Modeling Of Piezoelectric Energy Harvester Research Articles

Experimental admittance-based system identification for equivalent circuit modeling of piezoelectric energy harvesters on a plate

Equivalent circuit modeling is a useful tool for piezoelectric energy harvesters to analyze the electromechanical response of the system especially when complex host structure geometries and nonlinear circuits are used in the harvesting systems. Previous studies have used analytical and finite element models to estimate the equivalent circuit model (ECM) of piezoelectric energy harvesters (PEH) on beam- and plate-like structures. However, those methods require accurate analytical and/or numerical representation of the PEH. Here, we present an experimental admittance-based system identification method that allows us to identify the multi-modal ECM without prior knowledge of the host plate's geometry and/or physical properties of the piezoelectric patches. Using the proposed experimental method, we obtain the electromechanical frequency–response admittance of the PEH system at each vibration mode, and thereby, we calculate the equivalent system parameters. Additionally, a novel experimental technique is presented for the identification of the equivalent voltage sources associated with each LCR branch of the ECM. The derived ECM is experimentally validated for single and multiple piezoelectric patch harvesters on a plate. The electrical frequency response of the system has been validated for standard AC and rectifier circuits using SPICE software. Overall, the proposed admittance-based system identification is an accurate and robust method to identify the equivalent system parameters, making it a practical and reliable tool for modeling piezoelectric energy harvesting systems.

Performance analysis of nonlinear piezoelectric energy harvesting system under bidirectional excitations

In this paper, a cantilever beam piezoelectric energy harvester model of nonlinear partial differential equation based on Hamilton's Principle is established. A piezoelectric device using a bimorph cantilever beam with a fixed is subjected to horizontal and vertical excitation. Based on the Euler-Bernoulli thin beam model assumptions and inextensible deformation, the analysis further includes the effects of geometric nonlinearity and damping nonlinearity. The reduced-order nonlinear partial differential equations of motion with electro-mechanical coupling distributed parameter are derived by using Galerkin method. By using the method of multiple scales and solving the equations of motion, the energy harvester in its fundamental first-order resonance response is analyzed and the amplitudes of fundamental transverse deflection, output voltage and output power are determined. The major influence aspects of excitation amplitude, linear damping coefficient, nonlinear damping coefficient, impedance, nonlinear electro-mechanical coupling coefficient on transverse deflection, voltage and power are analyzed. The result shows that the linear damping coefficient and resistance affect the initial threshold of parametric excitation. The combination of parametric excitation and direct excitation gives full play to the advantages of parametric excitation and improve the energy conversion efficiency of the energy harvesting system.

Multi-physics modeling of piezoelectric energy harvesters from vibrations for improved cantilever designs

This study investigated piezoelectric cantilevers for energy harvesting using multi-physics modeling. The cantilevers with multiple degree-of-freedoms (DOFs) were designed with higher potential to match multiple-frequency vibrations of structures. Finite element models (FEMs) of cantilevers with different design parameters were built and verified with laboratory measurements. As results, multiple vibration modes with different bending conditions were captured by FEM outputs under resonant frequencies. The parametric analysis was performed to analyze the effects of cantilever length, width, thickness and mass. It was found that adjusting the cantilever design acquired the resonant frequencies in a wide range of 5 Hz–35 Hz, which potentially fitted the vibration scenario of a typical bridge structure. Under the cantilever design principle proposed in this study, as the DOF was increased, the maximum voltage outputs or the power outputs still remained the same level, respectively at 30 V or 5 mW, with no extra coverage area required from the multiple-DOF cantilever. All trends of resonant frequency changes via design parameter adjustments captured in this study will also serve as references for achieving specific design optimization strategies on the multiple-DOF cantilever designs, which will be varied based on the structure vibration scenarios in the field.

Design and Modeling of Piezoelectric Energy Harvester Under Variable Pressure in Pipe Flow

Design and Modeling of Piezoelectric Energy Harvester Under Variable Pressure in Pipe Flow

Modeling and analysis of energy harvester based on galloping considering the non-homogeneous beam

ABSTRACT This paper proposes a piezoelectric energy harvester based on non-homogeneous beam, which is employed to capture wind energy by galloping. A distributed parameter model of piezoelectric energy harvester with the nonuniformity of cantilever beam is developed. The quasi steady state approximation is used to simulate the fluid force. The model is verified by the experimental results reported previously. The influences of load resistance, the position of piezoelectric patch, and the size of beam on the output power are studied. Finally, a set of optimization parameters are generated to study the performance of the energy harvester. The results show that compared with rectangular beam, the output power of piezoelectric energy harvester with non-homogeneous beam can be increased by 32%.

Piezoelectric Impact Energy Harvester Based on the Composite Spherical Particle Chain for Self-Powered Sensors.

In this study, a novel piezoelectric energy harvester (PEH) based on the array composite spherical particle chain was constructed and explored in detail through simulation and experimental verification. The power test of the PEH based on array composite particle chains in the self-powered system was realized. Firstly, the model of PEH based on the composite spherical particle chain was constructed to theoretically realize the collection, transformation, and storage of impact energy, and the advantages of a composite particle chain in the field of piezoelectric energy harvesting were verified. Secondly, an experimental system was established to test the performance of the PEH, including the stability of the system under a continuous impact load, the power adjustment under different resistances, and the influence of the number of particle chains on the energy harvesting efficiency. Finally, a self-powered supply system was established with the PEH composed of three composite particle chains to realize the power supply of the microelectronic components. This paper presents a method of collecting impact energy based on particle chain structure, and lays an experimental foundation for the application of a composite particle chain in the field of piezoelectric energy harvesting.

Piezoelectric energy harvesting from roadway deformation under various traffic flow conditions

Many laboratory tests and in situ measurements have been conducted to study piezoelectric energy harvesting from roadway deformation. However, the performance of piezoelectric energy harvesters under real traffic flow conditions is still unknown. In this study, an electromechanical model of piezoelectric energy harvesters with detailed parameters (including the geometric parameters, material parameters, and circuits) is established, and the influences of traffic flow conditions (i.e. traffic speed and traffic density) on the output power of piezoelectric energy harvesters are analyzed by employing a scaling law method and traffic flow theory. The results indicate that remarkable differences exist in the load patterns and the frequencies between the laboratory tests (or in situ measurements) and real traffic flow conditions. Because of these differences, the results (especially the output electric power and optimization design methods) of previous studies may be inapplicable for piezoelectric energy harvesters embedded in roadways. Considering the distinguishing features of the traffic load pattern, the optimization criteria to determine the geometric parameters and the intrinsic system parameter of piezoelectric energy harvesters are obtained, and the corresponding optimal output power densities of the piezoelectric energy harvesters are also quantitatively calibrated. These theoretical results may serve as guidelines for optimizing the design of piezoelectric energy harvesters embedded in roadways under different traffic flow conditions.

Stable compact modeling of piezoelectric energy harvester devices

Purpose Based on the framework of Krylov subspace-based model order reduction (MOR), compact models of the piezoelectric energy harvester devices can be generated. However, the stability of reduced piezoelectric model often cannot be preserved. In previous research studies, “MOR after Schur,” “Schur after MOR” and “multiphysics structure preserving MOR” methods have proven successful in obtaining stable reduced piezoelectric energy harvester models. Though the stability preservation of “MOR after Schur” and “Schur after MOR” methods has already been mathematically proven, the “multiphysics structure preserving MOR” method was not. This paper aims to provide the missing mathematical proof of “multiphysics structure preserving MOR.” Design/methodology/approach Piezoelectric energy harvesters can be represented by system of differential-algebraic equations obtained by the finite element method. According to the block structure of its system matrices, “MOR after Schur” and “Schur after MOR” both perform Schur complement transformations either before or after the MOR process. For the “multiphysics structure preserving MOR” method, the original block structure of the system matrices is preserved during MOR. Findings This contribution shows that, in comparison to “MOR after Schur” and “Schur after MOR” methods, “multiphysics structure preserving MOR” method performs the Schur complement transformation implicitly, and therefore, stabilizes the reduced piezoelectric model. Originality/value The stability preservation of the reduced piezoelectric energy harvester model obtained through “multiphysics structure preserving MOR” method is proven mathematically and further validated by numerical experiments on two different piezoelectric energy harvester devices.

Improved Multilayered (Bi,Sc)O3-(Pb,Ti)O3 Piezoelectric Energy Harvesters Based on Impedance Matching Technique.

As a piezoelectric material, (Bi,Sc)O3-(Pb,Ti)O3 ceramics have been tested and analyzed for sensors and energy harvester applications owing to their relatively high Curie temperature and high piezoelectric coefficient. In this work, we prepared optimized (Bi,Sc)O3-(Pb,Ti)O3 piezoelectric materials through the conventional ceramic process. To increase the output energy, a multilayered structure was proposed and designed, and to obtain the maximum output energy, impedance matching techniques were considered and tested. By varying and measuring the energy harvesting system, we confirmed that the output energies were optimized by varying the load resistance. As the load resistance increased, the output voltage became saturated. Then, we calculated the optimized output power using the electric energy formula. Consequently, we identified the highest output energy of 5.93 µW/cm2 at 3 MΩ for the quadruple-layer harvester and load resistor using the impedance matching system. We characterized and improved the electrical properties of the piezoelectric energy harvesters by introducing impedance matching and performing the modeling of the energy harvesting component. Modeling was conducted for the piezoelectric generator component by introducing the mechanical force dependent voltage sources and load resistors and piezoelectric capacitor connected in parallel. Moreover, the generated output voltages were simulated by introducing an impedance matching technique. This work is designed to explain the modeling of piezoelectric energy harvesters. In this model, the relationship between applied mechanical force and output energy was discussed by employing experimental results and simulation.

Acoustic Energy Harvesting Through Multilayer Piezoelectric Harvester Model

Low-power requirements of contemporary sensing technology attract research on alternate power sources that can replace batteries. Energy harvesters’ function as power sources for sensors and other low-power devices by transducing the ambient energy into usable electrical form. Energy harvesters absorbing the ambient vibrations that have potential to deliver uninterrupted power to sensing nodes installed in remote and vibration rich environments motivate the research in vibrational energy harvesting. Piezoelectric bimorphs have been demonstrating a pre-eminence in converting the mechanical energy in ambient vibrations into electrical energy. Improving the performance of these harvesters is pivotal, as the energy in ambient vibrations is innately low. In this paper, we propose a mechanism namely Multilayer-PEHM (Piezoelectric Energy Harvester Model) which helps in converting the waste or unused energy into the useful energy. Multilayer-PEHM contains the various layer, which is placed one over the other, each layer is placed with specific element according to their properties and size, the size of the layer plays an important part for achieving efficiency. Furthermore, this paper presents an audit of the energy available in a vibrating source and design for effective transfer of the energy to harvesters, secondly, design of vibration energy harvesters with a focus to enhance their performance, and lastly, identification of key performance metrics influencing conversion efficiencies and scaling analysis for these acoustic harvesters. Typical vibration levels in stationary installations such as surfaces of blowers and ducts, and in mobile platforms such as light and heavy transport vehicles, are determined by measuring the acceleration signal. The frequency content in the signal is determined from the Fast Fourier Transform.

Phenomenological model of piezoelectric energy harvesting from galloping oscillations

We present an experimentally validated phenomenological model that directly predicts levels of energy harvested from large oscillations of an object subjected to wake galloping. This model is superior to currently used quasisteady models, which are applicable only at low-reduced frequencies and small amplitudes. In the model, the damping controlled instability and manifestation of limit cycle oscillations due to nonlinearities are represented by linear and nonlinear damping terms. The model coefficients are then identified from measurements using analytical expressions obtained by implementing the method of multiple scales. The validation is performed by comparing time series and spectra obtained from the model and experiments.

Normalized Modeling of Piezoelectric Energy Harvester Based on Equivalence Transformation and Unit-Less Parameters

Micro-electromechanical systems are ubiquitous in several energy harvesting solutions and can be used in applications such as bio-implantable devices and wireless micro-sensors. Piezoelectricity is an interesting key to perform the interface between environmental extracted energy and the power delivered to the load due to the use of mechanical vibration and resonance features. However, it is necessary for a detailed analysis in order to obtain an accurate understanding of the system. In this regard, some works deal with the normalization procedures to analyze the piezoelectric component behavior based on the mechanical resonance frequency. In order to enhance the system modeling, the electromechanical resonance frequency must also be analyzed. This paper deals with an approach to model the piezoelectric component that allows analyzing several unitless parameters that are critical to improve the performance of the system. In addition, a state-space model for the piezo-harvester based on the Class-E resonant rectifier is presented. Some experimental results are shown to validate the theoretical approach. [2019-0082]

Piezoelectric energy harvesting based on macro fiber composite from a rotating shaft

Piezoelectric energy harvesting from rotating applications can be realized by the use of harvesters, the basic part of which is a piezoelectric material. Such harvesters have various structures but most of them contain a cantilever composite beam, which consists of the carrying material and the piezoelectric material. A diversification of the harvester structures is, above all, the result of the application of additional mechanical structures, the task of which is to deform the cantilever composite beam. In contrast to these approaches, this article presents the simulation and laboratory investigation of the piezoelectric energy harvesting from a rotating shaft without the use of any additional mechanical structure. Energy harvesting was realized by the use of macro fiber composite (MFC), which was directly glued onto the rotating shaft surface, instead of on a cantilever beam being a part of the additional mechanical structure. In the theoretical part of the article, a mathematical model of piezoelectric energy harvesting from the rotating shaft with the use of MFC was elaborated. This model was verified on the basis of the laboratory experiments. On the basis of the simulation and laboratory experiments it was found that both an increase in the rotation frequency of the shaft and an increase in the stress in a rotating shaft caused a linear increase in the voltage generated by the MFC and caused an exponential increase in power generated by the MFC. These characteristics are significantly different to the characteristics obtained for harvesters consisting of a cantilever beam, in which the maximal value of a voltage and a power is generated only for a resonant frequency of a cantilever beam. In spite of these differences the optimal load resistance for the specific rotation frequency of the shaft can be calculated from the formula used to calculate the optimal load resistance for a harvester based on a cantilever beam.

Finite-element modeling of piezoelectric energy harvesters using lead-based and lead-free materials for voltage generation

ABSTRACTPiezoelectric energy harvesters are capable of sensing mechanical vibrations and converting them into usable energy to empower low-power microsystems. In this work, a novel seesaw cantilever structure-based broadband piezoelectric energy harvester has been designed using both lead-based and lead-free piezoelectric material. It has been observed that along with its structure dimensions and piezo material properties, a harvester’s load also determines its performance. An optimum load would yield maximum harvester power. The optimum value of a resistor generating peak power has been described in this work. The harvester is capable of producing a peak power of around 23 mW across a 0.14 MΩ load.

A Timoshenko like model for piezoelectric energy harvester with shear mode

In the present study a fully coupled electromechanical Timoshenko beam theory is developed for modelling an energy harvester operating in d31 (flexural mode with correction due to shear deformation/rotary inertia) and relatively rare d15 (pure shear) mode. The model is developed based on Variational Asymptotic Method (VAM). VAM is a dimensional reduction methodology, which asymptotically approximates the original 3D electromechanical enthalpy into an equivalent 1D electromechanical enthalpy functional, using small parameters present in the system. Firstly, we develop a fully coupled Timoshenko cross sectional model, which provides us a single common platform to analyze both d15 and d31 mode energy harvester. The developed cross sectional model is represented by a 7 × 7 electromechanical stiffness matrix with an additional 1D electrical variable along with 6 1D mechanical degrees of freedom commonly present in Timoshenko type analysis. The cross-sectional model is general enough to accommodate harvesters made of multilayer, arbitrary shaped cross-section, anisotropic material operating in both pure shear as well as in flexure mode. The coupled cross sectional output is fed subsequently into a 1D beam problem for a complete solution.

Implementation of multiphase piezoelectric composites energy harvester on aircraft wingbox structure with fuel saving evaluation

The multiphase composite with active structural fiber (ASF) has proven able to provide better optimization between actuating and load bearing capability compared to a pure piezoelectric material. In this paper, the multiphase composite application is further extended for energy harvesting purpose. The Double-Inclusion model combined with Mori-Tanaka method is implemented in a computational code to estimate the effective electro-elastic properties of the multiphase composite. The effective composite properties obtained via the present code are in good agreement with the analytical, experimental and finite element results. The multiphase composite with different composition is applied to a typical jet aircraft wingbox with 14.5 m halfspan. The energy harvesting evaluation by means of hybrid FEM/analytical piezoelectric energy harvester model is presented. A new procedure to investigate the trade-off between the aircraft weight, the fuel saving and the energy harvested is developed. The results pointed out that the equivalent fuel saved from the power generated by the wingbox is more than enough for 1 h Auxiliary Power Unit (APU) operation.

Reduced-order modeling of piezoelectric energy harvesters with nonlinear circuits under complex conditions

A fully coupled modeling approach is developed for piezoelectric energy harvesters in this work based on the use of available robust finite element packages and efficient reducing order modeling techniques. At first, the harvester is modeled using finite element packages. The dynamic equilibrium equations of harvesters are rebuilt by extracting system matrices from the finite element model using built-in commands without any additional tools. A Krylov subspace-based scheme is then applied to obtain a reduced-order model for improving simulation efficiency but preserving the key features of harvesters. Co-simulation of the reduced-order model with nonlinear energy harvesting circuits is achieved in a system level. Several examples in both cases of harmonic response and transient response analysis are conducted to validate the present approach. The proposed approach allows to improve the simulation efficiency by several orders of magnitude. Moreover, the parameters used in the equivalent circuit model can be conveniently obtained by the proposed eigenvector-based model order reduction technique. More importantly, this work establishes a methodology for modeling of piezoelectric energy harvesters with any complicated mechanical geometries and nonlinear circuits. The input load may be more complex also. The method can be employed by harvester designers to optimal mechanical structures or by circuit designers to develop novel energy harvesting circuits.

A dimensionally reduced order piezoelectric energy harvester model

Presently reduced power requirement for small electronic components have been the main motivation for developing vibration based energy harvesting. The ultimate objective in this research field is to provide an easy, sustainable and efficient technology to power such small electronic devices from the unused vibrational energy available in the environment. A comprehensive, reliable mathematical technique is thus in high demand which can model a piezoelectric energy harvester, predict its coupled dynamics (structural and electromechanical) accurately. The present work focuses on developing a mathematical model for a slender, piezoelectric energy harvester based on Variational Asymptotic Method, a dimensional reduction methodology. Variational Asymptotic Method approximates the 3D electromechanical enthalpy as an asymptotic series to formulate an equivalent 1D electromechanical enthalpy functional to perform a systematic dimensional reduction. For validation purpose, we have picked up experimental results for a bimorph PZT harvester, available in the literature. We have studied the extension-bending structural coupling along with the parameter dependence of the voltage, power output from the harvester and validated with the experiments. The present study provides a unique, accurate modeling technique which is capable of capturing material anisotropy, structural coupling and can analyse arbitrary cross section, surface mounted as well as embedded piezo layered energy harvester.

Verified nonlinear model of piezoelectric energy harvester

Energy harvesting is an important topic today. Complex monitoring systems with many nodes need energy sources and vibration energy harvesters (VEHs) could be one type of them. Mathematical model of the VEH is necessary instrument to estimate possible harvested power. This paper deals with piezoelectric VEH in setting as cantilever beam with tip mass. Traditional linear model of this type of VEH is simple, however, it represents the VEH only in one operating point and in another one (another amplitude of excitation vibrations) it could return wrong results. The nonlinear model of VEH is introduced in this paper with its parameters estimation. The nonlinear model is compared with linear model and experiment to demonstrate difference between them in amplitude frequency characteristics. Finally, the average harvested power from harmonic vibrations is measured experimentally and compared with prediction from linear and nonlinear model.

Modeling of Piezoelectric Energy Harvester and Comparative Performance Study of the Proof Mass for Eigen Frequency

This paper deals with the development of piezoelectric energy harvester and studied the effect of the proof mass on first ten eigen frequency modes, electric potential voltage output using finite element analysis software (ABAQUS). For piezoelectric energy harvester, there are two analyses performed, namely, eigenfrequency and transient/time-dependent analysis. The proof mass hugely affects on electrical potential output of piezoelectric energy harvester and natural frequency at first mode. Due to the additional attachment of the proof mass to piezoelectric energy harvester the peak potential voltage output reduces. Comparative results clearly suggest that the piezoelectric energy harvester with proof mass is providing lower electric potential output at first natural frequency.