Damping as a result of piezoelectric energy harvesting

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Abstract

Systems that harvest or scavenge energy from their environments are of considerable interest for use in remote power supplies. A class of such systems exploits the motion or deformation associated with vibration, converting the mechanical energy to electrical, and storing it for later use; some of these systems use piezoelectric materials for the direct conversion of strain energy to electrical energy. The removal of mechanical energy from a vibrating structure necessarily results in damping. This research addresses the damping associated with a piezoelectric energy harvesting system that consists of a full-bridge rectifier, a filter capacitor, a switching DC–DC step-down converter, and a battery. Under conditions of harmonic forcing, the effective modal loss factor depends on: (1) the electromechanical coupling coefficient of the piezoelectric system; and (2) the ratio of the rectifier output voltage during operation to its maximum open-circuit value. When the DC–DC converter is maximizing power flow to the battery, this voltage ratio is very nearly 1/2, and the loss factor depends only on the coupling coefficient. Experiments on a base-driven piezoelectric cantilever, having a system coupling coefficient of 26%, yielded an effective loss factor for the fundamental vibration mode of 2.2%, in excellent agreement with theory.

Introduction

A need for remote electrical power supplies for machinery condition monitoring [1], tunable vibration control devices [2], personnel tracking [3], networked radios [4] and numerous other applications has driven recent “energy harvesting” research. The general idea underlying this research is the extraction of electrical energy from the operating environment [5]. Potential sources of energy include solar, thermal, mechanical, electrical (radio), chemical, or some combination thereof; for each source, numerous specific energy transduction methods may be considered.

While a number of researchers have investigated the possibility of harvesting mechanical energy using piezoelectric devices [3], [6], [7], circuits that seek to maximize power output were developed only recently [8], [9]. A vibrating piezoelectric device differs from a typical electrical power source in that its internal impedance is capacitive rather than inductive in nature, and it may be driven by mechanical motion of varying amplitude.

Initial research by the authors [8] produced an adaptively controlled switching DC–DC converter that maximized harvested power. Results showed that use of this converter increased the power delivered to the energy storage element, an electrochemical battery, by 400% as compared to the case in which the battery was charged directly via a rectifier circuit. A single small piezoelectric element, however, could not power the adaptive control circuitry while providing enough power to the battery to justify use of the converter, even at high vibration levels.

Building on these results, a simpler circuit based on a step-down converter was pursued [9]. By considering the interaction of the piezoelectric element with the step-down converter operating in discontinuous current conduction mode (DCM), the existence of an optimal duty cycle that maximized power flow from the piezoelectric device was established. As the magnitude of the vibration excitation increases, the optimal duty cycle becomes essentially constant, greatly simplifying implementation of the step-down converter. Based on this result, a simplified control scheme for the converter was introduced. This design was validated by experiment, showing that the optimal duty cycle can be accurately determined and controlled to maximize harvested power. The self-powered converter increased the harvested power by approximately 325% as compared to the case in which the battery was charged directly via a rectifier circuit.

The removal of mechanical energy from a vibrating structure by a piezoelectric energy harvesting system necessarily results in damping. This research addresses the damping associated with a self-powered circuit consisting of a full-bridge rectifier, a filter capacitor, a switching DC–DC step-down converter, and an electrochemical battery [9]. The next section summarizes the configuration and operation of this energy harvesting circuit, while subsequent sections address the prediction and measurement of associated vibration damping.

Section snippets

Piezoelectric energy harvesting circuit

The electrical behavior of a vibrating piezoelectric element can be modelled to first order as a sinusoidal current source ip(t) in parallel with its electrode capacitance Cp; the magnitude of the polarization current Ip depends on the mechanical excitation level. As shown in Fig. 1, a full-bridge AC–DC diode rectifier is connected to the output of the piezoelectric device. The DC filter capacitor of the rectifier, CR, is assumed to be large relative to Cp so that the output voltage Vrect may

Damping analysis

The removal of electrical energy from the piezoelectric system results in structural damping. It does not matter whether this energy is dissipated in a resistor, stored in a battery, or used to run energy harvesting circuitry. As in the case of the energy harvesting analysis, the damping analysis that follows is simplified by the assumption that the voltage on the rectifier output capacitor is essentially constant; that is, it is unaffected by the addition or removal of small quantities of

Experimental procedure

Two sets of experiments were performed; the first to assess the performance of the energy harvesting system, the second to measure the associated vibration damping.

A commercially available piezoelectric device, an ACX QuickPack® QP20W, was used in these experiments as an energy source. A two-layer bimorph, it is designed for operation in bending, and generates a voltage when strained. The QP20 has nominal dimensions of 5.08×3.81×0.051 cm (2.00×1.50×0.03 in), a nominal capacitance of 200 nF

Results

The performance of the energy harvesting circuit was determined, as was the damping resulting from its operation.

Conclusions

This paper describes an approach to harvesting electrical energy from a mechanically excited piezoelectric structure, a process that simultaneously yields predictable structural damping. The harvesting system considered consisted of a full-bridge rectifier with a filter capacitor, a switching DC–DC step-down converter, and a battery. Motivated by the observation that a fixed duty cycle provides near-optimum performance when a persistent excitation exceeds a certain level, a standalone

Acknowledgements

The energy harvesting research was sponsored in part by the Office of Naval Research, under contract N00014-99-1-0450, and subcontract from the University of Florida. Encouragement from Dr. Kam Ng and Prof. Andrew Kurdila is gratefully acknowledged.

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