Bimorph Piezoelectric Energy Harvester Research Articles

A distributed parameter electromechanical model for bimorph piezoelectric energy harvesters based on the refined zigzag theory

In this paper, a distributed parameter electromechanical model for bimorph piezoelectric energy harvesters based on the refined zigzag theory (RZT) is developed. In this model, the zigzag function is incorporated into the axial displacement, and the zigzag distribution of the displacement between the adjacent layers of the bimorph structure can be considered. The governing equations, including three equations of motions and one equation of circuit, are derived using Hamilton’s principle. The natural frequency, its corresponding modal function and the steady state response of the base excitation motion are given in exact forms. The presented results are benchmarked with the finite element method and two beam theories, the first-order shear deformation theory and the classical beam theory. Comparing examples shows that the RZT provides predictions of output voltage and generated power at high accuracy, especially for the case of a soft middle layer. Variation of the parameters, such as the beam thickness, excitation frequencies and the external electrical loads, is investigated and its effects on the performance of the energy harvesters are studied by using the RZT developed in this paper. Based on this refined theory, analysts and engineers can capture more details on the electromechanical behavior of piezoelectric harvesters.

On developing an optimal design procedure for a bimorph piezoelectric cantilever energy harvester under a predefined volume

Abstract A typical vibration harvester is tuned to operate at resonance in order to maximize the power output. There are many design parameter sets for tuning the harvester to a specific frequency, even for simple geometries. This work studies the impact of the geometrical parameters on the harvested power while keeping the resonance frequency constant in order to find the combination of the parameters that optimizes the power under a predefined volume. A bimorph piezoelectric cantilever is considered for the study. It consists of two piezoelectric layers and a middle non-piezoelectric layer and holds a tip mass. A theoretical model was derived to obtain the system parameters and the power as functions of the design parameters. Formulas for the optimal load resistance that provide maximum power capability at resonance and anti-resonance frequency were derived. The influence of the width on the power is studied, considering a constant mass ratio (between the tip mass and the mass of the beam). This keeps the resonance frequency constant while changing the width. The influence of the ratio between the thickness of the middle layer and that of the piezoelectric layer is also studied. It is assumed that the total thickness of the cantilever is constant and the middle layer has the same mechanical properties (elasticity and density) as the piezoelectric layer. This keeps the resonance frequency constant while changing the ratio between the thicknesses. Finally, the influence of increasing the free length as well as of increasing the mass ratio on the power is investigated. This is done by first, increasing each of them individually and secondly, by increasing each of them simultaneously while increasing the total thickness under the condition of maintaining a constant resonance frequency. Based on the analysis of these influences, recommendations as to how to maximize the geometrical parameters within the available volume and mass are presented.

An Efficient Inductorless Dynamically Configured Interface Circuit for Piezoelectric Vibration Energy Harvesting

Vibration energy harvesting based on piezoelectric materials is of interest in several applications such as in powering remote distributed wireless sensor nodes for structural health monitoring. Synchronized switch harvesting on inductor and synchronous electric charge extraction circuits show good power efficiency among reported power management circuits; however, limitations exist due to inductors employed, adaption of response to varying excitation levels, and the synchronized switch damping (SSD) effect. In this paper, an inductorless dynamically configured interface circuit is proposed, which is able to configure the connection of two piezoelectric materials in parallel or in series by periodically evaluating the ambient excitation level. The proposed circuit is designed and fabricated in a 0.35 μHV CMOS process.The fabricated circuit is cointegrated with a piezoelectric bimorph energy harvester and the performance is experimentally validated. With a low power consumption (0.5 μW), the measured results show that the proposed rectifier can provide a 4.5 × boost in harvested energy compared to the conventional full-bridge rectifier without employing an inductor. It also shows a high power efficiency over a wide range of excitation levels and is less susceptible to SSD.

Near-Optimal Design of Scalable Energy Harvester for Underwater Pipeline Monitoring Applications With Consideration of Impact to Pipeline Performance

Underwater pipelines are often necessary to transport valuable resources between patches of land, and are expected to have increased utilization across the globe with the steep population increase on one hand, and unbalanced depletion of resources on the other. It is desirable to automate monitoring of various performance parameters associated with the pipelines through wireless sensor networks to ensure longevity of use and reduced running costs. However, such pipelines are not easily accessible, and are subject to harsh environments such as salt water and underwater currents. Therefore, an ideal node in this sort of network is embedded into the pipeline, and does not require batteries with regular replacement provisions. Using an energy harvester as the power source becomes a viable option. A method for near-optimal piezoelectric bimorph energy harvester module design is presented in this paper to enable a self-powered wireless sensor node for in-pipe monitoring using kinetic energy of water flow. A crude analytical model provides a starting point for the design, which is tuned through finite element modeling and simulation. Recently constructed Turkey-Cyprus water pipeline project is considered as a realistic application for determining boundary conditions. With an average water velocity of 1.4 m/s, the designed energy harvester is scalable to produce power between $820~\mu \text{W}$ (single) to 12.3 mW (15 in parallel) with a negligible impact of 1.5 mm additional head loss. The method developed to deliver a finely modeled, scalable harvester design with minimum quantified impact to pipe performance is first of its kind to our knowledge.

Bimorph piezoelectric energy harvester structurally integrated on a trapezoidal plate

A bimorph piezoelectric energy harvester is developed for harvesting energy under the vortex induced vibration and it is integrated to a host structure of a trapezoidal plate without changing its passive dynamic properties. It is aimed to select trapezoidal plate as similar to a vertical fin-like structure which could be a part of an air vehicle. The designed energy harvester consists of an aluminum beam and two identical multi fiber composite (MFC) piezoelectric patches. In order to understand the dynamic characteristic of the trapezoidal plate, finite element analysis is performed and it is validated through an experimental study. The bimorph piezoelectric energy harvester is then integrated to the trapezoidal plate at the most convenient location with minimal structural displacement. The finite element model is constructed for the new combined structure in ANSYS Workbench 14.0 and the analyses performed on this particular model are then validated via experimental techniques. Finally, the energy harvesting performance of the bimorph piezoelectric energy harvester attached to the trapezoidal plate is also investigated through wind tunnel tests under the air load and the obtained results indicate that the system is a viable one for harvesting reasonable amount of energy.

Design of MEMS piezoelectric harvesters with electrostatically adjustable resonance frequency

In this paper the analytical analysis of an adaptively tuned piezoelectric vibration based energy harvester is presented. A bimorph piezoelectric energy harvester is suspended between two electrodes, subjected to a same DC voltage. The resonance frequency of the system is controllable by the applied DC voltage, and the harvested power is maximized by controlling the natural frequency of the system to cope with vibration sources which have varying excitation frequencies. The nonlinear governing differential equation of motion is derived based on Euler Bernoulli theory, and due to the softening nonlinearity of the electrostatic force, the harvester is capable of working over a broad frequency range. The steady state harmonic solution is obtained using the harmonic balance method and results are verified numerically. The results show that the harvester can be tuned to give a resonance response over a wide range of frequencies, and shows the great potential of this hybrid system.

Improvements in energy harvesting capabilities by using different shapes of piezoelectric bimorphs

The small amount of power needed by microelectronic devices opens up the possibility to convert part of the vibration energy present in the environment into electrical energy, using several methods. One such method is to use piezoelectric material as an additional layer in cantilever beams to harvest vibration energy for self-powered sensors. The geometry of a piezoelectric cantilever beam will greatly affect its vibration energy harvesting ability. Tapering and changing the configuration as ways to increase the generated output power of cantilever piezoelectric energy harvesters have gained popularity in recent years. In this work vibration energy harvesting via piezoelectric resonant bimorph cantilevers is studied and new designs for obtaining optimal piezoelectric energy harvesters are suggested. This paper deduces a very precise and simple analytical formula that can be used as a rule of thumb for calculating the resonant frequency of bimorph trapezoidal V-shaped cantilevers using the Rayleigh–Ritz method. This analytical formula is then analyzed using MATLAB as well as finite element methods and validated by ABAQUS simulation. Also, mathematical derivations for the output voltage of bimorph piezoelectric energy harvesters are presented and validated by simulation and experimental results. These formulas provide a new perspective that, among all the bimorph trapezoidal V-shaped cantilever beams with uniform thickness, the bimorph triangular tapered cantilever can lead to the highest resonant frequency and therefore maximum sensitivity, and by increasing the ratio of the trapezoidal bases the sensitivity decreases. Also, the output voltage and strain distribution show that the triangular cantilever has the highest efficiency and power density.

Preloaded freeplay wide-bandwidth low-frequency piezoelectric harvesters

We propose a technique for increasing the bandwidth of resonant low-frequency (<100 Hz) piezoelectric energy harvesters based on the modification of the clamped boundary condition of cantilevers, termed here as preloaded freeplay boundary condition. The effects of the preloaded freeplay boundary condition are quantified in terms of the fundamental frequency, frequency response, and power output for two beam configurations, namely, classical cantilevered bimorph piezoelectric energy harvester and zigzag unimorph piezoelectric energy harvester. A comparative analysis was performed between both the harvesters to empirically establish the advantages of the preloaded freeplay boundary condition. Using this approach, we demonstrate that the coupled degree-of-freedom dynamics results in an approximate 4–7 times increase in half-power bandwidth over the fixed boundary condition case.

Unimorph and bimorph piezoelectric energy harvester stimulated by β-emitting radioisotopes: a modeling study

We use energy methods and lumped-element modelling in the analysis and optimization of a miniaturized aluminum nitride based piezoelectric energy harvester which utilizes tritiated silicon as an uninterrupted energy source. Tritiated silicon serves as a radioisotope source which emits energetic β particles that results in an electrostatic force between the radioactive source and collector that traps the emitted particles. The generated electrostatic force will drive the charging and actuating cycles of the piezoelectric cantilever leading to a continuous charge---discharge cycles, thus inducing vibrations in the piezoelectric cantilever. The energy generated from the piezoelectric thin-film is appropriately rectified and stored to provide continuous and uninterrupted electrical power to a low-power devices. The modelled results have been benchmarked against available experimental data for a unimorph piezoelectric harvester with very good agreement. Furthermore, the model was applied to a bimorph piezoelectric harvester, showing that the output power can be doubled in relation to a unimorph design. Moreover, the model accounts for the entire range of design and operating factors such as the ambient medium and associated damping losses, current leakage, and device scaling.

Design of a Bimorph Piezoelectric Energy Harvester for Railway Monitoring

Wireless sensor network is one of prospective methods for railway monitoring due to the long-term operation and low-maintenance performances. How to supply power to the wireless sensor nodes has drawn much attention recently. In railway monitoring, the idea of converting ambient vibration energy from vibration of railway track induced by passing trains to electric energy has made it a potential way for powering the wireless sensor nodes. In this paper, a bimorph cantilever piezoelectric energy harvester was designed based on a single degree-of-freedom model. Experimental test was also performed to validate the design. The first natural frequency of the bimorph piezoelectric energy harvester was decreased from 117.1 Hz to 65.2 Hz by adding 4 gram tip mass to the free end of the 8.6 gram energy harvester. In addition, the power generation of the piezoelectric energy harvester with 4 gram tip mass at resonant frequency was increased from 0.14 mW to 0.74 mW from <TEX>$2.06m/s^2$</TEX> base excitation compared to stand-alone piezoelectric energy harvester without tip mass.

Analysis of bimorph piezoelectric beam energy harvesters using Timoshenko and Euler–Bernoulli beam theory

Single-degree-of-freedom lumped parameter model, conventional finite element method, and distributed parameter model have been developed to design, analyze, and predict the performance of piezoelectric energy harvesters with reasonable accuracy. In this article, a spectral finite element method for bimorph piezoelectric beam energy harvesters is developed based on the Timoshenko beam theory and the Euler–Bernoulli beam theory. Linear piezoelectric constitutive and linear elastic stress/strain models are assumed. Both beam theories are considered in order to examine the validation and applicability of each beam theory for a range of harvester sizes. Using spectral finite element method, a minimum number of elements is required because accurate shape functions are derived using the coupled electromechanical governing equations. Numerical simulations are conducted and validated using existing experimental data from the literature. In addition, parametric studies are carried out to predict the performance of a range of harvester sizes using each beam theory. It is concluded that the Euler–Bernoulli beam theory is sufficient enough to predict the performance of slender piezoelectric beams (slenderness ratio &gt; 20, that is, length over thickness ratio &gt; 20). In contrast, the Timoshenko beam theory, including the effects of shear deformation and rotary inertia, must be used for short piezoelectric beams (slenderness ratio &lt; 5).

Designing maximum power output into piezoelectric energy harvesters

Energy harvesting from vibrational sources has been the focus of extensive research in the last decade, but fundamental questions remain concerning the design of these harvesters. We consider a piezoelectric bimorph energy harvester and seek to translate design requirements, such as mass and target natural frequency, into beam dimensions that maximize power output. Our method centers around optimizing the thickness of the piezoelectric layers of a beam relative to the total beam thickness, otherwise known as the thickness ratio. This method uses approximations for the fundamental frequency and mode shape. This allows for the development of algebraic expressions for the modal parameters required for the prediction of power output. The resulting expression for power is fully defined by the fixed system level requirements and the only unknown parameters, the piezoelectric thickness ratio and the damping ratio. We show in an example case that, for typical damping ratio values, the ideal thickness ratio is not significantly affected by changes in the damping ratio. As such, the method requires a simple sweep of the thickness ratio in order to determine the beam design which maximizes the power. We develop the design method for both systems where the piezoelectric material is continuous and where the thickness is selected from a discrete set of values. Because our method produces a single algebraic expression for the power, the resulting beam design can be developed extremely quickly from a set of design requirements, and thus does not require optimization algorithms. We also show that our design method achieves more power output and requires less piezoelectric material than an approach which maximizes the coupling coefficient.

Determination of maximum power transfer conditions of bimorph piezoelectric energy harvesters

In this paper, a method to find the maximum power transfer conditions in bimorph piezoelectric-based harvesters is proposed. Explicitly, we derive a closed form expression that relates the load resistance to the mechanical parameters describing the bimorph based on the electromechanical, single degree of freedom, analogy. Further, by taking into account the intrinsic capacitance of the piezoelectric harvester, a more descriptive expression of the resonant frequency in piezoelectric bimorphs was derived. In interest of impartiality, we apply the proposed philosophy on previously published experimental results and compare it with other reported hypotheses. It was found that the proposed method was able to predict the actual optimum load resistance more accurately than other methods reported in the literature.

Equivalent Circuit Simulation Model of Cantilevered Piezoelectric Bimorph Energy Harvester

This paper presented an equivalent circuit simulation model of the cantilevered piezoelectric bimorph energy harvester for predicting the electrical power output of the energy harvester. The alternating voltage in the equivalent circuit model is identified from FE transducer model and the parameters of the resistance, capacitance and inductance in the equivalent circuit model are identified from FE actuator model. To valid the equivalent circuit simulation model, the power output values are compared with those obtained from the coupled piezoelectric-circuit finite element analysis. The results demonstrate the accuracy of the equivalent circuit simulation model.

Analysis of Piezoelectric Energy Harvesters of a Moderate Aspect Ratio With a Distributed Tip Mass

Various mathematical beam models have been proposed for the efficient analysis of a piezoelectric energy harvester (PEH) and carrying out parameter study but there appears no beam model suitable for a PEH of a moderate width-to-length aspect ratio with a distributed tip mass, and so, moderate width-to-length aspect ratios and distribution effects of a tip mass over a finite length will be mainly focused on in the present beam analysis. To deal with a wide range of aspect ratios, the material coefficients appearing in the constitutive equations of a PEH beam will be interpolated by those of the limiting plane-strain and plane-stress conditions. The key idea in the interpolation is to derive the interpolation parameter analytically by using the fundamental frequency of a cantilevered beam of moderate aspect ratios. To deal with the distribution effects of a tip mass over a finite length, the use of a set of polynomial deflection shape functions is proposed in the assumed mode approach. The equations to predict the electrical outputs based on the proposed enhanced beam model are explicitly expressed in template forms, so one can calculate the outputs easily from the forms. The validity and accuracy were checked for unimorph and bimorph PEHs by comparing the results from the developed beam model, the conventional beam model, and a three-dimensional finite element model. The comparisons showed substantial improvements by the developed model in predicting the electrical outputs.

Design and Evaluation of a Piezoelectric Energy Harvester Produced with a Finite Element Method

Piezoelectric energy harvesting uses piezoelectric, which is able to convert unused mechanical vibration energy to electrical energy, such as with motor and machinery. The piezoelectric energy harvester was constructed with a cantilever made of lead zirconate titanate with a metal plate. The primary material was soft lead zirconium titanate (PZT-5H) due to the large strain availability, acceptable mechanical strength and high piezoelectric constant. This technique's drawback is that the energy efficiency is lower than the other energy harvesting methods, but this study increases the output electric power efficiency by analyzing a finite element method for the structure of the piezoelectric energy harvester. We manufactured two cantilever types as follows: the L-60 and L-33 bimorph piezoelectric energy harvesters. Their resulting energy harvesters were able to obtain high voltage values as follows: 27.4 mV and 40.6 mV. Moreover, these results have a similar band of resonance frequency it comparison to the simulation. Consequently, this study was confirmed with validity. The output electric powers of the L-60 and L-33 types have 3.1 mW/s and 5.8 mW/s with 47 Hz and 148 Hz of resonance frequency and then, the load resistivities were <TEX>$100k\Omega$</TEX> and <TEX>$10k\Omega$</TEX>, respectively.

Coupled analysis for the harvesting structure and the modulating circuit in a piezoelectric bimorph energy harvester

The authors analyze a piezoelectric energy harvester as an electro-mechanically coupled system. The energy harvester consists of a piezoelectric bimorph with a concentrated mass attached at one end, called the harvesting structure, an electric circuit for energy storage, and a rectifier that converts the AC output of the harvesting structure into a DC input for the storage circuit. The piezoelectric bimorph is assumed to be driven into flexural vibration by an ambient acoustic source to convert the mechanical energies into electric energies. The analysis indicates that the performance of this harvester, measured by the power density, is characterized by three important non-dimensional parameters, i.e., the non-dimensional inductance of the storage circuit, the non-dimensional aspect ratio (length/thickness) and the non-dimensional end mass of the harvesting structure. The numerical results show that: (1) the power density can be optimized by varying the non-dimensional inductance for each fixed non-dimensional aspect ratio with a fixed non-dimensional end mass; and (2) for a fixed non-dimensional inductance, the power density is maximized if the non-dimensional aspect ratio and the non-dimensional end mass are so chosen that the harvesting structure, consisting of both the piezoelectric bimorph and the end mass attached, resonates at the frequency of the ambient acoustic source.