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Research Papers

Dynamic Modeling and Experimental Validation of an Annular Dielectric Elastomer Actuator With a Biasing Mass

[+] Author and Article Information
Gianluca Rizzello

Polytechnic of Bari,
Via E. Orabona 4,
Bari 70125, Italy
e-mail: gianluca.rizzello@poliba.it

Micah Hodgins

University of Saarland,
ZeMA,
Gewerbepark Eschberger Weg Building 9, Saarbrücken 66121, Germany
e-mail: micah.hodgins@mmsl.uni-saarland.de

David Naso

Polytechnic of Bari,
Via E. Orabona 4,
Bari 70125, Italy
e-mail: naso@poliba.it

Alexander York

University of Saarland,
ZeMA,
Gewerbepark Eschberger Weg Building 9,
Saarbrücken 66121, Germany
e-mail: alexander.york@mmsl.uni-saarland.de

Stefan Seelecke

University of Saarland,
ZeMA,
Gewerbepark Eschberger Weg Building 9,
Saarbrücken 66121, Germany
e-mail: stefan.seelecke@mmsl.uni-saarland.de

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 2, 2014; final manuscript received August 21, 2014; published online November 12, 2014. Assoc. Editor: Ryan L. Harne.

J. Vib. Acoust 137(1), 011005 (Feb 01, 2015) (10 pages) Paper No: VIB-14-1123; doi: 10.1115/1.4028456 History: Received April 02, 2014; Revised August 21, 2014; Online November 12, 2014

This paper presents a model for the electromechanically coupled dynamic behavior of dielectric elastomer actuators (DEA). The main goal is to develop a lumped, dynamic model which can be used for the optimization of actuator design in specific applications as well as for the synthesis of high precision, model-based feedback control algorithms. A mass-biased membrane actuator with an annular geometry is chosen as a reference case to introduce the modeling concept. The mechanical model extends standard linear visco-elasticity through the introduction of a nonlinear hyperelastic Ogden element. Electromechanical coupling is implemented through the Maxwell stress concept. The DEA model is then experimentally calibrated and validated for both quasi static and dynamic loading conditions. It can be shown that both mechanical preloading and electric actuation can be reproduced over a relevant range of masses and frequencies.

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Figures

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Fig. 1

Sketch of the DEA membrane (a) and actuator (b)

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Fig. 2

Output displacement d1, d2, and d3 corresponding to different masses M1, M2, and M3. Note that the curves present hysteresis.

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Fig. 3

DEA electric actuation

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Fig. 4

Model block diagram

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Fig. 5

Free-body diagram of the biasing mass

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Fig. 6

Nonlinear Maxwell–Wiechert model

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Fig. 7

Block diagram representing the visco-elastic coupling between thickness axis and radial axis

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Fig. 8

Picture of the actuator

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Fig. 9

Input signal for the static identification measures

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Fig. 10

Static identification and validation results. Red circles and blue diamond correspond to the measures used in static identification and validation, respectively. Orange dots and light blue crosses represent the output predict by the best-fit model. Six different displacement measures, corresponding to six different voltage levels, were taken for each mass.

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Fig. 11

Nonlinear stress–strain curve (continuous line) and radial prestrain (dashed line)

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Fig. 13

Dynamic identification results: experimental (blue) and simulation displacement (red)

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Fig. 14

Inputs for dynamic validation, amplitude modulated square wave (upper) and unipolar sweep sine (lower)

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Fig. 15

10.52 g biasing mass experimental (blue) and simulation displacement (red); validation with square wave (left) and sweep sine input (right)

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Fig. 16

18.36 g biasing mass experimental (blue) and simulation displacement (red); validation with square wave (left) and sweep sine input (right)

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Fig. 17

4.05 g biasing mass experimental (blue) and simulation displacement (red); validation with square wave (left) and sweep sine input (right)

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Fig. 18

Dynamic validation results: experimental (blue) and simulation displacement (red). Each column corresponds to a different biasing mass. The first two rows represent results for square wave input and the last two rows show results for sweep sine input. Each spectrum is associated with the signal above.

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Fig. 19

Model response as the parameters change to 50% (blue), 75% (light blue), 150% (orange), 200% (red) of their nominal value (green) in Table 3. Each column represents a change in a different parameter. The first row exhibits the response over time for a 1 kV voltage step; the remaining rows show the input-output curve for a unipolar sine wave input. The sine peak-to-peak amplitude is 1 kV, the frequency is 0.1 Hz for the second row, 1 Hz for the third, and 10 Hz for the fourth one.

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