Piezoelectric Vibration Energy Harvester Research Articles

Parabolic tapering piezoelectric rotational energy harvester: Numerical analysis with experimental validation

Inadequate host beam design leads to the inefficiency of any piezoelectric vibration energy harvester. This article presents a parabolic tapering width piezoelectric energy harvester under rotational excitation. The Euler-Bernoulli theory, Hamilton's principle, and Galerkin's approach are used for mathematical modeling to investigate the frequency characteristics and open-circuit voltage response. Finally, experiments are conducted for validation. Compared to earlier reported designs, the proposed harvester produced high voltage-per-total mass (43.618 V/Kg) and performance amplification factor (4.18), besides the advantageous low natural frequency. This research’s findings can be used in real-time health monitoring of rotating machine components and fault detection mechanisms.

A novel soft encapsulated multi-directional and multi-modal piezoelectric vibration energy harvester

Advances in the design of various piezoelectric vibration-based energy harvesters (PVEHs), as a kind of power devices that can convert ambient energy to useable electrical energy, have become a hot topic in recent years due to their potential perspectives in wireless sensor networks, wearable electronics and low-power microelectronics. Unfortunately, conventional PVEHs modelled by beam- or plate-type planar structures are mainly restricted to harness kinetic energy in a single direction only. However, ambient vibration sources often work in multiple directions and broadband frequencies. To address this challenging problem, a mechanically-guided three-dimensional (3D) assembly structure is strategically designed to construct a soft cruciform-encapsulated PVEH in this work. Meanwhile, a reliable soft encapsulation technology is introduced to maintain the 3D configuration, which not only can avoid the collapse problem and also improve the dynamical performance. The entire system consists of a compressive buckling cruciform structure with a proof mass, PVDF thin film, and soft encapsulation. The dynamic characteristics of the system can be adjusted by changing the structural parameters, such as the pre-stressing force of the pre-stretched elastic substrate and the quality of the additional mass block. Finite element analysis and experimental studies are conducted to investigate the modal characteristics of system. A comparison of the vibration energy harvesting performance between the encapsulated and unencapsulated piezoelectric harvesters is presented. The results demonstrate that the encapsulated one can work well under multi-directional, multi-modal and low-frequency conditions. A maximum power output of 9.8 mW in the frequency range of 1–200 Hz can be achieved, which is almost 560 times more than that of the unencapsulated one. The proposed methodology also offers a new perspective for the fabrication design of soft-type PVEHs with higher working performance.

Investigation of boundary flexibility on the performance of piezoelectric vibration energy harvesting beam systems by DTFM

The purpose of this paper is to investigate the effect of boundary flexibility on the performance of piezoelectric vibration energy harvester (PVEH) beam systems, which has not been studied comprehensively in the literature despite its importance. The coupled electromechanical equations of motion of a piezoelectric cantilever beam with a tip mass are established, with the base boundary constrained by translational and rotational springs. An exact closed-form solution of the frequency response function (FRF) of the PVEH is obtained by the distributed transfer function method (DTFM). The DTFM is a systematic powerful tool for the dynamic analysis of distributed parameter continua with non-classical boundary conditions, intermediate constraints, coupled fields, and non-proportional damping without adding much complexity to the solution formulation. Moreover, the DTFM computes the derivatives of the response, that is, the strains, which are required in the electromechanical coupling formulation, simultaneously without any differentiation. Numerical results showing the effects of boundary flexibility on energy harvesting efficiency are presented. A first-order rational function relating the boundary stiffness parameters and the harvesting efficiency is determined by nonlinear curve fitting of the calculated data. Physical insights and applicability of this analytical function for end-of-line quality check of the boundary of PVEH are discussed.

Design and experimental validation of an exponentially tapering width rotational piezoelectric vibration energy harvester

The efficiency of any rotational piezoelectric vibration energy harvester (RVEH) can be improved by redesigning its host beam and making provision for self-tuning the harvester’s natural frequency with the rotational driving frequency. This article presents the design and analysis of an exponentially tapering width RVEH. The parameters for the proposed harvester’s natural frequency characteristics are acknowledged, and their effects on the peak open-circuit (OC) voltage response are discussed. A mathematical model of the system is formulated using the Euler-Bernoulli beam theory and Hamilton’s principle. Galerkin’s technique is used to acquire the system’s mass normalized mode shapes in matrix form. The proposed mathematical model is verified through ANSYS Mechanical APDL simulations and experimental methods. The harvester’s responses are obtained through MATLAB code. The two types of parameters that modify the harvester’s fundamental frequency are identified and analyzed. The proposed harvester delivered an improved power density (PD) of 5.27 [Formula: see text] and a performance amplification factor (PAF) of 3.14, operating at 7.968 Hz.

A Comparative Simulation Study of the Different Variations of PZT Piezoelectric Material by Using A MEMS Vibration Energy Harvester

In this article, the presented work aims to scavenge maximum electrical outputs by using the novel microelectromechanical system flared-U shaped spring based piezoelectric vibration energy harvester (PVEH). The performance studies were carried out by employing four different variations of lead zirconate titanate (PZT) piezoelectric material namely PZT-4, PZT-5A, PZT-5H, and PZT-8 in the same size and shape of the proposed device. The maximum output powers employing PZT-4, PZT-5A, PZT-5H, and PZT-8 piezoelectric materials are 7.156 nW, 8.657 nW, 10.738 nW, 5.701 nW over 30 Hz, 28.4 Hz, 28.6 Hz, and 30.2 Hz, resonant frequency, respectively, at input acceleration of 0.07 g. From the finite element method simulator COMSOL Multiphysics 5.4 (licensed version) simulation-based outcomes, it is inferred that PZT-5H piezoelectric material performs better than other variations of PZT, such as PZT-4, PZT-5A, and PZT-8 piezoelectric materials.

Uniform Stress Distribution of Bimorph by Arc Mechanical Stopper for Maximum Piezoelectric Vibration Energy Harvesting

To convert as much vibration energy as possible into electrical energy, the design of a high-performance piezoelectric vibration energy harvester (PVEH) has been studied widely in recent years. To overcome the low energy utilization of a traditional piezoelectric cantilever by inhomogeneous strain, a uniform stress distribution of bimorph by an ARC mechanical stopper structure has been designed for maximum piezoelectric vibration energy harvesting. Deflection equations and their simulation at the first-order modal of two classic bimorph cantilever beam models, with transverse tip force and with equal curvature, are derived based on the Euler–Bernoulli beam assumption. Piezoelectric energy from a beam model with equal curvature is four times that of a cantilever beam model with transverse tip force at the theoretical level. The nonlinear frequency response performance of bimorphs by an ARC mechanical stopper and point stopper model could be observed by the numerical simulations of the lumped parameter electromechanical model. PVEH prototypes were manufactured by 3D printing and tested. To verify the high-power generation capacity, PVEH with an ARC stopper has 1.756 times more voltage than that of a PVEH with a point stopper.

Design and Optimization of Piezoelectric Cantilever Beam Vibration Energy Harvester.

Piezoelectric cantilever beams are commonly utilized to harvest energy from environmental vibrations due to their simple structures. This paper optimizes a single crystal trapezoidal hollow structure piezoelectric cantilever beam vibration energy harvester with a copper substrate to achieve high energy density at a low frequency. Finite element analysis (FEA) is adopted to optimize the size of the copper substrate at first, and the piezoelectric energy harvester (PEH) is further optimized with a trapezoidal hollow structure under the optimal size of the copper substrate. The developed PEH with a trapezoidal hollow structure (La = 20 mm, Lb = 15 mm, and Lh = 40 mm), with a copper substrate of 80 mm × 33 mm × 0.2 mm, can obtain the best output performance. Under the condition of 1 g acceleration, the resonance frequency and peak voltage output were 23.29 Hz and 40.4 V, respectively. Compared with the unhollowed PEH, the developed trapezoidal hollow structure PEH can reduce its resonant frequency by 12.18% and increase output voltage by 34.67%, while also supplying a power density of 7.24 mW/cm3. This study verified the feasibility of the optimized design through simulation and experimental comparison.

Modeling and analysis of a three-degree-of-freedom piezoelectric vibration energy harvester for broadening bandwidth

This study proposes a multi-frequency response piecewise-linear piezoelectric vibration energy harvester (MFRPLP-VEH) by combining the linear multi-frequency resonance and nonlinear vibration bandwidth broadening methods to improve the working frequency bandwidth and environmental robustness of the piezoelectric vibration energy harvester. A theoretical model is established based on the electromechanical coupling and the dynamic response of the MFRPLP-VEH. The energy harvesting performance and broadening width efficiency of the MFRPLP-VEH were obtained through an experimental verification platform, where the resonant frequencies of the three beam are 28.9, 33.6, and 38.6 Hz, respectively. Furthermore, the operating frequency range is widened by 90.9% at an external excitation acceleration of 10 m/s2. The energy generated by the MFRPLP-VEH is 194% of the energy generated by its linear counterpart under the same excitation conditions. The numerical and experimental results verify the accuracy of the theoretical model and the broadband working frequency range of the MFRPLP-VEH.

A comparative study of electrical interfaces for tunable piezoelectric vibration energy harvesting

The present work deals with tunable electrical interfaces able to enhance both the harvested power and bandwidth of piezoelectric vibration energy harvesters. The aim of this paper is to propose a general, normalized, and unified performance evaluation (with respect to the harvested power and bandwidth) of the various electrical strategies that can tune the harvester’s frequency response. By mean of a thorough analysis, we demonstrate how such interfaces influence the electromechanical generator response through an electrically-induced damping and an electrically-induced stiffness. The choice of the strategy determines these two electrical quantities, and thus the achievable frequency response of the system. Thereafter, we introduce a collection of graphical and analytical tools to compare and analyze single- and multi-tuning electrical strategies, including a qualitative performance evaluation of existing strategies. Finally, we establish a unified comparison of single- and multiple-tuning strategies which is supported by the definition and evaluation of a new optimization criterion. This comparison reveals which strategy performs best depending on the electromechanical coupling of the piezoelectric harvester and on the losses in the electrical interface. Furthermore, it quantifies the power and bandwidth gain brought by single- and multi-tuning strategies. Such quantitative criterion provides guidance for the choice of a harvesting strategy in any specific applicative case.

Analytical Study of Piezoelectric Harvesters With SECE and SSHI Under Variable Excitation

A theoretical analysis aimed at predicting the power extracted from resonant piezoelectric vibration energy harvesters feeding synchronous switching-type electronic interfaces under variable mechanical excitation is proposed. In particular, for the widely used synchronous electric charge extraction (SECE) and synchronized switching harvesting on an inductor (SSHI) switching interfaces, the nonlinear equations describing the circuit behavior are solved under reasonable assumptions, and closed-form expressions of the extracted power are derived as a function of the circuit parameters and of the vibration characteristics, in the case of modulated mechanical vibrations. Numerical and experimental results validate the proposed closed-form expressions and show their usefulness for design purposes.

Multimodal Multidirectional Piezoelectric Vibration Energy Harvester by U-Shaped Structure with Cross-Connected Beams

This paper proposes a multidirectional piezoelectric vibration energy harvester based on an improved U-shaped structure with cross-connected beams. Benefitting from the bi-directional capacity of U-shaped beam and additional bending mode induced by cross-connected configuration, the proposed structure can well capture the vibrations in 3D space at the frequencies lower than 15 Hz. These features are further validated by finite element analyses and theorical formulas. The prototype is fabricated and the experiments under different conditions are carried out. The results show that the proposed harvester can generate favorable voltage and power under multidirectional vibrations at a low operating frequency. Practical applications of charging capacitors and powering a wireless sensor node demonstrate the feasibility of this energy harvester in supplying power for engineering devices.

Numerical and experimental evaluation of the magnetic interaction for frequency up-conversion in piezoelectric vibration energy harvesters

The purpose of this work is to improve the modelling process for the application of permanent magnets in a frequency up-conversion (FuC) mechanism for piezoelectric energy harvesters. More specifically, the aim is to avoid the burdensome finite element analyses (FEA) in the framework of electromechanical devices design. The analytical calculations are compared with experimental tests conducted by an ad-hoc set up and with FEA. After investigations on the interaction, an application of FuC mechanism is proposed on a meso-scale case study in which a low frequency seismic mass (LFM) interacts non-linearly, due to magnetic field, with an high frequency piezoelectric vibration energy harvester (PVEH). Numerical simulations have been carried out in the time domain (step-by-step analysis) under a harmonic low-frequency input acceleration signal. The peculiar behavior, due to non-linear dynamics, is investigated in both the repulsive and the attractive configurations of the magnets. The results confirm the effectiveness of magnetic FuC and show that the repulsive case allows the device to recover a larger amount of energy than the attractive configuration.

Ultra-low wide bandwidth vibrational energy harvesting using a statically balanced compliant mechanism

Structure design of ultra-low wide bandwidth vibrational energy harvesters remains an open issue. In this research, a statically balanced compliant mechanism (SBCM) is proposed, dynamically modelled, and experimentally demonstrated to address this need. This SBCM is designed based on the concept of stiffness compensation between a linear component with positive-stiffness (two double parallelograms in parallel) and a nonlinear component with negative-stiffness (two sets of post-buckled fixed-guided compliant beams in parallel). A design guideline of the SBCM starting from using rapid-design stiffness compensation equation is provided for reasonably approximate and accurate results. Subsequently, a dynamic analytical model of the displacement response of the SBCM to harmonic base excitation has been derived based on the averaging method. The nonlinear force-displacement relationship of the system was obtained through nonlinear finite element analysis (FEA) simulations in this regard and a 5th order polynomial fit was chosen taking only odd terms into account. The accuracy of this analytical model is confirmed by numerical analysis. Next, a prototype of the SBCM was fabricated and its applicability to piezoelectric vibrational energy harvesters (PVEHs) was demonstrated by integrating piezoelectric capacitors made of PVDF films with compliant beams of the SBCM to generate electric outputs in response to the bending of the beams. Static balancing is achieved over a continuous displacement range of 2 mm around the origin. Bi-stability and mono-stability were observed with the same prototype by adjusting the length of the positive-stiffness beams. Under static-balancing condition, the SBCM is able to respond to a wide range of ultra-low frequencies with low accelerations, which has been established experimentally, analytically and numerically. In dynamic experiments, the steady-state relative displacement amplitude H is 2.9 mm under an excitation condition of 6 Hz and 0.1g (1g=9.8 m/s2), and it reaches a maximum of 9.4 mm under 12.75 Hz and 0.25 g. A 30%-Hmax frequency bandwidth is introduced to assess the nonlinear dynamic performance of the SBCM from a mechanical perspective. The maximum experimental 30%-Hmax bandwidth of the structure is 6.75 Hz (from 6 Hz to 12.75 Hz) at 0.25 g and the corresponding theoretical value is 8.73 Hz (from 3.34 Hz to 12.07 Hz). Under the same excitation condition, it is shown that the maximum relative displacement amplitude deceases as the jump-down frequency increases. In addition, super-harmonic and sub-harmonic oscillations are observed in the dynamic experiments. The SBCM can provide a practical structural solution for harvesting energy from a range of vibrational scenarios (e.g. ocean waves, human motions and bridge vibrations) with ultra-low wide bandwidth frequencies and weak accelerations. The concept of SBCM is suitable to be combined with various energy conversion principles and is not limited to piezoelectric sources alone. When miniaturized, the SBCM concept can be of particular interest to researchers active in energy harvesting for microelectromechanical systems (MEMS) technology.

Nonlinear analysis of the internal resonance response of an L-shaped beam structure considering quadratic and cubic nonlinearity

The nonlinear behaviors of the L-shaped beam structure based on 1:2 internal resonance are investigated. The governing equations considering quadratic and cubic nonlinearity of the L-shaped beam structure are verified by the transient dynamic analysis of the finite element model. The approximate analytical solution for this system is derived by the method of multiple scales, and verified by the numerical solution. The Jacobian matrix of the modulation equation is employed to determine the equilibrium stability of the vibration response. The effects of the excitation frequency, amplitude and cubic nonlinear terms on the nonlinear responses of the primary resonance of the first and second modes are discussed. The bifurcation diagram, spectrum, phase plane and Poincaré section are applied to investigate the nonlinear vibration response. The results reveal that many nonlinear phenomena are observed, such as double-jump, hysteresis, Hopf bifurcation, modal saturation, multiple solutions, multi-softening and so on. The influence of cubic nonlinear term on internal resonance response should be considered. The broadband characteristics of internal resonance system are broadened by the nonlinear softening and hardening in the frequency response curve. In the primary resonance of the second mode, the hardening region in the frequency response curve becomes the softening region with the increase of excitation amplitude. The double-jump phenomenon is found in this newly formed softening region, and up to five solutions are observed in this region, including three sink points and two saddle-nodes. The broadband characteristics of the system is of great benefit to the application of broadband piezoelectric vibration energy harvesting.

Recent Research Progress in Piezoelectric Vibration Energy Harvesting Technology

With the development of remote monitoring technology and highly integrated circuit technology, the achievement and usage of self-powered wireless low-power electronic components has become a hot research topic nowadays. Harvesting vibration energy from the environment can meet the power consumption requirements of these devices, while it is also of great significance to fully utilize the hidden energy in the environment. The mechanism and three typical working modes of piezoelectric vibration energy harvesting technology are introduced, along with the classification of different excitation types of collectors. The progress of research related to piezoelectric vibration energy harvesting technology is reviewed. Finally, challenging problems in the study of piezoelectric energy harvesting technology are summarized, and the future research and development trend of piezoelectric vibration energy harvesting technology is discussed in the light of the current research status of piezoelectric vibration energy harvesting technology.

A piezoelectric vibration energy harvester for multi-directional and ultra-low frequency waves with magnetic coupling driven by rotating balls

Wave vibration is a ubiquitous energy existing in our environment, but efficient vibration energy harvesting at ultra-low frequency and multi-directions is still a challenge. This paper proposes a piezoelectric vibration energy harvester for multi-directional and ultra-low frequency waves driven by a rotating rolling ball. The energy harvester is designed to float on the water's surface; it will be tilting vibration in the corresponding direction once driven by the wave from any direction. The energy harvester converts the vibration wave energy into electrical energy due to the basic characteristics of frequency up-conversion. The proposed harvester can efficiently scavenge not only ultra-low frequency but also multi-directional vibration wave energy. The energy harvester is modeled and designed. A simulation wave device is used to evaluate the proposed harvester's performances. Simulation and experimental results are in good agreement. The energy harvester can harvest energy from single-direction or multi-direction excitation. When the external frequency is 0.9 Hz, and the external load is 47KΩ, the power output of the whole energy harvester is 6.32mW, which shows great application prospects in the power supply of ocean buoys.

Performance analysis of nonlinear vibration energy harvesting system with inelastic barrier under colored noise excitation

The vibro-impact structures are introduced into the piezoelectric vibration energy harvesting (VEH) systems, which can broaden the operating bandwidth of the piezoelectric VEH systems and thus improve the harvesting efficiency. The process of vibro-impact not only causes energy loss during the impact process but also causes the local deformation between two impact bodies. Therefore, this manuscript proposes a class of stochastic non-classical inelastic impact VEH models, whose non-classical impact processes are described by Hertz contact forces. Firstly, the relationship between the total energy of the unperturbed system and the potential energy of the system at the barrier position is used to determine whether the impact phenomena have occurred or not, then used to derive the period and frequency of the system. Secondly, using the quasi-conservative stochastic averaging method, the averaged drift term and the averaged diffusion term of the piecewise smooth averaged Ito^ equation are derived. The stationary probability density functions (PDFs), the mean square output (MSO) voltage and the root mean square (RMS) voltage of the system response can be obtained from solving the corresponding Fokker-Planck-Kolmogorov (FPK) equation for averaged Ito^ equation. Finally, an example is provided to verify the effectiveness of the proposed method, and the effects of the model parameters on the MSO voltage and power conversion efficiency (PCE) are analyzed. The relationship between the MSO voltage and the PCE is also analyzed. It is of great significance for the design and optimization of stochastic VEH systems.

Performance of a dual piezoceramic cantilever for low frequency energy harvesting applications: modeling and experiment verification

Vibration-based energy harvesting is a growing field for generating low-power electricity to use in wireless electronic devices. These applications are usually in an environment of abundant low frequency vibration, which can be collected through an appropriate energy conversion structure. However, traditional energy conversion architectures such as cantilever-cantilever type or spring-mass type have the problem of high working frequency and narrow bandwidth (limiting its use and far from the frequency found in the surrounding environment). To overcome these challenges, this work proposes a study of a piezoelectric vibration energy harvester based on a dual cantilever structure. The energy harvesting system is designed, analyzed and verified with the finite element analysis method and an experimental study. The results show that the bandwidth is enlarged of 30 Hz and a power is generated and equals to the sum of the power generated by each cantilever (190 nW) with an output voltage supplying a resistive load of 110 KΏ.

Design, Characterization and Testing of Magnetically Coupled Piezoelectric Vibration Energy Harvester Using Double Magnets

Design, Characterization and Testing of Magnetically Coupled Piezoelectric Vibration Energy Harvester Using Double Magnets

A new type of piezoelectric self-excited vibration energy harvester for micro-actuator's energy storage

In this paper, a new type of potassium-sodium niobate (K0.5Na0.5NbO3, KNN) piezoelectric self-excited vibration energy harvester (VEH) for micro-actuator's energy storage is proposed, and the system's nonlinear dynamic characteristics are studied. The KNN piezoelectric VEH has self-excited vibration characteristics, which can convert the random vibration energy from the environment into the harmonic currents for storage. New nonlinear differential terms are introduced to describe the hysteretic phenomena of a KNN piezoelectric ceramics. The nonlinear dynamic model of a KNN piezoelectric VEH subjected to stochastic disturbance is developed, the stochastic stability of the system is analyzed, and the conditions of stochastic bifurcation are obtained. The numerical results show that the system's motions can keep periodic when the outside random excitation is not very strong. The experimental results show that the KNN piezoelectric VEH can convert the harmonic excitation to harmonic currents, and the maximum output voltage is 237.99mv; there is a certain platform in the acceleration-output voltage curves of the system, which implies that there is an optimal amplitude for excitation force; the KNN VEH can convert the narrowband excitation to the narrowband currents, and the maximum output voltage is 572.89mv; the KNN VEH successfully convert a Gauss white noise excitation to narrowband currents, and the maximum output voltage is 99.35mv. The new KNN self-excited VEH can obtain the narrowband currents from the environment, which implies a new way to obtain green energy.