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.

Modeling and power performance improvement of a piezoelectric energy harvester for low-frequency vibration environment

A novel oscillator structure, bimorph piezoelectric cantilever beam with two-stepped variable thicknesses,is proposed to improve the energy harvestingperformance of the vibration energy harvester (VEH) under low-frequency vibration environment. Firstly, the piezoelectric cantilever is segmented to obtain the energy functions based on the Euler-Bernoulli beam assumptions, and the Galerkin approach is utilized to discretize the energy functions. Applying boundary conditions and continuity conditions enforced at separation locations, the electromechanical coupled governing equations for the piezoelectric energy harvesterareintroduced by means of the Lagrange equations. Furthermore, the steady state response expressions are obtained for harmonic base excitations at arbitrary frequencies. Numerical results are computed and the effects ofthe lengths-ratio, thicknesses-ratio,end thicknessand load resistance on the output voltage, harvested power and power density are discussed. Moreover, to verify thecorrectness ofanalytical results, the finite element method (FEM)simulationis also conducted to analyze performance of the proposed VEH, where a good agreement is presented. All the results show thatthe present oscillator structureis moreefficient than the conventional uniform beam structure, specifically, for vibration energy harvesting in low-frequency environment.

Low-frequency and broadband vibration energy harvester driven by mechanical impact based on layer-separated piezoelectric beam

Vibration energy harvesting is to transform the ambient mechanical energy to electricity. How to reduce the resonance frequency and improve the conversion efficiency is very important. In this paper, a layer-separated piezoelectric cantilever beam is proposed for the vibration energy harvester(VEH) for low-frequency and wide-bandwidth operation, which can transform the mechanical impact energy to electric energy. First,the electromechanical coupling equation is obtained by the Euler-Bernoulli beam theory.Based on the average method, the approximate analytical solution is derived and the voltage response is obtained. Furthermore, the physical prototype is fabricated, and the vibration experiment is conducted to validate the theoretical principle. The experimental results show that the maximum power of 0.445 μW of the layer-separated VEH is about3.11 times higher than that of the non-impact harvester when the excitation acceleration is 0.2 g. The operating frequency bandwidth can be widened by increasing the stiffness of the fundamental layer and decreasing the gap distance of the system. But the increasing of operating frequency bandwidth comes at the cost of reducing peak voltage. The theoretical simulation and the experimental results demonstrate good agreement which indicates that the proposed impact-driving VEH device has advantages for low-frequency and wide-bandwidth. The high performance provides great prospect to scavenge the vibration energy in environment.

Energy harvester array using piezoelectric circular diaphragm for rail vibration

Generating electric energy from mechanical vibration using a piezoelectric circular membrane array is presented in this paper.The electrical characteristics of the functional array consisted of three plates with varies tip masses are examined under dynamic conditions.With an optimal load resistor of 11 k,an output power of 21.4 m W was generated from the array in parallel connection at 150 Hz under a pre-stress of 0.8 N and a vibration acceleration of9.8 m/s2.Moreover,the broadband energy harvesting using this array still can be realized with different tip masses.Three obvious output power peaks can be obtained in a frequency spectra of 110 Hz to 260 Hz.The results show that using a piezoelectric circular diaphragm array can increase significantly the output of energy compared with the use of a single plate.And by optimizing combination of tip masses with piezoelectric elements in array,the frequency range can be tuned to meet the broadband vibration.This array may possibly be exploited to design the energy harvesting for practical applications such as future high speed rail.

Analysis on Output Power for Multi-direction Piezoelectric Vibration Energy Harvester

To predict the performance of multi-direction piezoelectric vibration energy harvester,an equation for calculating its output power is obtained based on elastic mechanics theory and piezoelectricity theory.Experiments are performed to verify theoretical analysis.When the excitation direction is along Y direction,a maximal output power about 0.139 mW can be harvested at a resistive load of 65kΩ and an excitation frequency of 136 Hz.Theoretical analysis agrees well with experimental results.Furthermore,the performance of multi-direction vibration energy harvester is experimentally tested.The results show that the multi-direction vibration energy harvester can harvest perfect energy as the excitation direction changes in XY plane,YZ plane,XZ plane and body diagonal plane of the harvester.

Spiral piezoelectric transducer in torsional motion as low-frequency power harvester

A structure consisting of a spiral piezoelectric transducer and a concentrated mass is proposed as a low-frequency piezoelectric power harvester. A theoretical model is developed for the system from the theory of piezoelectricity. An analysis is performed to demonstrate the low-frequency nature of the system. Other basic characteristics of the power harvester including the output power, voltage, and efficiency are also calculated and examined.

Nonlinear characteristics of circular-cylinder piezoelectric power harvester near resonance based on flow-induced flexural vibration mode

The nonlinear behaviors of a circular-cylinder piezoelectric power harvester （CCPPH） near resonance are analyzed based on the flow-induced flexural vibration mode. The geometrically-nonlinear effect of the cylinder is studied with considering the in-plane extension incidental to the large defection. The boundary electric charges generated from two deformation modes, flexure and in-plane extension, were distinguished with each other because the charge corresponding to the latter mode produces no contribution to the output current. Numerical results on output powers show that there are multi- valuedness and jump behaviors.

Performance improvement of the stochastic-resonance-based tri-stableenergy harvester under random rotational vibration

In this paper,the stochastic-resonance-based tri-stable energy harvester(TEH)is proposed to enhance harvesting performance under random rotational vibration.An electromechanical coupled system interfaced with a standard rectifier circuit driven by colored noise is considered.The stationary probability density function(SPDF)of the harvester is obtained by the improved stochastic averaging.Then,with the adiabatic approximation theory,the analytical expression of signal-to-noise ratio(SNR)for the TEH is deduced to characterize stochastic resonance(SR).To enhance direct current(DC)power delivery from a rotational TEH,the influences of system parameters on SR is discussed.The obtained results suggest that there are damping-induced resonance and noise-intensity-induced SR in the tri-stable system.The TEH has higher harvesting performance under the optimal SR.That is,the optimal parameter combinations can induce optimal SR and maximize harvesting performance.Thus,the stochastic-resonance-based TEH can be optimized to enhance energy harvesting through choosing the optimal parameter.

Integration of a nonlinear energy sink and a piezoelectric energy harvester

A mechanical-piezoelectric system is explored to reduce vibration and to harvest energy. The system consists of a piezoelectric device and a nonlinear energy sink （NES）, which is a nonlinear oscillator without linear stiffness. The NES-piezoelectric sys- tem is attached to a 2-degree-of-freedom primary system subjected to a shock load. This mechanical-piezoelectric system is investigated based on the concepts of the percentages of energy transition and energy transition measure. The strong target energy transfer occurs for some certain transient excitation amplitude and NES nonlinear stiffness. The plots of wavelet transforms are used to indicate that the nonlinear beats initiate energy transitions between the NES-piezoelectric system and the primary system in the tran- sient vibration, and a 1：1 transient resonance capture occurs between two subsystems. The investigation demonstrates that the integrated NES-piezoelectric mechanism can re- duce vibration and harvest some vibration energy.

The effect of the beam shapes on the doubly-clamped piezoelectric energy harvester

For a piezoelectric energy harvester composed of a doubly-clamped beam with arbitrary width shapes and a proof mass, the influence of beam shapes and electrode arrangements on different electric outputs is analyzed. The output performances of piezoelectric energy harvesters with rectangular shape, concave trapezoidal shape, and concave parabolic shape are compared, and an optimization way is given. The experimental results validate the effectiveness of the methods.

Design and Characterization of a Low-Cost Piezoelectric Vibration Energy Harvester with Bulk PZT Film

To improve the efficiency of MEMS piezoelectric vibration energy harvesters(PVEHs), the bulk lead zirconate titanate(PZT) has been used to substitute the thin film PZT for the higher mechanical-electrical coupling coefficients. The expensive equipment of micromachining set a high entry barrier on the research of PVEHs with high efficiency. To solve this issue, this paper developed an efficient PVEH with bulk PZT using common precision machining, whose dimensions and electrical outputs are comparable to the MEMS devices. After numerically analyzing the effects of the length ratio of the proof mass to the harvester on the output power, a compact PVEH consisting of a cantilevered uni-morph and a tungsten proof mass was designed. Simulations show that the mechanical damping ratio and the thickness have little effects on the optimized length ratio. By using a uni-morph with the copper structural layer of about 80-90μm and the bulk PZT-5 H layer of 139μm, a low-cost harvester prototype was assembled. The key parameters of the prototype were experimentally identified and compared with the theoretical predictions. Under the harmonic base excitation of 0.4 g(where g = 9.8 m/s^2) at 160 Hz, the maximum output power of the prototype is about 76.7μW, with the normalized power density of about 3.35 mW/cm^3/g^2. Under base excitation of 0.4 g at 159 Hz, the prototype charged a 680μF capacitor from 0 to 4.84 V in about 154 seconds.

Electroaeroelastic Modeling and Analysis for Flow Energy Piezoelectric Harvester

An electroaeroelastic model for wind energy harvesting using piezoelectric generators is presented.The flow field is mapped in detail.The force which the fluid flow exerts on the generator is formulated.The output voltage levels generated from the mechanical strain within the piezoelectric elements are determined.An analytical model is developed with consideration of the interactions between the fluid,solid and electric.Various analytical results are obtained,such as flow velocity contour and pressure contour for the flow,moving trajectories,stress contour and output voltage of the harvester.A prototype is fabricated and tested.The simulation result is close to the experimental result.The model developed in this paper can predict the performance and behavior of different energy harvesters.And it also can be used as a design tool for optimizing the performance of the harvester.

Power Analysis for Piezoelectric Energy Harvester

Piezoelectric energy harvesting technology is used to design battery less microelectronic devices such as wireless sensor nodes. This paper investigates the necessary conditions to enhance the extracted AC electrical power from exciting vibrations energy using piezoelectric materials. The effect of tip masses and their mounting positions are investigated to enhance the system performance. The optimal resistive load is estimated to maximize the power output. Different capacitive loads are tested to store the output energy. The experimental results validated the theoretical analysis and highlighted remarks in the paper.

Disk Bimorph-Type Piezoelectric Energy Harvester

The study of the experimental investigation of a disk-type piezoelectric energy harvester presented. The harvester contains disk bimorph piezoceramic element of the umbrella form and contains two disk PZT plates. The element is excited at the base point at its center. The element is supplied by a loading ring mass to decrease its resonance frequency. The dependences of the vibration displacement along the radii of the bimorph and the ring mass from the frequency of excitation are presented and the output voltage frequency response is also presented as well. The idle mode and the load duty are investigated. The value of the internal resistance of the harvester is obtained using the load characteristic. The piezoelectric specific power is estimated experimentally.

Performance of beam-type piezoelectric vibration energy harvester based on ZnO film fabrication and improved energy harvesting circuit

We demonstrate a piezoelectric vibration energy harvester with the ZnO piezoelectric film and an improved synchronous electric charge extraction energy harvesting circuit on the basis of the beam-type mechanical structure,especially investigate its output performance in vibration harvesting and ability to generate charges.By establishing the theoretical model for each of vibration and circuit,the numerical results of voltage and power output are obtained.By fabricating the prototype of this harvester,the quality of the sputtered film is explored.Theoretical and experimental analyses are conducted in open-circuit and closed-circuit conditions,where the open-circuit mode refers to the voltage output in relation to the ZnO film and external excitation,and the power output of the closed-circuit mode is relevant to resistance.Experimental findings show good agreement with the theoretical ones,in the output tendency.It is observed that the properties of ZnO film achieve regularly direct proportion to output performance under different excitations.Furthermore,a maximum experimental power output of 4.5 mW in a resistance range of 3 kΩ-8 kΩis achieved by using an improved synchronous electric charge extraction circuit.The result is not only more than three times the power output of classic circuit,but also can broaden the resistance to a large range of 5 kΩunder an identical maximum value of power output.In this study we demonstrate the fundamental mechanism of piezoelectric materials under multiple conditions and take an example to show the methods of fabricating and testing the ZnO film.Furthermore,it may contribute to a novel energy harvesting circuit with high output performance.

Finite Element Analysis on a Square Canister Piezoelectric Energy Harvester in Asphalt Pavement

A novel square canister piezoelectric energy harvester was proposed for harvesting energy from asphalt pavement. The square of the harvester was of great advantage to compose the harvester array for harvesting energy from the asphalt pavement in a large scale. The open circuit voltage of the harvester was obtained by the piezoelectric constant d33 of the piezoelectric ceramic. The harvester is different from the cymbal harvester which works by the piezoelectric constant d31. The finite element model of the single harvester was constructed. The open circuit voltage increased with increase of the outer load. The finite element model of the single harvester buried in the asphalt pavement was built. The open circuit voltage, the deformation difference percent and the stress of the ceramic of the harvester were obtained with different buried depth. The open circuit voltage decreased when the buried depth was increased. The proper buried depth of the harvester should be selected as 30 - 50 mm. The effects of structure parameters on the open circuit voltage were gotten. The output voltage about 64.442 V could be obtained from a single harvester buried under 40 mm pavement at the vehicle load of 0.7 MPa. 0.047 mJ electric energy could be gotten in the harvester. The output power was about 0.705 mW at 15 Hz vehicle load frequency.

Design and Analysis of MEMS Based Aluminum Nitride (AlN), Lithium Niobate (LiNbO₃) and Zinc Oxide (ZnO) Cantilever with Different Substrate Materials for Piezoelectric Vibration Energy Harvesters Using COMSOL Multiphysics Software

Interest in energy harvesters has grown rapidly over the last decade. The cantilever shaped piezoelectric energy harvesting beam is one of the most employed designs, due to its simplicity and flexibility for further performance enhancement. The research effort in the MEMS Piezoelectric vibration energy harvester designed using three types of cantilever materials, Lithium Niobate (LiNbO3), Aluminum Nitride (AlN) and Zinc Oxide (ZnO) with different substrate materials: aluminum, steel and silicon using COMSOL Multiphysics package were designed and analyzed. Voltage, mechanical power and electrical power versus frequency for different cantilever materials and substrates were modeled and simulated using Finite element method (FEM). The resonant frequencies of the LiNbO3/Al, AlN/Al and ZnO/Al systems were found to be 187.5 Hz, 279.5 Hz and 173.5 Hz, respectively. We found that ZnO/Al system yields optimum voltage and electrical power values of 8.2 V and 2.8 mW, respectively. For ZnO cantilever on aluminum, steel and silicon substrates, we found the resonant frequencies to be 173.5 Hz, 170 Hz and 175 Hz, respectively. Interestingly, ZnO/steel yields optimal voltage and electrical power values of 9.83 V and 4.02 mW, respectively. Furthermore, all systems were studied at different differentiate frequencies. We found that voltage and electrical power have increased as the acceleration has increased.

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule （GDQR） method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.

Complete Charging for Piezoelectric Energy Harvesting System

Under an in-phase assumption, the complete charging for an energy harvesting system is studied, which consists of a piezoelectric energy harvester(PEH), a bridge rectifier, a filter capacitor, a switch, a controller and a rechargeable battery. For the transient charging, the results indicate that the voltage across the filter capacitor increases as the charging proceeds, which is consistent with that reported in the literature. However, a new finding shows that the charging rate and energy harvesting efficiency decrease over time after their respective peak values are acquired.For the steady-state charging, the results reveal that the energy harvesting efficiency can be adjusted by altering the critical charging voltage that controls the transition of the system. The optimal energy harvesting efficiency is limited by the optimal efficiency of the transient charging. Finally, the relationship between the critical charging voltage and the equivalent resistance of the controller and rechargeable battery is established explicitly.

Harvesting Energy from Asphalt Pavement by Piezoelectric Generator

This paper presents the way to harvest mechanical energy from asphalt pavement by piezoelectric generator. Results show that the potential energy in asphalt pavement can be up to 150 kW/h per lane per kilometre. Part of the mechanical energy can be harvested by piezoelectric transducers. The performance of seven typical transducers is examined through finite element analysis. Results show that PZT piles and multilayer, cymbal and bridge can work in asphalt pavement environment. PZT piles and multilayer have higher energy converting rate, However, the total harvested energy is small if these transducers are embedded directly in pavement. A prototype pavement generator is developed using PZT piles to increase the harvested energy. The generator can harvest more than 50 kW/h energy from the pavement under heavy traffic. 8-16 PZT piles are recommended for one generator. Round shape is suggested for the PZT piles to reduce the concentration of stress. And multilayer structure is recommended for PZT piles to decrease the electric potential of generator. The generator can be extended as sensor in the asphalt pavement, which can be used to monitor the traffic, pavement stress and temperature.