. 4-9A,providedthemostaccurateresultsforasingleplyofbidirectional compositeundergoingbending.Inthislayup,thepseudo-epoxylayersmadeupa combined45%ofthethickness.However,whenasingleplywasincorporatedintoa multi-plylaminate,itwasfoundthatthebidirectionalplywasbettermodeledwithout epoxylayersasshowninFig. 4-9B.Thematerialpropertiesforboththeunidirectional andbidirectionalsamplesareshowninTable 4-3.Theelementsoftheniteelement modelwerequadrilateralshellelements,S4R. 57

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A B Figure 4-9.Bidirectionalcompositeapproximationforniteelementmodel.A)Single layerbidirectionalapproximation.B)Bidirectionalapproximationwhen incorporatedintoamulti-plylaminate. Table4-3.Finiteelementpropertiesforunidirectionalandbidirectionalcarbonber. Unidirectional Bidirectional CarbonFiberCarbonFiber E 1 GPa81.063.5 E 2 ,GPa5.5 5.0 12 0.3 0.3 G 12 ,GPa3.0 3.0 G 13 ,GPa3.0 3.0 G 23 ,GPa2.0 2.0 t,mm0.160.30 4.2.3 Results TheresultsfromtheexperimentsaresummarizedinFig. 4-10 .Afteradjustingthe niteelementmodelasdescribedinSection 4.2.1,theexperimentalvaluesmatchedup wellwiththeniteelementmodels.Overall,theniteelementmodelshadanaverage deviationfromtheexperimentsof5.5%.Acoupleoftheexperimentsdeviatedmore,but thiscouldbeattributedtomanufacturingdefects,variationsinthickness,ortheposition atwhichthesamplewasclamped. Aftergeneratingasuccessfulniteelementmodelforthecompositematerials, effortsprogressedtoanalyzingtheperformanceoftheMFCactuatoritselfandhowto applyittosubstrates. 58

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Figure 4-10.Resultsfromthecantileverbendingtests.59

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CHAPTER 5 MFCFREESTRAINEXPERIMENTALTESTS TherststepincreatinganaccurateFEAmodelrepresentinganMFCstructure istoexperimentallydeterminethefreestrainproducedbytheMFC.Todothis,a setupwithaDigitalImageCorrelation(DIC)systemandnecessaryelectronicswas assembled,asshowninFig. 5-1.ThissetupallowedtheMFCtobeactuatedthroughout itsvoltagerangeandthedeformationoftheMFCquantiedandconvertedtostrain. MFCsrequireahighvoltagesystem(describedinSection 5.3)capableofproducinga voltagerangeof-500Vto1500V.Thisrangeisslightlyexpandedbecauseresearch hasshownthattheMFCscanbesafelyactuatedupto1700V[ 22]. 5.1Setup AsmentionedinChapter 4,DICisanopticalmethodinwhichaspecklepatternis appliedtothesurfaceoftheexperimentalsubjectandtrackedusingacamerasystemto quantifythefull-eldpositionanddisplacementsinthreedimensions.DICisdescribed inAppendix A. Figure 5-1.TheexperimentalsetupusedtomeasurethestrainintheM8528-P1MFC actuator.TheDICcamerasarepositionedontheleft,theMFCsupportedby thetestxtureinthecenter,andthecorrespondingelectronicsarelocated ontheright.PhototakenbyBradleyLaCroix. 60

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The systemusedfortheseexperimentsiscomposedoftwocameras(PointGrey ResearchGrasshopper R r 2)outttedwithFujinon1:1.8/75mmHF75SA-1lensesand acomputersystemrunningVic-Snap2007andVIC-3D2009.Aspecklepatternwas appliedtotheMFCpriortotheexperimentusingValsparblackandwhitespraypaints. First,auniformlayerofwhitepaintwasapplied,thenaspecklepatternofblackdotswas appliedtocreatetheoverallhigh-contrastpattern.TheMFCwasclampedinplaceand thecameraswerefocusedonasmallsectionoftheMFCmeasuringapproximatelyone squarecentimeter. SincethemanufacturedMFCisnotperfectlysymmetric,itmovesout-of-planewhen actuated.Thisout-of-planemotionmustberestrictedduetotheextremelynarrowfocal planeofthecamerasetup,astopreventtheMFCfrommovingoutoffocus.Todothis,a smallweightwassuspendedfromtheendoftheMFC.ThisensuredthattheMFCcould stillstraininthein-planedirection,butwouldnotsignicantlybendout-of-planewhen actuated.Avarietyofsmallweightswereusedtoverifythatthepresenceoftheweight didnotaffectthemeasuredstrain. ThetechniqueusedtoconvertthemeasuredMFCdisplacementstostrainis describedinAppendix B.Theprocedureandresultsarediscussedinthefollowing section 5.2ProcedureandResults Atotaloffourtestswereconducted.Thethreecertiedmassesusedforthesetests were50,100,and500g.TwoseparatesectionsoftheMFCwereexamined:thecenter andthelowercenterportion.Theresults,showninFig. 5-2,demonstratethatthetests werequiteconsistent,withavariationinthepeak-to-peakmaximumdifferenceof8.4% inlongitudinalstrainand3.0%intransversestrainat1700V. Theresultsalsoindicatethatthelongitudinalstrainishigherthanthequotedvalue bySmartMaterialsCorp[ 61].OneexplanationforthisresultisthatSmartMaterials mayhavebeenreferringonlytothe0-1500Vrangeratherthantheentirerange. 61

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Figure 5-2.ExperimentallydeterminedfreestrainfortheM8528-P1MFC. Furthermore,thisexperimentexaminesarangeof-500to1700V.While1500Vis quotedastheupperlimitfortheMFCs,WilliamsandInmanconductedseveraltestsin whichtheydetermineditwassafetooperatetheMFCsupto1700Vwithnodecrease inperformance[ 22].Therefore,toencapsulatetheentireoperatingrange,testswere conductedfrom-500to1700V. Inaddition,theresultsshowthatthereissignicanttransversestrainexhibitedby theMFC,ontheorderof57%ofthelongitudinalstrain.Theshearstrain,ascanbe seeninthegure,isapproximatelyzero. AlthoughABAQUSallowsfortheinputofspecicpiezoelectricparametersfora piezoelectricmaterial,theimplementationiscomplicatedandultimatelyunnecessary foramacroscopicsetupsuchasthis.Therefore,asimplerthermalrelationisusedto modeltheMFCratherthanpiezoelectricparameters.Thestrainvaluesobtainedfrom theseexperimentswereconvertedtothermalstrainvaluestobeusedintheABAQUS FEAmodel.Thestrainvaluesfortheupperandlowerpartsofthehysteresisloopwere 62

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Figure 5-3.FreestrainapproximationfortheFEAmodel. averagedtoprovideasinglesetofuniquevaluesforthestrainvsvoltage,asshown inFig. 5-3.ThesearecompiledinTable 5-1.Forconvenience,thethermalstrainis shownbothintheunitsrequiredbyABAQUS(strainperdegreetemperaturechange) andinabsolutestrain.FortheFEAmodel,onedegreetemperaturechangeinABAQUS correspondstoonevoltchangeintheMFC. 5.3ElectricalSetup TheelectricalsetupconsistedofaGWGPC-3030Dpowersupply,EMCOQ15-5 HighVoltageAmplier,aFluke115multimeter,tworesistorsinseries,andtheMFC. TheEMCOhighvoltageamplierbooststheinitialvoltagebyafactorof300.Therefore, aninputvoltageof5Visampliedtoavoltageof1500V.Anillustrationofthesetupis showninFig. 5-4. Thevoltagedividerservesadualpurpose.Firstly,itallowstheampliedvoltage of1500Vtobescaleddownandmeasuredwithamultimeter,whichhasamaximum voltageof600V.Secondly,whenthepoweristurnedofftothecircuit,theresistors dissipatetheremainingvoltagepotentialstoredontheMFC.Theresistorswerecarefully 63

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T able5-1.FreestrainvaluesusedintheABAQUSFEAmodel. V oltage,V x / Temp y / Temp x y -5001.08E-06 -5.84E-07-540292 -4001.20E-06-6.69E-07-482267 -3001.31E-06-7.40E-07-392222 -2001.39E-06-7.98E-07-279160 -1001.46E-06-8.44E-07-14684 1001.54E-06-9.06E-07154-91 2001.56E-06-9.22E-07313-184 3001.57E-06-9.30E-07472-279 4001.57E-06-9.31E-07627-372 5001.56E-06-9.25E-07778-462 6001.53E-06-9.13E-07920-548 7001.50E-06-8.97E-071053-628 8001.47E-06-8.76E-071175-701 9001.43E-06-8.52E-071287-767 10001.39E-06-8.26E-071387-826 11001.34E-06-7.99E-071477-879 12001.30E-06-7.71E-071558-925 13001.26E-06-7.43E-071631-966 14001.21E-06-7.16E-071698-1003 15001.18E-06-6.92E-071763-1038 16001.14E-06-6.70E-071828-1072 17001.12E-06-6.52E-071898-1108 Figure 5-4.WiringsetupforMFCactuation. 64

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chosen tominimizetheeffectontheoverallcircuit.Ifthesecondresistor'sresistance istoohigh,thenitwillinterferewiththevoltagemeasuredbythemultimeter.Thisis becausethemultimeterhasabuilt-inimpedanceoverwhichitmeasuresvoltage.If theresistanceistoolow,thevoltagedropbecomesunmeasureable.Aresistorof1k n createsonly0.1%error,whereasalargerresistance,suchas1M n,wouldproducean errorof10%.ThistrendcanbeseeninFig. 5-5. Figure 5-5.Measurementerrorinvoltagereadingbasedontheresistorselectionfor highvoltagecircuit. Inaddition,aseriesofhighresistanceresistorsisnecesarysincetheEMCOdevice onlyproduces0.333mAofcurrent.UsingOhm'slaw, I = V R = 1500 V 10Mn = 0.15mA,wecan seethattheresistordissipates0.15mAofthe0.333mAproducedbytheEMCOdevice. Asmallerresistorwoulddissipatealargerportion,ifnotallof,thegeneratedcurrent.It shouldalsobenotedthattheEMCOdevicehasainputthresholdof0.7V.Therefore,no outputvoltageisproducedwhentheinputvoltageislessthan0.7V[ 62]. 65

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CHAPTER 6 UNIMORPHMODEL,EXPERIMENTALVALIDATION,ANDDESIGNSPACE EXPLORATION AfterconductingtheexperimenttomeasurethefreestrainintheMFC,thenextstep wastogenerateaniteelementmodelofaunimorphinABAQUSandvalidateitwith aseriesofexperiments.Itwasdecidedtomakeanexperimentalsetupsimilartothe congurationthatwouldbeusedonawing.FortheMAVwingsusedinourlaboratory, theleadingedgeisgenerallyreinforcedwhilethetrailingedgeisrelativelycompliant. ThisresultsinareinforcedleadingedgeinwhichonesideoftheMFCisapproximately rigidwhiletheotherend,onthetrailingedgeofthewing,isrelativelyfree.Thesetup mostsimilartothisisacantileverarrangement. Inthissetup,onesideoftheunimorphisclampedinawaythattheconnecting wiresarenotcompressedandtheotherendisleftunrestrained.Thesetup,withtwo 10gmassesapplied,isshowninFig. 6-1A.Analuminumtubeisadheredtothetip oftheunimorphandastringispassedthrough,asshowninFig. 6-1B.Weightsare suspendedfromthestringtoapplyloadsonthetipofthecantileveredunimorph.The stringandtubeinsurethattheloadsareappliedinapreciseandrepeatablemanner whilealsopreventingseverelocaldeformation. AsmentionedinSection 1.2 ,threesizesofMFCswereinitiallyexamined.The resultingunimorphsareshowninFig. 6-2.ThesmallerMFCswereusedontheinitial MAV,whichisdiscussedinChapter 8 .However,afterfurthertestingandexaminationof potentialdesignconcepts,itwasdeterminedthattheM8528-P1actuatorwasthebest candidateduetoitsstrainrangeandlargersize.Thisactuatorwasimplementedona MAVandisintroducedinChapter 9 .Someoftheexperimentalresultsareshownin Section 6.2. 6.1AdhesionMethod Twodifferenttypesofadhesionmethodswereinitiallyinvestigated.Therstmethod wasaco-curingmethodwherecarbonberpre-impregnatedwithepoxy,waslaidup 66

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A B Figure 6-1.CantileveredunimorphDICsetup.A)DICsetupwiththeunimorph cantileveredandtheloadsappliedtothefreeend.B)M8528-P1unimorph withthealuminumtubeandstringattached.PhotostakenbyBradley LaCroix. Figure 6-2.Unimorphspreparedforcantileverloadingexperiments.Phototakenby BradleyLaCroix. withtheMFC(showninFig. 6-3)andplacedintheovenforcuringwithvacuumpressure simultaneouslyapplied.Thismethodprovidesastrong,solidbondbetweentheMFC andthecarbonberinasinglestep. Thesecondmethodisatwo-stepprocess.First,thecarbonberiscuredin thedesiredgeometry.Next,thepiezoelectricisadheredtothecarbonberusing cyanoacrylateadhesive(CA).Pressurewasappliedmanuallyusingweights.Themain drawbacktothismethodistheaddedthicknessoftheadhesive,whichincreasesthe 67

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Figure 6-3.ExampleofbondinganMFCtounidirectionalcarbonberpre-preg.Photo takenbyBradleyLaCroix. momentofinertiaofthenallaminate,whichinturnincreasestheexuralstiffnessand therebyreducestheactuatedcurvature. CAisavailableinthreedifferentviscosities:thin,medium,andthick.Thelowerthe viscosity,thefasterthecuretime.Furthermore,itwasexpectedthatalowerviscosity wouldresultinathinnernallaminate.Thicknessmeasurementspartiallysupported thistheory,however,applyingthethinCAinauniformmannerproveddifcultduetothe rapidcuringtime.TheaveragethicknessofthemediumCAunimorphwas0.544mm withastandarddeviationof0.039mmwhilethethinCAunimorphwas0.534mmwith astandarddeviationof0.048mm.Figure 6-4 showstheDICresultsforthe3different adhesiontests. Despitebeingthinnerinsomelocations,thethinCAsampleprovedtobenobetter thanthemediumCAsamplewhiletheco-curesampleprovedtobesuperiortoboth. Therelativeup-deectionoftheco-curesamplewas23.1mmcomparedtothemedium CArelativeup-deectionof17.5mm.Thedown-deectionoftheco-curesamplewas slightlyworsethanthemediumCAatarelativedeectionof-8.8mmcomparedtothe mediumCArelativedown-deectionof-9.4mm.Therefore,forperformancecritical applications,theco-curingtechniqueappliedtotheunidirectionalcarbonber/epoxy 68

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Figure 6-4.Comparisonofthreeadhesiontechniquesatpositiveandnegativeactuation. isthepreferredmethod.Bothmethodsresultinastrongbondwhichmakesitvirtually impossibletoremoveandreusetheMFC.Therefore,eachMFCcanonlybeusedonce. Thiscanbeaneconomicdrawbackwhenintheearlytestinganddevelopmentphase. Aftersteelwasdeterminedtobeapotentiallysuperiorsubstrate,aslightlymodied adhesiontechniquewasdeveloped.First,thesteelsurfacewaspreppedusingnegrit sandpapertoremovetheprotectivecoatingonthesurface.Apartiallypreparedsample isshowninFig. 6-5.Next,thesteelisplacedonateonsheetonaatlayupsurface andWestSystemsepoxy(105resinand206hardener)isappliedtothesurface.The MFCisplacedontopandkaptontapeisplacedontopoftheMFCtopreventtheepoxy fromowingoverontotheexposedsurfaceandelectronicleads.Thissetupisshown inFig. 6-6.Thenalstepwastoplacethelayupinavacuumbagtoapplyconstant anduniformpressurewhiletheepoxycured.Aftertheepoxycured,theedgescouldbe sandedtoremoveexcesssteelandepoxy. 69

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Figure 6-5.Steelsubstratepartiallypreparedforbonding.PhototakenbyBradley LaCroix. Figure 6-6.SteelsubstrateandMFCpreparedandreadytovacuumbag.Phototaken byBradleyLaCroix. 6.2ExperimentalComparisonofMFCs EachoftheunimorphsshowninFig. 6-2 wereplacedinacantileveredconguration asshowninFig. 6-1A.Theunimorphswereactuatedto-500Vand1500Vandthe deformationmeasuredwithDIC.TheresultingdeformationsareshowninFig. 6-7. Contrarytotheexpectedresult,theM8507-P1unimorphhasalargeractuation rangethantheM8528-P1.TheM8528-P1hasaquotedstrainrangeof1800 whereastheM8507-P1hasaquotedstrainrangeof1380 ,asindicatedinTable 1-1. ThicknessmeasurementsindicatedthattheM8528-P1unimorphmeasuredapproximately 0.50mmwhereastheM8507-P1andM8503-P1unimorphsmeasuredapproximately 0.47mm.Thiscouldaccountforpartofthedifference,sincethinnersubstratesshould 70

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Figure 6-7.Experimentalcantileverresultsforthethreeunimorphs. producelargerdeections.Inaddition,theM8528-P1MFCcouldhavebeendamaged duringthemanufacturingprocessortheM8507-P1mayproducemorestrainthan thequotedvalues.Regardless,duetoitslargersizeandexpectedperformance,the M8528-P1wasstillchosenasthepreferredactuatorlaterinthedesignprocess.This decisionwasfurtherreinforcedbytheconvenientsizeoftheM8528-P1fora24inch MAV. 6.3SubstrateComparison Followingthetestsconductedintheprevioussection,ano-loadstudywiththe M8528-P1wasconductedinwhichavarietyofsubstratesweretestedwithnotipload applied.EachtestwasstartedwiththeMFCactuatedto-500V.Thevoltagewas increasedto1700Vinaseriesofsteps,withthevoltagerecordedandDICimages takenateachstep.Afterreaching1700V,thevoltagewasdecreasedto-500Vwhile recordingeachvoltageandtakingDICimages.Thetipdisplacementresultsofthese testsareshowninFig. 6-8. Twothicknessesofsteelweretested,0.05mm(0.002)and0.10mm(0.004),each bondedtotheMFCusingWestSystemsepoxy(105resinand206hardener)under vacuumpressure.Anothersubstratewaspre-curedunidirectionalcarbonberbonded totheMFCusingthinviscositycyanoacrylate(CA)adhesive.Theotherthreesamples 71

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Figure 6-8.Measuredtipdisplacementwithvarioussubstratesinacantileversetupwith theM8528-P1. wereco-curedwithcarbonberpreimpregantedwithepoxy(usuallytermedpre-preg forshort).Thecarbonberpre-preg,measuringapproximately0.16mmthick,was co-curedwiththeMFCundervacuumpressureatatemperatureof127 C(260 F).The rstofwhichwasco-curedwithunidirectionalcarbonberonaatlayupsurface.The othertwo(oneunidirectionalsampleandonebidirectionalsample)wereco-curedona pre-curvedsurface.Theradiusofcurvatureforthebidirectionalsampleaftercuringwas approximately0.33m )Tj /T1_2 7.97 Tf 6.59 0 Td (1 and0.21m )Tj /T1_2 7.97 Tf 6.59 0 Td (1 fortheunidirectionalsample. TheseresultsreinforcethosepredictedbyCLPTandthebimetallicbeamtheory, asdiscussedinChapter 3 .Asseeninthegure,steel,thematerialwiththehighest modulus,hasthelargestdeection.Theunidirectionalcarbonberisless,butstill outperformsthebidirectionalcarbonber.Furthermore,theseresultsclearlyshowthe hysteresisoftheMFCactuatorandcloselyfollowthetrendseenintheMFCfreestrain resultsseeninFig. 5-2 fromSection 5.2 72

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Figure 6-9.ExampleofFEAmodelwithcantileverboundaryconditionhighlighted(left) andaluminumpartitionhighlighted(right). 6.4ComparisonBetweenExperimentalandFiniteElementResults 6.4.1FiniteElementModel TheniteelementmodelwascreatedinABAQUS6.9-2usingaquadrilateralshell model.Themodelwasdividedintopartitionsandtherespectivematerialproperties assignedtoeachpartition.TheMFCmaterialwasassignedacoefcientofthermal expansionbasedontheresultsobtainedfromthefreestrainexperiments(Section 5.2). Next,atemperatureeldwasappliedtothemodeltosimulatethestrainproducedby theMFCactuation.Theothermaterialswerenotassignedacoefcientofthermal expansion,thereforeatemperatureelddidnotaffectthem.Alinearmodelwas usedsincethemagnitudeofextensibilitywasassumedtobesmallforallcases.The completecantileverFEAmodelisshowninFig. 6-9. 6.4.2ExperimentalProcedure Digitalimagecorrelationwasusedtomeasuretheshapeoftheunimorphthrough eachstepoftheexperiment.Fortheexperimentsinwhichnoloadwasapplied,the MFCwasactuatedto-500V,0V,1500V,1700V,then1500V,0V,and-500V.The deformationwascapturedusingDICfortheupwardpass(-500V,0V,1500V)andfor thedownwardpass(1500V,0V,and-500V). 73

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A B C Figure 6-10.Comparisonbetweentheexperimentalresultsandtheniteelementmodel forthe0.16mmunidirectionalunimorph.A)Noloadapplied.B)20gload applied.C)40gloadapplied. Fortheexperimentswithappliedloads,theloadswereappliedintwodifferentways. Intherstway,theMFCwasactuatedtoeither-500Vor1500Vandthentheload wasapplied.Intheotherway,theMFCwasloadedrstandthenactuatedto-500Vor 1500V.DICwasonceagainusedtomeasurethedeformationateachstep.Allofthe resultswereoutputfromVIC-3DandcompiledusingMATLAB. 6.4.3Results ThreesampleswerechosentobetestedandcomparedtotheFEAresults.One samplewasaco-curedunimorphcomposedofasinglelayerofunidirectionalcarbon ber.Theothertwosampleswerethesteelsubstratesmentionedpreviously,one measuring0.05mmandtheother0.10mmthick.Thelayerofadhesiveepoxybetween thesteelandtheMFCisalsomodeledineachcase,withathicknessof0.05mm.The results,ascomparedtotheFEAmodels,areshowninFigs. 6-10, 6-11,and 6-12. Duetothermalexpansionduringthemanufacturingprocess,theunimorphs containedasmallamountofpre-strainandthereforeexhibitedasmalldegreeof curvature.Toaccountforthis,thetemperatureeldintheABAQUSmodelwasshiftedto effectivelyzerothemodelontheunloaded,unactuatedposition. 74

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A B C Figure 6-11.Comparisonbetweentheexperimentalresultsandtheniteelementmodel forthe0.05mmsteelunimorph.A)Noloadapplied.B)20gloadapplied. C)40gloadapplied. A B C Figure 6-12.Comparisonbetweentheexperimentalresultsandtheniteelementmodel forthe0.10mmsteelunimorph.A)Noloadapplied.B)20gloadapplied. C)40gloadapplied. 6.5DesignSpaceExploration AftertheFEAmodelwasvalidated,itcouldbeusedtoexploreotherdesign possibilities.Forexample,thethicknessofthesteelsubstratecouldbeadjustedtosee itsimpactonthetipdeectionwithandwithoutloading.Twothickersubstrateswere examinedandcomparedwiththe0.10mmsteelsubstrateandtheresultsshownin Fig. 6-13.Ascanbeseeninthegure,theunloadeddisplacementofthe0.15mmsteel unimorphisslightlyless,andthe0.20mmsteelisevenless,butthethickersubstrates arebetteratopposingtheappliedload. 75

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A B C Figure 6-13.FEAunimorphcomparisonbetweenthreethicknessesofsteelsubstrate. A)Noloadapplied.B)20gloadapplied.C)40gloadapplied. A B C Figure 6-14.FEAunimorphcomparisonbetweentwoepoxythicknesses.A)Noload applied.B)20gloadapplied.C)40gloadapplied. Asimilarstudywasconductedcomparingtwothicknessesofepoxy.Theseresults areshowninFig. 6-14.Similartothetrendshownwiththeotherexperiments,the thinnestlayuphasthelargestunloadedtipdisplacementandthethickestsubstrate hasthesmallestdisplacement.However,theresultsaremixedoncetheloadis applied,sincethethickerlayupsholdtheirpositionbetterandthethinnerlayupshavea largerinitialdeection.Therefore,thethinnerlaminatesdeectfartherinitially,butare displacedfartherbyloading,sotheirresultingpositionaresimilartothethickerlayups. Togatheramorewidespreadunderstandingoftheimpactofthesubstrateonthe actuationoftheunimorph,alargeseriesofniteelementanalyseswereconducted.The substratethicknessandmoduluswasadjustedthrougharangeofvaluesandtheresults 76

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A B C Figure 6-15.FEAunimorphtipdisplacementforvarioussubstratesthicknessesand moduli.TheMFCisactuatedto1500V.A)Noloadapplied.B)20gload applied.C)40gloadapplied. A B C Figure 6-16.FEAunimorphtipdisplacementforvarioussubstratesthicknessesand moduli.TheMFCisactuatedto-500V.A)Noloadapplied.B)20gload applied.C)40gloadapplied. plotted.Figure 6-15 showstheFEAresultswhentheMFCisactuatedto1500Vwitha tiploadof0g,20g,and40gapplied.Similarly,Fig. 6-16 showstheFEAresultswhen theMFCisactuatedto-500V.Inthiscase,theloadisappliedinthesamedirectionas thedirectionofactuation. 6.6AlternativeDesigns AfewotherMFClayuppossibilities,inspiredfromtheliterature,werealso considered.Asimplebimorphcongurationispresentedrst.Then,twoalternative designsareexplored. 77

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Figure 6-17.Illustrationofbimorphactuation. 6.6.1BimorphConguration Buildingonthepreviousresults,abimorphcongurationwasexplored.Although bimorphexperimentswerenotconducted,theresultsfromtheprevioussetof experimentswereextrapolatedtoofferinsightintotherelativeperformanceofabimorph conguration.Furthermore,abimorphcongurationwasnotconsideredfortheMAV projectsinceoneofthemainobjectiveswastolimitthenumberofactuatorsonthe aircrafttoonlytwo.AMAVincorporatingasetofbimorphactuatorswouldrequirefour MFCactuators. Inabimorphconguration,thebottomMFCisactuatedindependentofthetop MFC,asshowninFig. 6-17.Inthissetup,thetopMFCisactuatedto1500Vwhile thebottomMFCisactuatedto-500V,orviceversa.Theresultingcurvaturecanbe predictedusingCLPTasoutlinedearlier,withtheresultsshowninFig. 6-18.Contrary totheunimorphconguration,theresultsshowthatinordertoincreasetheunloaded curvature,itispreferentialtominimizethethicknessofthesubstrate,butelasticmodulus hasaminimaleffectontheunloadedcurvature. Acomparisoncanbedrawnbetweenunimorphsandbimorphsbytestingacouple substratesinbothcongurationswithinFEA.ThisisshowninFig. 6-19.Inthesegures, 78

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Figure 6-18.PredictedcurvatureofabimorphusingCLPTforvarioussubstratemoduli andthicknesses. A B C Figure 6-19.Comparisonbetweenunimorphsandbimorphs.A)Noloadapplied. B)20gloadapplied.C)40gloadapplied. thebimorphandunimorphhaveasimilarunloadedtipdisplacementintheupward direction.However,inthedownwarddirection,thebimorphissuperior.However,when loadedwithamassatthetip,boththeunimorphandthebimorphsbehavesimilarly,with themaindifferencebeingthesubstrate. Totestthistheoryfurther,themodulusandthicknessofthebimorphconguration wasvaried.Loadswereappliedtothetipandthetipdisplacementmeasured.The resultsareshowninFig. 6-20.TheFEAmodelindicatesthatlowermodulusmaterials 79

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e xhibitthelargesttipdeectionsforabimorphconguration,butasignicantdrop-offis observedonceloadingisapplied.Theseresultsrevealthatthebimorphconguration hasasmallertipdeectionthantheunimorphforallcases.Thisismostlikelyaresult ofthebottomMFCworkingtoovercomethetopMFCwhiledeecting,duetothe asymmetryinactuationmagnitude.Inthisconguration,thetopMFCisactuatedtoonly -500VwhilethebottomMFCisactuatedto1500V.However,itmustbenotedthata bimorphprovidesequaldeectioninbothdirections,whichissomethingaunimorph isunabletoreplicate.Furthermore,abimorphwouldprovidefasteractuationforsome electronicsetupswherethechargeontheMFCisdissipatedusingaresistor,rather thanactivelyadjustingthevoltagetoalowervalue.Therefore,certainapplicationsmay makeabimorphcongurationthepreferredoption. Asanexample,wecancompareasinglesubstratewithamodulusof200GPa andathicknessof0.15mminbothcongurationswithM8528-P1MFCs.Inabimorph conguration,thissubstratewouldyieldatipdisplacementof15.5mmineachdirection foratotaldisplacementrangeof30.1mm.Inaunimorphconguration,thissubstrate wouldyieldanupwardtipdisplacementof21.7mmandadownwardtipdisplacementof 6.8mmforatotalrangeof28.5mm.However,whenloadedwith20gatthetip,thetip displacementofthebimorphisreducedto12.8mmandtheunimorphisonlyreducedto 17.6mm. Lastly,Fig. 6-21 demonstratesthepredictedbehaviorofthebimorphconguration whenloadsareappliedinthesamedirectionastheactuation.Theseresultsshow asimilarresponsetotheplotsinthepreviousgure.Ifthesubstrateistoothin,the structurewillcollapseunderloading.Furthermore,ifthesubstrateistoothick,thenthe structurewillnotdisplaceameasureableamount.Therefore,acompromisemustbe foundatapointinbetween. 80

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A B C Figure 6-20.FEAbimorphtipdisplacementvssubstratemoduliandthickness(with opposingload).A)Noloadapplied.B)20gloadapplied.C)40gload applied. A B C Figure 6-21.FEAbimorphtipdisplacementvssubstratemoduliandthickness(with supplementaryload).A)Noloadapplied.B)20gloadapplied.C)40g loadapplied. 6.6.2PrecompressedActuators Oncetheniteelementmodelwasvalidated,additionaldesignswereconsidered. Onesuchdesign,similartotheresultsobtainedbyVosandBarret[ 32, 34, 4345],was incorporatedintotheniteelementmodel.Inthisdesign,theMFCsandsubstrateare heatedupduringtheadhesionprocess.Duetothecoefcientofthermalexpansion,the substrateexpandsmorethantheMFC.Aftercoolingtoroomtemperature,thesubstrate contractsrelativetotheMFCsandisheldintensionwhiletheMFCsareincompression. ThiswasmodeledintheniteelementmodelandtheresultsshowninFig. 6-22. 81

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A B Figure 6-22.Predictedbehavioroftheprecompressedbimorphs(PBP)vsstandard bimorphsA)Noload.B)20gloadappliedtothetip. Thegurescomparetwosubstrates.Eachsubstrateismodeledasastandard bimorphandasaprecompressedbimorph.Thetwosubstratesexaminedwere:asteel substratewithathicknessof0.1mm,elasticmodulusof207GPa,andcoefcientof thermalexpansionof13 K ; andanaluminumsubstratewithathicknessof0.1mm, elasticmodulusof70GPa,andacoefcientofthermalexpansionof22.2 K The thermalcyclewasassumedtostartat22.2 C(72 F),elevateto126.7 C(260 F),and returnto22.2 C(72 F). Asnotedinthegures,theprecompressedaspectdoesnotyieldanoticeable benet.Itislikelythatcombiningthissetupwithapost-buckleddesignwouldyield betterresults,butsincethisdesignismorecomplexanddifculttoimplementona thinundercamberedwingitisnotconsideredfurther.Itshouldalsobenotedthat animprovementintipdisplacementwasachievedifthetemperaturegradientwas increased100-fold.However,thisisnotafeasibleoptionsinceitwouldrequiremore thana10,000 Ctemperaturechange. 82

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A B C Figure 6-23.ThedesignsmodeledinFEAsimilartotheLIPCAlayups.A)C1-M1 design.B)C1-M1design.C)C2design. 6.6.3LIPCAActuators LIPCAactuatorswerealsoconsidered.Inthistypeofactuator,theneutralaxisis shiftedawayfromtheactivematerialandintothesurroundinglaminate.Althoughthe researchforLIPCAactuatorswasconductedwithleadzirconatetitanatePZTactuators, itwasdecidedtoexaminethepotentialbenetspossiblewhenimplementingMFCsina similarconguration. IntheLIPCAactuatorsexamined[48, 49],theactuatingmaterialwasincorporated intoalaminatewithlayersofglass/epoxyandcarbon/epoxy,similartothatshownin Fig. 6-23.Threedesignswereexamined:C1-M1,C1-M2,andC2.TheC1-M1and C1-M2designsswitchtheorderofthetoptwolayersandtheC2layupcontainsanextra layerofglass/epoxy. TheresultsfromtheFEAareshowninFig. 6-24.Thestandardunimorph signicantlyoutperformsallthreeoftheLIPCAdesigns.Italsodeformslesswhenthe loadingisappliedatthefreeend.SincetheLIPCAactuatorshaveasmalleractuation rangeanddeectmoreunderloading,theseresultssafelyeliminateLIPCAsasa possibledesignoptionfortheresearchinthisdocument. 83

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A B Figure 6-24.TheresultsoftheLIPCAFEAmodelsvsastandardunimorphsamplewith unidirectionalcarbonberA)Noloadcomparison.B)20gload comparison. 84

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CHAPTER 7 FOURPOINTBENDTESTS Thecantileveredunimorphexperimentscoveredinthepreviouschapterprovided signicantinsightintotheperformanceoftheactuatorswhenbondedtovarious substrates.However,thedisplacementmeasuredinthecantileveredtestscouldbe especiallysensitivetotheclampposition.Smallchangesintheboundaryconditions wouldresultinlargechangesindisplacementswhenvariousloadswereappliedtothe actuatedunimorph. Therefore,anothersetofexperimentsweredevisedtotesttheloadbearing capacityoftheunimorphsduringactuation.Becausetheunimorph'smainresultof actuationiscurvature,itwasdecidedthatatestthatappliesabendingmomentwould beideal,sincethebendingwoulddirectlyopposethecurvature.Withthisinmind,afour pointbendtestwaschosensinceitprovidesauniformandconstantmomentbetween theinnertwosupports.Inaddition,positioningaunimorphonafourpointbendsetup wasdeterminedtobeeasierthanathreepointbendsetup.Overall,itwasexpected thatafourpointbendtestwouldyieldamoreaccuratecharacterizationoftheunimorph sinceitallowsfortheapplicationofapuremoment,therebycounteractingthemoment generatedbytheunimorph. 7.1Setup ThesetupandcorrespondingillustrationareshowninFig. 7-1.Thesupportsofthe fourpointbendsetupwereconnectedtothesameTestResourcesmachinedescribed inSection 4.1.Toimprovethetestresolution,aTestResources10lbfloadcell(model numberSM-10-294)wasincorporatedintothesetup.Thesupportswerespaced accordingtoASTMstandardsandpositionedsothattheoutersupportswereplacedjust insideoftheactiveportionoftheunimorph.Thisalsoallowedsufcientclearanceforthe wirestoruntotheMFCwithoutinterferringwiththesupports.Duringtheexperiments, 85

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A B Figure 7-1.Fourpointbendtestsetup.A)Exampleofthetestsetupforthefourpoint bendtest(wiresnotconnected).PhototakenbyBradleyLaCroix. B)Diagramofpinspacingandloadapplicationforfourpointbendtest. theoutermostsupportswerespacedat70mmandtheinnersupportswerespaced 35mmapart. 7.2Procedure The0.05mmsteelunimorph,0.10mmsteelunimorph,andaunidirectional unimorphweretested.Twotestswereconductedwitheachunimorph.Foronetest, theunimorphisactuatedto1500Vasthefourpointbendtestisconducted.Forthe othertest,theunimorphisinvertedandactuatedto-500Vwhilethetestisconducted. Thetestprocedureforthe1500VcaseisoutlinedinFig. 7-2 andthestepsaredetailed below. Theexperimentalstepsweredenedtominimizetheeffectsofhysteresis.Since thecurvatureoftheunimorphcannotbeaccuratelypredictedandreplicated,exceptat theminimumandmaximumvoltages,thesewerechosenasthestartingpointsforthe experiment.Therefore,theexperimentalprocedurewasdenedasfollows: 1.Actuatetheunimorphto-500V(or1500Vforinvertedcase). 2.Bringthextureintoslightcontactwiththeunimorphsoasmallloadismeasured (0.1Nor0.03lbf). 3.Adjusttheactuationoftheunimorphto1500V(or-500Vfortheinvertedcase). 86

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4.Record theloadasthexturesaremovedapartfromoneanother. 5.Stopandreversethedirectionofmotiononcetheloadisat0.44N(0.1lbf). 6.Recordtheloadasthexturesaremovedtowardoneanother. 7.Stopthextureswhentheyreturntotheirstartingposition. Forthe-500Vtest,theunimorphisippedsotheMFCpartoftheunimorphison top.Then,thestepsarerepeated,exceptthevoltagesareinterchanged,sothatthetest beginswith1500V.Theloadisappliedthroughouttheapplicationof-500V.Thecyclic natureofthisprocedureallowedforthemechanicalhysteresisoftheunimorphtobe studied.Furthermore,repetitions(notshown)indicatedthattheresultsdidnotvaryto anysignicantdegree. 7.3Results TheresultsoftheexperimentareshowninFig. 7-3.Reviewingtheresults,itis quicklyevidentthatthethickersteelsubstrateoutperformstheothertwosubstrates inloadbearingcapacity.Closerexaminationrevealsthatitalsooutperformsinterms ofoveralldisplacement.Thethinnersteelhasalargerdisplacementrangethanthe unidirectionalcarbonber,buttheunidirectionalcarbonberproducesalargerload bearingcapability.OneremarkableaspecttotheseresultsisthefactthattheMFCs aremuchweakerwhenactuatedinthe-500Vdirectionascomparedtothe1500V direction.Thedifferenceisapproximatelyafactoroftwo. Theseresultsindicatethatthe0.10mmsteelisthepreferredsubstrateforaMAV expectedtoencounteranythingbeyondveryslightaerodynamicloads.Aswasshown withtheFEAworkinSection 6.5,itispossiblethatathickersteelsubstratemayyield evenmoreloadbearingcapacitythanthe0.10mmsteelandmaybebettersuitedfor theMAVexaminedinthisresearch.Thiswillbeexploredusingtheoptimizationscheme inChapter 11 87

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A B C D E F G H Figure 7-2.Fourpointbendtestprocedureforthe1500Vtest. 88

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A B Figure 7-3.Fourpointbendexperimentalresults.a)MFCactuatedto-500V,thextures broughtintocontactwiththeunimorphsurface,thentheMFCactuatedto 1500V.b)MFCactuatedto1500V,thexturesbroughtintocontactwiththe unimorphsurface,thentheMFCactuatedto-500V. 89

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CHAPTER 8 INITIALMAVDESIGN,LESSONSLEARNED,ANDVALIDATIONOFAERODYNAMIC MODELASSUMPTION Shortlyafterthepreliminaryresultsweregenerated,apreliminaryMAVwith MFCswasmanufactured.Ratherthenspendsubstantialtimecreatingasophisticated computermodelaroundanunprovendesign,itwasdecidedthebestprocesswas toexperimentallytestpotentialdesignsuntilonewasfoundtoprovidesuitableight characteristics.Onceafunctionaldesignwasdetermined,additionalresourcescould becontributedtowardsmodelingandoptimizingthedesign.TheMAVdiscussedinthis chapteristherstattemptataMFCactuatedMAVdesign. ThegeometryofthisMAVwasbuiltonapreviouslyprovenservo-controlleddesign whichhadgonethroughnumerousrevisionsandimprovements.Tomaximizethe deectiongeneratedbytheMFCs,abattenreinforcedmembranewingwaschosen. Itwasexpectedthatthiswouldreducethebendingstiffnessofthestructure,allowing theMFCstodeectfurther.AtotaloffourMFCs,twoM8507-P1andtwoM8503-P1, wereplacedonthewing,asshowninFig. 8-1.WiththeMFCsoneachsideconnected inparallel,eachsideofthewingcouldbeactuatedindependently.Aservocontrolled elevatorandrudderwerealsoincorporatedintothedesign.Theintentwasnottocouple theMFCswiththeservos,buttousetheservoactuatedcontrolsurfacestotrimthe aircraftanduseonlytheMFCsforightcontrol. 8.1Manufacturing Manufacturingwasperformedusingapre-preglayuptechniqueasshownin Fig. 8-2.Themembranewasconstructedofripstoppolyesterandthebattenswere constructedofunidirectionalcarbonber.Theleadingedgewascomposedofthree layersofbidirectionalcarbonber.TheMFCswerelaidontopofthebattensbeforethe entirelayupwasplacedundervacuumpressureinsidetheovenforcuring.Afterthe curingprocess,theextramaterialwastrimmedoffthewingtoachievethenalproduct. 90

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Figure 8-1.ImagesoftherstMFCactuatedMAVconstructedunderthisresearch. PhotostakenbyBradleyLaCroix. Figure 8-2.ManufacturingoftherstMFCactuatedMAVwing.PhototakenbyBradley LaCroix. 91

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Figure 8-3.DICsetupforrstMFCactuatedMAVwing.PhototakenbyBradleyLaCroix. 8.2DICTesting Atthispoint,thewingwaspreparedforDICtesting,whereaspecklepatternwas appliedtothesurfaceofthewing.Next,thecamerasystemandlightingwassetupto illuminatethewingproperly,withoutoverexposingorsilhouettingthestructure.This setupisshowninFig. 8-3.Thewingwasactuatedthroughvariousvoltageswiththe horizontaltailpositionedinanapproximatepitch-up,pitch-neutral,andpitch-down position. Figure 8-4 showstheDICresultsforthreedifferentactuatedpostions.Arelatively largedisplacementcanbecommandedwhentheMFCsareactuatedtotheup-position. Conversely,arelativelysmalldisplacementoccurswhenactuatingtheMFCstothe downposition.Furthermore,thehorizontaltailstronglyaffectsthepositionofthe outboardportionsofthewingascanbeseeninFig. 8-4C. 92

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A B C Figure 8-4.DigitalimagecorrelationresultsfortherstMFCactuatedMAV.A)Neutral positionforallcontrolsurfaces.B)Fullroll-leftmaneuverwiththetailatthe neutralposition.C)MFCsactuatedtofull-uppositionwiththetailactuatedto apitch-downposition. 93

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8.3 FlightTesting Theighttestgoalwastorsttrimtheaircraftandreachadequatealtitudeand thenswitchtoMFCcontroltoevaluatetheMFCperformance.Numerousighttests showedthattheaircraftwasrelativelyheavyforitswingarea.Thismadeitdifculttoy formorethanafewseconds.Furthermore,themembraneatthewingtipsappearedto allowairowtospilloveranddumplift.Additionalstructurewasaddedatthetipstotry tomitigatethisproblem.Thenalighttestwassuccessfulinproducingrollcontrolof theairplanewiththeassistanceofpitchcontrolfromtheservo-actuatedhorizontaltail, buttherewasstillsubstantialroomforimprovement. 8.4DiscussionandLessonsLearned Oneofthemainaspectsthatmayhavelimitedtheperformanceoftheaircraft wastherelativelycompliantnatureofthewingandMFCs.Eventhoughthestationary actuationofMFCswasontheorderof25mm,aerodynamicloadsmayhavedrastically reducedthis.Furthermore,slackandvibrationinthewingmayhavemadestableight aninherentimpossibility.Inaddition,theMFCswerepositionedtowardsthetrailingedge ofthebattens.Duetoaeroelasticity,itislikelythattheMFCswerelikelybeingpushed upordownalongwiththerestofthewingmembrane.Lastly,therelativelylowaspect ratioofthewingmayhavemadeitlargelyinefcientanddifculttomaneuver. Therearealsodrawbackstotakeintoaccountwhenconsideringthecomputer modelingaspectoftheaircraft.Duetothelargedifferenceinthematerialpropertiesin themembranewing(transitioningabruptlyfromcarbonbercompositetopolyester), niteelementmodelingandaerodynamicpredictionscouldyieldavarietyofproblems. Thiswouldmakethecomputermodelingaspectextremelychallenging.Alongwith thepreviouslymentionednegativeightcharacteristics,itwasdeterminedthata solidcarbonberwingwouldbepreferential.Thenextchapterdetailstheattemptsto correcttheseissuesbyinvestigatingotherpotentialdesigns.Theremainingportion 94

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of thischapterconsidersthekeyassumptionmadewhenmodelingaexiblewingin aerodynamicsoftware. 8.5AerodynamicAssumptionValidation Oneofthekeyaspectsofthisresearchisthecalculationoftheaerodynamicload onanairframeforaparticulardesign.Todothisquicklyandefciently,aprogram calledAthenaVortexLattice(AVL)wasused[ 35].Thisprogramwasdevelopedby MarkDrelaandHaroldYoungrenatMIT.Itprovidesthenecessaryframeworkto calculatetheaerodynamicandight-dynamicpropertiesofarigidaircraftofarbitrary conguration.Itutilizesanextendedvortexlatticemodelfortheliftingsurfaces,as wellasaslender-bodymodelforthefuselage.OnedrawbackofAVListhatitonly givesaninviscidapproximation,whichtendstounderestimatedragandoverestimate lift.Nonetheless,ithasbeenwidelyusedintheresearcheldduetoitsrelatively fastcomputationaltime[ 6368]andhasbeenindependentlyvalidatednumerous times[ 69, 70]. AcoupleMAVswithasimilargeometrytotherevisedMAV(tobediscussedin Chapter 9 )alsouseAVLfortheiranalysis.TherstMAV,mentionedinSection 2.2,was developedbyStanfordandMujahidattheUniversityofFlorida,andincorporatedtorque rodsforactuatedrollcontrol[ 68].Thetorquerodenablestheoutboardsectionofthe wingtobetwistedupordownusingtraditionalservos.AnotherexamplefromAVLisan AirForceResearchLaboratoryMAV,GENMAV[ 69],intendedtobeusedforavariety ofmissions.ThisdesignwaslateroutttedwithMFCsasshowninOhanian'sworkin Section 2.1 [ 29]. ThekeyassumptioninAVListhatthestructureisperfectlyrigidanddoesnot deformunderloading.However,MAVsconstructedofmembranematerialsandtheones foundinthisproject,whichmaybeconstructedofonlyoneortwolayersofcarbonber composite,canberelativelycompliant.Toverifythatanadditionalphenomenaisnot present,suchasoscillationswhichmaycausetheowtoseparateor,conversely, 95

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impro veowattachment,aseparatesetofexperimentswereconducted.These experimentsaredescribedindetailinthefollowingsections. 8.5.1BackgroundandConceptOutline MicroAirVehicles(MAVs)areoperatedatlowReynoldsnumberswhichmakes themeasilyinuencedbysmalldisturbances.Arelativelysmalldegreeofturbulence canhaveprofoundeffectsontheightstabilityandightpath.Inaddition,thetip vorticesproducedatthewingtipscanbequitelargeincomparisontothewingdueto thelowaspectratio.Gustscanverylikelybeonthesameorderofmagnitudeasthe forwardvelocityoftheMAV(upto15m/s),whichcouldresultinimmediateinstability.A exiblemembranewingshapedampenssuchdisturbancesandcanhelptoresistow separation,reducingerraticbehaviorthatiscommonlyassociatedwithlowprolewings ofthissize[ 30 71 ]. However,theightmechanicsofexiblemembranewingsarenotfullyunderstood. Onecommonassumptionwhengeneratingacomputationalanalysisforsuchawing isthatthedeformedshape,insteadystate,behavesthesameasitsrigidcounterpart. Tothisextent,niteelementsoftwareisnormallycoupledwithAVLwhichpredicts thelift,drag,andmoments.TheniteelementsoftwareandAVLsoftwareiterateuntil theyconvergeonasolution.Whencalculatingtheaerodynamicloads,AVLtreatsthe structureasperfectlyrigid.Figure 8-5 showsthisgeneralconcept. Inthesoftwaresetupforthisresearch,theFEAsoftwarepredictsthedeformed shapeofthewingunderactuation.Next,AVLpredictstheaerodynamicloadsfor thisgeometry.TheaerodynamicloadsarepassedbacktotheFEAsoftware,which calculatesthenewgeometry.Theprocessisiterateduntiltheresultsconverge.This processisfurtherexplainedinChapter 10.However,theassumptionthatthewing canbetreatedasperfectlyrigidduringtheAVLanalysishasneverbeentested.The purposeofthissetofexperimentsistofurtherinvestigatetheightmechanicsofexible membranewingsandtodetermineiftheperfectlyrigidassumptionisappropriate. 96

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Figure 8-5.Conceptualillustrationofrigidvs.exiblewingloading. A B Figure 8-6.Flipsideviewofsiliconemembranewings.A)Battenreinforcedsilicone membranewing.B)Perimeterreinforcedsiliconemembranewing.Photos takenbyBradleyLaCroix. Totestthisassumption,twoexiblemembranewingsweremanufactured,one perimeterreinforcedandtheotherbattenreinforced,showninFig. 8-6.Siliconewas chosenforthemembranematerial.Thisisbecauseitisrelativelyeasytopretensionin auniformmanneranditdoesnotdegradewithtime[ 72],whichiscriticalforthissetof experiments.DICwasusedinthewindtunneltoacquirethethreedimensionalproles ofthewingswhileunderdifferentightconditions. 97

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The 3DprolesforeachwingwereconvertedtoCNCcodeandmoldswere manufacturedrepresentingthedeformedwingswhileunderload.Usingthesemolds, fourapproximatelyrigidwingswerefabricated:tworepresentingtheBRwingattwo ightconditionsandtworepresentingthePRwingattwoightconditions. Theintentwastomatchuptheexiblewinggeometrywiththerigidcounterpart underthesameightconditions.Detailedmeasurementsoftheliftanddragweretaken ofthefourrigidwingsaswellasthetwoexiblewingsusinga6DOFstingbalanceand DIC.TheDICcouldthenquantifythequalityoftbetweentherigidandexibleproles ofeachwing.Afterwards,themeasurementswereanalyzedandtheexible-rigid assumptionanalyzed. 8.5.2InitialExperiments Twosetsofexperimentswereconducted.Thegoaloftheinitialsetofexperiments wastomapthe3Dgeometryoftheexiblewingsatdifferentightconditions.This 3Dgeometrywasthenusedtogenerateasetofrigidwingsusedinthesecondsetof experiments.Duringthissecondsetofexperiments,theexiblewingswerecompared totherigidwingsatidenticalightconditionsinwhichtheexiblewingdeformedto thesameshapeastheirrigidcounterparts.Thisprocessisdescribedinthefollowing sections. 8.5.2.1Manufacturing Twowingswerefabricatedwithpre-pregcarbonberusingthemoldfortheinitial MAV.Thewingswerefabricatedinasingleprocessusingalay-upmethodwherethe pre-pregcarbonberandmembranematerialwerecutandassembledonthemold andthencuredundervacuumpressureat1atmosphereand260 F.Thisresultsina heterogeneouswingmanufacturedasasinglepart. ThePRframewasmadeupof4layersofbidirectionalcarbonber.Thislarge numberoflayerswasusedtoinsurethattheframeofthewingwouldberelativelyrigid, withonlythemembraneinthemiddledeforming.TheBRwinghadthesame4-layer 98

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A B Figure 8-7.Isometricviewofsiliconemembranewings.A)Battenreinforcedsilicone membranewing.B)Perimeterreinforcedsiliconemembranewing.Photos takenbyBradleyLaCroix. constructionontheleadingedge;howeverthebattenswerecomposedof2layersof unidirectionalcarbonber.ThesewingsareshowninFig. 8-7 aswellasintheprevious sectioninFig. 8-6.Themembranematerialforbothwingswasmadeofpre-fabricated silicone.Thesiliconematerialallowsforuniformandrepeatablepretensioning[ 72]. Furthermore,ithasbeenshownthattreatingthesiliconewithacoronatreatment machineimprovestheadhesionbetweenthepre-pregcarbonberandsilicone[ 73, 74]. Beforeapplyingthesilicone,itwastreatedwithacoronatreatmentdevice,ModelBD-20 manufacturedbyElectro-TechnicProducts,Inc,tostrengthenthebondbetweenthe epoxyinthecarbonberpre-pregandthesilicone. Aftercuring,theedgesofthewingweresandedandtrimmedsuchthattheir outlineswereidentical.ToutilizeDIC,ahighcontrastblackandwhitespecklepattern wasappliedtothetopsurfaceofeachwing.Thesilicone,whichwasalreadywhite,was maskedoffpriortoapplyingawhitecoatofpainttothecarbonber.Thentheblack specklepatternwassprayedovertheentiretopsurfaceofbothwings.Thesilicone isonlycoatedwithblackspeckles,sincethepaintcancrackandakeifappliedina uniformcoatonthehighlyelasticsilicone. 99

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Figure 8-8.FlexiblewingwindtunnelsetupwithDIC.PhototakenbyBradleyLaCroix. 8.5.2.2TestingProcedure Thetwowingswerepositionedinthewindtunnelandtestedundervariousangles ofattackrangingfrom0 to15 andwindspeedsof10to15m/s.Beforeeachrun,a referenceimagewastakenofthewingpositionedatitsrespectiveangleofattack.This imagewasusedtocalculatethedisplacementofthewingduringtesting.Duringthe runs,multipleimagesweretakenusingtheDICsystemandaccompanyingVIC-Snap 2007software.TheDICcamerasusedweremanufacturedbyPointGreyResearch (GRAS-50S5M-C)andthelensesareSchneider-KreuznachXenoplan1.4/17-0513. Tenpicturesweretakenateachconditionsothatanyoscillationscouldbeaveraged outnumericallyusingpost-processing.VIC-3D2009wasusedtoanalyzetheimages andtogenerateathreedimensionalsetofpointsrepresentingthedeformedshape ofthewings.Figure 8-8 showsthewindtunnelsetupwiththeDICsystemontheleft andthewingonarotatingangle-of-attackarmpositionedwithinthewindtunnelonthe right.Figure 8-9A showsaviewoftheBRwingplacedontheangle-of-attackarmand Fig. 8-9B showsthepositioningoftheDICcamerasystemovertheBRwingabovethe ceilingofthewindtunnel. 100

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A B Figure 8-9.Flexiblemembranewinginthewindtunnel.A)Rearviewofthemembrane wing.B)UndersideviewofthemembranewingwiththeDICcamerasinthe background.PhotostakenbyBradleyLaCroix. Liftanddragmeasurementswerenottakeninthissegmentoftestingsincethe exiblewingsneededtobere-testedatthenextstageoftestingtoensureproper matchingofgeometryanddynamicpressure.Forexample,evenifthesamewindspeed andangleofattackoftheinitialtestisusedduringthesecondsegmentoftesting, conditionssuchastemperatureandhumiditycanchange,whichaffectsthedynamic pressure.Thiscanhaveasignicanteffectonaerodynamicforces.Therefore,inthe secondstageoftesting,acombinationofvisualdifferencingbetweentheexiblewing andrigidwingtookplaceaswellasaleast-squareserrorcalculationtoaccuratelyadjust andcloselymatchthedeformedshapeoftheexiblewingtotheshapeoftherigidwing. 8.5.2.3DigitalImageCorrelationPostProcessing TheresultsofthewindtunneltestswereexportedfromVIC-2009asplainASCII textles.ThesetextlesincludetheX,Y,andZcoordinatesofapproximately40,000 pointsaswellastheirrespectivedisplacementsintheU,V,andWdirectionsforeach image.ThesetextleswereimportedintoMATLABandthenpost-processed. 101

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One ofthekeyadvantagesofpost-processingtheresultsinMATLABistheprecise transformationoftheresultsintothedesiredcoordinatesystem.Thedeformedvalues shownonthemonitorinFig. 8-8 makethewingappeartobeasymmetricallydeformed. Thisisbecausetheangle-of-attackarmcanpitchupwardsandrollslightlywhen aerodynamicallyloaded,therebycausingaseeminglylargerdeformationontheleftside ofthewing.Furthermore,thedefaultreferenceframeoftheDICmaynotbeorthogonal withrespecttotheplaneofthewing.MATLABwasusedtoeffectivelyremovetherigid bodyrotationandtransformthedatatothedesiredorientationwithinthecoordinate systemusingcoordinatetransformations. Thestepsforthis,whichareillustratedinFig. 8-10,areasfollow. 1.AfterloadingthedataintoMATLAB,thecoordinatesystemofthereferencedata wastransformedtothecorrectorientationbytakingthereferenceX,Y,andZ coordinatesandapplyingcoordinatetransformationsothattheX-Yplanewas alignedtotheplaneofthewing. 2.ThecoordinatetransformationswerealsoappliedtotheU,V,andWvectorsto maintainthecorrectdisplacementdirections. 3.TheXYZandUVWdatawasthencombined(X+U,Y+V,Z+W)togeneratea setofdeformeddataforeachimage. 4.Thisdatawastheninterpolatedintoauniformgridpatterntoassurestandardization acrossallimagesataparticularangleofattackandairspeed. 5.Finally,thisdatawastransformedtosubtractouttherigidbodyrotationofthewing duetothemovementoftheangle-of-attackarm. Figures 8-11 and 8-12 showthenalresultofthetransformationsalongwiththe out-of-planedeformationforboththePRandBRwing.Thetransformedgeometry,as showninFigs. 8-11A and 8-12A,illustratesthecontoursofthedeformedsurface.In contrast,theout-of-planedeformation,showninFigs. 8-11B and 8-12B showshow muchthewingdeformsintheout-of-the-pagesense.Inotherwords,itisthechange intheZ-position( Z)ratherthanaspecicZ-value.Additionalstepsarerequiredto convertthedataintoCNCformatwhichiscoveredinthefollowingsection. 102

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Figure 8-10.IllustrationofDICpostprocessingprocedure. A B Figure 8-11.DICresultsforthebattenreinforcedexiblemembranewing. A)Transformedreferencegeometryforthebattenreinforcedwing. B)Out-of-planedeformationforthebattenreinforcedwing. A B Figure 8-12.DICresultsfortheperimeterreinforcedexiblemembranewing. A)Transformedreferencegeometryfortheperimeterreinforcedwing. B)Out-of-planedeformationfortheperimeterreinforcedwing. 103

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Figure 8-13.GeometricedgetruncationofDIC. 8.5.3RigidWingManufacturing OneofthekeydrawbacksofDICwhenutilizingitasareplicationmethodisthatitis unabletocorrelatethesurfaceallthewaytotheedge.ThisisshowninFig. 8-13 where thecoloroverlaysuddenlystopsneartheedge.Thistruncationcanbemoderately reducedbychangingsettingsintheDICsoftware,butcannotbecompletelyeliminated. Therefore,itisnecessarytogenerateatechniquebywhichtheknowngeometrycan beextrapolatedtoapproximatelyreplicatethetruegeometry.Thisisdescribedinthe followingsection. 8.5.3.1ExtrapolationandConversionofDICDatatoCNCFormat Variousextrapolationtechniqueswereexaminedusingavarietyofcurvets. However,itwasdeterminedthatalinearextrapolationtechniquewasthebestapproach forthisproject.Sincetheextrapolationlengthwasrelativelysmallandalsobecause higherorderpolynomialshaveatendencytogiveasymptoticresults,alinearextrapolation techniquewasdeemedmostappropriate.Theextrapolationprocessitselftakes placeoverthreesteps.Therststepwastodesignatethepointsofinterestforthe extrapolation.Withthisinmind,asetnumberofpointsaroundtheperimeterwere selected,whichareshowninblackinFig. 8-14.Second,thedatawasextrapolated rowbyrowandcolumnbycolumnintwodirections,thelongitudinalandlateral direction,withtheconditionthatthereweretwodatapointsatthatroworcolumn. TheextrapolatedvaluesaredesignatedbytheredandgreencirclesinFig. 8-14.The 104

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Figure 8-14.ExtrapolationofDICdatatorestoreuncorrelatedgeometry.Theblackdots indicatethereferencepointsfortheextrapolationwhereastheredpoints designatethelongitudinalextrapolationandthegreenpointsdesignatethe lateralextrapolation. dataforthewingwasextrapolatedslightlybeyonditsoriginalplanformdimensionsto ensurethatthemoldwouldbelargeenoughtoproperlyfabricatethewing.Finally,any pointswherethedatawasextrapolatedbothinthelongitudinalandlateraldirectionwere averagedtogenerateasingledatapoint. Eventhoughthelinearextrapolationtechniquewasdeterminedtobethemost rigorous,itstillproducedsomeresultingdatapointsthatwereoutliers.Thiscanbe especiallyproblematiconaCNCmachinewheretheoutlyingpointscancommand thebittodivedeepintothematerialcausingalargegouge.Torectifythisissue,a smoothingfunctionwasutilizedaroundtheperimeterofthewing.Thistechniqueis showninFig. 8-15. Atthispoint,thedatapointscanbearrangedintoaCNCcodebasedonthedesired toolpath.ModiedMATLABcode,originallywrittenbyClaxton[ 70 ],wasusedtomake theconversion. 8.5.3.2Fabrication ThemanufacturingprocessisshowninFig. 8-16 wheretheCNCtoolpath, generatedinMATLABisshown,followedbythecompletedCNCmold,andtherigid counterpartfortheperimeterreinforcedwing.TheCNCtoolpathisgeneratedbasedon 105

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A B Figure 8-15.SmoothingtechniqueforextrapolatedDICdata.A)Indicationoftrailing edgedata(inblack)containingoutliers.B)Originaldata(bluedots)and smootheddata(redline). Figure 8-16.Illustratedrigidwingmanufacturingprocess.PhototakenbyBradley LaCroix. variousparameterssuchastooldiameter,scallopheight(ridgesbetweentoolpasses), andspacingofdatapoints. Thelay-upmethodfortherigidwingissimilartotheexiblewings(asdescribedin Section 8.5.2.1),butonlycarbonberpre-pregisused.4layersofbidirectionalcarbon 106

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Figure 8-17.Rigidwingcounterparts.Theperimeterreinforcedwingsareshownonthe leftandthebattenreinforcedwingsareshownontheright.Phototakenby BradleyLaCroix. berareusedtofabricateawingmeasuringapproximately1mminthickness.Thefour resultingrigidwingsareshowninFig. 8-17. BenchtopDICtestswereperformedontherigidwingstoverifythattherewas reasonableagreementbetweentherecordedprolesforthedeformedexiblewings. 8.5.4ValidationExperiments Inthevalidationsetoftests,eachrespectiveexiblewingwastestedrst.The ightconditionswereadjusteduntilthe3Dprolespresentedgoodagreementwith theoriginalrecordedproles.Thenew3Dprolewasrecordedandtheliftanddrag measurementstaken.Then,therigidwingcounterpartswereplacedinthewindtunnel atthesameightconditionsandthe3Dprolerecordedwhiletheliftanddragwas measuredusingthestingbalance.The3Dprolefortheexiblewingswerethen comparedwiththe3Dprolesfortherigidcounterparts.Thesecomparisonsareshown inFigs. 8-18 and 8-19. Apositivevalueindicatesthattherigidwingprotrudesabovetheexiblewing (out-of-the-page)whereasanegativevalueindicatesthattheexiblewingprotrudes abovetherigidwing.Thecolorscaleineachgureissetfrom-1mmto1mm.The 107

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A B Figure 8-18.Comparisonofexibleandrigidbattenreinforcedwings.A)Batten reinforcedwingat15m/sand8.5 angleofattack.B)Battenreinforced wingat15.5m/sand14 angleofattack. A B Figure 8-19.Comparisonofexibleandrigidperimeterreinforcedwings.A)Perimeter reinforcedwingat17m/sand4 angleofattack.B)Perimeterreinforced wingat17m/sand8 angleofattack. summaryofightconditions,proleagreement,andmeasuredliftanddragforces,are showninTable 8-1.Notethatthecoefcientofliftanddragarenearlyidenticalinevery case,withperimeterreinforcedwinghavingthelargestpercentdifferences.Eventhough thesepercentdifferencesarelarger,themagnitudeisstillquitesmall,especiallywhen consideringthemagnitudeofthecoefcients.Thisleadstotheconclusionthatthere isultimatelynodifferenceinsteadystateliftanddragbetweentheexiblewingandits rigidcounterpart. 108

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T able8-1.Resultsoftherigidandexiblewingcomparison. Prole RigidFle xible AgreementWingWing AoAVelocityRMSErrorAvgError C L C D C L C D %Diff%Diff (degrees)(m/s)(mm)(mm) in C L in C D BR 18.515.00.17-0.031.230.241.220.24-1.0-1.6 BR214.015.50.24-0.071.760.521.780.531.20.3 PR14.017.00.270.030.770.100.740.10-3.3-0.3 PR28.017.00.360.171.330.251.290.25-2.8-2.4 8.5.5 Discussion Thissetofexperimentssuccessfullydemonstratedthataperfectlyrigidwing assumptioninAVLisvalidaslongasthedeformedproleistheinputgeometry.This meansthatsaprogramincorporatingbothAVLandaniteelementsolver,suchas Abaqus,canbeusedtodeterminetheaerodynamicloadsanddeformedstateofawing onaMAV.Furthermore,thisprovidesamethodbywhichvariousdesignsutilizingMFCs canbestudiedrelativelyquicklyandefciently. Perhapsoneofthemostsignicantresultsofthissetofexperimentsistheproofof conceptthatDICcanbeusedtocreateareasonablyaccuratecopyofa3Dgeometry. Withadegreeoferroroflessthan 1mmfora305mmwing,thisisequivalenttoa replicationaccuracyof 0.3%.Thiswasseenwithallfourrigidwingcounterparts. 109

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CHAPTER 9 FORWARDSWEPTMAV AfterconductingnumeroustestightswiththeellipticalMAV,itwasdecidedto makeacompletedesignrevision.Thegoaloftheinitialstageofighttestingwas tonarrowdownthedesignspacefromabroadrangeofoptionstodevelopadesign capableofafewminutesofight.Onceaightworthyplanewasdeveloped,further analysiscouldbeconductedandrevisionscouldbemadetomakeawellrounded aircraft.Ultimately,themaingoalwastodevelopaplatformwhichwouldbecapable ofsufcientcontrolauthority,butwithonlytwoMFCactuators.Excludingelectronics, theMFCsonatwoactuatoraircraftaccountforroughly90%ofthematerialcosts. Therefore,doublingthenumberofactuatorswouldnearlydoubletheaircraft'scost. Fromlaboratorytestingandprevioustestights,itwasknownthattheMFCsgenerated relativelysmalldeectionscomparedtoservo-actuatedcontrolsurfaces.Therefore,in developinganewaircraft,itwasdecidedtomaximizethecontrolauthoritybychoosing thebestplanformandbyndingtheidealplacementfortheMFCs. 9.1ConceptEvaluation Figure 9-1 illustratestheconceptualthoughtprocessbehindtheconsiderationof thethreetraditionalaircraftdesigns.Witharearsweptwing,placingtheMFCsinboard wouldresultinpoorrollcontrolandpoorpitchcontrolbecausetheMFCsarelocated closetotheCenterofGravity(CG)bothinthelateraldirectionandinthelongitudinal direction.PlacingtheMFCsoutboardhasmorepotential,butsincethewingsare relativelycompliant,thisdesignissubjecttotheeffectsofaeroelasticityandcontrol reversal.Aeroelasticeffectsarearesultofaerodynamicloadschangingtheshapeofthe structure.Inamoreseverecase,theaeroelasticeffectswilldeformthewinginsucha waythatacontrolinputresultsinanoppositeresponse.Therefore,arearsweptwing withtheMFCsplacedoutboardwouldrequiresufcientstructuralreinforcement. 110

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Figure 9-1.DesignconsiderationsforMFCplanform. AstraightwingwouldbecapableofverylittlepitchautoritysincetheMFCscannot bepositionedmorethanasmalldistancefromtheCG.Rollcontrolwouldbeacceptable iftheMFCswereplacedoutboard. Fortheforwardsweptdesign,placingtheMFCsoutboardwouldresultinverylittle pitchauthoritysincetheMFCsarelongitudinallyclosetotheCG,butmayproduce acceptablerollcontrolwithsufcientstructuralreinforcement.Thebestpositionforthe MFCsmaybeneartheinboardsection,wheretheyarealargelongitudinaldistance fromtheCG.RollcontrolwouldbeacceptableifthedeformationoftheMFCactuator translatesoutboardonthewing.Inaddition,theaeroelasticresponseofthewingmay betunedbyadjustingtheberorientationinthewinglayup. Anotherconcern,forMAVsingeneral,istheoverallpitchauthority.MAVs,due totheiroperationatlowerReynoldsnumbersandmoreexiblewings,requirealarge degreeofpitchauthorityforadequatecontrol.However,rollauthorityisgenerallywithin anacceptableregionformostdesigns.Forthisreason,itisimportanttomaximizepitch authorityasmuchaspossibleandthenmaximizerollauthorityaccordingly.Therefore, theMFCsshouldbeplacedtowardstherear-mostportionofthewing,whichinthe forwardsweptwingcase,istowardstheinboardsection. Otherfactorsmaketheforwardsweptdesignslightlybetterthantherearswept design.Forexample,prop-washcanimprovecontrolsurfaceauthorityduetoincreased airow.Thisisespeciallytrueatlowerspeeds,whencontrolauthorityisusually 111

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Figure 9-2.Illustrationofanisotropicwingvsabend-twistcoupledwing. reduced,duetoreducedairow.However,iftheactuatedareaisintheprop-wash,ight controlcanbemaintainedevenatlowerspeeds.Furthermore,iftheMFCswereplaced outboardonthewing,theywouldnotbewithintheprop-washregionandhaveless controlauthorityforamajorityoftheightregime.Theseconsiderationsindicatethatthe forwardsweptwingmaybeasuperiorsolutionwhenselectingaplanformfortheMFCs. Tomitigateaerodynamicinstabilitiesfortheforwardsweptwingdesign,bend-twist couplingcanbeincorporatedintothewing.Bend-twistcouplingisaresponseof orthotropicmaterialsinwhichapurebendingmomentresultsinabendingANDtwisting responsefromthematerial.ThisbehaviorisdemonstratedextremelywellinFig. 4-8A, wherealoadappliedtoonlyonecornerofthecantileveredsubjectresultsinbending, butalsointwistingintheoppositedirectionoftheload.Thebenetofbend-twist couplinginaforwardsweptwingisdemonstratedbyFig. 9-2.Foranisotropicforward sweptwing,aerodynamicloadswillliftthefrontedgeofthewingupresultingintwist, whichinreturnincreasestheaerodynamicloadsevenfurther.Thiscancreatesevere instabilitiesduringight.Theupwardtwistisbecauseamajorityoftheliftonthewing isinfrontofthehalfwaypoint,nearthequarter-chordlocation.Astheisotropicwingis loaded,itwillcontinuetotwistupwards.Essentially,thisisapositivefeedbackloopthat canleadtootherproblemslikeutteranddivergence. Incomparison,whenaforwardsweptwingincorporatesbend-twistcouplingby orientingthebersinthedirectionshown,thetwistingofthewingwillbemitigated 112

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or evenslightlyreversed,thereforereducinglift.Thisresultsinanegativefeedback loopinwhichhighloadswillleadtoreducedloads,thereforealleviatinginstabilities. Theforwardsweptwingdesignwithbend-twistcouplingwillbestudiedindetailforthe remainderofthischapter. 9.2Motivation ForwardsweptwingsrstmadetheirdebutduringWorldWarII,intheformof theGermanbomber,JunkersJu287.Theairplanehadaforwardwingsweepof25 degrees.Severalyearslater,theMesserschmittofGermanyproducedtheHFB320 Hansaaircraft.Thenextforwardsweptwingaircraftwasnotuntil1984,withtherelease oftheGrummanX-29. Forwardsweptwingshaveafewadvantageswhencomparedtotraditonalstraight orsweptwings.Firstly,theypromisetobeslightlymoreefcient,sincetheairow overthewingforcesairinboardratherthanoutboard,whichreduceswingtipvortices. Secondly,assumingawelldesignedstructure,theycanbemoreagilewhenconducting complexmaneuvers.However,ifthestructureisill-designed,aeroelasticdivergencecan rapidlycausetheplanetobecomeunstable.Pamadifurtheraddsthatforwardswept wingsgenerallyhavefavorablestallcharacteristics.Contrarytorearsweptwings,the rootregionsstallrst,andthestallprogressesfromtheroottothetip.Thispreventsloss ofrollcontrolduringstallingandtherefore,forwardsweptdesignsarespinresistant[ 75 ]. Nonetheless,forwardsweptwingscansufferfromyawinstability.Thismeans thatastheplaneyawstooneside,onewinganglesforward,theotherrearward.This reducesthesweepoftherearwardwing,whichincreasesthedrag,whichpushesit fartherback.Thiscanleadtoadutchrollinreverse.However,averticalstabilizercould helptoalleviatethisproblem. 113

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9.3 PrototypesandFlightTesting Acoupleprototypeswithservoactuatedcontrolsurfaceswereconstructedand testedpriortomanufacturingawingwithMFCs.Theseprototypes,aswellastheMFC prototype,aredescribedinthefollowingsections. 9.3.1FirstPrototype-Testingtheforwardsweptwingdesign TheinitialprototypeisshowninFig. 9-3A.Tominimizetheresourcesinvested,the rstprototypewingwaslaiduponaatsurface,therefore,toolingwasnotnecessary. Twolayersofbidirectionalcarbonberwerepresentthroughoutthewing,withadditional layersofunidirectionalcarbonberplacedontheleadingedge.Theunidirectional wasangledat22 infrontofthesweepangleofthewing.Thisversionoftheplane hadservo-actuatedrudderandelevatorcontrolintheformofatraditionaltailforight control.Sinceyawandrollarecoupled,sufcientcontrolwasexpected. Aftertheinitialtesting,itwasquicklyrealizedthatthecenterofgravitywastoofar backandaprolongedtestightcouldnotbecompleted.Therefore,thewingwasmoved towardstherearoftheplanetoeffectivelyshiftthecenterofgravityforward.Additionally, extrasurfaceareawasaddedtotheruddertoincreaseyawauthority.Thisrevisedplane isshowninFig. 9-3B. Thisplaneewwellwithrespecttostability,butlackedsufcientrollcontrol.Since therewasnodihedralbuiltintothewing,theplanewasonlyslightlymorestablethan neutralintherollaxis.Furthermore,therudderwaslocatedverycloseverticallytothe centerofgravity.Therefore,iftheplaneenteredabankedorientationduringight,the rudderwasunabletorolltheaircraftbacktolevel. Toimproverollcontrolandtomakeanintermediatesteptowardsthenextprototype, aileroncontrolsurfaceswereaddedtotheinboardsectionofthewing.Thismodication isshowninFig. 9-4.Afterthisrevision,theaircrafthandledextremelywellandwas difculttodifferentiatebetweenatraditionalRCaircraft.Withtheseresults,thework beganonthenextprototype. 114

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A B Figure 9-3.Therstprototypeoftheforwardsweptwing.A)Protypewiththewinginthe initialposition.B)Prototypewiththewingintherevisedposition.Photos takenbyBradleyLaCroix. A B Figure 9-4.Therevisedversionoftherstprototype.A)Topview.B)Bottomview. PhotostakenbyBradleyLaCroix. 115

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A B Figure 9-5.Thesecondprototype.A)Topviewoftheairplane.B)Bottomview.Photos takenbyBradleyLaCroix. 9.3.2SecondPrototype-Testingelevoncontrol Forthenextprototype,thehorizontaltailwasremovedfromthedesignandelevons wereadded,asshowninFig. 9-5.Elevonsareasinglesetofcontrolsurfaceswhich serveboththeroleofailerons(rollcontrol)andelevators(pitchcontrol).Asmentioned previously,sincerollandyawarecoupled,sufcientightcontrolcanbemaintainedwith controlinoneofthetwoaxes.Therefore,therudderwasalsoeliminated,butthevertical tailwasretainedforstability. Acamberedwingdesignwasdevisedusinganin-housesoftwarepackagebuiltfor MATLABdevelopedbyDanielClaxton[ 70].Reexwasbuiltintothewingtoeliminate theneedforahorizontaltail.Oncethedesignwascomplete,thesoftwareproduceda CNCcodewhichallowedforthetoolingtobemanufactured.Thetoolingprovidesa3D surfaceonwhichtolayupthecompositewing,similartotheellipticalwinglayupinthe previouschapter(Fig. 8-2).Thewingwascomposedoftwolayersofbidirectional throughoutandaleadingedgewithtwolayersofunidirectionalsandwichingthe bidirectional.Theunidirectionalwasonceagainplacedatanangleof22 withrespectto thesweepofthewingtherebyincorporatingbend-twistcoupling.Anewsmallerfuselage wasalsoproduced.Similartotherstprototype,servoswereusedtoallowforsmall modicationsaswellastoreduceairframecosts. 116

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Figure 9-6.Initialforwardsweptwingdesignconcept. Flighttestingshowedthatthisversionoftheplanewasstableaslongasthe airspeedwasmaintained.Inaddition,bothrollandpitchauthorityweresufcientwith thisconguration.Withthesuccessofthisprototypeandthepreviousprototype,work beganontheMFCversion. 9.3.3ThirdPrototype(MFC1)-ImplementingMFCs Thersttwoprototypesshowedthataforwardsweptwingwithbend-twistcoupling wasafeasibleoptionforaMAVmeasuring0.61m(2ft).However,bothoftheseMAVs werecontrolledusingtraditionalservomotorsforactuation.Thenextstepwasto eliminatetheservosandincorporateMFCsintothedesign.Theinitialdesignconcept fortheMFCforwardsweptwingisshowninFig. 9-6. TheintentwastoplacetheMFCsinboardneartheveryrearoftheaircraftsothat theycouldproducethelargestpossiblepitchingmoment.Inaddition,theactuationof theMFCswouldalsotranslateoutboardonthewing,thereforeallowingrollcontrol.It wasanticipatedthatpositioningtheMFCsfartherinboardorfartheroutboardonthe wingwouldallowforabalancebetweenrollandpitchcontrol. TheMFCprototype,termedMFC1,waslaiduponthesamewingtoolingasthe secondprototype.ThesubstratefortheMFCswasunidirectionalcarbonberdue toeaseofmanufacturing.Tofabricatethewing,eachlayerofthewingwascutand 117

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A B C D Figure 9-7.TherstMFCprototype,MFC1.A)Topview.B)Bottomview.C)Angled view.D)CloseupofMFCactuator.PhotostakenbyBradleyLaCroix. placedintoposition,includingtheunidirectionalcarbonberfortheMFC.Thelast stepwasplacingtheMFCsontopoftheuncuredlayupandthenplacingthelayup insideavacuumbag.Thelayupwascycledthroughalay-upcyclewhichholdsa temperatureof126.7 C(260 F)forfourhours.Aftercuring,thewing,tail,andfuselage wereassembled.ThenalresultisshowninFig. 9-7. Thelayupforthiswingwascomposedofasinglelayerofbidirectionaltofacilitate morecompliancefortheMFCactuation.Theleadingedgewascomposedoftwolayers ofunidirectionalcarbonber,onelayerontopofthebidirectionalandonelayeronthe bottom.Theunidirectionalwasagainplacedat22 withrespecttothesweepangleof thewing.Battens,intheformofunidirectionalstiffeners,wereaddedtothewingfor reinforcementtopreventtheoutboardsectionofthewingfrombeingtoocompliant. 118

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Flight testingwasanimmediatesuccess.Therstightwasmorethanveminutes. Duringthistime,itwasobservedthattheairplanewasstableandhaddecentcontrol authority.Thelargestissuewasalackofsufcientrollauthority,butthetestpilotnoted thepitchauthoritywassufcient.Thetestightendedwhenthepilotenteredasteep bankandwasunabletorecover. 9.3.4FourthPrototype(MFC2)-Anattempttoimproverollcontrol Thenextprototype,termedMFC2,wasthersttoimplementsteelsubstratesinto thewing.Todothis,itwasnecessarytocombineapre-preglayupwithawetlayup. Sincestandardepoxiesusedinwetlayupsstarttodegradeathighertemperatures,it wasdecidedthebestoptionwastousehightemperatureepoxy.Toperformthiskindof layup,thecompositelayersofthewingwereassembledjustastheywereintheprevious prototypes.Asectionofmaterial,thesizeoftheactiveareaoftheMFC,wasremoved andsteelplacedinthevoid.TobondtheMFCtothesteel,hightemperatureepoxywas appliedtothesteelandtheMFCplacedontop. ThisprocesswasrsttestedwithaninoperativeMFConahalfwingtestpieceto verifyitseffectiveness.TheresultingtestpieceisshowninFig. 9-8.Thesteelisheldin placeduetothebondtotheMFC.TheMFCoverlapsbetweenthesteelandtherestof thewing.Inotherwords,thesteelissetwithinthesurfaceofthewingandtheMFCis placedonthesurfaceofthewingwhereitoverlapsboththecarbonberandthesteel. Oncetheprocesswasdemonstrated,theMFCprototypewasconstructed.The battensweredeterminedtobeunnecessaryandwerenotincludedinthisprototype. ThisalsohadtheaddedbenetofmakingtheFEAmodellesscomplex.Thenumber oflayersinthelayupandberorientationremainedthesameasMFC1.Inanattempt toincreaserollauthority,theMFCactuatorsweremovedfartheroutboard.Itwas alsoanticipatedthatthesteelsubstratewouldproducelargerdeections,therefore increasingbothrollandpitchauthority.TheseresultsarediscussedinSection 9.4. MFC2,completedafterassembly,isshowninFig. 9-9. 119

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A B Figure 9-8.Steelsubstratetestsection.A)Viewofwingfromthetrailingedge. B)Closeupofthetopsectionofthewing.PhotostakenbyBradleyLaCroix. Figure 9-9.ThesecondMFCprototype,MFC2.PhototakenbyBradleyLaCroix. Thisaircraftdidnotundergoighttesting,butitscharacteristicsandperformance wereexaminedinstaticworkbenchtestingaswellaswindtunneltesting.Boththe MFC1andMFC2underwentstaticworkbenchtestswithDICasawaytovalidatethe FEAmodelofeachairplane.Thesetestsandresultsarediscussedinthefollowing section.Thewindtunneltestsprovidedawaytostudytheaeroelasticnatureofthe aircraft,inwhichtheinteractionbetweenthewingstructureandaerodynamicloadswas 120

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Figure 9-10.Diagramoftheloadingpointsfortheworkbenchtests.LLE-Leftleading edge,LTE-Lefttrailingedge,LPZ-LeftMFC,RPZ-RightMFC, RTE-Righttrailingedge,RLE-Rightleadingedge. studiedwithacombinationofDICandloadmeasurements.Theseresultswereusedto validatetheaeroelasticmodelandarediscussedinChapter 10. 9.4WorkbenchTesting ThissectiondiscussesthestatictestsetupandexecutionforboththeMFC1and MFC2aircraft.Inthesetests,theaircraftweremountedinarigidmannerandvarious massessuspendedfromkeypointsonthewing.DICwasusedtomeasurethefull-eld deformationofthewingandtheresultsusedtovalidatetheFEAmodelinSection 9.6. Themasseswerepositionedatthreelocationsoneachsideofthewingasshownin Fig. 9-10.Staples,bentintotheshapeofhooks,wereusedasattachmentpointsforthe masses.Cyanoacrylateadhesive(CA)wasusedtobondthehookstothewing.Asmall pieceofstring,lessthan0.1g,wastiedtoeachmasssothatitcouldbeeasilyplaced ontheattachmenthooks.Thehooks,masses,andattachmentpointsforMFC1and MFC2areshowninFig. 9-11 9.4.1MFC1Tests Inthissetup,theMFC1aircraftwasplacedinavicewhichwassecuredtoalarge opticaltable.TheDICcameraswerepositionedovertheaircraftasshowninFig. 9-12. Theaircraftperformedighttestspriortoperformingtheworkbenchtestsmentioned 121

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A B Figure 9-11.LoadingpointsfortheMFC1andMFC2.A)MFC1withmassesapplied. B)MFC2attachmentpoints.PhotostakenbyBradleyLaCroix. here.Duringtheighttest,thepilotlostcontroloftheaircraftanditcrashednose-rst intotheground.Shortlyafterbeginningtheworkbenchtests,theleftMFCfailedand wouldnotrespondtovoltageinputs.ItislikelythattheleftMFCwasdamagedduring thecrash.Regardless,anumberoftestswerestillconductedandusedforthevalidation oftheFEAmodel. 9.4.2MFC2Tests AsimilarsetupwasusedfortheMFC2aircraft.Tofurtheranalyzethestructure, twomainsetupswereused.Therst,wassimilartothatusedfortheMFC1,andis showninFig. 9-13A.Thesecond,isaninvertedsetupinwhichtheplanewaspositioned upside-downandthecameraswereplacedbelow,showninFig. 9-13B. 9.5FiniteElementModel 9.5.1ModelSetup Theniteelementmodelwassetupinasimilarwaytotheunimorphmodelsin Chapter 6 andalsousedthecompositematerialpropertiesderivedinChapter 4.The modelitselfwascomposedofbothquadrilateralreducedintegrationshellelements (S4R)andtriangularshellelements(S3).TheresultinglayoutsforboththeMFC1and MFC2wing,withaseedspacingof5mm,areshowninFig. 9-14.Inbothcases,the portionattachedtothefuselageisassignedaxedboundarycondition. 122

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Figure 9-12.TheworkbenchsetupforMFC1.TheDICcamerasarepositionedabove theaircraftandtheaircraftismountedtothetableviaalargevice.Photo takenbyBradleyLaCroix. 9.5.2ConvergenceAnalysis Toensureaeconomicalbalancebetweencomputationaltimeandaccuracy,a convergenceanalysiswasperformed.Themaininterestinperformingaconvergence analysisistodeterminehownetomaketheniteelementmeshinordertoachieve sufcientaccuracy.Makingthemeshtoocoarsecanresultinlargeerrors,whilemaking themeshtoonecanresultinexcessivecomputationaltime.Itisespeciallyimportant todetermineasatisfactorybalanceincomputationaltimeandaccuracywhenrunninga niteelementanalysisontheorderofhundredsorthousandsoftimes,suchisthecase inthisresearch,whenusingthemodelforoptimization. FourpointsofinterestwereexaminedontheMFC2wingfortheniteelement convergenceanalysis.ThesecongurationsareshowninFig. 9-15.Thersttwopoints assessedtheunloadedMFCactuationofthewing,with1500Vappliedtotheleftside 123

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A B Figure 9-13.TheworkbenchsetupfortheMFC2.A)Thestandardloadingsetup.B)The invertedloadingsetup.PhotostakenbyBradleyLaCroix. A B Figure 9-14.FEAlayout.A)MFC1.B)MFC2. 124

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and -500Vappliedtotherightside.Inthisconguration,thedisplacmentsfortheleft andrightsideofthewingweremeasured.Themeasuredpointswereatthetrailing edgeofthewingnearestthecenterlineoftheaircraft.Next,thewingwasplacedinto theunactuatedcongurationanda100gloadappliedintheupwarddirectiononthe outboardleadingedgeofthewing.Thenalpointexaminedwasacombinedactuation andloadedconguration.Inthisconguration,bothsidesofthemodelwereactuatedto 1500Vanda20gloadwasappliedtotheoutboardcornerofeachtrailingedge. Ninemeshdensitiesweretested,rangingfrom776elementsto24,470elements. Eachofthe9meshesareshowninFig. 9-16.Theresultsoftheconvergenceanalysis areshowninFig. 9-17 andFig. 9-18. Theresultsshowthatthereisasignicantincreaseinthenumberofelements afterseedspacingdropsbelow5mm.Sincethecomputationaltimeisproportional tothenumberofelements,itincreasesrapidlyaswell.Takingalookatthechangein displacements,thereisnotasignicantchangeafterseedspacingisreducedto5mm. Therefore,itisdecidedthemostbalancedmeshsizeisthemeshwithaseedspacingof 5mmandslightlymorethan6,000elements. 9.6ModelValidation Asetofexperiments,asdescribedinSections 9.4.1 and 9.4.2 ,wereperformed tovalidatetheresultsoftheFEAmodel.Afewcomparisonsaregiveninthissection, however,amajorityofthedataispresentedinAppendix D. 9.6.1MFC1 Therstresultinthissectionisacomparisonbetweenbothsidesofthewingbeing actuatedto-500V,showninFig. 9-19.Keepinmind,thisisbeforetheleftMFCfailed, soitmayhavebeenfunctioningatareducedcapacity.Theseresultsshowthatthe experimentalresultsmatchtheFEAmodelwellontherightside,buttheexperiment doesnotachievethesamedegreeofdeectionontheleftside. 125

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A B C Figure 9-15.Pointsexaminedfortheconvergenceanalysis.A)Case1.B)Case2. C)Case3. 126

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A B C D E F G H I Figure 9-16.Meshesconsideredintheconvergenceanalysis.A)776elements. B)1,651elements.C)2,819elements.D)6,278elements. E)7,655elements.F)9,564elements.G)12,721elements. H)16,940elements.I)24,470elements. 127

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A B Figure 9-17.Resultsoftheconvergenceanalysis.A)Seedspacingvsnumberof elements.B)Seedspacingvscomputationaltime. Figure 9-18.Seedspacingvs.resultingdisplacements. 128

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Figure 9-19.MFC1workbenchcomparisonLV-500RV-500. Figure 9-20.MFC1workbenchcomparisonLV0000RV1500. Thenextcomparison,showninFig. 9-20 ,demonstratestherightsideofthewing actuatedto1500V.Theseresultsmatchextremelywell. Next,loadsareappliedtothewing,with100gbeingappliedtotheleadingedge intherstloadcomparison,showninFig. 9-21.Thedisplacementoftheleading edgematchesupwellbetweentheexperimentandtheFEAmodel.However,the displacementofthetrailingedgeofthewingdiffers.ThismaybecausedbytheFEA modelnotaccuratelyrepresentingthebend-twistcouplingforthisparticularcase.It mayalsobepossiblethattheberorientationoftheleadingedgewasnotcorrectly 129

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Figure 9-21.MFC1workbenchcomparisonLV0000RV0000RLE100. Figure 9-22.MFC1workbenchcomparisonLV0000RV1500RTE20. appliedduringthelayupprocedure.Sincetheotherresultsmatchedupwell,thisslight mismatchwasnotalargeconcern. Thenalcomparisonshowninthissectionisascenariowheretherightsideof thewingisactuatedto1500Vandtherighttrailingedgeofthewingissupportinga 20gload,showninFig. 9-22.Theseresultsmatchwell,includingthecontoursnearthe centeroftherightsideofthewing.AdditionalcomparisonsareshowninAppendix D. 130

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Figure 9-23.MFC2LV0000RV0000LLE-100gRLE-100g. Figure 9-24.MFC2LV1500RV-500. 9.6.2MFC2 AsmallportionoftheMFC2statictestingresultsarepresentedinthissection. TheremainingcomparisonsarepresentedinAppendix D.Therstcomparisonisan unactuatedconguration,with100gloadingappliedintheupwarddirectionatthe leadingedgeofthewingtips.TheseresultsareshowninFig. 9-23. Thenextcomparisonisanno-loadactuatedconguration,withtheMFCsactuated inanassymetricmanner.TheseresultsareshowninFig. 9-24. 131

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Figure 9-25.MFC2LV-500RV-500LTE-20gRTE-20g. Thenalcomparisonshowninthissectionisacombinedloadingandactuation setup.Inthiscomparison,showninFig. 9-25,theMFCsareactuatedto-500Vand loadingisappliedintheopposingdirectiononthetrailingedgeofthewingtips. Overall,theMFC1hasalargertrailingedgedisplacementthantheMFC2whenthe MFCisactuatedto1500V,buttheMFC2createsalargerspanwisedisplacement(more ofthetrailingedgeisdeformed).ThisindicatesthattheMFC2mayproducebetterroll authoritythantheMFC1. 9.6.3Discussion TheresultspresentedintheprevioussectionsshowthatboththeMFC1andMFC2 aircrafthavegoodagreementwiththeniteelementmodelunderstaticloads.The MFC1showedagreaterdiscrepancyinsomecases,butthiswasattributedtothe morecomplexgeometrywhichincludesbattens.TheaircraftMFC2andsuccessive designsarebuiltwithoutbattens.Thissimpliestheniteelementmodelandyields betteragreementbetweentheFEAmodelandexperimentalresults.Thenextstepof theproject,discussedinthefollowingchapter,willbetoapplyaerodynamicloadsandto calculatetheaeroelasticinteractioncomputationally. 132

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CHAPTER 10 AEROELASTICMODEL Aftertheniteelementmodelwasvalidated,itwaspossibletoaddthenextlayer ofanalysis:thecouplingofaerodynamicloadswiththeniteelementmodel.Thisis avitalaspecttothemodel,sincetheMAVsconsideredinthisresearcharecompliant structuressusceptibletosignicantdeformationunderloading.Thischapterexamines thedesignandsetupoftheaeroelasticmodelandcomparesthewindtunnelresultsto thecomputationalpredictions. 10.1ComputationalModel 10.1.1ABAQUS WhensettinguptheFEAmodelinABAQUS,meticulouscarewastakentoallow forchangestobemadetothemodel,suchasoverallgeometry,compositelayup, partitioningfortheMFCsandleadingedge,andaerodynamicloading.Ifaspectsof thecodeusedtogeneratethemodelarenotimplementedcorrectly,changestothe earlierpartsofthemodelwillpreventthemodelfrombeingregeneratedproperly.If implementedcorrectly,changescanbemadetothemodelautonomouslyandalarge setofmodelscanbeexaminedwithoutuserintervention. Thisiscritical,sincetheoptimizationroutine,discussedinChapter 11 examined hundredsofpossibledesignsanditwouldbefartootimeconsumingtoimplementthese changesmanually.Inaddition,thisallowedfortheaerodynamicloadstobecalculated andinputautomatically,alsoeliminatinganextensiveamountofmanualuserinput. ABAQUSprovidesthreeoptionsonhowtocreateamodel.Themostcommon optionusedistheGraphicalUserInterface(GUI).Thisallowstheusertovisuallygo throughtheirdesignstep-by-stepandspecifyeachportionoftheirmodel,suchas geometry,materials,andloads.Theuserisabletoseethemodelchangesasthey constructthemodelinawaysimilartoaComputerAidedGraphics(CAD)environment. Thismethodisgenerallythebestoptionwhensettingupamodelthatwillbeexamined 133

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under asmallnumberofloadsorconditions.However,thismethodbecomestediousto specifyalargernumberofscenariossincetheusermustinputchangesmanually. Iftheuserwishestoinputalargenumberofdesignpossibilitiesorscenarios,then theyhavetwooptions.Theusercanchoosetocreateaninputle(.inp)ordevelopa pythonscript(.py).Anexternalprogram,suchasMATLAB,canthenbeusedtoexecute theseleswithoutusingtheABAQUSGUI.ABAQUScreatesbothoftheseleswhen usingtheGUI,sodependingontheparametersbeingchangedfromonescenarioto thenext,theusermaybeabletouseoneofthesegeneratedleswithoutimplementing verymanychanges.Forinstance,iftheonlyaspectbeingchangedisapointload,and theloadisactingonthesamepointinallscenarios,thentheusercancreateashort routineinMATLABwhichwillchangetheloadvalueinthepythonorinputlebefore runningtheanalysiseachtime. However,ifmorecomplexchangesarenecessary,suchasachangeingeometry, thenthedifferencesbetweentheinputlemethodandthepythonscriptmethodbeginto arise.Theinputlemethodgivestheusermorecontroloverhowthemodeliscreated inABAQUS.Inthismethod,theusermustspecifyeveryaspectofthemodelgeometry, suchasthepositionofeverynodeandhowthenodesareconnectedtoformelements. Thiscouldbeadvantageousifaveryspecicniteelementmeshisdesired,however, itrequiressubstantialprogrammingtoexecute.Furthermore,asimilarlevelofdetailis involvedwhendeningdistributedloadsorboundaryconditions,sincetheloadsare appliedtothenodesandelementsindividually. Forthepythonscriptmethod,theuserspeciestheshapeofthegeometryand partitions,butABAQUSisresponsibleforgeneratingthemesh.Therefore,ABAQUS determineshowtoarrangethenodesandelementsbasedonitsownalgorithms.This relievessomeoftheworkloadfromtheuserandmakesiteasiertodeneanarray ofdesignsusingapythonscriptroutine.Inaddition,distributedloadsandboundary conditionsarespeciedforentiresectionsofthemodelandABAQUScalculateshowto 134

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apply thesepropertiesacrossthenodesandelements.Itisalsopossibletogenerate outputsusingthismethodsothattheexternalprogram,suchasMATLAB,canretrieve specicresultsfromtheanalysisanddeterminehowtoadaptthenextrun. Regardingthisresearch,thebestmethodwasdeterminedtobethepythonscript method.Thismethodallowedforthegeometry,partitions,anddistributedloadsof themodeltobechangedquicklyandautonomouslywithoutuserinput.Withproper scripting,theusercouldspecifychangeslikewingsweep,MFCposition,andloading conditionsbyspecifyingthevaluesinMATLABandeverythingelsewouldbeexecuted autonomously. 10.1.2AthenaVortexLattice(AVL) Oneofthemaincriterionforcalculatingtheaerodynamicloadsonthewingwas therequiredcomputationalcosts.Reducingthetimerequiredtoruntheaerodynamic codemeantthattheaeroelasticmodelcoulditeratefasterandreachasolutioninless time.Therefore,fullscaleComputationalFluidDynamics(CFD)wasconsideredtootime consuming. Afaster,yetprovenprogramwasrequired.Anextensivenumberofjournalarticles andconferenceproceedingshavebeenpublisheddetailingtheperformanceand limitationsofAthenaVortexLattice(AVL)programdevelopedbyMarkDrelaandHarold YoungrenatMIT[ 35 6369, 76, 77].AVLisaprogramusedforaerodynamicand ight-dynamicanalysisofrigidaircraftfornearlyanygeometry.Itutilizesanextended vortexlatticemodelfortheliftingsurfaces,togetherwithaslender-bodymodelfor fuselagesandnacelles.Ithasbeenshowntoprovidereasonablepredictionsforlift,roll, pitch,andyaw,aswellasdynamicstability.Itisnotoriouslypooratcalculatingdrag,but thatisnotaprimaryrequirementforthisresearch. AVLoperatesinaDOS-likeenvironmentrequiringkeystrokecommandsbythe usertospecifytextlescontainingaircraftdesign,airfoils,andmassles.Fig 10-1 isan exampleoftheinterfacewithsomecommands.Whileitisprimitivebytodaysstandards, 135

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Figure 10-1.ExampleoftheAthenaVortexLattice(AVL)interface. thesesamecharacteristicsmakeitrelativelystraightforwardtobuildprogramming around. OneofthemainlimitationsofAVLisitsrigidaircraftassumption.Itassumesthat anygeometryspeciedisperfectlyrigidanddoesnotdeformunderaerodynamicloads. Morerecentprograms,suchasASWING[ 78],incorporatethestiffnessofthewing similartoacantileverbeam,butthistypeofmodelwouldnotworkforthisresearch.This isbecausetheMFCsactuatetodeformthecompliantstructure,ratherthanactinglikea controlsurface,sothereisnowaytoincorporatetheMFCsintoacodelikethis. However,itispossibletoiteratethestructuralmodel(ABAQUS)withtheaerodynamic model(AVL)tocreateanaeroelasticmodel.Similarmethodshavebeenused before[ 68].Inaddition,theassumptionthatacompliantstructuredeformedunder aerodynamicloadinginaquasi-staticmannerbehaveslikearigidstructurewiththe identicalgeometrywastestedandisdescribedinChapter 8.Theresultsindicatethatit ispossibletoderiveaccuratepredictionsusingacombinationofABAQUSandAVL. 136

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10.1.3 CouplingABAQUSandAVL TheaeroelasticcalculationstartswithMATLAB.Theuser,oroptimizationscheme, denesanaircraftdesignwithinaMATLABle,calledanm-le,withdetailssuchas thewingshape,MFCposition,andmaterialcomposition.Next,theMATLABcode assemblesthisinformationintoapythonscriptandpassesittoABAQUS.ABAQUS assemblesthemodelandconductsapreliminaryrunwhichcalculatesthewing deectionasaresultoftheMFCactuation.ThisgeometryisthenpassedtoAVL,which calculatestheaerodynamicloadsbasedonthegeometry.Theseaerodynamicloadsare passedbacktoABAQUSwheretheyareappliedtothesameFEAmodelandthenew geometryiscalculated.ThenewgeometryispassedtoAVLandtheprocesscontinues untilthereisnosignicantchangefromoneiterationtothenext.Nosignicantchange isdenedaslessthan0.1mmforallcases.ThisprocessisillustratedinFig. 10-2. Figure 10-2.Overviewoftheprogrammingarchitecturefortheaeroelasticmodel. 137

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T ypically,sixorseveniterationswerenecessarytoreachconvergence.The geometryofthewingandthepredictedaerodynamicloadswerethemainoutputsfrom theanalysis.Theresultsofthecomputationalanalysiswillbepresentedandcompared withtheexperimentsinSection 10.3.Thenextsectiondescribesthewindtunneltests andaccompanyingprocedure. 10.2WindTunnelTests 10.2.1Facilities ThewindtunneltestswerecompletedataremoteUniversityofFloridafacility, knownastheAerodynamicCharacterizationFacility(ACF)locatedintheResearch andEngineeringEducationFacility(REEF)inShalimar,FL.AlthoughtheUniversityof FloridahasanumberofwindtunnelfacilitiesonitsmaincampusinGainesville,FL, thesewereundergoingrenovationatthetimeofthisresearch.TheACF,designedby EngineeringLaboratoryDesign,Inc.(ELD),becameoperationalinNovemberof2007.It isanopensectionwindtunnelwitha1.07m(42inch)squarecross-sectionandalength of3.0m(10feet).TheaxialfanwasmanufacturedbyHowdenBuffaloandispowered bya50HPRelianceElectricmotor.Apitottubeconnectedtoaheiseisplacedatthe beginningofthetestsectiontomeasuretheincomingwindspeed.Thetemperature andabsolutepressurearealsomeasureddigitallyandincludedinthewindtunnel calculations.PicturesofthewindtunnelareshowninFig. 10-3. Twolinearmotorsworkincombinationtocontroltheheightandangleofattackof thetestarm.Adigitalinclinometerisattachedattherearofthetestarmtomeasure theangleofattackduringtesting.AJR330E12loadcell(I40boltpattern)ismounted totheendofthetestarmtomeasuretheloads.Aclose-upoftheseitemsareshownin Fig. 10-4.ThedistancefromthereferencepointontheloadcelltotheCGoftheaircraft wasmeasuredinboththelongitudinalandverticaldirection.Finally,allaspectsofthe windtunnelarecontrolledthroughasuiteofLabVIEWsoftware. 138

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A B Figure 10-3.TheREEFwindtunnel.A)Viewfromoutsidethewindtunnelroom. B)Viewfrominsidethewindtunnelroom(MFC2shown).Photostakenby BradleyLaCroix. Figure 10-4.Aclose-upofthewindtunnelsetup.PhototakenbyBradleyLaCroix. 139

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10.2.2 Setup TheighttestedMFC1aircraftwastakentothewindtunnelalongwithtwoMFC2 wings.Sincetestingwasconductedataremotefacility,itwascriticaltohaveabackup testwing.TwoMFC2wingswereproducedasaprecautionintheeventonemightfail eitherduetomanufacturingdefectsorhandling.Altogether,threewingswereprepared fortesting. AsmentionedinSection 9.4.1 ,theMFC1aircraftsufferedanMFCfailureduring workbenchtesting.However,itwasstillincludedinthetestingtoobserveitsperformance withoneMFC.Inaddition,itwasdiscoveredafterarrivingattheREEFthattheMFCsin oneoftheMFC2wingswerealsodamaged.Whenapplyingvoltage,theMFCsbegan toshortoutandquicklystoppedworking.Thedamagelikelyoccuredduringtheintial testingofthewing,whichwasperformedwhileitwasonapowersupply.Itispossible thatthevoltagepotentialbetweentheMFCsandthepowersupplywasgreatenoughto causepermanentdamagetotheMFCs.Fortunately,theotherMFC2wingmaintained functionality. TheDICsystemwasalsoanintegralpartoftheexperiments.Tominimizethe infrastructurerequiredtosetuptheDIC,itwasdecidedtotestthewinginaninverted orientation.Thisallowedthecamerastobeplacedneartheoorwhichrequiredminimal structuraladditiontotheexistingsetup.Italsoallowedeasieraccesstothecamerasfor adjustmentssuchasfocusandaperture.Themainassumptioninthisinvertedsetupis thatthewingdoesnotdeformsignicantlyundergravitationalloads.Thiswasexpected tobetruebasedonvisualinspection.Figure 10-5 showsthewindtunnelsetupincluding theDICcameras. 10.2.3Procedure Priortobeginningthewindtunnelexperiments,theloadcellwaspoweredon overnighttoreachsteadystate.Beforetestingeachaircraft,asetoftaresweretaken fortheentirerangeofangleofattacks.Duringthetareprocedure,thewindtunnelwould 140

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Figure 10-5.Theoverallwindtunnelsetup.TheDICcamerasarelocatedbelowthe aircraft.PhototakenbyBradleyLaCroix. runfor60secondstobringtheloadcelltothermalequilibrium.Thenthewindwouldbe shutoffandtheprogramwouldrunthroughtheanglesofattackinarandomorder,to mitigatetheeffectsofhysteresis. Next,aseriesofcongurationsweretested.TheMFC1planewasconguredto: LV0000RV0000 LV0000RV1500 LV0000RV-500 TheMFC2planewasconguredto: LV0000RV0000 LV1500RV1500 LV-500RV-500 LV1500RV-500 LV-500RV1500 141

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Each wingwastestedat10m/sand15m/s,butforbrevity,onlythe15m/scases areincludedinthisdocument.DICimagesweretakenateachangleofattackforeach conguration.Eachtestincludedrunningthroughtheanglesofattacksinarandom orderatagivenvelocity. 10.3Results Inthissection,thepredictionsfromtheaeroelasticmodelarecomparedtothewind tunneltests.Onlyasmallsampleoftheresultsarepresentedinthissection,withthe remainingdatabeingshowninAppendix E 10.3.1DICResults DICwasperformedoneachwinginbothstaticconditions(nowind)andwithwind appliedat15m/s.Inaddition,eventhoughthecomputermodelwasbuiltoffoftheDIC resultsforthestatic,unactuatedwing,thereisstillasmalldiscrepancyintheshape. Therefore,theout-of-planedifferencebetweenthecomputermodelandthestatic, unactuatedwingiscalculatedforboththeMFC1andtheMFC2wing.Thisprocess isillustratedinFig. 10-6.Thisdifferenceistakenasthetareandsubtractedfromthe otherimagesinthegroup.Thedifferenceinmostcasesisnomorethan1mmineither direction.Thisdiscrepancycanbecausedbyvariationsinmanufacturingincludingthe thermalexpansionofthecompositematerials.Furthermore,themountingofthewingto thefuselagecancauseaslightchangeintheshapeofthewing. ThetarefortheMFC2wingisshowninFig. 10-7A.Thistarevalueissubtracted fromtheotherresultsforthewingasitisactuated.Theresultsforthewingasitis actuatedthroughvariouscongurationsareshowninpartsB,C,andDofFig. 10-7. Theseresultsarecalculatedbytakingtheout-of-planepositionoftheexperimental results(DIC)andsubstractingtheniteelementmodel(FEA)out-of-planeposition. Therefore,positivevaluesindicatetheexperimentalresultsarehigherthanthenite elementmodelandnegativevaluesindicatetheexperimentalvaluesarelowerthanthe niteelementmodel. 142

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A B Figure 10-6.Illustrationoftheout-of-planetare.A)Overallviewofthecomputational model(FEA)andtheexperimentalresults(DIC)overlayedononeanother. B)Close-upviewofthesamemodeldemonstratingtheout-of-plane differencebetweenthetworesults. Table10-1.MFC2qualityoftforeachcongurationtested. V elocity,m/sCongurationNumberofpointsRMSerror,mm 0 L V0000RV000043437 0.38 LV1500RV150043269 0.53 LV-500RV-50043273 0.15 LV-500RV150043009 0.33 15 LV0000RV000042903 0.19 LV1500RV150043225 0.48 LV-500RV-50043352 0.35 LV-500RV150042989 0.46 The windtunnelarm,althoughrelativelystiff,stillhasasmalldegreeofcompliance inalldirections.Tofurtherenhancethetbetweenthecomputermodelandthewind tunnelresults,anoptimizationroutinewasinvoked.Theoptimizationroutineadjusted thetofthemodelstoreducetheoverallRMSerror.TheRMSerrorwascalculated bytakingtheout-of-planedistancebetweeneachcorrespondingpointonthewing, squaringit,andthensummingallthepoints.Then,thesquarerootwastakento produceasinglevaluecorrespondingtotheoveralltoftheFEAandDICmodels. Thesevalues,forMFC2,aretabulatedinTable 10-1.Thenumberofpointsanalyzedis slightlymorethan40,000.TheRMSerroraveragesto0.36mmforall8cases.Similar valuesforMFC1arepresentedinAppendix E. 143

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A B C D Figure 10-7.ComparisonoftheMFC2niteelementmodeltotheexperimentalresults understaticconditions.A)Noactuation.B)ActuatedtoLV1500and RV1500.C)ActuatedtoLV-500andRV-500.D)ActuatedtoLV1500and RV-500. 144

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The sameresultsareshownfortheMFC2wingwhensubmittedto15m/s conditionsasshowninFig. 10-8 .Alloftheseresultsindicateextremelygoodagreement, withthelargesterrorbeingontheorderof2mm.SimilarresultsareshownforMFC1in Appendix E .However,theresultsfortheMFC1aircrafthaveslightlyworseagreement andareontheorderofa3-4mm.Thisislikelyduetodifcultiesinaccuratelymodeling thebattensintheniteelementmodel.Thisisnotalargeconcern,sincetheMFC2and successivemodelswillnotincorporatebattens. 10.3.2AerodynamicResults TheaerodynamicloadmeasurementsfollowatrendsimilartothatofthetheDIC resultsandmatchreasonablywell.TherstresultsareshowninFig. 10-9.Thisgure showstheaerodynamicloadsfortheMFC1aircraftastherightactuatorisactuatedat 0V,1500V,and-500V.OnlyonesideisactuatedsincetheleftMFCactuatorfailed duringtestingaspreviouslymentioned. Theseresultsshowgoodagreementbetweenthecomputationalmodelandthe experimentalresults.Inparticular,thedistancebetweeneachlinematchupwellfor thepitchandrollcoefcient.Thismeansthatthemodelpredictsthepitchandroll authoritywell.Theexperimentalresultsfortherollcoefcientalsoindicatethatthewing isundergoingunsymmetrictwistingasitisloaded,whichmakestherollcoefcient changewithrespecttoangleofattack.Inaddition,theslopeofthepitchcoefcientsare negative.Thisisapreferredcharacteristicwhichindicatestheplane'stendencytonose downwillincreaseastheangleofattackincreases.Lastly,theliftcoefcientchanges asthewingisactuated.Thisisexpectedsincetheliftcoefcientisadirectresultof thewingcamber.SincetheMFCchangestheoverallwingcamber,thiswillhavea proportionalaffectontheliftcoefcient. Goingonestepbeyondtheexperiment,thepitchandrollauthorityfortheMFC1 aircraftcanbecalculatedbysimulatingwhatwouldhappenifbothactuatorswereactive andtheresultscomparedtotheMFC2results.Thiswillallowforabettercomparison 145

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A B C D Figure 10-8.ComparisonoftheMFC2niteelementmodeltotheexperimentalresults at15m/s.A)Noactuation.B)ActuatedtoLV1500andRV1500. C)ActuatedtoLV-500andRV-500.D)ActuatedtoLV1500andRV-500. 146

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Figure 10-9.Comparisonbetweenthecomputationalandexperimentalresultsforthe MFC1. betweenthetwoaircraft.ThechangeinpitchauthorityisshowninFig. 10-10.Ascan beseeninthegure,thepitchcoefcientinbothdirectionsisapproximatelydoubled. Next,therollauthoritycanbecompared,asseeninFig. 10-11.Theseresultsaresimilar becausetheoverallrollrangeisdoubled. TheseresultscanbecomparedtotheresultsfortheMFC2aircraft,whichare showninFigs. 10-12 and 10-13.ThepitchrangefortheMFC1withbothactuators activeisapproximately0.135.ForMFC2,thepitchrangeisapproximately0.125. Comparingtherollcoefcients,theMFC1hasarollcoefcientofapproximately0.0105, whereastheMFC2hasasimilarrollcoefcientof0.0100.Overall,theexperimental 147

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Figure 10-10.PitchcomparisonbetweentwocomputationalmodelsoftheMFC1.Oneis onlyactuatingtherightMFCandtheotherisactuatingbothMFCs. Figure 10-11.RollcomparisonbetweentwocomputationalmodelsoftheMFC1.Oneis onlyactuatingtherightMFCandtheotherisactuatingbothMFCs. pitchandrollcoefcientsmatchtheaeroelasticmodelreasonablywell,butthemodel slightlyoverpredictsboth. TwosetsofmeasurementswererecordedwiththeMFC2ontwodifferentvisits totheREEF.TheresultsshowninFigs. 10-12 and 10-13 arebasedonthesecond visit.Theresultsfromtherstvisitindicateaslightlylargeractuation.Theseresults areshowninFigs. 10-14 and 10-15.Itispossiblethattheactuatorswerecompromised atsomepointbetweenthetwovisitsorduringtransportanddidnotactuatetothe samerangeonthesecondtriptothewindtunnel.Thiscouldaccountforpartofthe discrepancy. 148

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Figure 10-12.Pitchcomparisonbetweenthecomputationalandexperimentalresultsfor theMFC2. 10.4Discussion Theaeroelasticmodelwasabletopredictthelift,drag,pitch,anddragcoefcients quitewellfortheMFC1andMFC2.Differencesbetweentheexperimentalresultsand computationalmodelcanbeattributedtovariationsinmanufacturing.Thenextstepwill beimplementingtheaeroelasticmodelintoanoptimizationschemetodeterminethe bestconguration.Tocutdownoncomputationalcosts,themodelwasonlyexaminedat 15m/s,0 angleofattack.AdditionalspecicsarediscussedinChapter 11 149

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Figure 10-13.Rollcomparisonbetweenthecomputationalandexperimentalresultsfor theMFC2. 150

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Figure 10-14.MFC2comparisonbetweenrstandsecondsetofmeasurements(pitch maneuver). Figure 10-15.MFC2comparisonbetweenrstandsecondsetofmeasurements(roll maneuver). 151

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CHAPTER 11 OPTIMIZATIONROUTINE Aftercompletingandvalidatingtheaeroelasticmodel,itwaspossibletobeginthe optimizationprocess.FlighttestingshowedthattheMFC1providedsufcientpitch authority,butlackedrollauthority.Therefore,theoverallgoaloftheoptimizationwasto improverollauthoritywhilemaintaining,orslightlyimproving,pitchauthority.Thiswas tobedonewiththesamewinggeometryandwingtooling,therebyminimizingcosts. Furthermore,asmentionedpreviously,theendgoalwastolimitthenumberofMFC actuatorstoonlytwoperaircraft. Beforebeginningtheoptimizationprocess,asensitivityanalysiswasconducted. Thisanalysisconsistedofadjustingeachdesignparameterasmallamountand observingitsaffectontherollandpitchascalculatedbytheaeroelasticanalysis. Thesensitivityanalysiswasanecessarystep,sincetheaircraftdesigniscomposed ofdozensofparameters,andeachparameterincludedintheoptimizationdrastically increasesthesizeofthedesignspace.Thisdrasticallyincreasesthetimerequiredto runaneffectiveoptimization. Figure 11-1 and 11-2 showtheresultsofthesensitivityanalysis.Thepitchand rollaregivenaspercentageimprovements,wherethebaselinemodelusedthroughout theoptimizationschemeistheMFC2aircraft.Theightconditionsusedforallparts oftheoptimizationare15m/swiththewingat5 angleofattack.5 angleofattack correspondsto0 forthewindtunneldata,butthisistakenintoaccountforallgures anddatapresentedinthisdocument.Thedynamicpressurefortheaeroelasticmodel wasassignedbasedonroomtemperature,22.2 C(72 F),andpressurewassetforsea levelat101,325Pa(14.7psi). Fourcongurationswereanalyzedduringtheoptimizationroutine.Torunone functionevaluation(analyzeonedesign)atoneangleofattackandonevelocitywith 152

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these fourcongurationstookapproximately20minutes.Thefourcongurations examinedforeachdesignwere: LV0000RV0000 LV1500RV1500 LV-500RV-500 LV1500RV-500 FromtheresultsshowninFigs. 11-1 and 11-2,tenparameterswerechosen,and arelistedbelow: numberofleadingedgeunidirectionalcarbonberlayers(topoflaminate) numberofleadingedgebidirectionalcarbonberlayers(middleoflaminate) numberofleadingedgeunidirectionalcarbonberlayers(bottomoflaminate) chordwiselengthoftheleadingedgesectionatwingroot chordwiselengthoftheleadingedgesectionatwingtip angleofunidirectionalcarbonberintheleadingedge spanwisepositionoftheMFC chordwisepositionoftheMFC angleoftheMFC thicknessofMFCsubstrate Surprisingly,theleadingedgelayuphadasignicantaffectontheperformance oftheaircraft.Otherproperties,suchasMFCangleandsubstratethickness,were previouslyconsideredtohavealargeimpactonaircraftperformance.Thefollowing sectionswilldescribehowthese10variablesareincorporatedintotheoptimizationand describeeachstepoftheoptimizationprocess. 153

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Figure 11-1.Variablesensitivity.Thevariablesarenormalizedandcolor-codedaccordingtoimprovement(Page1of2).154

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Figure 11-2.Variablesensitivity.Thevariablesarenormalizedandcolor-codedaccordingtoimprovement(Page2of2).155

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11.1 ImplementationofOptimizationScheme Theoptimizationroutinetakestheaeroelasticsimulationdevelopedinthelast chapterandessentiallyexecutesitlikeablackboxsystem.Asetofinputvaluesare denedbasedontheparametersspeciedintheprevioussectionandtherollandpitch valuesareoutputintheformoftheobjectivefunction.Theobjectivefunctionisaway toresolvemultipleperformanceaspectsofthedesignintoasinglevaluewhichthe optimizationusestorankeachdesign.Itisessentiallyagradingrubric.Inthiscase,it combinestherollandpitchcoefcientsintoasinglevalueonwhichtorankthedesign. Boththepitchrangeandrollwerenormalizedbeforecalculatingtheobjective function.Thenormalizedpitchrangewascalculatedasfollows: pitchrange norm = pitchup i )Tj /T1_2 11.955 Tf 11.95 0 Td [(pitchdown i pitchup MF C 2 )Tj /T1_2 11.955 Tf 11.95 0 Td [(pitchdown MFC 2 (11) Where i designatesthecurrentdesignbeingconsideredand MFC 2 designates thepitchupandpitchdowncoefcientsfortheMFC2aircraft.Thenormalizedrollwas calculatedbysimplydividingbytheMFC2rollcoefcient.Theobjectivefunctionis calculatedasshowninEq. 11. ObjectiveFunction= )Tj /T1_2 11.955 Tf 10.5 8.09 Td (pitchrange norm + roll norm 1 + (11) Aweightingfactor, ,wasincludedtoincreasetheoptimization'spreferencefor increasingroll.Thisisbecausethepitchauthoritywassufcientinthetestightof MFC1,buttherollauthoritywassignicantlylacking. wassetto2atthebeginningof theEGOoptimizationandgraduallyreducedto1.05attheend.Theobjectivefunctionis recalculatedforallofthedesignseachtime changes. 11.1.1LatinHypercubeSampling(LHS)ofDesignSpace Beforebeginningtheoptimizationroutine,itwasnecessarytoexplorethedesign space.Theintentwastoproduceasurrogaterepresentingthedesignregion.A surrogateisawaytoconnecttheinputsofthemodeltotheoutputsofthemodel, 156

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essentially mappingthedesignregion.Inthecaseofthisresearch,itishoweachofthe 10parametersaffecttheobjectivefunction. Themaingoalofasurrogateistocreateadescriptionofthedesignspaceusingas fewfunctionevaluationsaspossible.Sinceeachfunctionevaluationtakes20minutes torun,itisinfeasibletomaptheentiredesignspaceindetail(itwouldtakeoneweekto runabout500functionevaluationsifrunningcontinuously).Therefore,LatinHypercube Sampling(LHS)ischosentomapthedesignspaceinthemoststrategicwaypossible withagivennumberofpoints. Contrarytointuition,exploringamulti-dimensionaldesignspacewithagrid-like patternishighlyinefcient.Itrequiresfartoomanypointstomapthedesignspace effectively.Ifplacingapointateachcornerofa3variabledesignspace(acube),it wouldrequire8functionevaluations.However,ina10variabledesignspace,itwould require 2 10 functionevaluations,oratotalof1,024.Thiswouldtakeabouttwoweeksto runiftheprogramwasrancontinuously.However,thetimemappingthedesignspace mustalsobebalancedwiththeoptimizationroutine.Thegoalistosufcientlymapthe designspacesothattheoptimizationroutinecanprogresstowardstheglobaloptimum. Toomuchtimeevaluatingthedesignspace,andtheoptimizationroutineishardly utilized.Toolittletimemappingthedesignspaceandtheoptimizationroutinewillspend toomuchtimetryingtondthegenerallocationoftheoptimumorconvergeonalesser localoptimum. LHSdesignprovidesawaytomapthedesignspaceinamoreeffectivewaywith fewerpoints.Theresultmayseemsimilartorandomsampling,exceptitstrategically placesthepointswithinthedesignspacetogenerateabettersetofdataforthe surrogate.Itworksbybreakingthedesignspaceupintoagridformat.Itthenplaces pointswithinthegridsothateachpointoccupiesadifferentrowandcolumnthenall theotherpoints.ThisisshowninatwovariablecaseinFig. 11-3.Anextraproperty 157

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Figure 11-3.LHSdesignmethodologyforatwovariabledesignspace. denedwithinMATLABwasamaximinfunction.Thismaximizestheminimumdistance betweenpointsintheLHSdesignbyiteratingthroughmultiplecases. TheLHSdesignstartedoutwith250points.Itwasknownfromperformingasmall LHSdesign,thatroughly40%ofthepointswouldbeinfeasible.Thereforealargerinitial groupsizewaschosen.Aftereliminatingthepointsthatcreatedconictsingeometry (theMFCprotrudingfromthewing),146pointswereleft.Thefeasiblepointswerethen evaluated.BoththefeasibleandinfeasiblepointsareshowninFig. 11-4.Theboxinthis gureillustratesthedesignspaceconsidered,albeitinonlythreedimensions.Thetrue designspaceisintendimensions.ThreeexamplesofdesignsevaluatedintheLHS methodareshowninFig. 11-5 .IncludedamongtheseisoneexampleinwhichtheMFC protrudesfromtheperimeterofthewing,whichwasdesignatedaninfeasiblepointdue tothegeometryconict.Toencouragetheoptimizationtoavoidinfeasibleregionsofthe designspace,theobjectivefunctionisautomaticallysetto1.2,whichisgreaterthanthe baseline,butstilllessthanthebetterdesigns. Tolimitthedesignspacetoonlytheareawiththeliklihoodofhavingthebest designs,boundsareplacedontheLHSdesignandthesuccessiveoptimization.The boundsonthedesignspacearegiveninTable 11-1.Themaximumnumberoflayers fortheleadingedgeisspeciedas9,duetoweightconcerns.However,weightisnot 158

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Figure 11-4.LHSdesignregion,withthefeasibleandinfeasiblepointsshown. A B C Figure 11-5.ExamplesofthreeLHSdesigns.A)LHS167-Feasiblegeometry. B)LHS168-Infeasiblegeometry.C)LHS170-Feasiblegeometry. consideredduringthispartoftheanalysis.Theotherboundsarechosenbasedmainly ongeometricalconstraints. 11.1.2EGOOptimization EfcientGlobalOptimization(EGO)isarelativelynewoptimizationschemerst discussedina1998journalarticle[ 79].Additionalworkhasbuiltonthiscoreconcept withgreatsuccess[ 8087]. 159

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T able11-1.Boundsforforwardsweptoptimizationdesignregion. Design Property LowerboundUpperbound Uni layersontopofLE 1 3 BilayersinLE 1 3 UnilayersonbottomofLE1 3 LEchordroot,% 21 45 LEchordtip,% 21 45 LEuniangle,degrees 14 30 MFCspanwiseposition,%10 40 MFCchordwiseposition,%60 72 MFCangle,degrees -10 45 substratethickness,mm0.100.15 The fundamentalgoalofEGOistobalanceexplorationandexploitation.Exploitation isstrategicallyplacingthenextpointinanareawherethesurrogatesuggestsan improvedobjectivefunction.Thispointgenerallyhaslowuncertainty.Ontheotherhand, explorationiswhenapointisplacedinanareawithhighuncertaintywhichalsooffers anopportunityforimprovement.Evaluatingthispointdecreasestheuncertaintyofthe surrogateandimprovestheplacementoffuturepoints.Thispracticeisbestillustrated byFig. 11-6 [88],inwhichaonevariabledesignspaceisshown.Inthiscase,the functionisbeingminimized. Inthisseriesofgures, y (x ) representsthetruefunction,evaluateddatapoints arerepresentedbycircles, y KRG (x ) istheKrigingsurrogate,and y T isthetargeted improvement.InKriging,theuncertaintygoestozeroatthedatapoints.Inaddition, theshadedarearepresentstheuncertaintyassociatedwiththeKrigingsurrogate. Therefore,therearethreeareaswhichmightyieldanimprovement.Theseareaslie around0.21,0.62,and0.75.Basedontheuncertaintyandtheexpectedimprovement, EGOwillselectoneofthethreepoints.Thesurrogatewillthenberettotheoriginal datapointsplusthenewdatapoint.Then,theprocesswillrepeat. TherearetwopredominantadaptationsofEGO,eachwithmanyvariations. Probabilityofimprovement(PI)wastherstoptionexploredandwaslaterfollowed withexpectedimprovement(EI).TheinitialauthorsfavoredPIoverEI.However,setting 160

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A B C Figure 11-6.ConceptualillustrationofEGOmethodology.Imagescourtesyof Viana[88].A)EGOEI-Maximizationofexpectedimprovement. B)EGOPI-Maximizationoftheprobabilityofimprovementwithtargetset at-4.6.C)EGOPI-Maximizationoftheprobabilityofimprovementwith targetsetat-5.5. thetargetforPIwasachallengingtaskinmanyscenarios.Therefore,EIwaswidely adopted. EIfollowstheoptimizationschemeshowninFig. 11-6A.EGOEIproducesthe curveshownonthebottombasedontheuncertaintyofthefunction.Thisfunction isessentiallyarepresentationofuncertaintyinthefunctionandthepossibilityof improvement.Therefore,sincetheareaaround0.21hasthelargestuncertaintyand mayproduceanimprovementbeyondthepresentbestsolution(pointat0.68),EGOEI choosesthispointtoevaluatenext. EGOPIrequirestheusertospecifyatarget.Itusesthistargettodeterminewhere toplacethenextpoint,asshowninFigs. 11-6B and 11-6C.Thismethoddetermines whichpotentialpointwillhavethehighestprobabilityofimprovementbasedonthe function'suncertainty,ratherthansimplyapossibilityofimprovement.Recentworkby Chaudhuri[ 89 ],hasproducedanewEGOmethodology.Thismethod,calledAdaptive Targeting,adjuststhetargetaftereachiteration.Therefore,ifthetargetissettoo 161

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high ortoolow,itwillbeadjustedtolieinthecorrectregion.Earlyresultssuggestthat EGOATmayperformbetterthanEGOEI,showingcontinuousimprovementfromone iterationtothenext,ratherthanplateauing,asiscommonwithEGOEI. Forthisresearch,theEGOoptimizationprocesswasconductedinseveralparts. TheinitialseriesofrunswereconductedwithEGOEI.AfterconductingseveralEGOEI iterations,acombinationofEGOATandEGOIEwereutilized.However,theinitialEGO EIimprovedvastlyontheinitialdesignandleftlittleroomforthelateroptimizationsto continuetoimprove. TheresultsoftheinitialLHSdesignandEGOoptimizationsareshowninFig. 11-7. Boththenormalizedpitchrangeandnormalizedrollareshownwiththeobjective function.TheLHSdesignisclearlyseenattheleftsideoftheguresincethedesign pointsarespreadacrossalargerangeofvalues.TheEGOroutinequicklyndsafew designsthatimproveontheinitialMFC2design.Anythingwithavaluegreaterthan1 (abovethehorizontalgreyline)isanimprovement.Inotherwords,avalueof1.2,can beconsidereda20%improvementontheMFC2design.Asmentionedpreviously,a of2wasusedatthebeginningoftheEGOoptimizationandgraduallyreducedto1.05 towardstheend. Figure 11-8 showstheEGOpointssuperimposedwiththeLHSdesignpointsfor thethreefeaturesaffectingMFCposition.ItcanbeseeninthegurethattheEGO optimizationwasseekinganoptimiumnearthepointwheretheMFCspanwiseposition wasbetween20and30%,theMFCchordwisepositionwasnear60%boundary,and theMFCanglewasbetween25and35%.Theother7variablesarenotshowninthis plot. Asmentioned,acombinationofEGOEIandEGOATwereusedtosearchfor anoptimumdesign.Sinceeachfunctionevaluationtakesapproximately20min, optimizationrunsweregroupedinsetsof20-30.Thismeanttheoptimizationcould runfor7-10hourswithoutmanualinterventionandthentheresultsevaluatedtomake 162

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Figure 11-7.LHSDesignandEGOresults.( =1.05) Figure 11-8.LHSandEGOdesignpoints,withthefeasibleandinfeasiblepointsshown. 163

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an yadjustments,suchas ,forthenextset.Inaddition,eachtimeanewdesign wasevaluated,theresultswereincorporatedintothesurrogatewhichimprovedthe optimization. Anotherwaytoviewtheresultsisbyplottingthepresentbestsolutionduring eachstepoftheoptimization.Thepresentbestsolutionisthedesignwiththebest objectivefunction,whichmaynotbethemostrecentevaluation.Thistypeofplotshows howtheoptimizationisimprovingduringthecourseoftheoptimizationandifithas reachedaplateau.Figure 11-9 showsthepresentbestsolutionoverthecourseofthe EGOoptimizationcyclesalongwiththeobjectivefunctionforeachcycle.Asthegure demonstrates,theEGOoptimizationwasquicktoimproveonthedesign,producinga designwithin14iterationswitha40%improvedobjectivefunction.Itisnotuntilthe85th iterationthatthisisimproveduponforatotalimprovementof43.5%.Thisisnoteworthy sinceiteration14producesabout92%ofthetotalimprovement.Noneofthesucceeding iterationsimproveontheobjectivefunctionafteriteration85,however,somecomeclose andrepresentalternativedesigns. Figure 11-9.EGOpresentbestsolutionduringtheoptimizationcycles.Theobjective functionforeachcycleisalsoshown. 164

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Fiv edesignsstandoutfromthegroupandarenotedinthegure.Thenormalized pitchrangeandrollvaluesforeachofthesevedesignsarehighlighted.Theseve designsaretheonesthatrankedthebestaccordingtotheobjectivefunctionandalso representdesignswithnotabledifferences.Thevedesignsaresuperimposedon eachotherinFig. 11-10.Inaddition,thespecicsoftheseresultsaresummarizedin Tables 11-2 and 11-3. Figure 11-10.ThetopveEGOdesigns. Afterconductingtheglobaloptimization,itwasdecidedthatthereshouldbean equalnumberoflayersofunidirectionalcarbonberinthetopandbottomoftheleading edge.Thisisbecausewarpingtakesplacewheneveralayupisunsymmetricdueto orthotropicthermalexpansionofthecompositesduringthecuringprocess.Anexample ofanunsymmetric[2uni,3bi,1uni]layupisshowninFig. 11-11.Thislayupwas performedonaatsurface,yetduetoresidualstrains,thelaminateiscurved.This couldhaveasignicanteffectonthewingdesignbyunintentionallymodifyingthewing twist. 165

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Figure 11-11.Exampleofanunsymmetriclayupexhibitingwarping.Thelayupis[2uni, 3bi,1uni].PhototakenbyBradleyLaCroix. 11.1.3Fmincon Thenalstepoftheoptimizationprocessistoapplyalocaloptimizer.Fmincon operatesbystartingatauserspeciedpoint,perturbingeachdesignvariableasmall amount,andthenmovinginadirectionbasedonthatinformation.Inotherwords,its decisionisbasedonthenumericalderivativesfromthepertubations.Onceitarrivesat thenextdatapoint,itevaluatestheresultandthendecideswhichdirectiontomovenext. Fmincondoesnottakeintoaccountdatafromanypriorpointintheoptimization,such astheEGOorLHSdesignresults.Tables 11-2 and 11-3 showthedesignresultsofthe EGOoptimization,initialfminconpoints,andthenalfminconresults.Figure 11-12 and 11-13 showtheevaluationofeachpointduringthefminconoptimization. Forthispartoftheoptimization,30functionevaluationswereconductedforeach design.Asmentionedintheprevioussection,thetopandbottomlayersoftheleading edgelayupareconstrainedtobeanequalnumberoflayersandlessthan3(i.e.1and 1,2and2,3and3).Thisisincorporatedinordertopreventwarping.Inaddition,a penaltyforeachlayeraddedisincorporatedintotheobjectivefunction.Thisisintended topreventtheoptimizationfromstiffeningthewingtoomuch.Stiffeningthewingwas inferredtobeaerodynamicallybenecial,butdeterminednottobebenecialfroma weightperspective.Therefore,eachadditionallayeraddedtotheleadingedgelayup hadapenaltyontheobjectivefunctionof0.015.Thebestresultingdesignswere 166

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T able11-2.BestcasesfromEGOandtheinitialandbestpointsfromfmincon.Leading edgeproperties.(Table1/2) Design LayersofLayersofLayersofRootTipLE unionbidirectionalunionchordchorduni top bottom%%angle EGO 142 3 132.037.018.3 EGO852 3 133.040.017.4 EGO1563 3 133.037.024.0 EGO1623 3 132.037.023.4 EGO2221 3 132.036.016.0 Fmincon131 2 132.338.024.2 initialpoint Fmincon142 3 233.040.017.4 initialpoint Fmincon132 3 232.338.324.2 bestpoint Fmincon142 3 232.940.317.4 bestpoint T able11-3.BestcasesfromEGOandtheinitialandbestpointsfromfmincon.General wingpropertiesandresults.(Table2/2) Design MFCMFCMFCSubstratePitchRoll SpanwiseChordwiseangle,thickness,Range(coefcient) %%degreesmm(coefcient) EGO 1428.460.527.50.100.12110.0199 EGO8526.161.226.90.100.12750.0201 EGO15623.260.026.70.150.13370.0188 EGO16223.460.027.40.150.13250.0189 EGO22229.160.027.50.100.12020.0203 Fmincon1324.560.027.00.100.13480.0168 initialpoint Fmincon1426.161.226.90.100.12610.0190 initialpoint Fmincon1325.360.026.90.150.13110.0212 bestpoint Fmincon1426.461.027.40.150.12960.0211 bestpoint 167

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Figure 11-12.Localfminconoptimizationforthefmincon13design. determinedtobeiteration28ofFmincon13anditeration29ofFmincon14.These designswillbetermedMFC13andMFC14fortheremainderofthisdocument. AParetofrontfortheoptimizationprocessisshowninFig. 11-14.Thisplot comparestherollauthorityandpitchauthorityofeachdesignandisusefulinillustrating thetradeoffbetweenthetwoobjectives.ThetopveEGOpointsoccupyapoint neartheParetofront,butarenotonthefrontbecauseEGOtendstofunctioninan exploratorymannerratherthanexploitatory.Inotherwords,EGOcontinuestolookfor othergoodpointsratherthanfocusinginonaregiontodeterminegreatpoints.The localoptimizer,fmincon,followsupontheEGOresultsbyproducingtwoadditionally 168

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Figure 11-13.Localfminconoptimizationforthefmincon14design. improveddesigns,whicharelikelyontheParetofront.TheroundnessofthePareto frontregionindicatesthatrollandpitcharecompetingobjectivesandsacricingsome pitchauthoritywouldresultinasmallincreaseinrollauthorityandviceversa. 11.1.4ResultsandDiscussion Overall,theoptimizationpredictsthatMFC13willhavean86%improvedroll authorityanda13%improvedpitchauthoritywhencomparedtotheoriginalMFC2 prototype.TheoptimizationalsopredictsthatMFC14willhave83%improvedroll authorityand10%improvedpitchauthorityovertheoriginalMFC2prototype.These designswerebuiltandtestedandtheresultsdiscussedinChapter 12. 169

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Figure 11-14.Paretofrontfortheforwardsweptoptimization. ThecomparisonbetweenthedesignsoftheMFC1,MFC2,MFC13,andMFC14are showninFig. 11-15.ThedarkbluelineindicatetheperimeterofthewingfortheMFC2, MFC13,andMFC14,whereasthelightbluecolorindicatestheMFC1design.Variations inmanufacturingledtoadifferentperimeter,however,additionalcarewastakentomake MFC13andMFC14matchupwithMFC2.Overall,itappearsthatthelargestfactors correspondingtoanimprovementinperformanceistheproximityoftheMFCtothe leadingedge(closerisbetter),substratematerialandthickness,andtheleadingedge stiffness.Otherfactorswerethelayupgeometryandtheberorientation. MFC1seemedtoparalleltheserequirementsquitewellbycoincidence.However, thesubstratematerialselectionwasnotoptimized.Inaddition,thelocationofthe MFContheMFC13andMFC14arefartherforwardandtheleadingedgeisalso narrower.Thenextchapterwilldetailthetestingforthenalroundofexperiments. Theseexperimentsarethenusedtovalidatethemodelpredictions. 170

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Figure 11-15.ComparisonbetweentheoriginalMFCprototypesandoptimizeddesigns. 11.2ApplicationtoaRearSweptWingDesign Themethoddescribedintherstpartofthischaptercanbeusedtoexamineother aircraftdesigns,includingarearsweptwingdesign.Arearsweptdesignisparticularly interestinginthecaseofthisresearchsinceitmayprovideaplanformwithsimilar pitchandrollcharacteristicstotheforwardsweptdesign.Insuchadesign,theMFCs wouldbeplacedfartheroutboard(andrearward),sothattheycanprovidesufcient pitchauthority,aswasdemonstratedinFig. 9-1 inChapter 9.Thegoalofthissection istodeterminewhetheranoptimizedrearsweptdesignwouldprovideasatisfactory alternativedesignandhowsuchadesignwouldcomparetotheforwardsweptdesign. 11.2.1MaintaininganAnalogousComparison Tomakeafaircomparison,anumberofvariableswereheldxedandothers,which couldnotbeheldconstant,werecarefullymodied.Variablesthatwereheldconstant includethewingarea,airfoilshape,andtaperratio.Theslotfortheverticalstabilizerin thetrailingedgesectionofthewingwasmaintainedintherearsweptwing,eventhough 171

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A B Figure 11-16.Centerofgravitydeterminationfortherearsweptwing.A)Centerof gravityfortheforwardsweptwing.B)Centerofgravityfortherearswept wing. theverticalstabilizerwasmovedfartherbackandbehindthewing.Thesweepangle wasmaintained,butreversed,withrespecttothehalfchord. Thetwovariableswhichcouldnotbeheldconstant,buthadtobeadjustedcarefully werethecenterofgravity(CG)positionandtheboundaryconditionsforthefuselage. ThepositionfortheCG,whichwasdeterminedduringtheighttestingofMFC1,was maintainedwithrespecttothebisectionofthequarterchord.Thesweepangleand centerofgravitydeterminationareshowninFig. 11-16.Todeterminethepointof referencefortheCG,thequarterchordlinewasdrawnonthewingandthereference pointtakenatthehalf-spanpoint.Then,theCGwasmovedforwardthesameamount forbothcases. Theothervariable,theboundaryconditionsforthefuselage,wasmodiedslightly fortherearsweptdesign.Tomaintainafaircomparison,theperimeterlengthofthe 172

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A B Figure 11-17.Forwardandrearsweptboundaryconditions.A)Boundaryconditionsfor theforwardsweptwing.B)Boundaryconditionsfortherearsweptwing. boundaryconditionswasmaintained.Theshapeoftherearportionoftheboundary conditionswasalsomaintained.ThisisshowninFig. 11-17 11.2.2LatinHypercubeSampling(LHS)ofDesignSpace Thesameoptimizationvariablesusedfortheforwardsweptwingwereusedforthe rearsweptwingoptimization.Oneminorrevision,whichwasimplementedduringthe fminconphaseoftheoptimizationfortheforwardsweptwing,wasthecombinationof theleadingedgelayupvariableforthenumberoflayersofunidirectionalcarbonber. AsmentionedinSection 11.1.2,tomaintainasymmetriclayupandpreventwarping, thenumberofunidirectionallayersonthetopoftheleadingedgeandthebottomof theleadingedgemustbeequal.Therefore,thenumberofdesignvariablesfortherear sweptwingwasreducedfrom10variablesto9. TheboundsfortheoptimizationareshowninTable 11-4.Asmentionedpreviously, theMFCpositionwasmovedfartheroutboardontherearsweptwingsothatitwouldbe atareasonablelongitudinaldistancefromtheCG.Inaddition,theboundsforthechord oftheleadingedgepartitionattherootwasincreasedtoprovideadditionalcapacityfor materialreinforcement.Theboundsforthechordatthetipwerealsoadjustedtoallow morespacefortheMFC. TheLHSprocesswasreducedfrom250initialpointsto150toreducecomputational time.Eachiterationfortherearsweptdesigntookapproximately40minutesratherthan 173

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T able11-4.Boundsforrearsweptoptimizationdesignregion. Design Property LowerboundUpperbound Uni layersontop/bottomofLE1 3 BilayersinLE 1 3 LEchordroot,% 27 50 LEchordtip,% 1 30 LEuniangle,degrees -15 15 MFCspanwiseposition,%55 91 MFCchordwiseposition,%55 68 MFCangle,degrees -25 25 substratethickness,mm 0.100.15 A B C Figure 11-18.ExamplesofthreerearsweptLHSdesigns.A)LHS2.B)LHS48. C)LHS86. 20minutes,sincetheaeroelasticconvergencerequiredadditionaliterationstoreachthe convergencecriteria.ReducingthenumberofpointsintheLHSdesignwasconsidered acceptablesincethe250pointsfortheforwardsweptwingdesignseemedtoprovidea verythoroughinvestigationofthedesignspaceasindicatedbytherapidoptimization.In addition,thenumberofvariablesinthiscasewasreducedfrom10to9.Aftereliminating theinfeasibledesign,67feasiblepointsremained.Figure 11-18 showsthreefeasible rearsweptdesignsthatwereexaminedduringtheLHSdesignspaceexploration.These provideanillustrationoftherangeofgeometriesexaminedduringtheoptimization process.Toencouragetheoptimizationtoavoidinfeasibleregionsofthedesignspace, theobjectivefunctionfortheinfeasiblepointswassettoavalueofapproximately90%of thepresentbestdesignduringeachstageoftheoptimization. 174

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11.2.3 EGOOptimization AftertheLHSdesign,severalsmallrunsofEGOwereagainusedtotrytoimprove thepitchauthorityoftherearsweptwingdesign.Theobjectivefunctionwasmodiedto placeadditionalweightonthepitchauthorityasfollows. ObjectiveFunction= )Tj /T1_4 11.955 Tf 10.5 8.09 Td ( pitchrange norm +roll norm 1 + (11) Thepitchandrollcoefcientswerenormalizedbasedontheoptimizedforward sweptMFC13design.Thismakesiteasytodeterminewhichdesignsarebetteror worseintermsofrollandpitchauthority.Anythingwithavaluelessthan1hasless controlauthoritythanMFC13andviceversa.Figure 11-19 showstheresultsoftheLHS designandthesubsequentEGOoptimizations.Thetopveiterationswiththehighest normalizedpitchcoefcientarenotedinthegure.Onceagain,bothEGOATandEGO EIwereused. wasincreasedduringeachsubsequentrunwithoutanynotableeffect. Forthelast10runs,theobjectivefunctionwasmodiedsothatitsvaluewassimplythe normalizedpitchcoefcient,takingtherollcoefcientcompletelyoutoftheequation.It wasexpectedthatthismayyieldadesignwithalargerpitchcoefcient,buttheresults didnotsurpassthepreviousEGOiterations. Figure 11-20 showsthepresentbestsolutionoverthecourseoftheEGO optimizationcyclesalongwiththeobjectivefunctionforeachcycle.Asthegure demonstrates,theEGOoptimizationwasquicktoimproveonthedesign,producinga superiordesignwithin13iterations.Noneofthesucceedingiterationsimproveonthe objectivefunctionafterthisdesign,althoughsomecomeclose.Thegeometryandother specicationsofthetopvedesignsareillustratedinFig. 11-21 11.2.4Fmincon AftercompletingtheEGOportionoftheoptimization,fminconwasusedasalocal optimization.Atotalof30functionevaluationswereconducted,withanelapsedtime ofabout20hours.ThebestdesignisshowninTables 11-5 and 11-6 whereitisalso 175

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Figure 11-19.LHSdesignandEGOresultsfortherearsweptwing.Thetopvedesigns withrespecttopitchauthorityarenoted.Theobjectivefunctionvalues werecalculatedwith =3.0 Figure 11-20.EGOpresentbestsolutionduringtheoptimizationcycles.Theobjective functionforeachcycleisalsoshown. 176

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Figure 11-21.LHSdesignandEGOresultsfortherearsweptwing.Thetopvedesigns withrespecttopitchauthorityarenoted.Theobjectivefunctionvalues werecalculatedwith =3.0 comparedtotheinitialfmincondesignandtopveEGOdesigns.Theoptimizeddesign has95%ofthepitchauthorityastheforwardsweptdesignand75%morerollauthority. However,theoptimizeddesignrequires9layersofcarbonberfortheleadingedgein ordertoproducetheseresults. TheprogressionofthefminconoptimizationisillustratedinFig. 11-22.Oneofthe initialpertubationsfailedduetoinfeasiblegeometry,thereforeitisnotshowninthe plot.Aftertheinitialsequenceofpertubations(rst8points),theoptimizationsteadily increasesthepitchandrollauthority.Point25yieldsthebestsolutionoutofthepoints evaluated.Figure 11-23 showsaside-by-sidecomparisonoftheoptimizedrearswept designandtheoptimizedforwardsweptdesign.Itisimportanttonotehowinboth cases,theMFCisorientedinawaywhichfollowsthecurvatureofthewing.Inthisway, itisnotactuatingagainstthestiffnessproducedbythewingcurvature,butisactuatingin themostcompliantdirection. AParetofrontfortherearsweptwingoptimizationisshowninFig. 11-24.Contrary totheParetofrontshownfortheforwardsweptoptimization(Fig. 11-14),thisPareto frontindicatesthatthetwoobjectivesarenotcompeting.Generallyspeaking,an 177

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Figure 11-22.Localfminconoptimizationfortherearsweptdesign. A B Figure 11-23.Side-by-sidecomparisonofoptimizedforwardsweptandrearswept designs.A)Layoutofrearsweptdesign.B)Layoutofforwardswept design. 178

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T able11-5.BestcasesfromEGOandtheinitialandbestpointsfromfminconforthe rearsweptwing.Leadingedgeproperties.(Table1/2) Design LayersofLayersofLayersofRootTipLE unionbidirectionalunionchordchorduni top bottom%%angle EGO 1633 2 347.413.415.0 EGO1853 3 343.816.49.0 EGO1873 3 342.318.411.5 EGO2003 3 341.316.913.0 EGO2113 2 337.916.715.0 Fmincon3 2 347.413.415.0 initialpoint Fmincon3 3 347.811.117.9 bestpoint T able11-6.BestcasesfromEGOandtheinitialandbestpointsfromfminconforthe rearsweptwing.Generalwingpropertiesandresults.(Table2/2) Design MFCMFCMFCSubstratePitchRoll SpanwiseChordwiseangle,thickness,Range(coefcient) %%degreesmm(coefcient) EGO 16371.862.8-9.90.150.12120.0350 EGO18570.363.7-5.70.150.12070.0347 EGO18771.264.2-3.60.150.12070.0346 EGO20068.563.4-3.10.150.12020.0345 EGO21170.761.9-1.90.150.11940.0339 Fmincon71.862.8-9.90.100.11970.0344 initialpoint Fmincon71.761.3-9.80.150.12510.0372 bestpoint increase inrollauthoritywillresultinanincreaseinpitchauthority.Thefminconresult furtherimprovesontheEGOresultsasdemonstratedbyitspositionontheplot. 11.2.5ManualTestCase Onenalcheckontherearsweptoptimizationwasconducted.Thiswasa manualtestcase,inwhichtheMFCwasplacedfartheroutboardonthewingnear thewingtipandorientedlongitudinally,withoutanyangleofrotation.Thisdesign,shown inFig. 11-25,wasexpectedtogivegoodresultssincetheMFCwasplacedfartheraway fromthecenterofgravityinboththelateralandlongitudinaldirectionsascomparedto theoptimizeddesigns.However,thisdesignhad27%lessrollauthorityand9%less 179

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Figure 11-24.Paretofrontfortherearsweptoptimization. pitchauthorityascomparedtofmincondesign.Therefore,theoptimizedfmincondesign stillperformsthebest.ThisislikelybecauseplacingtheMFCfartheroutboardresultsin lesswingareabeingactuatedaswellastheMFCactingagainstthe3Dcurvatureofthe wing. 11.2.6Discussion Intheend,theoptimizedrearsweptdesignhasslightlylesspitchauthorityand signicantlymorerollauthoritythantheoptimizedforwardsweptdesign.Additional considerationswhicharenotincludedintheanalysisincludetheeffectsofprop-wash onthecontrolsurfaceauthoritythroughoutthevariousightregimes.Asmentioned previously,fortheforwardsweptdesign,theMFCsarelocatedintheprop-washregion, whichmayincreasetheireffectivenessforlowtomoderateightspeeds.Couplingthis withthefavorablestallcharacteristicsofaforwardsweptwingfurtherimprovesthe potentialadvantagesofaforwardsweptwingoverarearsweptdesign.Theforward 180

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Figure 11-25.Rearsweptuser-speciedtestcase. sweptgeometryisalsofavorablefortheplacementoftheMFCsonthewingsurface, whereastherearsweptdesignhasmorespacerestrictions.Inaddition,theforward sweptdesignprovidedaresearchtopicwithachallengingcombinationofdisciplines byincorporatingbend-twistcouplingwiththestandardaeroelasticmodelingaspects. Finally,eventhoughtheforwardsweptdesignhasslightlybetterpitchauthoritythanthe comparablerearsweptdesign,itispossiblethatafurtheroptimizedrearsweptdesign (withanoptimizedairfoil,wingsweep,orgeometry)couldperformbetter. 181

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CHAPTER 12 CONCLUDINGTESTS Thischapterpresentsandanalyzestheresultsfromthenalsetofwindtunnel tests.Threewingsweretested,theMFC2,MFC13,andMFC14,wheretheMFC2isthe baselinedesignandtheMFC13andMFC14aretheoptimizeddesigns.Thesamesetup andequipment,describedinSection 10.2,usedintherstseriesoftestswasused againforthissetoftests.TheDICsetupwasmodiedslightlyandisshowninFig. 12-1. 12.1Manufacturing Thefabricationofthewingtookplaceinasimilarmannertothatdescribedin previouschaptersandinSection 9.3.4 .Anareaofthepre-pregwingwascutoutforthe steelsubstrateandthesubstrateplacedinthevoid.Hightemperatureepoxywasused toadherethesteelsubstratetotheMFC.Thesteelsubstrateplacedintothewingmold isshowninFig. 12-2A.Aclose-upoftheresultingwingisshowninFig. 12-2B. 12.2Procedure Thesamecongurationsweretestedinthisseriesoftestsaswereusedforthe MFC1andMFC2rstroundoftests(Section 10.2.3).However,duetothestifferleading edgeoftheMFC13andMFC14,alargerrangeofangleofattackscouldbeexamined. Inaddition,theMFC2wastestedunderaslightlylargerrangeofangleofattacks. SignicantutterwasnotedfortheMFC2atnegativeanglesofattackbeyond-2 and beyond15 .Therefore,testingwaslimitedintheseregions. Duringtesting,theleftMFConMFC13begantoshortout.Thisbehaviorwasnoted duringthepreliminarytestspriortovisitingtheREEF.Itissuspectedthatwhileremoving thetapeprotectingtheMFC'selectricalleads,excessivepressurewasplacednearthe edgeoftheMFC.Asaprecaution,oncearrivingattheREEFaroundofwindtunnel testswerecompletedathalfpower(750V),inwhichshortingwasnotobserved.After acquiringsufcientdata,theMFCsweretestedat1500V,atwhichpointtheleftMFC begantoshort. 182

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Figure 12-1.Windtunnelsetupforsecondseriesoftests.PhototakenbyBradley LaCroix. A B Figure 12-2.ManufacturingoftheMFC13wing.A)Steelsubstrateplacedinthecutout sectionofMFC13priortocuring.B)PictureoftheMFC13wing,post-cure. PhotostakenbyBradleyLaCroix. 183

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Figure 12-3.RepairmadetotheMFConMFC13.PhototakenbyBradleyLaCroix. Itwasdeterminedthatthebestcourseofactionwastoattemptarepaironthe MFC.Iftheareainwhichtheshortwasoccuringwasremovedfromthecircuit,then ideallytheproblemshouldberesolved.ADremel c r andagrindingdiskwereusedto carefullycuttheelectricalconnectionsleadingtothedamagedareaoftheMFC.The resultisshowninFig. 12-3,inwhichtheblackshortedareaisremovedfromthecircuit viathecutmadeintheMFC.Aftermakingthecut,acoatofinsulatingadhesivewas appliedtopreventtheexposedconnectionsfromarching.Testingrevealedthatthe repairhadsuccessfullyresolvedtheproblem. 12.3Results Theresultsfromthewindtunneltestsaregroupedintothreesections.Therst sectionpresentstheDICresultscomparingthegeometryoftheaeroelasticcomputer modeltotheexperimentalresultsobtainedusingDIC.Thesecondsectionpresentsa comparisonoftheactuatedwingsatvariousspeedstoexaminetheaffectofloadson thewingdeformation.Thethirdsectionexaminestheaerodynamicloadresults. 12.3.1DICResults Acomparisonbetweentheaeroelasticcomputermodelandtheexperimental resultsfortheMFC13wingisshowninFig. 12-4.Theseresultsareforstaticconditions 184

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T able12-1.MFC13qualityoftforeachcongurationtested. V elocity,m/sCongurationNumberofpointsRMSerror,mm 0 L V0000RV000043908 0.75 LV1500RV150043308 0.59 LV-500RV-50043388 0.56 LV-500RV150043356 0.56 15 LV0000RV0000N/A N/A LV1500RV150043575 0.53 LV-500RV-50043411 0.63 LV-500RV150043410 0.57 in whichtheMFCsareactuatedtovariouspositions.Somesharpvariationsincolor arepresentintheseimages.ThisisduetotheDICsoftwarebeingunabletocorrelate properlyfortheseareasduetothecombinationofinsufcientcontrastintheDIC specklepatternandglareonthewing. JustasinChapter 10 ,therstimageiswiththeMFCsplacedintheunactuated position,andisusedasatarevaluefortheotherwings.Thisremovesanyinitial discrepancybetweentheexperimentalmodelandthecomputermodel.Overall,the resultsindicatethatthecomputermodelmatchestheexperimentalresultswithin 1mm. Thenextgure,Fig. 12-5 ,providesacomparisonbetweenthecomputermodeland theexperimentaltestsat15m/s.Nodatawasrecordedfortheunactuatedpositionfor thiswing.Regardless,theresultsshowthatthemodelmatchestheexperimentverywell withadiscrepancyoflessthan 1mm. Thequalityoftofthecomputermodelswithrespecttothewindtunnelexperiments istabulatedinTable 12-1.Thistablewascalculatedinthesamewayasspecied inSection 10.3.TheRMSerrorisslightlymore,onaverage,forthissetofresults (averaging0.60mmcomparedto0.36mm).Thiscanbeattributedtothefactthatthe modelwastunedtomatchupwellwiththeMFC2results,butwasnotadjustedforthis setofresults. 185

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A B C D Figure 12-4.ComparisonoftheMFC13niteelementmodeltotheexperimentalresults understaticconditions.A)Noactuation.B)ActuatedtoLV1500and RV-500.C)ActuatedtoLV1500andRV1500.D)ActuatedtoLV-500and RV-500. 186

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A B C Figure 12-5.ComparisonoftheMFC13niteelementmodelandtheexperimental resultsat15m/s.Note:Nodatawasrecordedfortheunactuated experiment.A)ActuatedtoLV1500andRV-500.B)ActuatedtoLV1500 andRV1500.C)ActuatedtoLV-500andRV-500. 187

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T able12-2.MFC14qualityoftforeachcongurationtested. V elocity,m/sCongurationNumberofpointsRMSerror,mm 0 L V0000RV000044578 0.50 LV1500RV150044283 0.43 LV-500RV-50044479 0.27 LV-500RV150044273 0.31 15 LV0000RV000044086 0.43 LV1500RV150044228 0.36 LV-500RV-50044084 0.55 LV-500RV150044109 0.41 A similarseriesofresultsareshowninFigs. 12-6 and 12-7 fortheMFC14wing. Onceagain,theresultsmatchupverywellwithnearlythewholesurfacebeingwith 1mm. ThequalityoftfortheseresultsareshowninTable 12-2.Asthevaluesindicate, theMFC14resultsmatchupslightlybetter,withanaverageRMSvalueof0.41mm. 12.3.2EffectsofSpeed Anextraseriesoftestswereconductedforthisroundoftesting.Toexaminethe affectsofaerodynamicloadsontheactuatedwing,eachwingwasputthroughaseries ofvelocities.TheresultsareshowninFigs. 12-8 and 12-9.Itisevidentfromthese guresthatduetothereexinthetrailingedgepartofthewing,the-500Vactuated partofthewingisfurtherassistedbyaerodynamicloads,pushingitfartherdownasthe velocityincreases.Forthe1500Vside,theaerodynamicloadsopposetheactuation andpushitdownasthevelocityincreases.Thisisthecaseforbothwingsandtoa similardegree. 12.3.3AerodynamicResults Thefollowingseriesofgurescomparetheaeroelasticcomputermodelresults totheexperimentalresultsmeasuredinthewindtunnel.Alltestswereconductedat 15m/s.Therstgure,Fig. 12-10,showsthepitchrangewhentheMFC13isactuated throughitspitchupandpitchdownactuations.Similarly,Fig. 12-11 showstheMFC13 188

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A B C D Figure 12-6.ComparisonoftheMFC14niteelementmodelandtheexperimental resultsunderstaticconditions.A)Noactuation.B)ActuatedtoLV1500and RV-500.C)ActuatedtoLV1500andRV1500.D)ActuatedtoLV-500and RV-500. 189

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A B C D Figure 12-7.ComparisonoftheMFC14niteelementmodelandtheexperimental resultsat15m/s.A)Noactuation.B)ActuatedtoLV1500andRV-500. C)ActuatedtoLV1500andRV1500.D)ActuatedtoLV-500andRV-500. 190

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Figure 12-8.MFC13deformationundervariousvelocitieswhenactuatedtoLV1500 RV-500at0 angleofattack. Figure 12-9.MFC14deformationundervariousvelocitieswhenactuatedtoLV1500 RV-500at0 angleofattack. 191

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Figure 12-10.MFC13pitchcomparisonbetweenthecomputationalandexperimental models. wingconguredinthetworollcongurations.Theresultsinbothcasesmatchextremely well,withthecomputermodelbeginningtodeviateatthehigheranglesofattack. AlsoworthnotingiswhentheMFCrepairtookplace.LV0000RV0000,LV-500 RV1500,andLV-500RV-500congurationsweretestedbeforetheleftMFCbeganto exhibitproblems.TheMFCwasthenrepairedandtheothertestsperformed,LV1500 RV-500andLV1500RV1500.Evenwiththerepair,therollrangeissymmetricandthe rollwhenpitchingupisnearlyzero,indicatingsymmetricactuation. SimilarresultsareshowninFigs. 12-12 and 12-13 fortheMFC14aircraft.Thepitch coefcientvaluesmatchupverywell,buttheexperimentalrollrangeislessthanthe 192

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Figure 12-11.MFC13rollcomparisonbetweenthecomputationalandexperimental models. predictedvalues.Therollactuationisalsonotsymmetric.Bothoftheseissuesmaybe duetovariationsinmanufacturing. ThevaluesforrollarecomparabletotheresultsobtainedbyOhanian.Duringhis testingwiththeGENMAV,mentionedinSection 2.1,heobtainedrollcoefcientvalues of0.0324and0.0382fortwoofhisMFCactuatedaircraft[ 46 ].Therstaircraftutilized 4setsofM8514-P1bimorphspositionedattheoutboardsectionofwing(twobimorphs ontheleftsideandtwobimorphsontherightside).Thesecondaircraftutilized4 setsofM8528-P1bimorphspositionedat45 anglesonathinairfoilwing.Theroll coefcientfortheseMAVsisapproximately53-80%morethantheMFC13.However, whencomparedtotheoptimizedrearsweptdesigninSection 11.2,theoptimized 193

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Figure 12-12.MFC14pitchcomparisonbetweenthecomputationalandexperimental models. designproduced15%morerollthantheOhanian'srstdesignandonly3%lessthan theseconddesign.TheseresultsareespeciallynoteableconsideringOhananian's aircraftused8actuatorsforrollcontrol,comparedtothe2actuatorsusedontheMFC13 andrearsweptdesign. Althoughthestabilityoftheoptimizeddesignswasnotevaluated,itislikelythat theimproveddesignshavesimilarstabilitytraitstotheoriginaldesign,MFC1.Thisis becausethewinggeometryhasremainedvirtuallythesameandthewingstructure istheonlyaspectthathaschanged.Inaddition,theimproveddesignsarestifferand deformlessthantheoriginalMFC1,therefore,aeroelasticinstabilitieswouldbelessofa 194

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Figure 12-13.MFC14rollcomparisonbetweenthecomputationalandexperimental models. consideration.Asaresult,sincetheMFC1exhibitedacceptableightcharacteristics,it islikelytheimproveddesignswouldalsoexhibitacceptableightcharacteristics. 12.4Conclusion Intheend,theMFC13andtheMFC14arebothmuchimprovedovertheoriginal prototypes.TheMFC13producesabouttwicetherollastheMFC2andtheMFC14 producesabout75%more.TheMFC13hadsignicantlymorerollthantheMFC14,and slightlymorepitchauthority.Thefactorsmostimportantfortheseimprovementsare likelythesubstratematerial,placementoftheMFCneartheleadingedge,andthestiffer leadingedgecontainingmorelayersofcomposite. 195

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This processhasprogressedthroughoptimizationonboththelocalscale,looking attheindependentunimorphperformance,aswellasontheglobalscale,lookingatthe overallwinggeometryandlayup.InitialtestsexaminingtheMFCactuation,unimorphs, andcompositematerialspavedthewayforamoreaccuratecomputermodel.Thisis especiallycriticalwhenconductinganoptimization,sincedefectsinthecomputermodel canbeexploitedbytheoptimizationroutine. Ultimately,thisresearchhasbeensuccessfulindemonstratingthattwoMFC actuatorsaresufcienttoadequatelyyanaircraft.Thisisbenecialintermsof weight,electroniccomplexity,andcost.Furthermore,theresearchcontainedwithinthis documentwouldbebenecialtoothergroupswhomaybeinterestedinachievingmore actuationfromtheirMFCactuatorsforavarietyofapplications,notlimitedtoMAVs. 196

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APPENDIX A DIGITALIMAGECORRELATION(DIC) DigitalImageCorrelation(DIC)isaclassofnon-contactingmethodsthatacquires imagesofanobject,storestheimagesindigitalform,andperformsimageanalysis toextractfull-eldshapeanddeformationmeasurements.Itissometimesreferredto asVisualImageCorrelation(VIC),however,thisterminologyismildlyredundant.The digitalimagecorrelationsetupusedwithinthisresearchisa3Dsystem,whichmakes useoftwoGrasshopper c r2cameras,manufacturedbyPointGreyResearch.The imagesarerecordedusingVicSnap2007andprocessedusingVIC-3D2009.Byusing stereotriangulation,thesystemisabletoreconstructathreedimensionalgeometry utilizingtwopre-calibratedimagingsensors.ThisconceptisshowninFig. A-1A. A B Figure A-1.Digitalimagecorrelationconceptualillustration.A)Demonstrationofthe3D perceptionwhenviewedthroughthestereographicsystem.B)Measurement of3Ddisplacementwithrespecttotime. BeforeconductingaDICexperiment,ablackandwhitespecklepatternisappliedto thesurfaceofinterest.Thisprovidesadistinct,high-contrastpatternthatcanbetracked bythesystem.Sincethepatternisunique,thetranslation,rotation,andstraincanbe acquiredfromthecorrelation.Furthermore,sincethesystemusesstereotriangulation, displacementcanbemeasuredinallthreecoordinatedirections.Thisprincipleis illustratedinFig. A-1B .Thesameconceptisillustratedwithastandardspecklepattern inFig. A-2,wherethetranslationofthedotsismeasuredbytheDICsystem.DICtries 197

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Figure A-2.Digitalimagecorrelationexamplepattern. tondaregioninthedeformedimagethatmaximizesacross-correlationfunction correspondingtoasmallsubsetwithintheun-deformedimage. DICisscalabletoalargevarietyoflengthscales,rangingfromtensofmetersto micrometers.2Dsurfacedeformationsatthenanoscaleusingatomicforcemicroscopy andscanningelectronmicroscopyhavebeenperformed[ 90 ].Optimalaccuracyis obtainedwhencamerasarepositionedat90 withrespecttooneanother,but45-90 isgenerallyaccepted.Lessthan45 reducesout-of-planeaccuracy,butthecorrelation analysiscanstillbeperformed. Theimagingprocesstakesplacestartingwiththeconversionofintensityoflight oneachpixeltoanumericvalue.Theintensityoflightisconvertedwith8-bitresolution toavaluerangingfrom0to255.Anintensityvalueof255indicatesthatthepixelis oversaturated.DICutilizesgrey-valueinterpolationschemes,whichallowsforoptimal sub-pixelaccuracy.Becauseofthis,in-planeaccuracyisontheorderof1/50 th ofapixel andout-of-planeaccuracyisontheorderofZ/50,000whereZisthedistancefromthe cameratothesubject.Thisisassumingthecamerasystemispositionedwithatleasta 45 angle. Figure A-3 illustratestheDICsetupusedforthecantileveredunimorphexperiments describedinChapter 6.Inthissetup,theDICcameraswerepositionedoverthe cantileversetupwhiletheMFCwasactuatedtovariousvoltagesanddifferentloading conditionswereapplied.TheDICsystemallowedforthefull-eld3Ddisplacementof theunimorphtobemeasuredatanygiventime. 198

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Figure A-3.DICsetupforcantileverexperiment. ThereareavarietyofissuesthatcanarisewhenusingaDICsystem.Possible problemsincludecontinuityofcorrelationregionswhenadisconinuityispresent,such asacrack,hole,orshadow.Lossofcontrastcanalsooccurduetodebondingor delaminationofthespecklepattern.Inaddition,achangeinthediffusereectivityofthe surfaceduringloadingcanresultinlossofcontrastintherecordedimages.Ifsucha discontinuityorsurfaceimperfectionispresent,thecorrelationwillonlytakeplaceonthe startingsubsetareaandwillnotbeabletoprogressacrosstheentiresurface. ThiswasaconsiderationwhenusingDICinthewindtunnelonthemembrane wings,asshowninFig. A-4 .Thelightingandreectivesurfaceshadtobecarefully positionedtopreventanyshadoworsilhouettingfromoccuring.Toomuchback-lighting andthecarbonberportionofthewingbecomessilhouetted.Toomuchfrontlighting andportionsofthewingcanbecomeover-exposed.Ineithercase,theDICsystem wouldbeunabletocorrelatetheentirewingsurface. TwootherparametersthatmustbeconsideredwhensettingupaDICsystem includeshutterspeedandaperture.Shutterspeedisthedurationoverwhichtheimage iscaptured.Thismayhaveveryminuteeffectsforquasi-staticsystems,butiftheuser isattemptingtocaptureasurfacethatisinmotion,ahighshutterspeedmustbeused. 199

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Figure A-4.Digitalimagecorrelationsetupinthewindtunnelwithcarefullyadjusted lighting.PhototakenbyBradleyLaCroix. Ifahighshutterspeedisnotanoption,analternativewouldbetouseastrobeashto illuminatethesurfaceforabriefperiodoftime,ontheorderofathousandthofasecond, whilethecamerashutterisopen.Thiswillessentiallyfreezetheobjectinmotion,as demonstratedwithasetofpropellerexperimentsIconductedinFall2009(Figure A-5). Thesametechniquehasalsobeenusedextensivelyfortheappingwingprojectatthe UniversityofFlorida[ 9195]. ApertureadjustmentiscrucialforobtainingvalidDICresults.Thecameraaperture determinestheproportionoflightthatreachesthesensor.Buttheaperturesettingalso effectsthedepthofeld.Ifthedepthofeldissmall,itemswithintheeldofviewthat areoutsideofthefocalplanewillappearextremelyoutoffocus.Ifthedepthofeldis large,thenitemswithintheeldofviewthatarenearthefocalplanewillstillappear tobeinfocusandthefocalplanewillbelessdistinct.Optically,thedepthofeldis inverselyrelatedtotheaperturesize.Therefore,alargeaperture,whichallowsalarge amountoflighttofallonthesensor,willproduceasmalldepthofeld.Soonlytheitems 200

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A B Figure A-5.DigitalimagecorrelationofarotatingUAVpropeller.A)Theexperimental setupwiththepropellerfrozeninmotionusingthestrobelight.Phototaken byBradleyLaCroix.B)ResultsoftheDICanalysisfortwopropellers. locatedatthefocalplanewillbesharplyinfocus.Conversely,asmallaperture,which wouldlimitthelightfallingonthesensor,wouldcreatealargedepthofeldandmore itemswouldbeinfocus. AlloftheseoptionsmustbecarefullyweighedwhensettingupaDICsystemand performinganexperiment.Incertainsituations,compromisesmayhavetobemadeto achievesatisfactoryresults.Nonetheless,DICprovidesarelativelyquickandsimple architecturebywhichalargevarietyofexperimentscanbeperformed.Withtheright setup,full-elddisplacementsand3Dprolescanbeaccuratelycapturedandmodeled in3D. 201

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APPENDIX B USINGDICDISPLACEMENTSTOCALCULATESTRAIN TheprimaryoutputfromVIC-3Dsoftwareare3Dpositionsanddisplacements (X,Y,Z,andU,V,W).VIC-3Dofferstheuseranoptiontoconverttheresultsintostrain, butsincetheareaofinterestinsomeapplicationsisrelativelysmallcomparedtothe overallsample,thestrainisexpectedtobeconstantineachdirection.Withthisinmind, thelongitudinalstrain xx ,transversestrain yy ,andshearstrain xy ,werecalculated basedonGreen'sstrainequationsshowninEquations B, B,and B usingthe measuredpositionsanddisplacementsfromVIC-3D. xx = @ u @ x + 1 2 @ u @ x 2 + @ v @ x 2 + @ w @ x 2 # (B) yy = @ v @ y + 1 2 @ u @ y 2 + @ v @ y 2 + @ w @ y 2 # (B) xy = 1 2 r xy = 1 2 @ v @ x + @ u @ y + @ u @ x @ u @ y + @ v @ x @ v @ y + @ w @ x @ w @ y (B) Figure B-1.Illustrationofhowthestraincomponentsarecalculatedusingpositionsand displacements. 202

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T odothis,eachdisplacement(U,V,orW)isplottedagainsttheXandYpositions, asshowninFig. B-1.Aplanetisthenappliedtothedata.Thestraincomponents areobtainedfromtheslopeoftheplane,whichcanthenbepluggedintotheabove equations. 203

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APPENDIX C UNIMORPHBANDWIDTHMEASUREMENT FlightcontrolofaMAVrequirespreciseandrapidcontrolsurfaceactuation,usually ontheorderof2Hzorgreater.ToverifythatMFCscouldobtainanactuationatthis rateandtoquantifytheexactdynamics,aseriesofhighspeedcameratestswere conducted.Thesetestsprovidedinsightintothehighspeeddynamicsoftheactuator andareexplainedinthefollowingsections. C.1HighSpeedCameraSetup Thesetup,showninFig. C-1A,consistsofahighspeedcamera,unimorphina cantileveredsetup,andproperlighting.Theproperelectronicstodrivetheunimorph from-500Vto1500Vatvariousfrequencieswasalsoincludedinthesetup. A B Figure C-1.A)Highspeedcamerasetupfordynamictesting.B)Triangleadheredtothe tipoftheunimorphtovisuallytrackthetipdisplacement.Photostakenby BradleyLaCroix. Atriangle,madeoutofcarbonberandspraypaintedwhite,isadheredtothe tipoftheunimorph,asshowninFig. C-1B.Thisallowedthetipoftheunimorphtobe visuallytrackedthroughoutitsrangeofmotion.Sincetherewasonlyonecamera,it wasimportanttokeepthecameraperpendiculartotheplaneofmotiontominimizethe effectsofperspective. 204

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C.2 Analysis Theunimorphwasactuatedthrougharangeoffrequenciesandthedisplacements capturedusingthehighspeedcamera.Basedonthedimensionsofthetriangle,a mm-to-pixelratiowasdevelopedandutilizedtomeasurethetipdisplacementsofthe unimorph.MATLABwasusedtondeachcornerofthetriangleforeachimageand compiletheresultsintoaplot.ThisprocessisillustratedinFig. C-2. Figure C-2.Unimorphdynamicspost-processing. C.3Results TheresultsofthehighspeeddynamictestsandthesubsequentMATLABanalysis areshowninFigs. C-3 and C-4.The1Hzresponseisanidealexampleofthenatural 205

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frequency oftheunimorph,wherethesmalloscillationsareanartifactofthenatural frequencyandthelargedisplacementiscommandedbyapplyingthechangeinvoltage. Thisisapparentinthe5Hzplotaswell,butislessevidentintheotherplots.Thetip displacementishighestat23.3Hz,whichisthenaturalfrequency,andthenbegins todecreaseasthefrequencyincreases.Fromtheseresults,itcanbeconcludedthat theMFCscanbeactuatedontheorderof20Hzormore,withhigherfrequencies dependentonthenaturalfrequencyoftheoverallstructure. Figure C-3.M8528-P1unimorphdynamicsfor1cycleat1Hz. 206

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Figure C-4.M8528-P1unimorphdynamicsfrom5-40Hz. 207

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APPENDIX D MFC1ANDMFC2WORKBENCHCOMPARISONS D.1MFC1 IncludedinthissectionareadditionalcomparisonsfortheMFC1aircraft.The gurescomparetheABAQUSFEAmodelandtheexperimentaltestscompletedwith DIC.ThesetupandadditionaldetailsaregiveninSection 9.6.Adiagramexplainingthe loadingdirection,Fig. 9-10 canbefoundinSection 9.4 Figure D-1.MFC1workbenchcomparisonLV0000RV0000RPZ20. Figure D-2.MFC1workbenchcomparisonLV0000RV0000RTE20. 208

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Figure D-3.MFC1workbenchcomparisonLV0000RV1500RLE100. Figure D-4.MFC1workbenchcomparisonLV0000RV1500RPZ20. 209

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D .2MFC2 IncludedinthissectionareadditionalcomparisonsfortheMFC2aircraft.The gurescomparetheABAQUSFEAmodelandtheexperimentaltestscompletedwith DIC.ThesetupandadditionaldetailsaregiveninSection 9.6.Adiagramexplainingthe loadingdirection,Fig. 9-10 canbefoundinSection 9.4 D.2.1Noactuation Figure D-5.MFC2LV0000RV0000LLE100gRLE100g. Figure D-6.MFC2LV0000RV0000LTE20gRTE20g. 210

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Figure D-7.MFC2LV0000RV0000LTE-20gRTE-20g. Figure D-8.MFC2LV0000RV0000LPZ20gRPZ20g. 211

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Figure D-9.MFC2LV0000RV0000LPZ-20gRPZ-20g. D.2.2Noload Figure D-10.MFC2LV0000RV1500. 212

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Figure D-11.MFC2LV1500RV0000. Figure D-12.MFC2LV1500RV1500. 213

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Figure D-13.MFC2LV-500RV1500. Figure D-14.MFC2LV-500RV-500. 214

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D .2.3LV1500RV1500 Figure D-15.MFC2LV1500RV1500LLE100gRLE100g. Figure D-16.MFC2LV1500RV1500LLE-100gRLE-100g. 215

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Figure D-17.MFC2LV1500RV1500LTE20gRTE20g. Figure D-18.MFC2LV1500RV1500LTE-20gRTE-20g. 216

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Figure D-19.MFC2LV1500RV1500LPZ20gRPZ20g. Figure D-20.MFC2LV1500RV1500LPZ-20gRPZ-20g. 217

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D .2.4LV-500RV-500 Figure D-21.MFC2LV-500RV-500LLE100gRLE100g. Figure D-22.MFC2LV-500RV-500LLE-100gRLE-100g. 218

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Figure D-23.MFC2LV-500RV-500LTE20gRTE20g. Figure D-24.MFC2LV-500RV-500LPZ20gRPZ20g. 219

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Figure D-25.MFC2LV-500RV-500LPZ-20gRPZ-20g. 220

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D .2.5Miscellaneous Figure D-26.MFC2LV-500RV-500LPZ-20gRPZ-20gLLE-100gRLE-100g. Figure D-27.MFC2LV1500RV0000LLE-100gRLE-100g. 221

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APPENDIX E MFC1AEROELASTICCOMPARISONS Thissectionshowsthecomparisonofthewindtunnelexperimentalresultstothe aeroelasticcomputermodel.AdditionaldetailscanbefoundinSection 10.3.Duetoa failureoftheleftMFC,onlytherightsideoftheMFC1modelisactuated.Figure E-1 showstheresultsfortheactuatedwingunderstaticconditions.Asstatedpreviously,the resultsfromtheunactuated,staticconditionsareusedasatarefortheothercases. Theresultsinthisrstsetofguresmatchupwell.Theresultsforthe15m/stest conditionsareshowninFig. E-2 .Theseresultsdifferslightlymore,mostlikelydueto theniteelementmodelnotbeingabletomodelthebattensontheMFC1correctly.The resultsdifferbyabout3mminsomepartsofthemodel. ThetwasoptimizedandtheRMSerrorforeachcongurationcalculated,as describedinSection 10.3.TheRMSerroristabulatedinTable E-1.Ascanbeseenin thetable,anaverageofslightlymorethan45,000pointswereanalyzedtodeterminethe qualityoft.TheRMSerrorwaslessthan1mmforallcasesandaveragedlessthan 0.5mmforthegroupofcongurations. TableE-1.MFC1qualityoftforeachcongurationtested. V elocity,m/sCongurationNumberofpointsRMSerror,mm 0 L V0000RV000045736 0.65 LV0000RV150045558 0.23 LV0000RV-50045702 0.27 15 LV0000RV000045639 0.46 LV0000RV150045491 0.57 LV0000RV-50045637 0.49 222

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A B C Figure E-1.ComparisonoftheMFC1niteelementmodeltotheexperimentalresults understaticconditions.A)noactuation.B)actuatedtoLV0000andRV1500. C)actuatedtoLV0000andRV-500. 223

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A B C Figure E-2.ComparisonoftheMFC1niteelementmodeltotheexperimentalresultsat 15m/s.A)noactuation.B)actuatedtoLV0000andRV1500.C)actuatedto LV0000andRV-500. 224

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APPENDIX F SMARTMATERIALSCORPORATION'SMFCENGINEERINGPROPERTIES High-eld( jE j>1kV/mm),biased-voltage-operationpiezoelectricconstants: d33 4.6E+02 pC/N4.6E+02pm/V d31 -2.1E+02pC/N-2.1E+02pm/V Low-eld(jE j< 1kV/mm),biased-voltage-operationpiezoelectricconstants: d33 4.0E+02 pC/N4.0E+02pm/V d31 -1.7E+02pC/N-1.7E+02pm/V Free-strain pervolt(low-eld-high-eld) 0.75-0.9ppm/V 0.75-0.9ppm/V ford33MFC(P1) Free-strain pervolt(low-eld-high-eld) 0.75-0.9ppm/V 0.75-0.9ppm/V ford31MFC(P2) Free-strainhysteresis 0.2 0.2 DCpolingvoltage,Vpolford33MFC(P1)+1500V+1500V DCpolingvoltage,Vpolford31MFC(P2)+360V +360V Poledcapacitance @ 1kHz,roomttemp,Cpol 0.42nF/cm 2 2.7nF/in 2 ford33MFC(P1) Poledcapacitance @ 1kHz,roomttemp,Cpol 4.6nF/cm 2 29nF/in 2 ford31MFC(P2) OrthotropicLinearElasticProperties(constantelectriceld): T ensilemodulus, E 1 30.336GPa4.4E+06psi Tensilemodulus, E 1 15.857GPa2.3E+06psi Poisson'sratio, 12 0.31 0.31 Poisson'sratio, 21 0.16 0.16 Shearmodulus, G 12 5.515GPa8.0E+05psi Roddirection Electrodedirection Rules-of-mixtureestimate 225

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Oper ationalParameters: Maxim umoperationalpositivevoltage, +1500V+1500V V max ford33MFC(P1) Maximumoperationalpositivevoltage, +360V +360V V max ford31MFC(P2) Maximumoperationalnegativevoltage, -500V -500V V max ford33MFC(P1) Maximumoperationalnegativevoltage, -60V -60V V max ford31MFC(P2) Linear-elasticstrainlimit 1000ppm1000ppm Maximumoperationaltensilestrain < 4500ppm < 4500ppm Peakwork-energydensity 6.9 m MN=m 3 1000 in lb=in 3 Maximumoperatingtemperature-StandardVersion < 80 C < 176 F Maximumoperatingtemperature-HighTempVersion < 130 C < 266 F Operationallifetime( @ 1kVp-p,incycles) > 10E+09 > 10E+09 Operationallifetime( @ 2kVp-p,500VDC,incycles) > 10E+07 > 10E+07 Operationalbandwidthasactuator,highelectriceld0Hz-10kHz0Hz-10kHz atlowelectriceldlevels(<33%ofmaxop.voltage)0Hz-700kHz0Hz-700kHz Additionalmechanicalparameters Thic knessofallMFCtypes 300 m 10%12mil 10% VolumeDensity,activearea 5.44g/cm 3 0.197lb/in 3 AreaDensity,activearea 0.16g/cm 2 0.328lb/ft 2 226

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BIOGRAPHICAL SKETCH Bradley'scollegecareerbeganatUFinFall2004.Firstslatedtowardsmechanical engineering,hesoonaddedaerospaceengineeringtopursueadualdegree.Spending severalyearsinAIAA'sDesignBuildFly,hequicklylearnedvariousmanufacturing, design,andtestingtechniquesforsmallUAVs.Healsogainedsignicantcommercial airplaneexperienceduringhisthreesummerinternshipswithTheBoeingCompanyin theSeattlearea. Bradgraduatedwithdualbachelordegreesinmechanicalengineeringand aerospaceengineeringinSpring2009andbegunhisgraduatecareerintheFall of2009.Hisworkhasbeenmainlyfocusedonsolidmechanicswithanapplication towardsmicroairvehicles.Throughthisresearch,hehasgainedextensiveexperience withcompositelayups,digitalimagecorrelation,materialtesting,andniteelement modeling. 236