Piezoelectric Actuators and Generators for Energy Harvesting

189 Pages·2018·9.63 MB·English

by  Sergey N. Shevtsov

Innovation and Discovery in Russian Science and Engineering
Sergey N. Shevtsov · Arkady N. Soloviev
Ivan A. Parinov · Alexander V. Cherpakov
Valery A. Chebanenko
Piezoelectric
Actuators and
Generators for
Energy Harvesting
Research and Development
Innovation and Discovery in Russian Science
and Engineering
Serieseditors
CarlosBrebbia
WessexInstituteofTechnology,Southampton,UnitedKingdom
JeromeJ.Connor
Department of Civil & Environmental Engineering, Massachusetts Institute of
Technology,Cambridge,Massachusetts,USA
Moreinformationaboutthisseriesathttp://www.springer.com/series/15790
(cid:129)
Sergey N. Shevtsov Arkady N. Soloviev
(cid:129)
Ivan A. Parinov Alexander V. Cherpakov
Valery A. Chebanenko
Piezoelectric Actuators
and Generators for Energy
Harvesting
Research and Development
SergeyN.Shevtsov ArkadyN.Soloviev
RussianAcademyofSciences DonStateTechnicalUniversity
SouthScientificCenteroftheRussian Rostov-on-Don,Russia
AcademyofSciences
Rostov-on-Don,Russia AlexanderV.Cherpakov
I.I.VorovichMathematics,Mechanics
IvanA.Parinov andComputerScienceInstitute
I.I.VorovichMathematics,Mechanics SouthernFederalUniversity
andComputerScienceInstitute Rostov-on-Don,Russia
SouthernFederalUniversity
Rostov-on-Don,Russia
ValeryA.Chebanenko
RussianAcademyofSciences
SouthScientificCenteroftheRussian
AcademyofSciences
Rostov-on-Don,Russia
ISSN2520-8047 ISSN2520-8055 (electronic)
InnovationandDiscoveryinRussianScienceandEngineering
ISBN978-3-319-75628-8 ISBN978-3-319-75629-5 (eBook)
https://doi.org/10.1007/978-3-319-75629-5
LibraryofCongressControlNumber:2018935963
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Preface
A great problem for modern science and modern techniques is the receiving,
transformation,andstorageofenergyobtainedfromtheenvironmentandgenerated
by working mechanisms and moving objects. While there is a fairly extensive
scientificliteratureonR&Dandapplicationofenergy-harvestingdevices,significant
breakthroughsinthisfieldofscience,technique,andtechnologyhavenotyetbeen
achieved.Atpresent,investigationsareplannedintooptimalconstructionsthatallow
obtaining maximum output characteristics of piezoelectric devices by using the
specificgeometryofthegoodsandhighphysicalandmechanicalcharacteristicsof
piezoelectric materials and composites, as well as the development of promising
experimental, theoretical, and numerical methodsfor studying thesecomplextech-
nicalsystems.
This book presents some achievements and results in this field, obtained by the
so-called Rostov Scientific School on Ferro-piezoelectricity. Investigations of the
three-component systems, based on lead zirconate titanate (PZT), started in the
Rostov State University (now Southern Federal University) at the end of the
1960s. Almost immediately, intensive studies of four- and five-component solid
solutions were undertaken, and thereafter studies of six-component systems, based
onPZTattheendofthe1990s.PiezoelectricCeramicRostovskaya(PCR)isawell-
knownbrandthatoriginallypresenteditselfasPZT-typeceramics.Rostovscientists
havedevelopedandmanufacturedmorethan100systemsofPCRovertime,based
onPZTcompositionasonthebaseofotherferro-piezoelectricsolidsolutions.Many
materials, composites, and devices were developed, researched, and manufactured
by these scientists in Rostov-on-Don. They have published more 5,000 journal
papers and books on these topics and have been granted more 200 Soviet,
Russian, and international patents (see, for example, monographs [4–8, 20, 50,
64,120,130,135–139],andthereferencestherein).
This book includes some of the latest results obtained by the scientists of the
South Scientific Center of the Russian Academy of Sciences, Southern Federal
University, and Don State Technical University (Rostov-on-Don). It also presents
newapproachestoR&Dinpiezoelectricgeneratorsandactuatorsofdifferenttypes
v
vi Preface
basedonthedevelopedoriginalconstructionsandmodernresearchintotheoretical,
experimental,andnumericalmethodsofphysics,mechanics,andmaterialsscience.
Improvedtechnical solutionsofthedevicesarepresented, whichdemonstrate high
outputvaluesofvoltageandpower,allowingapplicationoftheseproductsinvarious
areasofenergyharvesting.
Thebookisdividedintosevenchapters.
Chapter 1 considers a general overview of the problems of electro-elasticity in
applicationtotheinvestigationofenergyharvesting,morespecificallytothestudy
ofpiezoelectricgenerators(PEGs).Thischapterdiscussesconstitutiveequationsof
electro-elasticityintensorform,andstatescorrespondingboundary-valueproblems.
Mathematicalmodellingofcantileverandstacktypesofpiezoelectricgeneratorsare
presentedindetail.Inparticular,weconsiderbimorphpiezoelectricstructureswith
whole and partial covering of substrate by piezoelements. Numerous numerical
results are presented for a broad spectrum of characteristics (in particular, first
resonancefrequency,voltage,andoutputpower).
Chapter 2 discusses the developed original set-ups for testing the above-
mentioned harvesters, samples of piezoelectric generators, and also the
corresponding experimental methods and original computer algorithms. Compari-
sonsoftheobtainedanalyticalandfinite-elementresultswiththeexperimentaldata
obtained by using the developed test set-ups, are presented and discussed with the
goal of optimizing construction of piezoelectric generators of both types. Experi-
mental,numerical,andcomparativeresultsareobtainedforcasesofdifferentkinds
ofloading(harmonical,pulsed,andquasi-statical).
Chapter3isdevotedtomathematicalmodelingoftheflexoelectriceffect,arising
in unpolarized piezoceramics under mechanical (in particular, bending) loading.
There is discussion of the developed original set-up for estimation of this effect
and the obtained experimental results for flexo-electrical beam under three-point
bending. We formulate a corresponding boundary-value problem and obtain a
theoretical solution that allows us to perform numerical experiments. The results
allow studying the possibility of obtaining an electrical response, caused by the
flexoelectric effect in ferroelectric ceramic plates of a certain composition. The
numerical results show the possibility of the appearance of an electric potential in
an unpolarized piezoceramic beam and also allows us to make conclusions on
qualitativeconstituentsofthetheoreticalmodelwiththeexperiment.
Chapter 4 deals with the analytical and numerical modeling of the power of a
high-stroke flex-tensional piezoelectric actuator, which consists of a high-power
piezoelectric stack and polymeric composite shell, intended for amplification of
the stroke. In order to overcome the principal drawback of the piezoelectric trans-
ducers,whichisaverysmallstrokeatrelativelyhighoperatingforce,anoptimiza-
tion problem is formulated and solved for the actuator’s construction. For
simultaneous provision ofsufficient strokeand stiffness,allowingcounteraction of
the external loads, the shape of the amplified shell is parameterized by the rational
Beziercurves.Theirparameters(coordinatesandweightsofthecontrolpoints)are
changediterativelybyageneticalgorithmaccordingtotheobjectivefunctionvalue,
which is calculated by the finite element model of the transducer through varied
geometryoftheshell.
Preface vii
Sincedamageanddefectshaveacrucialinfluenceonallpossiblecharacteristics
oftheconsideredpiezoelectricharvesters,thesecondpartofthebookisdevotedto
experimental-theoretical methods, computer simulation, and devices developed for
the study and identification of defects in cantilever elastic rod constructions.
Chapter5presentsthecurrentbackgroundforourstudiesinthisarea.
Chapter 6 is devoted to the development of methods for identifying the param-
eters of defects in an elastic cantilever with a notch, and theoscillation parameters
are investigated in the context of dependence on the type of defect. The finite-
elementcalculationofthemodalparametersoffull-bodymodelsofacantileverrod
withdefectusingthefinite-elementmethodisperformedandtheoscillationformsof
the model are presented. The dependencies of natural frequencies on the defect
location and size are investigated. The most sensitive modes of oscillations are
determinedwithrelation todependenceon thedefectsize atits different locations.
Thecalculationofthedependencebetweenthedefect(notch)sizeofthecantilever
rod of the full-body finite element model and the flexural rigidity of the elastic
element is performed for the analytical model on the base of the dynamic equiva-
lenceofmodels.
Chapter 7 presents the measuring set-up that allows one to conduct technical
diagnostics of rod constructions. It is based on the methods developed in the
previous chapter. In addition, the results of the development and implementation
of the algorithm of the calculation-experimental approach for the identification of
defects in elements of cantilever structures are discussed. For this purpose, the
original software and a laboratory information-measuring set-up have been devel-
oped,whichprovideanautomatedcollectionofinformationonconstructionvibra-
tionsandperformdiagnosticsofthedefects.
TheauthorsofthebookespeciallythankV.A.AkopyanandE.V.Rozhkovfor
participating in the development of experimental approaches and creating test
setups. We also acknowledge the Russian Foundation for Basic Research and
Russian Ministry of Education and Science, grants from which helped to perform
thisresearch.
This self-standing book, covering the necessary theoretical, experimental, and
numericalmodelingapproaches,isaimedatawiderangeofstudents,engineers,and
specialists interested and participating in R&D of modern energy-harvesting
devices,thematerialsforthesedevices,thedevelopmentofphysicalandmathemat-
icalmethodsfortheirstudy,andalsoexperimentalequipmentfordefinitionoftheir
characteristics.
Rostov-on-Don,Russia SergeyN.Shevtsov
December,2017 ArkadyN.Soloviev
IvanA.Parinov
AlexanderV.Cherpakov
ValeryA.Chebanenko
Contents
1 MathematicalModelingofPiezoelectricGenerators. . . . . . . . . . . . . 1
1.1 GeneralFormulationoftheProblemofElectroelasticity. . . . . . . . 2
1.2 MathematicalModellingofCantilever-typePEGs. . . . . . . . . . . . . 4
1.2.1 StatementoftheProblemforCantilever-typePEGs. . . . . . 4
1.2.2 NumericalExperiment. . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 MathematicalModellingofStack-typePEGs. . . . . . . . . . . . . . . . 26
1.3.1 StatementoftheProblemforStack-typePEGs. . . . . . . . . 26
1.3.2 NumericalExperiment. . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2 ExperimentalModelingofPiezoelectricGenerators. . . . . . . . . . . . . 33
2.1 Cantilever-TypeGenerators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.1.1 DescriptionofTestSet-upandSamples. . . . . . . . . . . . . . 33
2.1.2 Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.1.3 TheoryandExperiment. . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2 Stack-TypeGenerators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.1 HarmonicLoading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.2 PulsedLoading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.3 Quasi-StaticLoading. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3 MathematicalModelingofFlexoelectricEffect. . . . . . . . . . . . . . . . . 49
3.1 InvestigationofOutputVoltageinUnpolarizedCeramics. . . . . . . 49
3.1.1 SamplesforStudyandExperimentalProcedure. . . . . . . . . 49
3.1.2 ResultsoftheExperimentandDiscussion. . . . . . . . . . . . . 51
3.2 InvestigationoftheFlexoelectricEffect
inUnpolarizedCeramics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2.1 FormulationoftheProblemforFlexoelectricalBeam. . . . . 52
3.2.2 BoundaryConditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.3 Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2.4 NumericalExperiment. . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
ix
x Contents
4 AmplifiedHigh-StrokeFlextensionalPZTActuator
forRotorcraftApplication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 ModelingandNumericalOptimizationoftheActuatorShell. . . . . 66
4.3 ActuatorDesignandManufacture. . . . . . . . . . . . . . . . . . . . . . . . 71
4.4 ActuatorStaticTests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.5 NumericalandExperimentalTestsoftheActuator’s
DynamicProperties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.6 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5 DefectsinRodConstructions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.1 DiagnosisofDefectsandMonitoringofRodConstruction. . . . . . 81
5.2 ReconstructionofDefectParametersBasedonBeamModels. . . . 82
5.3 ReconstructionofDefectsBasedonFinite-ElementModeling. . . . 85
5.4 GoalsofFollowingStudy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6 IdentificationofDefectsinCantileverElasticRod. . . . . . . . . . . . . . . 89
6.1 MathematicalFormulationoftheProblemofDefect
ReconstructioninCantilever. . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2 FiniteElementModelingofCantileverwithDefects
andAnalysisofVibrationParameters. . . . . . . . . . . . . . . . .. . . . . 90
6.2.1 Full-BodyRodModelwithDefect. . . . . . . . . . . . . . . . . . 90
6.2.2 AnalysisofModalParametersofFull-Body
ModelwithDefect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2.3 ComparisonofModalParametersofOscillations
withStress-StrainStateofFECantileverModel
withVariousNotches. . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.3 AnalysisoftheVibrationParametersofCantilever
withDefectsBasedontheAnalyticalModeling. . . . . . . . . . . . . . 106
6.3.1 IdentificationofCantileverRodDefects
WithintheEuler–BernoulliModel. . . . . . . . . . . . . . . . . . 106
6.3.2 AnalysisofSensitivityofNaturalFrequenciestoSize
andLocationofDefectinAnalyticalModeling. . . . . . . . . 111
6.4 MethodsofIdentifyingDefectsinCantilever. . . . . . . . . . . . . . . . 116
6.4.1 ComparisonofFinite-ElementandAnalyticalModels
ontheBaseofDynamicEquivalence. . . . . . . . . . . . . . . . 119
6.4.2 ReconstructionofDefectParametersinCantilever. . . . . . . 122
6.5 InvestigationoftheFeaturesofResonanceModes
ofCantileverwithDefect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.5.1 ComparisonofOscillationModesofFE
andAnalyticalModels. . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.5.2 ChoiceofCharacteristicsforIdentificationofDefects
inCantilever,BasedontheAnalysisofEigen-Forms
ofBendingOscillations. . . . . . . . . . . . . . . . . . . . . . . . . . 128
Contents xi
6.5.3 IdentificationofCantileverDefectParameters,
BasedontheAnalysisofEigen-Forms
ofBendingOscillations. . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.5.4 AlgorithmoftheMethodforIdentifying
theParametersofDefectsinCantilever. . . . . . . . . . . . . . . 138
6.5.5 IdentificationofDefectsinRodswithDifferent
VariantsofFixing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.6 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7 Set-upforStudyingOscillationParametersandIdentification
ofDefectsinRodConstructions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.1 TechnicalDiagnosticsofDefectsinRodConstructions. . . . . . . . . 145
7.2 MeasuringSet-upforIdentificationofDefects
inRodConstructions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.2.1 TechnicalCapabilitiesoftheSet-up. . . . . . . . . . . . . . . . . 145
7.2.2 DevelopmentofStructuralParametersoftheSet-up. . . . . . 147
7.2.3 AlgorithmforMultiparametricIdentification
ofDefectsinRodConstructions. . . . . . . . . . . . . . . . . . . . 148
7.2.4 TechniqueofCarryingOutTestMeasurements
ofModalCharacteristicsoftheBeamConstruction. . . . . . 151
7.2.5 SoftwareforAutomationoftheMeasurements
oftheOscillationParametersofBeamConstructions. . . . . 152
7.3 Calculation-ExperimentalApproachtoDetermination
ofDefectsinCantilever-ShapedBeamConstruction. . . . . . . . . . . 157
7.3.1 DescriptionofStudiedObject. . . . . . . . . . . . . . . . . . . . . . 157
7.3.2 Full-ScaleExperiment. . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.3.3 ApprobationofCalculation-TestApproach
forDeterminationofCantileverBeamDefects. . . . . . . . . . 158
7.4 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179