Experimental Study of Dielectric Elastomer Actuator Energy Conversion Efficiency

IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 1, FEBRUARY 2013 169

Experimental Study of Dielectric ElastomerActuator Energy Conversion Efficiency

Jean-Philippe Lucking Bigue and Jean-Sebastien Plante

Abstract—Dielectric elastomer actuators (DEAs) have raised in-terest in the field of mobile robotics. In such a field, actuator de-sign requires a fundamental understanding of DEA energy conver-sion performance. To provide insight into DEA mechanical work,energy consumption, and efficiency, this paper proposes a sim-ple thermodynamic description completed by experimental lossfactors obtained over a broad range of operating conditions andmodes. Extensive data gathered on cone actuators show practicalefficiency limits of ∼26% for acrylic actuators (VHB 4905) operat-ing under constant charge mode and ∼18% for silicone actuatorsoperating under constant voltage mode. While charge recoverycould raise these limits to ∼60%, the study of a DEA rotary motorshows significant efficiency degradation caused by unconstrainedelectrode boundaries.

Index Terms—Dielectric elastomer actuator (DEA), efficiency,energy, orbital motor, thermodynamics.

I. INTRODUCTION

A. Background

D IELECTRIC elastomer actuators (DEAs) are known fortheir impressive force-to-weight ratios (>500:1) [1] and

for their high strain potential (>200%) [2], [3]. Studies also sug-gest that DEAs can theoretically achieve 80% overall efficiencyunder constant charge operating mode [4]. These characteris-tics, combined with their inexpensive nature and self-sensingcapabilities [5], make DEAs a promising power source for mo-bile robotic systems, such as flapping-wing insects [6], rollingrovers [7] or hopping microbots [8]. As a power source, DEAmotors have also been proposed, either guided by an orbitinginner rotor design [9], or by transforming linear actuation intorotary motion with ratchet mechanisms [10].

Designing DEAs for energy-sensitive applications impliesevaluating design requirements, such as actuator efficiency andpower output. However, to date, very limited work has beendone regarding the energy conversion efficiency of DEAs.

An experimental study performed limited tests on diamondactuators made of VHB material and operating under constantvoltage. Results revealed a peak efficiency of 18%, significantly

Manuscript received April 9, 2011; revised July 15 2011; accepted July 252011. Date of publication September 19, 2011; date of current version Septem-ber 12, 2012. Recommended by Technical Editor G. Alici. This work wassupported by a FQRNT New Researchers Start-Up Grant and the CRSNG grad-uate scholarships program.

The authors are with the Universite de Sherbrooke, Sherbrooke,QC J1K2R1, Canada (e-mail: [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMECH.2011.2164930

lower than the theoretical maximum. The study identified vis-coelasticity and current leakage as the main culprits for theefficiency degradation [1].

Traditional modeling of DEAs relies heavily on continuummechanics. Indeed, models that account for large material defor-mation, nonlinear elasticity and viscoelasticity have been shownto accurately predict DEA dynamics when proper material char-acterization is used [11]. To predict overall efficiency however,these models must include the effect of electrical losses. Theo-retical work regarding this issue coupled linear resistive heatingand current leakage to a visco-hyperelastic model [12]. Thework predicted that DEA strip actuators could reach 90% max-imal efficiency in optimal conditions, but that electrical lossescan rapidly undermine this limit. The work also pointed out thata significant gap exists between theoretical and experimentalefficiency of DEAs.

An alternative approach to study DEA efficiency relies on thefundamental thermodynamic process of charge expansion [4].The work explored dielectric material deformations (dots) in-duced by an electrical field, in order to determine their max-imal energy coupling efficiency factor (k2), defined as the ra-tio of output mechanical work over the input electrical energy.Mainly used for high-level technology comparison (e.g., withpiezoelectric), the work was amongst the first to predict maxi-mal theoretical efficiency of different materials. However, it didnot quantify the impact of electrical and viscous losses, whilethe impact of DEA geometry and operating modes were notconsidered.

In summary, the causes underlining the experimental effi-ciency limits of DEAs have yet to be fully characterized andunderstood. Hence, design guidelines to maximize DEA energyconversion have yet to be established.

B. Approach

This paper builds upon the thermodynamic behavior of DEAsand describes the charge expansion process that characterizesideal DEAs operating under constant voltage, constant charge,and constant electrical field modes. The thermodynamic descrip-tion is accompanied by extensive experimental performancemapping of main loss factors, to provide an understanding ofpractical DEA energy conversion performance.

A computerized test bench, designed to monitor actuator workoutput and energy consumption during simulated work cycles,is used to map the performance of cone actuators operatingover a wide range of speeds, electrical fields, and capacitanceratios (Cr ). This is done for the constant voltage and constantcharge processes, and for two DEA materials, VHB4905 andNusil CF19-2186. The impact of geometry is also considered

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170 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 1, FEBRUARY 2013

Fig. 1. DEA deformation from (1) an initial contracted state to (2) a uniformlydeformed state (applied voltage).

by comparing the performance of cone actuators and multicellDEA rotary motors.

It is shown that, together, the proposed thermodynamic de-scription and experimental loss factors can explain the main per-formance trends that characterize practical DEAs. The resultsprovide guidelines that can be used for preliminary efficiencypredictions based on actuator size, geometry, material, appliedvoltage, displacement, and operating mode.

II. ANALYTICAL DEVELOPMENT

A. Problem Statement

As shown in Fig. 1 in its contracted and expanded states, aDEA can be described as a flexible capacitor, composed of apair of compliant electrodes applied on each side of a dielectricpolymer.

This ideal DEA has a uniform film thickness u and area A.The film is incompressible and its constant volume ψ is givenby

ψ = Au. (1)

The deformation of the film occurs under the action ofMaxwell stresses, generated by electric charges placed on theelectrodes. The total electrical charge Q placed on the film’selectrodes under voltage V is given by

Q = CV (2)

where the actuator capacitance C is found by the flat plate ca-pacitor equation

C = εdε0A

u(3)

where ε0 is the permittivity of free space and εd is the mate-rial dielectric constant. The Maxwell stresses resulting from theelectrostatic attraction are combined into an equivalent Maxwellpressure (P). The proven electromechanical relationship govern-ing this phenomenon [13] is given by:

P = εdε0E2 (4)

where E = V/u is the electrical field, defined by the ratio of theapplied voltage V over the actuated film thickness u.

The following development is based on the ideal DEA ofFig. 1, deforming between its initial contracted state (1) and afinal expanded state (2), here driven by three ideal operatingmodes, self-described as the constant voltage, constant charge,and constant electrical field modes.

Fig. 2 Energy flow across a DEA.

The charge expansion process that characterizes DEA opera-tion is a capacitive process, similar to the gas expansion processof internal combustion engines. With respect to the thermody-namics of such engines, a fundamental understanding of DEAenergy conversion is derived by the simple thermodynamic pro-cess that describes ideal DEA behavior, and a number of lossmechanisms that can affect performances according to differ-ent operating conditions. With high amounts of experimentaldata, such analysis can lead to robust performance predictions,as widely proven through the preliminary design of internalcombustion engines [14], [15].

B. DEA Thermodynamic Description

The proposed energy flow across a typical DEA is illustratedin Fig. 2. Starting from the available input energy UE , the ther-modynamic efficiency ηT is defined as

ηT =WT

UE(5)

where WT is the theoretical mechanical work generated by anideal thermodynamic process, further developed in Section II.C.The thermodynamic loss QT associated with this ideal processis nothing but unused electrical energy left on the capacitorafter its expansion, an amount of energy that can theoreticallybe recovered.

The electromechanical loss QEM is defined as input energythat does not contribute to mechanical work, such as electricallosses due to leakage and resistive heating, as well as undesir-able capacitor overexpansion. These losses, therefore, reducethe theoretical mechanical work WT to the indicated amountof energy available for mechanical work WI . Finally, viscousand friction losses QV lower the output mechanical work to thebrake actuator work WB .

The measurable quantities on a physical system are UE , WB ,and QV , which allow the computation of the mechanical ηM ,indicated ηI , and brake ηB efficiencies, as defined by:

ηM =WB

WI(6)

ηI =WI

UE(7)

ηB =WB

UE. (8)

While these efficiencies are determined experimentally, the ther-modynamic ηT and electromechanical ηEM efficiencies are not.The thermodynamic work WT is difficult, if not impossible, to

BIGUE AND PLANTE: EXPERIMENTAL STUDY OF DIELECTRIC ELASTOMER ACTUATOR ENERGY CONVERSION EFFICIENCY 171

TABLE ITHERMODYNAMIC PERFORMANCE OF DEAS

measure (hence illustrated by dashed lines in Fig. 2) and is there-fore determined from theoretical expressions derived in SectionII.C. The electromechanical efficiency ηEM is determined indi-rectly by considering the product of subsidiary efficiencies

ηEM =ηI

ηT. (9)

C. Thermodynamic Charge Expansion Process

The equivalent Maxwell pressure P applied on the flexiblesurface A of the ideal DEA, presented in Fig. 1, generates amechanical work WT during expansion. For a uniform actuator,such as considered here, this work reduces to

WT =∫ u2

u1

PAdu. (10)

Substituting the Maxwell pressure by (4) and the film area of(1) yields (11), which is only a function of the applied voltageand material thickness when εd is assumed constant

WT = εdε0ψ

∫ u2

u1

V 2

u3 du. (11)

Solving the voltageversusthickness relation (11) for the threeoperating modes, leads to the equations listed in the first row ofTable I. These relations are expressed in terms of the actuatorcapacitance taken in its initial and deformed states, respectivelyC1 and C2 .

Electrical energy consumption is composed of the initialcharging energy U1 and actuation energy U12 , where UE =U1 + U12 . The charging energy is the energy stored on theinitial actuator capacitance C1 at an applied voltage V1

U1 =12C1V

21 . (12)

The actuation energy depends on the work done by the addedcharges during the process: dW = VdQ, and is found from

U12 =∫ Q2

Q1V dQ. (13)

Actuation energy is thus a function of the voltageversuschargerelation imposed by the actuator operating mode. In the constantcharge case, no actuation energy is added (U12 = 0) since the

Fig. 3 Thermodynamic efficiency ηT and normalized thermodynamic me-chanical work wT as a function of Cr for three different operating modes.

actuator is disconnected from the power source during deforma-tion. However, in the constant voltage and constant field cases,electrical energy is added and the corresponding relations foundfrom (13) are presented in Table I.

The efficiency of the thermodynamic process is defined asthe ratio of the mechanical work over the total electrical energyconsumption,

ηT =WT

U1 + U12 − UREC(14)

where UREC is the recovered energy from recovery electronics,if used. The amount of recovered energy is further defined bythe efficiency of the recovery electronics ηREC and the energystored on the capacitor at the end of the charge expansion process(state 2)

UREC = ηRECU2 . (15)

By neglecting charge recovery (ηREC = 0), the thermodynamicefficiency is developed for each operating mode and presentedin Table I. Note that when taken in the constant charge mode, asshown in Table 1, the thermodynamic efficiency equation is thetheoretical basis used to calculate the energy coupling efficiencyfactor (k2) proposed in previous work [4].

D. Fundamental DEA Performance

With respect to the defined charge processes, the actuatorefficiency and normalized mechanical work (wt = WT /U1) areplotted in Fig. 3 in terms of capacitance ratio (Cr = C2 /C1). A100% film area deformation, which corresponds to a Cr of 4,is drawn as a typical upper deformation boundary for practicalactuators, made from the best polymer materials available at thetime of writing.

Fig. 3 shows that the constant voltage process generates sig-nificantly more mechanical work when Cr is increased. How-ever, it is the least efficient and presents an asymptotic efficiencylimit of 50% at large Cr , where the impact of the charging energybecomes gradually negligible.

The origin of the constant voltage efficiency limit is deter-mined by analyzing current consumption during actuation. Thetime derivative of the electromechanical coupling written as


Fig. 4 Cone-shaped DEA used in the experimental study (cut view).

P = Q2/Cψ gives, after rearranging

dQ

dt=

Cψ

2Q

dP

dt+

Q

2C

dC

dt. (16)

Equation (16) shows that the current consumption has two con-tributors: the first term, mechanical work, and the second, energystorage. After further simplifications, these two terms are foundto be of equal magnitude, which explains the 50% limit seen atlarge Cr .

Finally, as shown in Table I, actuator efficiency is solely afunction of actuator Cr for all operating modes, suggesting thatusing high expansion ratios has a positive effect on efficiency.The key performance trend between the three processes is asfollows: increasing the stored energy level during deformationshows high mechanical work but low thermodynamic efficiency,while decreasing the stored energy level produces less mechan-ical work but higher thermodynamic efficiency. Thus, the con-stant charge process is the most efficient and does not presentany theoretical limit.

III. EXPERIMENTAL PERFORMANCE MAPPING

The objective of this section is to determine the main lossfactors and efficiencies that characterize a typical DEA design.This is done by measuring the energy input (UE = U1+U12),work output (WB ), as well as viscous losses (QV ) of acrylicand silicone cone actuators, forced to operate in various con-trolled conditions of speed, Cr , voltage and operating mode.From these measures, the indicated efficiency (ηI ), electrome-chanical efficiency (ηEM ), and mechanical efficiency (ηM ), aremapped in a postprocess, while their impact on brake efficiency(ηB ) is assessed according to the different operating conditions.The proposed description and maps are then compared to datataken on a DEA motor to illustrate the importance of actuatorgeometry on performance.

A. Standard Uniform Actuator

For the experimental performance mapping, a cone actuatoris chosen because its geometry does not present any free bound-aries that could significantly modify film deformation underdifferent loading conditions. A cone-shaped actuator with innerradius ri = 25 mm and outer radius ro = 45 mm is chosen tofulfill such requirements, and is shown in Figs. 4 and 5.

Acrylic actuators are made from two active film layers, eachbeing a 1 mm laminate of VHB4905 with a moderate prestretch

Fig. 5 TA.XTPlus Texture Analyser mounted with a cone actuator.

of λpre,1 × λpre,2 = 3×3 (i = 1 and j = 2 are the main prestretchdirections). Silicone actuators are made from one 400 μm layerof Nusil CF19-2186 film with a much smaller prestretch ofλpre,1 × λpre,1 = 1.4×1.4. Carbon grease is used for bothmaterials as it offers good adherence to the silicone films. Smallgaps (∼2 mm) are left between electrode and frame edges tomaximize reliability during tests [16], [17]. For all actuators,the minimal electrical field tested is Emin = 30 kV/mm, whilethe maximal applied electrical field is Emax = 60 kV/mm foracrylics and Emax = 50 kV/mm for silicones. Note that theelectrical field is calculated from prestretched film thickness,and not from the actuated film thickness, as this value woulddepend on the Cr (or displacement) of the actuator.

B. Work and Actuation Energy Measurements

Mechanical work output WB and actuation energy U12 aremeasured through the work cycle method [1], used to mimicDEA operation in a controlled environment of preset conditions(displacement, speed, voltage, and operating mode). Shown inFig. 5, a TA.XTPlus Texture Analyzer traction device is con-trolled by Labview to cycle an actuator at constant velocity,between two desired positions (s1 and s2), which correspond totwo actuator capacitance states (C1 and C2). Fig. 6 presents atypical work cycle force measurement under constant voltageoperation, here from an initial position s1 = 10 mm to a finalposition s2 = 20 mm. Voltage is only applied during actuatorexpansion, so that net mechanical work is produced over a com-plete cycle. Mechanical work output is, therefore, the closedintegral of the force F by the infinitesimal stroke ds

WM =∮

Fds. (17)

Actuation energy is the integral of the input electrical powerbetween s1and s2

U12 =∫ s2

s1

V i ds. (18)

Current i is measured by placing a small resistance (2 kΩ) inseries with the actuator and amplifying the voltage drop withan instrumentation amplifier, while voltage V is read from the


Fig. 6 Typical force and current measurements during a constant voltage workcycle where E = 57 kV/mm.

output port of a high voltage power source. Fig. 6 also presentsa typical current measurement during actuator rise.

To measure the viscous losses QV , the work cycles are re-peated while no voltage is applied to the actuator. In such con-ditions, the viscous losses QV are associated to the negative me-chanical work output over a complete cycle, determined from(17). All results gathered from the test bench are then storedautomatically for later post-processing in MATLAB.

C. Capacitance Ratio and Charging Energy Measurements

Capacitance measurements are automatically performed priorto the DEA work cycles. Fixed in a given position (s) by thetraction device, the DEA is charged with low voltage (∼ 0.5 kV)where current leakage is negligible, and then discharged througha high resistance value (R = 502 MΩ) where the electroderesistance is negligible in front of R. In such conditions, thevoltage drop is typical of an RC circuit and the capacitance isdetermined from the time constant τ = RC. Capacitance ratioCr is then calculated by dividing the measurements from anytwo given positions Cr = C2 /C1 .

Due to the fast dynamics involved, charging energy (U1) isnot measured directly, but estimated from the measured actuatorcapacitance C1 using (12) and the applied voltage V1 . Whenenergy recovery is accounted for, the discharge energy U2 isestimated with the same equation using capacitance C2 andvoltage V2 . For the constant charge process, the voltage V2 iscalculated by (2), assuming that the charge Q is constant duringthe expansion process.

Note that when submitted to high electrical fields, the actua-tor was found to expand (∼1 mm) within the gap left betweenelectrode edges and actuator frame, slightly changing the ca-pacitance from the value measured at low voltage. This overex-pansion was found mostly independent of the actuator position(s), and therefore to have no impact on the Cr . The impact ofoverexpansion on charging energy (U1) was also assessed, andfound to have limited effect on brake efficiency, as calculatedfrom (8). It was estimated to a maximal 3% deviation of thebrake efficiency in the constant charge process and less than 1%for the constant voltage process.

Fig. 7 DEA swashplate motor on the test bench.

Fig. 8 Schematic of a DEA swashplate motor (cut view).

D. DEA Swashplate Motor

To investigate the effect of free boundary conditions on theenergy conversion performance of DEAs, a novel DEA motoris presented in Fig. 7. As seen in Fig. 8, an inclined swashplatemechanism is fixed to an output shaft and coupled to a cone DEAby means of a bearing (not shown). By alternately activating apattern of four separate electrodes with high voltage relays, theswashplate rotates about the upper plate to accommodate thedeformation of the film. Note that for this study, two electrodesare activated at every time, as this pattern has been shown toproduce the most power output in 4-cell orbital DEA motors [9].

The advantage of this concept for experimental studies is itsdesign flexibility, as the angle of the swashplate α, the inner ri orouter ro plate radius as well as static height h of the actuator caneasily be modified. Even an offset can be added to the alignmentof the inner and outer plates (not shown) to produce a wobblemovement. For this study, the test geometry has α = 7.5◦, ri

= 27.5 mm, ro = 45 mm and h = 20 mm. These parameterswere selected without any extensive optimization but resultedin good overall performance.

To evaluate the performances of the DEA motor, a pinion gearis attached to the output shaft of the DEA motor, while a linearrack gear is used to transfer the rotary motion of the pinion gearinto the linear motion of the automated test bench described inSection III.B. The added friction of this mechanism was mappedas needed to correct the torque measurements. As seen in Fig. 9,


Fig. 9 Friction torque versus input torque of the rack and pinion mechanism,measured at 5 mm/s.

the friction torque was found repeatable, load dependant, andspeed independent.

To ensure that the high voltage relays were properly timedwith the forced rotation of the motor during the work cycles,many tests were performed and only the best results were used.These tests were also compared to an experimental simulationof optimal timing. In such a simulation, two cells are kept athigh voltage during a complete work cycle (360◦). The maximalamount of work produced over 90 consecutive degrees is thenextrapolated to account for the highest possible work that wouldbe produced by all four cells over a complete cycle. The resultsfrom this simulation were ∼5% higher than the best resultstaken with high voltage relays, suggesting that proper timingwas achieved.

IV. RESULTS

This section presents the experimental results gathered oncone actuators and on DEA rotary motors. The energy conver-sion performance of these devices is analyzed with respect tothe thermodynamic description presented in Section II.B (seeFig. 2). A detailed analysis is given for acrylic actuators oper-ating under constant voltage mode, while only most interestingresults are shown for the acrylic actuators operating under con-stant charge mode, as well as for the silicone actuators and DEAmotors.

For uniformity, efficiency maps and loss factors, here pre-sented in percentage values, are always plotted according tospeed and Cr . Results are only shown for the highest testedelectrical fields of Emax = 60 kV/mm for acrylics and of Emax= 50 kV/mm for silicones, since, unless noted otherwise, themaximum efficiencies were always reached at the highest ap-plied electrical field, for both materials and in both operatingmodes.

A. Acrylic Cone Actuators

With respect to the energy flow through a DEA, Fig. 10presents the different loss factors and efficiencies associatedwith the thermodynamic, electromechanical and mechanicalprocesses of acrylic actuators operating under the constant volt-age mode.

Starting from the top, the (a) thermodynamic efficiency and(b) electromechanical loss factor are multiplied to provide the (c)

Fig. 10 Acrylic actuators operating at constant voltage and Em ax = 60kV/mm: (a) Thermodynamic efficiency ηT . (b) Electromechanical loss fac-tor ηEM . (c) Indicated efficiency ηI . (d) Mechanical loss factor ηM . (e) Brakeefficiency ηB .

indicated efficiency. The thermodynamic efficiency, improvedby high Cr , is diminished by up to 35% at slow operating speedsand high Cr , due to major electrical losses as well as electrodeoverexpansion (e.g., buckling). Away from this critical region,the average electromechanical efficiency is ∼85% and is at-tributed to the electrical losses during the expansion process.


Fig. 11 Brake efficiency ηB of an acrylic actuator under constant voltage andEm ax = 60 kV/mm, where charge recovery ηREC = 90%.

The energy left at this stage is then further reduced by (d)mechanical losses, providing the (e) brake (or global) efficiencyof the actuator. Here the mechanical efficiency mainly affectsthe performances at high Cr and high speeds. Combined, theelectromechanical and mechanical loss factors bound the effi-ciency to an 18% peak, measured at slow speeds (0.5 mm/s) andmoderate Cr (∼2). This value is roughly 50% of the thermo-dynamic process prediction (a). Note that around this operatingpoint, increased electrical field does not improve maximal effi-ciency. In fact, peak efficiency was slightly better at electricalfields just under Emax (E = 54 kV/mm).

When optimistic charge recovery is considered (ηREC =90%) for the constant voltage mode, the brake efficiency valuecan significantly improve, particularly at slow speeds and lowCr . As seen in Fig. 11, brake efficiency of Fig. 10 (e) improveswhen the combined electromechanical and mechanical lossesare low. Note, that while actual best DEA driving circuits show∼60% efficiency [18], the design of efficient bi-directional elec-tronic circuits is an area of growing interest and should lead tofurther improvements of recovery efficiency values [19].

The main performance trends of the constant charge operatingmode are presented in Fig. 12. As seen in (a), the low mechanicalwork produced by the constant charge process is more rapidlydominated by viscous losses than the constant voltage mode. Itsimpact on brake efficiency (b) is significant, as efficiency quicklyreduces with speed and Cr . Note that electromechanical lossesare negligible and maximum efficiencies are produced by themaximum tested electrical field. Brake efficiency (b) is, there-fore, bound by mechanical losses, thermodynamic efficiencyand maximum electrical field. A peak brake efficiency of ∼26%is measured at a Cr of ∼1.6 and low speed (0.5 mm/s). Whencharge recovery is added in Fig. 12 (c), the constant charge pro-cess is found almost twice as efficient as the constant voltageprocess, reaching ∼60%.

B. Silicone Cone Actuators

Shown in Fig. 13 (a), silicone actuators operating under con-stant voltage mode (and Emax ) reach a brake efficiency plateauat a Cr of ∼1.5. This interesting design target is attributedto a tradeoff between mechanical losses and thermodynamicefficiency. In terms of Cr , thermodynamic efficiency increasesfaster than mechanical losses up to a Cr∼1.5. Over this value, the

Fig. 12 Acrylic actuators operating at constant charge and Em ax = 60 kV/mm.(a) Mechanical loss factor ηM . (b) Brake efficiency ηB . (c) Brake efficiencyηB with charge recovery ηREC = 90%.

Fig. 13 Brake efficiency ηB of silicone actuators operating at Em ax = 50kV/mm. (a) Constant voltage. (b) Constant Charge.


Fig. 14 Brake efficiency ηB of silicone actuators operating at Em ax = 50kV/mm with energy recovery (ηREC = 90%). (a) Constant voltage. (b) Constantcharge.

asymptotic behavior of thermodynamic efficiency (see Fig. 3)starts to wear off as mechanical losses continue to increase,thus creating the optimal design target. For the tested condi-tions, speed is found to have almost no effect on mechanicalefficiency, and a slight role in electromechanical losses. Whileelectromechanical losses are mostly negligible at high speeds,at slow speeds (<5 mm/s) they account for up to 5% reductionin brake efficiency, compared to the peak brake efficiency of∼19%, reached at the highest tested speed of 30 mm/s and Cr

of ∼1.5.Under constant charge operating mode in Fig. 13 (b), a peak

brake efficiency of ∼15% is observed at a Cr of ∼1.4. Thelow work output of this operating mode is mainly dominated bymechanical losses, however small mechanical losses are.

When charge recovery (ηREC = 90%) is considered, bothcharge modes seem to reach potentially high efficiencies of∼50% at very low Cr (∼1.2) as seen in Fig. 14. At low speeds,the constant charge mode (b) is more efficient, while at highspeeds, the constant voltage mode (a) is found superior.

Globally, these results demonstrate that in terms of energyconversion efficiency, silicone actuators reach their best perfor-mance at smaller Cr than acrylic actuators (∼1.5 versus ∼2).The main advantage of silicones is their reduced viscoelasticity,allowing peak efficiencies at higher speeds. In fact, to completethe mapping of the silicone loss factors, a new experimentalsetup that can achieve higher speeds should be developed infuture work.

C. Acrylic DEA Motor

The purpose of this section is to further investigate the effectof electrode boundary on energy conversion performance. Asseen in Fig. 15, when voltage is applied to a device that uses

Fig. 15 Direction of undesirable overexpansion in a multicell DEA motor.

TABLE IIAVERAGE EFFICIENCY COMPARISON BETWEEN DEA MOTORS

AND DEA CONES

multiple cells on a same film, the free boundary condition cancause overexpansion in a direction that does not contribute tooutput work.

To evaluate the effect of this overexpansion on actuation ef-ficiency, Table II compares the electromechanical and brakeefficiencies of the DEA motor to the performance of cone ac-tuators operating under similar Cr . The values were measuredon two identical acrylic DEA motors operating at the maximalelectrical field of Emax = 60 kv/mm and under the constantvoltage mode.

At slow operating speeds, the electromechanical efficiencyshows a 40% drop attributed to the overexpansion process,which not only can diminish the indicated work, but also in-crease the energy consumption. At higher speeds, the viscoelas-ticity of the material slows overexpansion and reduces energyconsumption. For acrylics, however, higher speeds do not im-prove overall efficiency as they also increase mechanical losses.Globally, best peak brake efficiency was 70% lower than peakefficiency of cone-shaped actuators, due to the overexpansionlosses as well as higher mechanical losses induced by the cycli-cal movement of the DEA motor.

While this evaluation should be further pursued on differentgeometries and materials, results demonstrate that free elec-trode boundary conditions can hinder the energy conversionperformance of DEAs. Improper boundary conditions should,therefore, be considered as an important loss mechanism. Strate-gies to avoid or reduce this phenomenon should be envisionedwhenever efficiency is considered an important design metric.

V. CONCLUSION

The thermodynamic description presented in this paper por-trays the energy flow across a DEA. Together with the experi-mental loss factors, this thermodynamic description can be used


to understand the influence of operating conditions on actua-tor performance. With the significant amount of data gathered,this method provides a simple and robust design tool to quicklyevaluate DEA energy conversion performance.

As a subset of the thermodynamic description, equations weredeveloped to understand the thermodynamic behavior of a uni-form DEA operating under constant voltage, constant charge,and constant electric field modes. This description shows thatthe constant charge process is associated to high efficiencies asit maximizes the work output done by DEA charging energy,while the constant voltage process is associated with higherwork output, generated from the additional electrical energyinput. In different operating conditions, these idealistic ther-modynamic behaviors are reduced by electromechanical andmechanical loss factors, which are mapped experimentally oncone-shaped actuators and a swashplate DEA motor.

The understanding provided by this thermodynamic descrip-tion yields the following design guidelines for actuator effi-ciency.

1) The constant charge process does not predict any theoreti-cal efficiency limit, but an actual peak efficiency of ∼26%was measured for acrylic actuators (at Cr∼1.6) and∼15%for silicone actuators (at Cr ∼1.4).

2) The constant voltage process presents a 50% theoreti-cal efficiency limit due to increased energy strorage, butan actual peak efficiency of ∼18% was measured forboth acrylic actuators (at Cr∼2) and silicone actuators(at Cr∼1.5).

3) For the tested conditions, highest efficiencies were alwaysreached at the maximal electrical fields, except for acrylicactuators operating at the peak brake efficiency conditions.

4) With ideal charge recovery (ηREC = 90%), efficiency val-ues can increase up to 60% in optimal conditions, while ithas less effect on operating conditions where loss factorsare important.

5) Free electrode boundary conditions have an important im-pact on the efficiency of practical DEAs, as they can de-crease output mechanical work and increase energy con-sumption.

Some trends highlighted in this paper may apply to dielec-tric elastomer used in the generator mode, but this remains tobe confirmed. The conclusions of this paper apply to the mate-rial and actuator geometries tested in this work. Generalizationshould be done with care.

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Jean-Philippe Lucking Bigue received the B.Sc.A.and M.Sc.A. dregrees in mechanical engineeringfrom the Universite de Sherbrooke, Sherbrooke, QC,Canada, in 2009 and 2011, respectively.

He is currently a member of the Conceptiond’Actionneur et de Moteur de l’Universite de Sher-brooke (CAMUS) Laboratory team, where he is pur-suing the Ph.D degree. His most recent researchinterests include design and optimization of high-performance actuators.

Jean-Sebastien Plante received the B.Sc.A. andM.Sc.A. degrees in mechanical engineering from theUniversite de Sherbrooke, Sherbrooke, QC, Canada,in 1998 and 2001, respectively, and the Ph.D. de-gree from the Massachusetts Institute of Technology(MIT), Cambridge, in 2006.

Following postdoctoral studies in MIT’s Field andSpace Robotics Laboratory, he joined the Depart-ment of Mechanical Engineering, Universite de Sher-brooke, as an Associate Professor, in 2007, where hefounded the Conception d’Actionneur et de Moteur

de l’Universite de Sherbrooke Laboratory, a laboratory dedicated to the devel-opment of new actuator and engine technologies for robotics and transportation.He has an eclectic approach and studies actuation technologies ranging fromshock wave hydrogen engines to polymer actuators. His current research inter-ests in mechatronics include high-energy and power-density actuators based ondielectric elastomers and pneumatic air muscles. He develops applications ofthese actuators to MRI-compatible medical devices.

Documents

Experimental Study of Dielectric Elastomer Actuator Energy Conversion Efficiency