Linear Vibration Energy Harvester Research Articles

Frequency Response for Sweep-Up and Sweep-Down of Piezoelectric Energy Harvester

PurposeThe aim of this work is to study the frequency response of linear and nonlinear piezoelectric vibration energy harvester (pVEH) based on Duffing-type nonlinearity and Kirchhoff’s law, and the effect of the effective electromechanical coupling on the frequency response of nonlinear pVEH.MethodsThe analytical technique based on the harmonic balance method (HBM) is used to obtain the mechanical and electrical frequency responses of linear and nonlinear pVEH, and the Jacobian matrix is used to analyze the solutions’ stability. The Runge–Kutta fourth-order method as a numerical technique is used to solve the ordinary differential equations of pVEH.ResultsThe analytical calculations are completed, and the frequency response solution of displacement of pVEH is contained in real and complex values and those of electrical responses are presented. The harmonic balance results are compared with numerical simulations for various hardening nonlinear springs. Simple analytical expressions for the jump points are suggested for the sweep-up and sweep-down frequencies of pVEH.ConclusionsThe analytical analysis shows that the jump-down frequency ratios have definite behaviors for each low and high effective electromechanical coupling of hardening-nonlinear pVEHs. Moreover, the jump-up frequency ratio is directly proportional to the effective electromechanical coupling of hardening nonlinear pVEHs.

Effect of geometric non-linearity and tip mass on the frequency bandwidth of a cantilever piezoelectric energy harvester under tip excitation

The research community is investigating a variety of approaches to convert mechanical energies to useful electrical energy in order to fulfil the ever-increasing demand for energy and fulfil the requirements of the various sectors. In this regard, numerous contributions toward increasing the capacity and efficiency of the various energy harvesting techniques have been proposed in recent times; one such promising technology is piezoelectric-based vibration energy harvesting. In the present work, the effect of geometric nonlinearity and tip mass is investigated on the operational frequency range of a cantilever nonlinear piezoelectric energy harvester. The proposed mathematical model is based on an energy-based variational approach. The methodology is formulated for the piezoelectric patched cantilever beam and, eventually solved using an efficient numerical technique . An amplitude incremental iterative algorithm is used to solve the non-linear governing equations of motion for the proposed non-linear broadband harvester along with the experimental validation. Firstly, a parametric study is performed to determine the optimum piezoelectric patch dimensions. Subsequently, the attempt is made to increase the frequency bandwidth for optimum energy harvesting by taking advantage of geometrically non-linear behaviour. Additionally, a tip mass, appropriate for the excitation level, can be added to the harvester design to make it effective for lower excitation frequency. Increased frequency bandwidth for improved energy harvesting capacity with the hardening type nonlinearity and tip mass is meaningfully shown with the help of frequency-amplitude response. Furthermore, to interpret the efficacy of nonlinear harvesters in terms of frequency band-width, power spectral density plots with improved harvesting capability are presented and compared with the conventional linear vibration energy harvester.

Comparison of L-Shaped and U-Shaped Beams in Bidirectional Piezoelectric Vibration Energy Harvesting.

The traditional single degree of freedom linear piezoelectric vibration energy harvester (PVEH), such as the cantilever type, mainly works and resonates in a single direction and at a single frequency. To adapt broadband and bidirectional ambient vibration, this paper designs and compares two PVEHs of L-shaped beam and U-shaped beam through COMSOL simulation and prototype test. FEA modeling is introduced for accurate structure design with modal analysis, voltage frequency response analysis, and proof mass analysis with multiphysics electromechanical coupling simulation. Two PVEH prototypes with different gravity angles and clamping angles are tested at 0.1 g acceleration to find the optimal angle for maximum output power. The best clamping angle of L-PVEH is 135° with RMS power of 0.3 mW at 7.9 Hz, and that of U-PVEH is 45° with RMS power of 0.4 mW at 5.0 Hz. The proposed U-PVEH shows more advantages in low broadband and bidirectional vibration energy harvesting.

Power expectation as a unified metric for the evaluation of vibration energy harvesters

Vibration energy harvesters (VEHs) allow the extraction of ambient mechanical energy. The proposed analysis focuses on bistable harvesters with Duffing nonlinearity. Bistable harvesters exhibit larger frequency bandwidth than linear monostable harvesters, but they exhibit complex behaviors (i.e., multiple periodic orbits and chaos), making their evaluation challenging. To assess the quality of a VEH, it is necessary to evaluate its energy performance generically. In this paper, we offer a new quantitative metric that can be used to evaluate bistable harvesters while taking into account the richness and diversity of their dynamics. This metric – called power expectation – is based on the average harvested power of each existing orbit weighted by its occurrence probability. The value of this power expectation depends on the harvester characteristics and potential orbit jump strategy implemented. Finally, we define a new figure of merit (FoM) based on the integral of the power expectation over all vibration frequencies. This FoM can be used for a generic evaluation of nonlinear vibration energy harvesters (NVEHs), by taking into account the various orbits and their respective probability of occurrence depending on the orbit jump strategy used. The proposed FoM also makes it possible to ensure a fair comparison with linear VEHs and quantitatively assess the effectiveness of orbit jump strategies for a given VEH.

Dynamic performance of the energy harvester with a fractional-order derivative circuit

Vibration energy harvesters are expected to replace chemical batteries and achieve self-power for low-power electronic devices, and their design has attracted significant attention. In previous studies, circuits consistent with the constitutive relationship with integer derivatives were frequently used, but fractional-order derivative circuits have received less attention. Because of the dissipation effects, such as internal friction and thermal memory, the fractional-order derivative is an effective mathematical approach for determining such nonconservative behaviors. In this study, the dynamic performance of a vibration energy harvester with a fractional-order derivative circuit in a random environment was investigated. Both linear and nonlinear vibration energy harvesters were evaluated using the linear random vibration theory and the equivalent linearization technique. The effects of the system parameters on the mean output power were analyzed, and the optimal system parameters, such as the oscillation frequency of the circuit and the coupling coefficient, were determined. Furthermore, the relationships between the optimal parameters and the order of the fractional derivative were established. Our study will potentially guide future designs of vibration energy harvesters.

Design, Modeling, and Characterization of a Tubular Linear Vibration Energy Harvester for Integrated Active Wheel System

Design, Modeling, and Characterization of a Tubular Linear Vibration Energy Harvester for Integrated Active Wheel System

Resource Allocation in Vibration Energy Harvesters

This paper studies the optimization of mechanics and resource allocation in linear vibration energy harvesters operating under an overall size constraint. In such harvesters, the volume aspect ratio and the stroke direction should be carefully selected to maximize output power and power density. Further, because the proof mass and spring stroke must share the available size along the stroke direction, a mass-stroke design trade-off results; the trade-off is optimized here. The optimization further leads to a universal metric the enables the comparison of linear vibration energy harvesters designed to operate in a limited volume. Examination of this metric results in guidelines and best practices for selecting harvester dimensions and shape for a given volume constraint, all based on the dimensional harvester optimization for maximum size-constrained output power. This paper offers several key contributions. First, it provides an evaluation and optimization of the impact that volume shaping and volumetric resource allocation have on the output power of linear vibration energy harvesters. Second, it develops a “universal normalized surface” relating output power to dimensional harvester design. The surface expresses the performance limit of space-constrained linear vibration energy harvesters in terms of their output power density. This leads to universal guidelines for harvester design. Finally, benchmarking harvesters reported in the literature against the universal surface demonstrates that their output performances lie on or below the surface, despite large variations in their exogenous design variables such as vibration amplitude, frequency, volume etc. Thus, this paper offers an effective method to evaluate mechanical design and optimization in state-of-the-art linear vibration energy harvesters under volume constraints, a scenario suited for IoT applications. [2021-0074]

A wide band nonlinear dual piezoelectric cantilever energy harvester coupled by origami

Since the traditional linear piezoelectric vibration energy harvester has narrow energy conversion frequency band and low energy conversion, a wide band nonlinear dual piezoelectric cantilever energy harvester coupled by origami is proposed. Apart from using two piezoelectric cantilevered beams to broaden the working frequency band of the device, the nonlinear origami component is introduced into the upper and lower beams to realize the dynamic coupling of the two piezoelectric beams. The origami structure can change the stiffness and increase the nonlinearity of the system by dynamic folding, so as to further broaden the frequency band and increase the output power. The structure of the proposed energy harvester is designed. Based on the Euler Bernoulli beam theory, Hamilton principle and the dynamic analysis of origami component, the electromechanical coupling dynamic model of two piezoelectric beam subsystems is established, and the approximate solutions of the output voltage and output power of each subsystem are obtained by harmonic balance method. The numerical simulation of each subsystem is implemented by the Runge–Kutta method, and the influences of excitation frequency and amplitude on the output voltage and power of each subsystem are explored respectively. The results show that this energy harvester that has a nonlinear characteristics of hardening stiffness can significantly broaden the working frequency band of each piezoelectric beam, and the maximum voltage value is about 1.2 V. Via the simulated analysis of motion, it is further proven that the proposed energy harvester has strong nonlinear characteristics. Furthermore, the coupling position of origami component on the voltage output is explored and the optimal coupling position is determined. Finally, the experimental results show that both of two beams can obtain effective voltage output between 0.5 and 0.6 V in the frequency range of 0–50 Hz, which validates the effectiveness and correctness of the simulation model.

Tapered nonlinear vibration energy harvester for powering Internet of Things

The lack of a sustainable power source to substitute batteries for long-term applications limits the widespread deployment of wireless sensor nodes in this era of the Internet of Things. Conventional linear Vibration Energy Harvesters are inefficient in converting ambient mechanical energy into usable electrical energy owing to their narrow frequency bandwidth when harnessing mechanical energy that is spread over a wide range of frequencies. In this work, we design, develop and demonstrate high power density nonlinear wideband energy harvesters using novel tapered spring architectures in an autonomous wireless sensor node system. These spring structures exhibit a nonlinear restoring force arising from the atypical stress distribution that can be additionally tuned by changing the taper-ratio in the structure. We investigate different tapering designs in order to achieve optimal spring hardening nonlinearities. This nonlinearity aids in widening the operable bandwidth, making the harvesters suitable for scavenging energy from real-world broadband vibrations. We obtain power densities of the order of 2660 μW/cm3g2 in the nonlinear energy harvester, outpacing most contemporary energy scavengers. We present a modified Perturb and Observe algorithm that allows tracing of the maximum power point in the context of non-stationary vibration conditions. We use the fabricated nonlinear device to power a wireless sensor node that reports on vital physical parameters (humidity, temperature), thereby enabling a resilient remote data acquisition system. This demonstrates the potential of our design to provide a sustainable energy source for platforms within the Internet of Things.

A two degree-of-freedom linear vibration energy harvester for tram applications

This paper presents an innovative two degree-of-freedom (DoF) electromagnetic vibration energy harvester used in a railway environment and its optimization based on complete multi-physics modeling, coupling an analytical model, numerical magnetic flied simulations and experimental data used as input parameters. It highlights that the resonance frequencies of the harvester must not be equal to the predominant frequencies of the input signal, which differs greatly compared to the optimization of a one DoF device. Characteristic frequency hopping dependent on the mechanical quality factors linked to the two DoF is also observed. Two prototypes were designed and tested with real tram acceleration signals. An average electrical power of 6.5 mW was obtained experimentally with a prototype of 710 g and 141 cc, validating the multi-physics model and the optimization process.

Efficient optimal load and maximum output power determination for linear vibration energy harvesters with a two-measurement characterization method

This paper presents a new characterization method allowing to efficiently characterize vibration energy harvesters (VEH). It enables to determine for example the optimal electrical loads at any frequency or the maximum output power; and this with only two measurements (two frequency sweeps on a shaker with two well-chosen electrical loads). This technique, while being time-efficient, greatly simplifies the determination of the maximum output power of VEH without requiring a measurement of the output power with many resistors; it is also compatible with finite element simulations. The proposed methodology has been tested and validated on a piezoelectric VEH.

Vortex-induced vibrational tristable energy harvester: Design and experiments

Wind energy harvesters have been widely studied for their great application potential to power small wireless sensors. Meanwhile, the unique dynamic characteristics of vibrational tristable energy harvesters have been theoretically and experimentally verified. More importantly, such vibrational tristable energy harvesters have excellent broadband energy harvesting performance under low-frequency and low-level excitations. This paper aims to develop a new kind of aeroelastic energy harvesters for enhancing wind energy harvesting performance. In detail, a vortex-induced vibrational tristable energy harvester is designed by using the magnetic force to realize the tristable configuration. A mathematical model of the presented harvester is provided. Experimental results verify that the presented vortex-induced vibrational tristable energy harvester performs better than the traditional linear vortex-induced vibration energy harvester.

Design Procedure and Experimental Verification of a Broadband Quad-Stable 2-DOF Vibration Energy Harvester.

Vibration-based energy harvesters brought the idea of self-powered sensors to reality in the past few years. Many strategies to improve the performance of linear vibration energy harvesters that collect energy over a limited bandwidth have been proposed. In this paper, a bi-stable two degrees of freedom (2-DOF) cut-out vibration energy harvester employing a pair of permanent magnets is designed through a proposed design methodology. Based on this methodology, the nonlinear harvesters can be optimally designed such that the bandwidth can be widened for a targeted output voltage. The proper selection of the harvester parameters as well as the gap distances between the tip and the fixed magnets are the bases of this methodology. The mathematical modeling of the proposed harvester and the formula for the potential energy between the tip and the fixed magnets are presented. Additionally, to enhance the performance of the bi-stable energy harvester (BEH), a quad-stable energy harvester (QEH) was configured by adding more fixed magnets. Experiments were performed to validate the numerical simulations and the results showed that, the simulation and experimental results are consistent. The results indicate that, the QEH covers a wider bandwidth than the BEH and based on a figure of merit the QEH shows the best performance among many harvesters presented in the literature.

Bandwidth broadening through stiffness merging using the nonlinear cantilever generator

Nonlinear systems are more attractive for the wide bandwidth in contrast to linear vibration energy harvesters. Most available generators belong to a certain type of nonlinear systems and the Duffing oscillator is a most popular kind. Once the system type is determined with a specific equation form, the performance optimization is limited in a certain range, generally related to the parameter study of the system within a given frame. In this paper, a novel generator is proposed by merging the stiffness curves of two different source generators through utilization of the nonlinear cantilever with a curve fixture. The special merged stiffness characteristics break the response limitation of the specific stiffness profile such as the Duffing equation and bring new benefits with the generator bandwidth further broadened by integrating the advantages of the source generator. In order to verify the stiffness-merging concept, two Duffing generators and a proposed generator with stiffness fitted from the former two are fabricated using the nonlinear cantilever with specially designed fixture curves. Experimental and numerical investigations reveal that the proposed generator with the merged stiffness has better performance than the generators with the typical stiffness characteristics of Duffing systems. The effectiveness of the stiffness-merging method is well demonstrated.

On the energy localization in weakly coupled oscillators for electromagnetic vibration energy harvesting

The present paper investigates the implementation of the energy localization phenomenon for enhancing the output harvesting performance. Also in this paper, a linear electromagnetic vibration energy harvester with weakly-magnetic coupling is proposed. The designed device is two degree-of-freedom oscillators, which functionalizes the energy localization phenomenon via a spring-magnet array. The proposed concept is made up of moving magnets held by elastic springs and coupled by a repulsive magnetic force with a very low mechanical damping. The energy localization is achieved by mistuning the mass of one of the moving magnets. The experimental and theoretical results showing the benefits of the energy localization phenomenon are reported. The maximal average power density harvested by functionalizing the energy localization is for a magnetic coupling β = 0.015.

A new concept of speed amplified nonlinear electromagnetic vibration energy harvester through fixed pulley wheel mechanisms and magnetic springs

Abstract This paper proposes a novel design of speed amplified nonlinear electromagnetic vibration energy harvester through fixed pulley wheel mechanisms and magnetic springs. The new vibration energy harvester consisting of fixed pulley wheel mechanisms, nonlinear magnetic springs, inner and outer rectangular ring Halbach arrays of magnets and a four-phase coil connection has potential to generate more output voltage than that with the speed amplified linear electromagnetic vibration energy harvester and conventional non-speed amplified nonlinear electromagnetic vibration energy harvester. By so far no one has worked on increasing the relative speed of the magnets with respect to the coils by adopting the fixed pulley wheel mechanisms. The nonlinear vibration was achieved by adopting repulsive magnetic springs with nonlinear spring stiffness. Analytical and simulation solutions of the speed amplified nonlinear electromagnetic vibration energy harvester system considering the effects of the rotational inertia of the pulley wheels have been verified by experimental results. The dimensionless formulae of the relative displacement, output voltage and harvested power of the speed amplified nonlinear electromagnetic vibration energy harvester system have been established and experimentally validated.

Modeling and Analysis of Piezoelectric Energy Harvesting With Dynamic Plucking Mechanism

Nonharmonic excitations are widely distributed in the environment. They can work as energy sources of vibration energy harvesters for powering wireless electronics. To overcome the narrow bandwidth of linear vibration energy harvesters, plucking piezoelectric energy harvesters have been designed. Plucking piezoelectric energy harvesters can convert sporadic motions into plucking force to excite vibration energy harvesters and achieve broadband performances. Though different kinds of plucking piezoelectric energy harvesters have been designed, the plucking mechanism is not well understood. The simplified models of plucking piezoelectric energy harvesting neglect the dynamic interaction between the plectrum and the piezoelectric beam. This research work is aimed at investigating the plucking mechanism and developing a comprehensive model of plucking piezoelectric energy harvesting. In this paper, the dynamic plucking mechanism is investigated and the Hertzian contact theory is applied. The developed model of plucking piezoelectric energy harvesting accounts for the dynamic interaction between the plectrum and the piezoelectric beam by considering contact theory. Experimental results show that the developed model well predicts the responses of plucking piezoelectric energy harvesters under different plucking velocities and overlap lengths. Parametric studies are conducted on the dimensionless model after choosing appropriate scaling. The influences of plucking velocity and overlap length on energy harvesting performance and energy conversion efficiency are discussed. The comprehensive model helps investigate the characteristics and guide the design of plucking piezoelectric energy harvesters.

Electromagnetic Linear Vibration Energy Harvester Using Sliding Permanent Magnet Array and Ferrofluid as a Lubricant.

We present an electromagnetic linear vibration energy harvester with an array of rectangular permanent magnets as a springless proof mass. Instead of supporting the magnet assembly with spring element, ferrofluid has been used as a lubricating material. When external vibration is applied laterally to the harvester, magnet assembly slides back and forth on the channel with reduced friction and wear due to ferrofluid, which significantly improves the long-term reliability of the device. Electric power is generated across an array of copper windings formed at the bottom of the aluminum housing. A proof-of-concept harvester has been fabricated and tested with a vibration exciter at various input frequencies and accelerations. For the device where 5 μL of ferrofluid was used for lubrication, maximum output power of 493 μW has been generated, which was 4.37% higher than that without ferrofluid. Long-term reliability improvement due to ferrofluid lubrication has also been verified. For the device with ferrofluid, 1.02% decrease of output power has been observed, in contrast to 59.73% decrease of output power without ferrofluid after 93,600 cycles.

Global stabilization of high-energy response of a nonlinear wideband electromagnetic energy harvester

This paper presents a resonance-type vibration energy harvester with a Duffing-type nonlinear oscillator which is designed to perform effectively in a wide frequency band. For the conventional linear vibration energy harvester, the maximum performance of the power generation and its bandwidth are in a relation of trade-off. Introducing a Duffing-type nonlinearity can expand the resonance frequency band and enable the harvester to generate larger electric power in a wider frequency range. However, since such nonlinear oscillator may have coexisting multiple steady-state solutions in the resonance band, it is difficult for the nonlinear harvester to maintain the high performance of the power generation constantly. The principle of self-excitation and entrainment has been utilized to give global stability to the high-energy orbit by destabilizing other unexpected low-energy orbits by introducing a switching circuit of the load resistance between positive and the negative values depending on the response amplitude of the oscillator. In this paper, an improved control law that switches the load resistance according to a frequency-dependent threshold is proposed to ensure the oscillator to respond in the high-energy orbit without ineffective power consumption. Numerical study shows that the steady-state responses of the harvester with the proposed control low are successfully kept on the high-energy orbit without repeating activation of the excitationmode.

An experimentally validated analytical model for the coupled electromechanical dynamics of linear vibration energy harvesting systems

Recent technological advancements in the efficiency of microprocessors, sensors, and other digital logic systems have increased research effort in vibration energy harvesting, where trace amounts of energy are scavenged from the ambient environment to provide power. Due to the complexity and nonlinearity of most vibration energy harvesting systems, existing research has relied primarily on numerical and finite element methods for harvester design and validation. Although these methods are useful, a vetted analytical model provides intuitive understanding of the governing dynamics and is useful for obtaining rough calculations when designing vibration energy harvesting systems. In this article, an analytical framework for linear electromechanical transducer modeling is developed into the coupled electromechanical model; a transfer function characterizing the dynamics of second-order VEH systems, which includes inputs for mechanical and electrical domain lumped parameters as complex impedances. The coupled electromechanical model transfer function is validated against frequency sweep data from a linear vibration energy harvesting experimental setup. The experimental setup demonstrated good correlation with the coupled electromechanical model, with not more than 0.9% error in natural frequency overall, 6% error in damping ratio for purely resistive loads, and 11% for reactive loads.