Dynamic Electromechanical Coupling of Piezoelectric Bending Actuators.

Mostafa Nabawy,William Crowther

doi:10.3390/mi7010012

Abstract

Electromechanical coupling defines the ratio of electrical and mechanical energy exchanged during a flexure cycle of a piezoelectric actuator. This paper presents an analysis of the dynamic electromechanical coupling factor (dynamic EMCF) for cantilever based piezoelectric actuators and provides for the first time explicit expressions for calculation of dynamic EMCF based on arrangement of passive and active layers, layer geometry, and active and passive materials selection. Three main cantilever layer configurations are considered: unimorph, dual layer bimorph and triple layer bimorph. The actuator is modeled using standard constitutive dynamic equations that relate deflection and charge to force and voltage. A mode shape formulation is used for the cantilever dynamics that allows the generalized mass to be the actual mass at the first resonant frequency, removing the need for numerical integration in the design process. Results are presented in the form of physical insight from the model structure and also numerical evaluations of the model to provide trends in dynamic EMCF with actuator design parameters. For given material properties of the active and passive layers and given system overall damping ratio, the triple layer bimorph topology is the best in terms of theoretically achievable dynamic EMCF, followed by the dual layer bimorph. For a damping ratio of 0.035, the dynamic EMCF for an example dual layer bimorph configuration is 9% better than for a unimorph configuration. For configurations with a passive layer, the ratio of thicknesses for the passive and active layers is the primary geometric design variable. Choice of passive layer stiffness (Young’s modulus) relative to the stiffness of the material in the active layer is an important materials related design choice. For unimorph configurations, it is beneficial to use the highest stiffness possible passive material, whereas for triple layer bimorph configurations, the passive material should have a low stiffness. In all cases, increasing the transverse electromechanical coupling coefficient of the active material improves the dynamic EMCF.

Highlights

Piezoelectric bending actuators are an important class of micro electro-mechanical systems (MEMS) that find wide use in applications involving relatively large displacements in millimeter scale applications
Dynamic operation at resonance with light damping significantly increases the achievable displacement of the actuator compared to the achievable static displacement for the same magnitude of electrical input
For the double layer bimorph is 9% higher than that of the unimorph

Summary

Introduction

Piezoelectric bending actuators are an important class of micro electro-mechanical systems (MEMS) that find wide use in applications involving relatively large displacements in millimeter scale applications. Dynamic operation at resonance with light damping significantly increases the achievable displacement of the actuator compared to the achievable static displacement for the same magnitude of electrical input. Whilst piezoelectric bending actuators are geometrically simple, the solution of the dynamic design problem is non-trivial, and, in recent years, there has been significant interest in providing theoretical, numerical and experimental contributions to dynamic characterization of these devices [13,14,15,16,17,18,19]. Micromachines 2016, 7, 12; doi:10.3390/mi7010012 www.mdpi.com/journal/micromachines non-trivial, and, in recent years, there has been significant interest in providing theoretical, numerical and experimental contributions to dynamic characterization of these devices [13,14,15,16,17,18,19].

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