Analysis and Modeling of Electro-Mechanical Coupling in an Electroactive Polymer-Based Actuator
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Analysis and Modeling of Electro-Mechanical Coupling in an Electroactive Polymer-Based Actuator Thomas A. Bowers1, Patrick Anquetil2, Ian Hunter1, and Neville Hogan1 1 Department of Mechanical Engineering, Institute for Soldier Nanotechnologies, MIT 2 Department of Mechanical Engineering, MIT Cambridge, MA 02139, U.S.A. ABSTRACT A non-linear constitutive model was formulated for ionic electroactive polymers (EAP) to describe the energetic coupling between electrical and mechanical domains. The polymer was modeled as a multi-port energy storage element with inputs from the electrical and mechanical domain. Using energy conservation methods, general relationships between stress, strain, voltage, and charge were determined. A solution to the uniaxial loading boundary condition was developed fully and compared to a linear model published by Madden and an electrochemical model published by Mazzoldi et al. Experimental results from a conducting polymer actuator composed of polypyrrole were used to validate the electro-mechanical coupling model. It was found that the correlation between the model and experimental data was very good for strains up to 3% and applied voltages up to 1 Volt; these are within the typical operating range of polypyrrole. The model is sufficiently simply to allow real-time control while also exceeding the linear coupling models in its ability to predict polymer behavior in normal operating ranges. INTRODUCTION Many electroactive polymers (EAP) exhibit volumetric strains when loaded electrically in the presence of an electrolyte. Expansion and contraction result from the insertion and removal of electrolyte ions and can be utilized for actuation [1]. While the electrochemical interactions in EAP have been studied extensively and are understood fairly well [1,2,3], interactions with the mechanical domain are still incomplete. For instance, it has been noted that although electrical inputs can produce linear strains of more than 10% [1], mechanical loads cause little observable back effect in the electrical domain [2]. As energy-storing transducers, EAP actuators should exhibit equivalent energy transduction between domains. There is no existing model of EAP that properly describes equivalent transmission of energy between the electrical to mechanical domains. It is necessary, therefore, to derive a set of constitutive equations capable of demonstrating symmetric coupling and revealing the nature of the interactions between domains. After considering the mechanics of the system and realizing that electrical energy storage depends on the volume rather than the length of the polymer, it is theorized that the apparent asymmetry in the coupling is the result of the Poisson Effect. This describes how the dimensions of an object will change under a uniaxial load. The three-dimensional polymer constitutive equations were analyzed by Mazzoldi, De Rossi, and Della Santa [3] who developed a detailed continuum model of EAP. While their model describes how mechanical, fluid, and electrical stresses result
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