Frequency Analysis of Vibration Energy Harvesting Systems

307 Pages·2016·21.569 MB·English

by  Xu Wang

Frequency Analysis
of Vibration Energy
Harvesting Systems
Xu Wang
School of Engineering
College of Science Engineering and Health
RMIT University
AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON
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List of Figures
Figure1.1 Asingledegreeoffreedomspring-mass-dashpotsystem
drivenby(A)directforceand(B)inertialforce. 3
Figure1.2 Predictionofthemassrelativedisplacementresponse
fromthebasedisplacementexcitationusingMatlabSimulink
transferfunctionmethod. 5
Figure1.3 Predictionoftherelativedisplacementresponsefromthe
baseaccelerationexcitationinputusingtheMatlabSimulink
integrationmethod:(A)IntegrationschematicofEq.(1.12);
(B)MatlabSimulinkschematicfollowingEq.(1.12). 6
Figure1.4 SchematicoftheMatlabSimulinkstatespacemethod
forpredictionoftherelativedisplacementresponsefrom
thebasedisplacementexcitation. 8
Figure1.5 Asinewaveexcitationsignalinputwithafrequency
of275HzandRMSaccelerationof9.8m/s2. 9
Figure1.6 Parameterinputsofsinewaveexcitationacceleration
forthesourceblockoftheMatlabSimulink. 10
Figure1.7 Thetimetraceoftherelativedisplacementresponse. 11
Figure1.8 AMatlabcodeforcalculationoftherelativedisplacement
frequencyresponsefunctionamplitudeversusfrequencycurve. 11
Figure1.9 Relativedisplacementfrequencyresponsefunction
(therelativedisplacementamplitudeovertheexcitationacceleration
amplitude). 12
Figure2.1 Schematicofsingledegreeoffreedompiezoelectric
vibrationenergyharvestersystemconnectedtoasingleelectric
loadresistor(A)theharvesteroscillatorelectromechanicalsystem
(B)energyharvestingcircuit. 16
Figure2.2 SimulationschematicforEq.(2.10)inMatlabSimulink
withasinewavebaseexcitationinputandasinusoidal
voltageoutputatafrequencyusingthetransferfunctionmethod. 20
Figure2.3 (A)Relativeaccelerationintegratedtotherelative
displacement;(B)Derivativeoftheoutputvoltageintegrated
totheoutputvoltage;(C)SimulationschematicforEq.(2.11)
withasinewavebaseexcitationinputandasinusoidal
voltageoutputatafrequencyusingtheintegrationmethod. 22
Figure2.4 TheMatlabSimulinkstatespacemethodschematic
forthepredictionoftheresponserelativedisplacementand
outputvoltagefromthebaseexcitationacceleration. 24
Figure2.5 Outputsinusoidalvoltagesignal(volt)fromaninput
excitationaccelerationsignalwitharootmeansquare
accelerationvalueof1g(9.8m/s2)atanexcitation
frequencyof275Hz. 25
Figure2.6 Theoutputvoltageamplitudeversusthebaseexcitation
accelerationamplitudeatanexcitationfrequencyof275Hz. 26
xi
xii List of Figures
Figure2.7 Harvestedresonantpowerversusthebaseexcitation
accelerationamplitudeatanexcitationfrequencyof275Hz. 27
Figure2.8 Theoutputvoltageamplitudeversusthemechanical
dampingunderaninputexcitationaccelerationsignal
ofanRMSvalueof1g(9.8m/s2)atanexcitationfrequencyof275Hz. 27
Figure2.9 Harvestedresonantpowerversusthemechanical
dampingunderaninputexcitationaccelerationsignalofan
RMSvalueof1g(9.8m/s2)atanexcitationfrequencyof275Hz. 28
Figure2.10 Theoutputvoltageamplitudeversustheelectricalload
resistanceunderaninputexcitationaccelerationsignal
ofanRMSvalueof1g(9.8m/s2)atanexcitation
frequencyof275Hz. 28
Figure2.11 Harvestedresonantpowerversustheelectricalload
resistanceunderaninputexcitationaccelerationsignal
ofanRMSvalueof1g(9.8m/s2)atanexcitation
frequencyof275Hz. 29
Figure2.12 Harvestedresonantpowerversustheforcefactor
underaninputexcitationaccelerationsignalofanRMS
valueof1g(9.8m/s2)atanexcitationfrequencyof275Hz. 29
Figure2.13 Matlabcodesforsimulationofthefrequencyresponse
functionsoftheoutputrelativedisplacementandvoltage
overtheinputexcitationacceleration. 30
Figure2.14 Amplitudeoftherelativedisplacementfrequencyresponse
functiondtheoutputrelativedisplacementdividedbytheinput
excitationacceleration. 31
Figure2.15 Amplitudeofthevoltagefrequencyresponse
functiondtheoutputvoltagedividedbytheinputexcitation
acceleration. 32
Figure2.16 Harvestedresonantpowerandoutputvoltageversusfrequency. 34
Figure2.17 Dimensionlessharvestedresonantpowerversus
dimensionlessresistanceandforcefactorsforthe
singledegreeoffreedomsystemconnectedtoaloadresistor. 36
Figure2.18 Resonantenergyharvestingefficiencyversus
dimensionlessresistanceandforcefactorsforthe
singledegreeoffreedomsystemconnectedtoaloadresistor. 38
Figure3.1 Extractionandstorageinterfacecircuitsforvibration
energyharvesters,(A)standard;(B)synchronouselectric
chargeextraction(SECE);(C)parallelsynchronousswitch
harvestingoninductor(SSHI);(D)seriesSSHICircuit. 44
Figure3.2 Workingprincipleofafullcycleofbridgerectification.
(A)Positivehalf-cycle;(B)negativehalf-cycle;(C)positiveoutput
waveform. 45
Figure3.3 Theresonantenergyharvestingefficiencyversusdimensionless
resistanceandforcefactorsforthesingledegreeoffreedom
piezoelectricharvesterconnectedtothefourtypesof
List of Figures xiii
interfacecircuits.(A)Standard;(B)synchronouselectric
chargeextraction;(C)parallelsynchronousswitchharvesting
oninductor(SSHI);(D)seriesSSHI. 56
Figure3.4 Thedimensionlessharvestedresonantpowerversus
dimensionlessresistanceandforcefactorsforthesingle
degreeoffreedompiezoelectricharvesterconnectedto
thefourtypesofinterfacecircuits.(A)Standard;(B)synchronous
electricchargeextraction;(C)parallelsynchronousswitch
harvestingoninductor(SSHI);(D)seriesSSHI. 57
Figure3.5 Outputvoltageandharvestedresonantpowerversusthe
inputexcitationacceleration.(A)Harvestedresonantpower
versustheexcitationacceleration;(B)outputvoltageversus
theexcitationacceleration. 61
Figure3.6 (A)Outputvoltageand(B)harvestedresonantpower
versusmechanicaldampingunderthebaseacceleration
of9.8m/s2. 62
Figure3.7 Outputvoltage(A)andharvestedresonantpower(B)versus
electricresistanceunderthebaseaccelerationof9.8m/s2. 63
Figure3.8 Harvestedresonantpowerversusforcefactorunderthebase
accelerationof9.8m/s2. 63
Figure4.1 Schematicofasingledegreeoffreedomelectromagnetic
vibrationenergyharvesterconnectedtoasingleloadresistor. 71
Figure4.2 SimulationschematicforEq.(4.9)inMatlabSimulinkwitha
sinewavebaseexcitationinputandasinusoidalvoltage
outputatafrequencyusingthetransferfunctionmethod. 72
Figure4.3 (A)Relativeaccelerationintegratedtotherelativedisplacement.
(B)Derivativeoftheoutputvoltageintegratedtotheoutputvoltage.
(C)SimulationschematicforEq.(4.10)withasinewavebaseexcitation
inputandasinusoidalvoltageoutputatafrequencyusingthetime
domainintegrationmethod. 73
Figure4.4 Matlabcodesforsimulationofthefrequencyresponsefunctionsof
theoutputrelativedisplacementandvoltageoverthebaseinput
excitationacceleration. 77
Figure4.5 Resonant energy harvesting efficiency versus dimensionless
resistance and equivalent force factors for the single degree of
freedom electromagnetic harvester connected to a load resistor. 81
Figure4.6 Dimensionless harvested resonant power versus dimensionless
resistance and equivalent force factors for the single degree of
freedom electromagnetic harvester connected to a load resistor. 82
Figure4.7 Theresonantenergyharvestingefficiencyversusdimensionless
resistanceandforcefactorsforthesingledegreeoffreedom
piezoelectricharvesterconnectedtothefourtypesofinterfacecircuits.
(A)Standardinterface;(B)synchronouselectricchargeextraction;
(C)parallelsynchronousswitchharvestingoninductor(SSHI);
(D)seriesSSHI. 96
xiv List of Figures
Figure4.8 The dimensionless harvested resonant power versus dimensionless
resistance and force factors for the SDOF electromagnetic harvester
connected to the four types of interface circuits. (A) Standard
interface; (B) synchronous electric charge extraction;
(C) parallel synchronous switch harvesting on inductor (SSHI);
(D) series SSHI. 101
Figure5.1 Dimensionlessresonantenergyharvestingefficiencyofpiezoelectric
andelectromagneticvibrationenergyharvestersversusdimensionless
resistanceandforcefactorsforthesingledegreeoffreedom
harvestersconnectedtoaloadresistance;(A)piezoelectric;
(B)electromagnetic. 109
Figure5.2 Dimensionlessharvestedresonantpowerversusdimensionless
resistanceandforcefactorsforthesingledegreeoffreedom
piezoelectricandelectromagneticharvestersconnectedtoaload
resistor;(A)piezoelectric;(B)electromagnetic. 111
Figure5.3 Dimensionlessharvestedresonantpowerversusthedimensionless
forcefactorbyfixingthedimensionlessresistanceof0.5. 113
Figure5.4 Dimensionlessharvestedresonantpowerversusthedimensionless
forcefactorbyfixingthedimensionlessresistanceof1.5. 113
Figure5.5 Dimensionlessharvestedresonantpowerversusthedimensionless
resistancebyfixingthedimensionlessforcefactorof0.5. 114
Figure5.6 Dimensionlessharvestedresonantpowerversusthedimensionless
resistancebyfixingthedimensionlessforcefactorof1.5. 114
Figure6.1 Schematicofatwodegreeoffreedompiezoelectricvibrationenergy
harvestingsystemmodel. 125
Figure6.2 Thedimensionlessharvestedresonantpowerandenergyharvesting
efficiencyversusvariousmassratio(M ¼m /m ). 132
R 2 1
Figure6.3 Thedimensionlessharvestedresonantpowerandenergyharvesting
efficiencyversusvariousstiffnessratio(K ¼k /k ). 133
R 2 1
Figure6.4 Casestudyofaquartervehiclesuspensionmodelwithpiezoelectric
elementinsert. 133
Figure6.5 SimulationschematicforEqs.(6.1)and(6.2)withasinewavebase
excitationinputandasinusoidalvoltageoutputatafrequency
usingtheintegrationmethod. 135
Figure6.6 Outputvoltagefortheinputexcitationaccelerationamplitudeof
1g(9.80m/s2)andexcitationfrequencyof1.45Hz. 135
Figure6.7 Outputpowerfortheinputexcitationaccelerationamplitudeof1g
(9.80m/s2)andexcitationfrequencyof1.45Hz. 136
Figure6.8 Displacementamplituderatiosofmass1andmass2withrespectto
theinputdisplacementamplitudeversusfrequency. 137
Figure6.9 Outputvoltageandharvestedresonantpowerversustheinput
excitationaccelerationamplitude. 137
Figure6.10 Theoutputvoltageandharvestedresonantpowerversusfrequency. 138
Figure6.11 Outputvoltageandharvestedresonantpowerversuselectric
loadresistance. 139
List of Figures xv
Figure6.12 Outputvoltageandharvestedresonantpowerversusthe
wheeletiredamping. 140
Figure6.13 Outputvoltageandharvestedresonantpowerversusthesuspension
damping. 141
Figure6.14 Outputvoltageandharvestedresonantpowerversustheforce
factor. 142
Figure6.15 Outputvoltageversusfrequencyforvariouswheeletiremass. 143
Figure6.16 Outputvoltageversusfrequencyforvariousquartervehiclemasses. 144
Figure6.17 Outputvoltageversusfrequencyforvariouswheeletirestiffness. 145
Figure6.18 Outputvoltageversusfrequencyforvarioussuspensionstiffness. 145
Figure6.19 Thedimensionlessharvestedresonantpowerversusthestiffness
ratio(k /k ). 147
2 1
Figure6.20 Outputvoltageversusfrequencyforvariouswheeletiredamping
coefficients. 148
Figure6.21 Outputvoltageversusfrequencyforvarioussuspensiondamping
coefficients. 148
Figure6.22 Dimensionlessharvestedresonantpowerversusthedampingratio
(c /c ). 149
1 2
Figure7.1 Schematicofatwodegreeoffreedompiezoelectricvibrationenergy
harvesterinsertedwithtwopiezoelectricpatchelements. 157
Figure7.2 Thedifferenceofthetwodimensionlessresonantfrequenciesversus
themassratioM anddimensionlessfrequencyratioU underthe
1 1
synchronouschangesofthecouplingstrengthofthepiezoelectric
patches.(A)Lz21¼Lz22¼0:02;(B)Lz21¼Lz22¼5;(C)Lz21¼Lz22¼10;
1 2 1 2 1 2
and(D)Lz21¼Lz22¼40. 162
1 2
Figure7.3 Thedifferenceofthetwodimensionlessresonantfrequencies
versusthemassratioM andtheU underthecoupling
1 1
strengthchangesoftheprimaryandauxiliaryoscillatorsystems.
(A)Lz21¼0:02Lz22¼5;(B)Lz21¼0:02Lz22¼10;(C)Lz21¼0:02Lz22¼40;
1 2 1 2 1 2
and(D)Lz21¼40Lz22¼0:02. 163
1 2
Figure7.4 Thedimensionlessharvestedpowerofthetwodegreeoffreedom
piezoelectricvibrationenergyharvesterversusthedimensionless
frequencyfordifferentdimensionlessmassratio(M ).(A)The
1
dimensionlessharvestedpowerofthefirstpiezopatchelement;
(B)thedimensionlessharvestedpowerofthesecondpiezopatch
element;and(C)thetotaldimensionlessharvestedpowerofthefirst
andsecondpiezopatchelements.DOF,degreeoffreedom. 164
Figure7.5 Thedimensionlessharvestedpowerofthetwodegreeoffreedom
piezoelectricvibrationenergyharvesterversusthedimensionless
frequencyfordifferentU .(A)Thedimensionlessharvestedpowerof
1
thefirstpiezopatchelement;(B)thedimensionlessharvestedpower
ofthesecondpiezopatchelement;and(C)thetotaldimensionless
harvestedpower.DOF,degreeoffreedom. 165
xvi List of Figures
Figure7.6 Dimensionlessharvestedpowerofthetwodegreeoffreedom
piezoelectricvibrationenergyharvesterversusFandz .
1
(A)Dimensionlessharvestedpowerofthefirstpiezopatchelement;
(B)dimensionlessharvestedpowerofthesecondpiezopatch
element;and(C)totaldimensionlessharvestedpower. 166
Figure7.7 Dimensionlessharvestedpowerofthetwodegreeoffreedom
piezoelectricvibrationenergyharvesterversusFandz .
2
(A)dimensionlessharvestedpowerofthefirstpiezopatchelement;
(B)dimensionlessharvestedpowerofthesecondpiezopatch
element;and(C)totaldimensionlessharvestedpower. 167
Figure7.8 Theenergyharvestingefficiencyofthefirstpiezoelectricpatch
elementversusFandM fordifferentcouplingstrengths.
1
(A)Lz21¼Lz22¼0:02;(B)Lz21¼Lz22¼5;(C)Lz21¼Lz22¼10;and
1 2 1 2 1 2
(D)Lz21¼Lz22¼40. 168
1 2
Figure7.9 Theenergyharvestingefficiencyofthesecondpiezoelectricpatch
elementversusFandM fordifferentcouplingstrengths.
1
(A)Lz21¼Lz22¼0:02;(B)Lz21¼Lz22¼5;(C)Lz21¼Lz22¼10;and
1 2 1 2 1 2
(D)Lz21¼Lz22¼40. 169
1 2
Figure7.10 Schematicofathreedegreeoffreedompiezoelectricvibration
energyharvesterinsertedwiththreepiezoelectricpatchelements. 170
Figure7.11 Thedimensionlessharvestedpowerofthe3DOFpiezoelectric
vibrationenergyharvesterversusthedimensionlessfrequencyfor
differentmassratioM .(A)Dimensionlessharvestedpowerofthe
1
firstpiezopatchelement;(B)dimensionlessharvestedpowerofthe
secondpiezopatchelement;(C)dimensionlessharvestedpowerof
thethirdpiezopatchelement;and(D)totaldimensionless
harvestedpower.DOF,degreeoffreedom. 172
Figure7.12 Thedimensionlessharvestedpowerofthe3DOFsystemversusthe
dimensionlessfrequencyfordifferentU (A)dimensionless
1.
harvestedpowerofthefirstpiezopatchelement;(B)dimensionless
harvestedpowerofthesecondpiezopatchelement;(C)
dimensionlessharvestedpowerofthethirdpiezopatchelement;
and(D)totaldimensionlessharvestedpower.DOF,degreeoffreedom. 173
Figure7.13 Dimensionlessharvestedpowerofthe3DOFpiezoelectricvibration
energyharvesterversusFandz .(A)dimensionlessharvestedpower
1
ofthefirstpiezopatchelement.(B)dimensionlessharvestedpowerof
thesecondpiezopatchelement.(C)dimensionlessharvested
powerofthethirdpiezopatchelement.(D)totaldimensionless
harvestedpower.DOF,degreeoffreedom. 174
Figure7.14 Dimensionlessharvestedpowerofthe3DOFpiezoelectric
vibrationenergyharvesterversusFandz .(A)dimensionless
2
harvestedpowerofthefirstpiezopatchelement.(B)dimensionless
harvestedpowerofthesecondpiezopatchelement.
List of Figures xvii
(C)dimensionlessharvestedpowerofthethirdpiezopatchelement.
(D)totaldimensionlessharvestedpower.DOF,degreeof
freedom. 175
Figure7.15 Theharvestedefficiencyofthe3DOFpiezoelectricvibrationenergy
harvesterversusM andF.(A)theefficiencyofthefirstpiezo
1
patchelement.(B)theefficiencyofthesecondpiezopatchelement.
(C)Theefficiencyofthethirdpiezopatchelement.(D)Total
efficiency.DOF,degreeoffreedom. 175
Figure7.16 Schematicofageneralizedmultipledegreeoffreedompiezoelectric
vibrationenergyharvesterwithpiezoelectricelementsbetweenall
twonearbyoscillators. 177
Figure7.17 Thedimensionlessharvestedpowerandtheharvestedpower
densityversusthenumberofdegreesoffreedomofpiezoelectric
vibrationenergyharvester(PVEH). 179
Figure8.1 Acantileveredbimorphbeamclampedbywasherswithanut
massgluedatthefreeend. 188
Figure8.2 Thebimorphcantileveredbeamsetupontheshakerforlabtesting. 189
Figure8.3 PolytecLaserDopplerVibrometersystemdisplay. 190
Figure8.4 Themeasuredvibrationspectrumandfirstnaturalfrequency
of24.375Hzforthecantileveredbeamunderawhitenoise
randomforceexcitation. 191
Figure8.5 Thepredictedandmeasuredvoltageoutputversusexcitation
frequencyforthePZT-5Hcantileveredbeam. 192
Figure8.6 Thepredictedandmeasuredharvestedresonantpowerversusthe
excitationfrequencyforthePZT-5Hcantileveredbeam. 192
Figure8.7 Thepredictedandmeasuredresonantoutputvoltageversusthe
externalelectricloadresistanceforthePZT-5Hcantilevered
beam. 193
Figure8.8 Thepredictedandmeasuredresonantoutputvoltagesversusthe
excitationaccelerationamplitudeforthePZT-5Hcantileveredbeam. 194
Figure8.9 Atwodegreeoffreedompiezoelectricvibrationenergyharvester
withonepiezoelectricelementwasmountedontheshaker. 195
Figure8.10 Thepredictedandexperimentallymeasuredvoltageoutputvalues
versustheexcitationfrequencyforatwodegreeoffreedompiezoelectric
vibrationenergyharvesterinsertedwithonepiezoelectricelement. 196
Figure8.11 Thepredictedandexperimentallymeasuredvoltageoutputvalues
versustheexternalelectricloadresistanceforatwodegreeof
freedompiezoelectricvibrationenergyharvesterinsertedwith
onepiezoelectricelement. 197
Figure8.12 Theexperimentalsetupofthetwodegreeoffreedom(2DOF)
piezoelectricvibrationenergyharvester(PVEH)builtwithtwo
piezoelectricelements. 198
Figure8.13 Theisolatedtestsfortheprimaryandauxiliaryoscillatorsofthetwo
degreeoffreedom(2DOF)piezoelectricvibrationenergyharvester
(PVEH)builtwithtwopiezoelectricelements. 199
xviii List of Figures
Figure8.14 Theanalyticallypredictedandexperimentallymeasuredvoltage
outputsversustheexcitationfrequencyforatwodegreeoffreedom
piezoelectricvibrationenergyharvesterinsertedwithtwopiezoelectric
elements.(A)Theanalyticallypredictedandexperimentallymeasured
voltageoutputofthefirstpiezopatchelement;(B)Theanalytically
predictedandexperimentallymeasuredvoltageoutputofthesecond
piezopatchelement. 201
Figure9.1 Statisticalenergyanalysismodelofalinearvibrationenergy
harvestingsystem. 218
Figure9.2 Dimensionlessmeanharvestedresonantpoweroflinearsingle
degreeoffreedompiezoelectricandelectromagneticvibration
energyharvestersforthecasesoftheweakandnon-weakcoupling
(h ¼h ). 223
M E
Figure9.3 Resonantenergyharvestingefficiencyoflinearsingledegreeof
freedompiezoelectricandelectromagneticvibrationenergy
harvestersforthecasesofweakandnon-weakcoupling
(h ¼h ). 224
M E
Figure10.1 Timerecord,autocorrelation,andautospectrumfunctionsof
broadbandrandomorwhitenoiseexcitationinputoftheinertiaforce. 236
Figure10.2 Timerecord,autocorrelation,andautospectrumfunctionsoffinite
narrowbandwidthrandomexcitationinputoftheinertiaforce. 238
Figure10.3 Timerecord,autocorrelation,andautospectrumfunctionsof
harmonicexcitationinputoftheinertiaforce. 240
Figure10.4 Schematicforthedirectmethodsformeasurementofthemean
inputandharvestedpowerandenergyharvestingefficiencyofa
vibrationenergyharvester.DC,directcurrent;FFT,fastFourier
transform;FRFP,frequencyresponsefunctionofpowerfluctuation. 242
Figure11.1 HydraulicactuationtypeofPelamis. 250
Figure11.2 Waveenergyconvertertypes:(A)thePSFrogpointabsorber;
(B)heavingbuoypointabsorber;(C)archimedeswaveswing. 251
Figure11.3 Rotationalturbinetype. 251
Figure11.4 Asingledegreeoffreedomnonlinearoscillatorinacylindrical
tubegenerator. 256
Figure11.5 SimulationschematicforEq.(11.7)forpredictionoftheoscillator
relativedisplacementresponse(x-y)andoutputvoltagevfrom
asinewavebaseexcitationaccelerationinputy€atafrequency
usingMatlabSimulinktimedomainintegrationmethod. 257
Figure12.1 Schematicofatwodegreeoffreedomelectromagneticvibration
energyharvesteroscillatorsystem. 272
Figure12.2 SimulationschematicforEq.(12.3)forpredictionoftheoscillator
relativedisplacementresponsesandoutputvoltagesfromthebase
excitationaccelerationusingMatlabSimulinktimedomainintegration
method. 274
Figure12.3 Schematicofafourdegreeoffreedomelectromagneticvibration
energyharvesteroscillatorsystem. 275