Research Papers: Design Innovation and Devices

Performance Prediction and Scaling Laws of Circular Dielectric Elastomer Membrane Actuators

[+] Author and Article Information
Steffen Hau

Department of Systems Engineering,
Department of Materials Science
and Engineering,
Saarland University,
Saarbrücken 66121, Germany;
ZeMA gGmbH,
Gewerbepark Eschberger Weg,
Gebäude 9,
Saarbrücken 66121, Germany
e-mail: steffen.hau@imsl.uni-saarland.de

Alexander York

Parker Hannifin Corporation,
Diversified Technology Business Unit,
8145 Lewis Road,
Minneapolis, MN 55427
e-mail: alex.york@parker.com

Gianluca Rizzello

Department of Systems Engineering,
Department of Materials Science
and Engineering,
Saarland University,
Saarbrücken 66121, Germany;
ZeMA gGmbH,
Gewerbepark Eschberger Weg,
Gebäude 9,
Saarbrücken 66121, Germany
e-mail: gianluca.rizzello@imsl.uni-saarland.de

Stefan Seelecke

Department of Systems Engineering,
Department of Materials Science and
Saarland University,
Saarbrücken 66121, Germany;
ZeMA gGmbH,
Gewerbepark Eschberger Weg,
Gebäude 9,
Saarbrücken 66121, Germany
e-mail: stefan.seelecke@imsl.uni-saarland.de

Contributed by the Design Innovation and Devices of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 1, 2017; final manuscript received January 12, 2018; published online September 7, 2018. Assoc. Editor: Massimo Callegari.

J. Mech. Des 140(11), 113501 (Sep 07, 2018) (8 pages) Paper No: MD-17-1599; doi: 10.1115/1.4039104 History: Received September 01, 2017; Revised January 12, 2018

For a number of emerging mechatronics applications, dielectric elastomers (DEs) appear as a more energy efficient, lightweight, and low-cost solution with respect to established actuation technologies based, e.g., on solenoids or pneumatic cylinders. In addition to large strain, low power consumption, and high flexibility, DE actuators (DEA) are also highly scalable. Since DE membranes can be easily manufactured in different sizes and shapes, an effective approach to scale their performance is based on properly designing the material geometry. Clearly, to perform an optimal scaling the relation between material geometry and performance has to be properly investigated. In this paper, performance scaling by means of geometry is studied for circular out-of-plane (COP) DEAs. Such actuators consist of a silicone elastomer membrane sandwiched between two electrodes (carbon black silicone mixture). DEAs with six different geometries are manufactured, and a model-based strategy is used to find an experimental relationship between geometry and electro-mechanical behavior. In addition, an effective and computationally efficient method for predicting force–displacement characteristics of different geometries is presented. The proposed method allows to easily adapt DEAs to different applications in terms of stroke and force requirement, while minimizing at the same time both characterization and prototyping effort.

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Fig. 1

DE before and after application of high voltage (left). By applying a voltage the elastomer gets squeezed by electrostatic forces, which lead to an increase in area (right).

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Fig. 2

Sketch of flat circular membrane DEA (left) and deflected one (right)

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Fig. 3

2 in DEA showing where the ID and OD is measured (right) and three 1 in DEAs with same OD and different IDs: small, medium, and large (left)

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Fig. 4

Sketch of the test setup for DEA characterization [32]

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Fig. 5

Example of force–displacement data for a 1 in DEA medium at 0 V and 2500 V applied. The inner disk is displaced between 0 and 4.1 mm with a speed of 1 Hz to gain the data. The maximum displacement corresponds to a strain of 1.3. In case this DEA would acting against a precompressed spring load spring load (dash-dot line), ΔF and Δs would determining the force and stroke output of such a combination.

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Fig. 6

(a) Cross section through the deflected DEA shown in Fig. 2, right. The sketch shows the truncated-cone approximation (straight lines) in comparison to an exaggerated actual membrane shape (dashed lines). (b) Sketch with nomenclature for calculations.

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Fig. 7

Transformation of the COP-DEA design (a) to an equivalent pure shear DEA design with a width of equal to the average circumference cave (c); (b) shows the intermediate step where the COP-DEA is just unwound into a strip DEA configuration

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Fig. 8

Averaged force–displacement data for six different geometries at 0 V and 2500 V (upper part) and out of it calculated stress–strain plots. The dashed line represents the results of the 2 in DEA small (lower part).

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Fig. 9

Training data and photograph (1:2.5) of a 1 in DEA medium (upper part); calculate material data using Eqs. (4) and (10) (center part); measured versus predicted data and photograph (1:2.5) of a 2 in DEA large (lower part)

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Fig. 10

Results of blocking force measurements for a single DEA at different strain levels for triangular input voltage

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Fig. 11

Results of blocking force measurements for all DEAs of Table 1 at three different strain levels. Plotted quantities represent mean values (n = 8) with error bars and linear regression. The three data points for each data set represent the different inner disk diameters: small, medium, and large (left to right).

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Fig. 12

Boxplot showing the blocking force normalized on the average circumference cave grouped by the two different DEA sizes at three different strain levels

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Fig. 13

Estimated stroke at two different strain levels for all six different DEAs over electrode ring width l0. Marker indicate mean values (n = 6). Error bars are neglected because they are smaller than the marker.

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Fig. 14

Scaling laws for stroke and force output of COP-DEAs: (a) for constant OD, (b) constant ID, and (c) constant electrode ring width



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