Design, Fabrication and Testing of Angled Fiber Suspension for Electrostatic Actuators

118 Pages·2012·5.83 MB·English

Design, Fabrication and Testing of Angled Fiber
Suspension for Electrostatic Actuators
Bryan Edward Schubert
Electrical Engineering and Computer Sciences
University of California at Berkeley
Technical Report No. UCB/EECS-2012-51
http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-51.html
May 1, 2012
Copyright © 2012, by the author(s).
All rights reserved.

Permission to make digital or hard copies of all or part of this work for
personal or classroom use is granted without fee provided that copies are
not made or distributed for profit or commercial advantage and that copies
bear this notice and the full citation on the first page. To copy otherwise, to
republish, to post on servers or to redistribute to lists, requires prior specific
permission.
Design,FabricationandTestingofAngledFiberSuspensionforElectrostaticActuators
by
BryanEdwardSchubert
Adissertationsubmittedinpartialsatisfactionofthe
requirementsforthedegreeof
DoctorofPhilosophy
in
Engineering-ElectricalEngineeringandComputerSciences
inthe
GraduateDivision
ofthe
UniversityofCalifornia,Berkeley
Committee incharge:
ProfessorRonaldS.Fearing,Chair
ProfessorAliJavey
ProfessorRoyaMaboudian
Spring2011
Design,FabricationandTestingofAngledFiberSuspensionforElectrostaticActuators
Copyright 2011
by
BryanEdwardSchubert
1
Abstract
Design,FabricationandTestingofAngledFiberSuspensionforElectrostaticActuators
by
BryanEdwardSchubert
DoctorofPhilosophyinEngineering-ElectricalEngineeringandComputer Sciences
UniversityofCalifornia,Berkeley
ProfessorRonaldS.Fearing,Chair
Asuspensioncomprisedofangledfibersisproposedasanewmeansforachievinghighstrain,
high stress, energy dense electrostatic actuators. Angled fiber arrays have low density and can
be placed between the electrodes of a parallel plate or comb-drive type actuator to create a self-
contained actuator sheet with low mass and volume. Angled fibers also have a Poisson’s ratio of
zero,allowingtheuseofrobust,rigidelectrodes,andtheycanbecomposedofstiffmaterialswith
lowviscoelasticproperties. Thisisincontrasttothealternativetechnologyofdielectricelastomers
that depend on unreliable compliant electrodes and highly viscoelastic dielectrics. Performance
limitsofanidealnanometer-scaleactuator,suchasenergydensity,stressandstrain,andefficiency
are considered through theoretical modeling. A micrometer scale prototype is fabricated using a
novel fiber peeling technique that easily produces high-aspect-ratio (1.8 µm radius, 66 µm long),
angled microfibers. The microfibers are used as a suspension for a parallel plate actuator. The
prototype actuator is characterized through static and dynamic tests, to reveal a maximum static
strainof3.4%atastaticstressof0.8kPa(electricfieldof13.9V/µm),afastunloadedstepresponse
of< 2ms,aQof12.9andapowerdensityof12.8W/kgwhendrivinganinertialloadinresonance
at845Hz.
i
Tomyamazingwife,Jessica.
ii
Contents
ListofFigures iv
ListofTables x
1 Introduction 1
1.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 SurveyofActuators 4
2.1 PiezoelectricCeramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 ElectroactivePolymers(EAPs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 ElectronicEAPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 IonicEAPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 CarbonNanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 ShapeMemoryAlloys(SMA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 ThermalActuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 MagneticActuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6.1 Electromagnetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6.2 Magnetostrictive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7 ElectrostaticActuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7.1 ParallelPlateActuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7.2 CombDriveActuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.7.3 ElectrostaticInductionLinearActuator . . . . . . . . . . . . . . . . . . . 23
2.8 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 DesignandModellingofElectrostaticActuator 26
3.1 Dielectric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 DielectricBreakdowninAir . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.2 DielectricBreakdowninPorousMaterial . . . . . . . . . . . . . . . . . . 28
3.1.3 DielectricLosses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 IdealStiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
iii
3.2.2 ViscoelasticLosses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.3 PorousSupports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.4 AngledFiberSupports . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3.1 Squeeze-FilmDamping . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3.2 ForceControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3.3 Performance-Stress,StrainandWorkDensity . . . . . . . . . . . . . . . 52
3.4 SystemModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.5 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Fabrication 58
4.1 FabricationinCombDriveActuator . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 Methodsandmaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Fabricationresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.4 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4.1 Radiusandlengthlimit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.5 Concludingremarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5 CharacterizationandTesting 76
5.1 TestSetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2 BreakdownLimit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.3 Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.4 DCTesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.4.1 Displacementvs. ElectricField . . . . . . . . . . . . . . . . . . . . . . . 81
5.4.2 DCStepResponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.5 ACResponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6 Conclusion 90
6.1 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Bibliography 93
A Fiberpullingangles 101
iv
List of Figures
2.1 (a) Reference axes for piezoelectric subscripts. (b) Example hysteresis curve for
PZT [91]. Marked positions correspond to a. unpolarized, b. polarized to satura-
tionandc. defaultstateafterpolarization. . . . . . . . . . . . . . . . . . . . . . . 6
2.2 (a)Comparisonofapproximatehysteresisloopsforanormalferroelectric(dashed
line)andarelaxorferroelectric(P(VDF-TrFE))(solidline)[19]. (b)Illustrationof
crystallized,polarpolymersgraftedtoaflexibleelastomerbackbone. . . . . . . . . 9
2.3 Illustration of trapped charge in a cellular polymer foam with bonded electrodes.
Avoltageappliedtotheelectrodeswillcausethisstructuretocompress. . . . . . . 10
2.4 Illustrationofdielectricelastomerwithcompliantelectrodescompressinginthick-
nessandexpandingtransverselyunderanappliedvoltage. . . . . . . . . . . . . . 11
2.5 A sample of dielectric elastomer actuator configurations. (a) Spring roll actua-
tor with elastomer peeled back to show spring. (b) Folded actuator. (c) Bowtie
actuator. (d)Bimorph (top)andunimorph (bottom). . . . . . . . . . . . . . . . . . 14
2.6 IPMC actuation. Top figure is the neutral state. Middle figure is the state just
after a voltage is applied to the electrodes, causing cations to move toward the
cathode. Bottomfigureisafterthepressuregradientcausesflowtowardstheanode,
relievingsomestress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.7 CNT actuator in aqueous solution of NaCl. Two gray regions are SWNT sheets
bonded together by double-sided tape. The polarity of the applied voltage causes
theionstoformachargeddoublelayerontheSWNTs. Thechargeinjectioncauses
mechanicaldeformations intheSWNTs,makingthecantileverbend[9]. . . . . . . 17
2.8 ToprowshowscrystalstructureofthematerialduringthedifferentstagesofSMA
actuator use. (a) SMA spring in low-temperature, undeformed martensite state.
(b)SMAspringinlow-temperature,deformedmartensitestate. (c)SMAspringin
hightemperatureaustenitestate. . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.9 Parallelplateactuator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
v
2.10 (a) Integrated force array. The polyimide beams are t = 0.35 µm thick, the metal
p
layers are t = 30 nm thick, and the air gap between beams is t = 1.2 µm thick.
m g
The support spacing is d = 22 µm long. This actuator is only 2 to 4 µm thick into
the page [11, 43]. (b) Macroscale, distributed electrostatic micro actuator. This
actuator is composed of flexible 7.5 µm thick polyimide film coated with 12.5 nm
ofnickel. Thedouble-sidedtapeis25µmthick. Thisactuatoris28mmthickinto
thepage[58]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.11 Comb drive actuator shown at an angled perspective, and detail of a single finger
fromthetopview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.12 Linearinductionmotor. In(1)chargesareinducedonthesliderbytherotor. In(2)
the charge on the rotor is switched, causing it to repel the slider and force it over
byonestep. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1 Electrical limits based on Paschen effect and field emission in air. (a) Maximum
voltage versus gap spacing. (b) Maximum field strength versus gap spacing. The
shadedregionsdenotethesafedesignlimits. . . . . . . . . . . . . . . . . . . . . . 27
3.2 Electrostatic actuators using angled fibers and porous foam as support structures.
(a,b) Parallel plate. (c,d) Comb drive. Drawings on left side show the actuators in
theirdefaultstate,anddrawingsontherightshowtheactuatorscompressingunder
electrostaticpressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 (a) Spring force for linear spring and buckling spring plotted with electrostatic
force for a parallel plate actuator with arbitrary units. The filled dots are unsta-
ble points and the open dots are stable points. The arrow shows the direction of
increasingvoltage. (b)Illustration ofspringbetweenparallelplates. . . . . . . . . 33
3.4 Models for linear viscoelasticity in a material, and plots showing approximate
displacement behavior for a constant applied force. (a) Voigt-Kelvin model. (b)
Maxwell model. (c) Combined Voigt-Kelvin and Maxwell model called the Stan-
dardSolid[72] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 Example compressive stress-strain behavior for different cellular foams. (a) Elas-
tomeric foam, where plateau region is from elastic buckling of cell walls. (b)
Polymeric foam that shows a plateau region as a result of plastic yielding of cell
walls. (c) Brittle foam with jagged plateau region resulting from brittle fracture of
cellwalls[31]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.6 Normalized stress as a function of strain for an elastic open cell foam with m = 1
andD = 1. Thevaluesonthelinesaretherelativedensitiesρ /ρ . . . . . . . . . . 40
f s