Cantilevered Harvester Research Articles

A simulation of the performance of a self-tuning energy harvesting cantilever beam

A vibration energy harvester is typically a cantilever beam made up of one or two layers of piezoelectric material that is clamped at one end to a vibrating host structure. The harvester is typically tuned to the frequency of the ambient vibration to ensure maximum power generation. One method to ensure that the system stays tuned in the presence of a varying frequency is to attach a mass to the cantilever and apply a control system to adjust its position along the cantilever according to the ambient frequency. This paper presents a simulation of the performance of such a system, based on a distributed parameter electromechanical model of the sliding-mass beam. A variety of control systems are used to adjust the position of the movable mass during operation and are compared for their efficacy in maintaining resonance over a varying excitation frequency. It was found that the resonance frequency of a bimorph cantilever VEH (Vibration Energy Harvester) could be successfully tuned over a wide frequency range. Moreover, it is also found that much of the voltage output reduction at higher frequencies could be compensated for by a separate control system used to adjust the capacitor load.

A Broadband Internally Resonant Vibratory Energy Harvester

The objective of this paper is twofold: first to illustrate that nonlinear modal interactions, namely, a two-to-one internal resonance energy pump, can be exploited to improve the steady-state bandwidth of vibratory energy harvesters; and, second, to investigate the influence of key system’s parameters on the steady-state bandwidth in the presence of the internal resonance. To achieve this objective, an L-shaped piezoelectric cantilevered harvester augmented with frequency tuning magnets is considered. The distance between the magnets is adjusted such that the second modal frequency of the structure is nearly twice its first modal frequency. This facilitates a nonlinear energy exchange between these two commensurate modes resulting in large-amplitude responses over a wider range of frequencies. The harvester is then subjected to a harmonic excitation with a frequency close to the first modal frequency, and the voltage–frequency response curves are generated. Results clearly illustrate an improved bandwidth and output voltage over a case which does not involve an internal resonance. A nonlinear model of the harvester is developed and validated against experimental findings. An approximate analytical solution of the model is obtained using perturbation methods and utilized to draw several conclusions regarding the influence of key design parameters on the harvester’s bandwidth.

Fabrication of a 2-DOF electromagnetic energy harvester with in-phase vibrational bandwidth broadening

A vibration structure with two-degrees-of-freedom is proposed to increase the usable bandwidth of a micromachined electromagnetic energy harvester. Compared with the structure of a pure cantilever harvester, the proposed structure is formed by integrating a spiral diaphragm into a U-shaped cantilever diaphragm. By performing finite element analysis, the resonance frequencies of the two diaphragms are designed with a slight shift, both lower than 300 Hz. In addition, to achieve output bandwidth broadening, electroplated copper coils on the spiral and the U-shaped cantilever are coupled and the connection sequences of the coupled coils are arranged such that single- or duo-mode tuning of the energy harvester can be realized. The harvester delivers powers of 22.1 and 21.5 nW at two resonance frequencies of 211 and 274 Hz, respectively, in the duo-mode operation. The proposed spiral–cantilever coupled energy harvester has lower resonance frequencies and broader bandwidth than a pure cantilever-type harvester of equal area, and can therefore harvest more energy from the environment.

A broadband bi-stable flow energy harvester based on the wake-galloping phenomenon

Linear wake-galloping flow energy harvesters have a narrow frequency bandwidth restricted to the lock-in region, where the vortex shedding frequency is close to the natural frequency of the harvester. As a result, their performance is very sensitive to variations in the flow speed around the nominal design value. This letter demonstrates that the lock-in region of a wake-galloping flow energy harvester can be improved by exploiting a bi-stable restoring force. To demonstrate the enhanced performance, the response behavior of a bi-stable piezoelectric cantilever harvester is evaluated in a wind tunnel. A Von Kármán vortex street is generated by placing a rectangular rod in the windward direction of the harvester and the voltage response of the harvester is evaluated as a function of the wind speed. It is shown that, compared to the linear design, bi-stability can be used to improve the steady-state bandwidth considerably.

An optimization of rectangular shape piezoelectric energy harvesting cantilever beam for micro devices

The vibration based piezoelectric energy harvester system is considered as an alternative solution for micro-devices, especially for remote area. This paper presents an optimization approach to determine the optimal cantilever beam of a rectangular shape piezoelectric energy harvester to run the micro devices in which power is unavailable. In this study, PZT-5H material has been utilized. The motivation behind this research is to maximize the power behavior by optimizing the cantilever beam’s length, width and thickness. Therefore, the proposed rectangular cantilever beam has been optimized by using modified particle swarm optimization (MPSO) algorithm and designed in COMSOL software. Finally, the optimization results of MPSO are compared with other technique to validate the outcomes. The findings show that the performance of the proposed technique is better than other technique in terms of quality and convergence speed.

Adaptive tuned piezoelectric MEMS vibration energy harvester using an electrostatic device

In this paper an adaptive tuned piezoelectric vibration based energy harvesting system based on the use of electrostatic device is proposed. The main motivation is to control the resonance frequency of the piezoelectric harvester with the DC voltage applied to the electrostatic system in order to maximize the harvested power. The idea is demonstrated in a hybrid system consisting of a cantilevered piezoelectric harvester combined with an electrostatic harvester which is connected to a variable voltage source. The nonlinear governing differential equation of motion is derived based on Euler Bernoulli theory, and solved to obtain the static and dynamic solutions. The results show that the harvester can be tuned to give a resonant response over a wide range of frequencies, and shows the great potential of this hybrid system.

Experimental and theoretical studies on piezoelectric energy harvesting from low-frequency ambient random vibrations

In this paper, an analytical approach was used to formulate for gathering energy from ambient sources of vibrations. The apparatus consists of a cantilevered beam harvester with a piezoelectric patch. A coupled electromechanical modal model based on Euler–Bernoulli theory is used. The governing equations were extracted using Hamilton’s principle and then were discretized by using the Rayleigh–Ritz approach. The expected value of the electrical power output was obtained for a weakly stationary, Gaussian bandpass with zero mean base excitation. Next, a numerical solution for the beam under band-limited ambient random acceleration as the input was calculated and validated by experiment. The numerical results closely correlated to the experimental data with a deviation of about 10%.

A Shear-Mode Energy Harvesting Device Based on Torsional Stresses

The shear-mode of a piezoceramic material offers improved energy harvesting potential as compared to other modes. This paper presents a concept of using torsional stresses induced by nonrotational vibrations in an energy harvesting device to produce electrical power. A finite-element model of this concept is presented to illustrate the principle and a prototype is demonstrated to validate the design. This prototype harvester is found to be capable of producing a maximum power of 0.57 mW at its resonant frequency of 620 Hz with a base acceleration of 1 g in amplitude. When compared to conventional cantilever harvester designs, this torsion-based harvester is found to suffer from fewer electrical power losses and has a greater potential in producing high power outputs.

Optimization of cantilevered piezoelectric energy harvester with a fixed resonance frequency

Piezoelectric energy harvesting is widely used to scavenge vibration energy in the environment. For some vibration sources with fixed frequency, cantilevered harvester can generate the energy effectively, so the optimization theory for cantilevered harvester in such an application is needed. In this article, we present the theoretical and experimental studies of the cantilevered piezoelectric energy harvester with a fixed resonance frequency. An analytical model based on energy method is used to estimate the open-circuit voltage and generated energy. Considering that the harvester may be subjected to the static force or steady-state sinusoidal vibration excitation, static and dynamic analysis is performed for device structure to achieve efficient energy. In the analysis, the effects of geometrical dimension on the energy harvesting performance are discussed comprehensively. Eventually, a prototype is designed and fabricated using (1−x)Pb(Mg1/3Nb2/3)O3−x PbTiO3 (PMN-PT) single crystal with ultrahigh piezoelectric properties and coupling factor. Performances of the cantilever with different clamped length are evaluated under sinusoidal vibration excitation, proving the good consistency between experimental results and theoretical prediction. The established analysis can provide useful guidelines for the structure design of cantilevered piezoelectric energy harvester with a fixed resonance frequency.

Power evaluation of flutter-based electromagnetic energy harvesters using computational fluid dynamics simulations

H- and T-shaped cross sections are known to be susceptible to rotational single-degree-of-freedom aerodynamic instabilities. Here, such self-excited aerodynamic response of a T-shaped cantilever structure is used to extract energy, which is then converted into electric power through an electromagnetic transducer. The complex fluid–structure interaction between the cantilever harvester and wind flow is analyzed numerically and experimentally. To study the dynamic response of the cantilever and estimate the power output from the harvester, numerical simulations based on the vortex particle method are performed to determine the aerodynamic damping of the harvester section and to analyze the stability behavior of the section. The estimated aerodynamic damping parameter together with the mechanical and electrical damping parameters in the harvester are used to find the critical wind speed of flutter onset as well as the optimum load resistance. Wind tunnel experiments are conducted to validate the simulation results.

Analytical modeling and experimental validation of a structurally integrated piezoelectric energy harvester on a thin plate

Vibration-based energy harvesting using piezoelectric cantilevers has been extensively studied over the past decade. As an alternative to cantilevered harvesters, piezoelectric patch harvesters integrated to thin plates can be more convenient for use in marine, aerospace and automotive applications since these systems are often composed of thin plate-like structures with various boundary conditions. In this paper, we present analytical electroelastic modeling of a piezoelectric energy harvester structurally integrated to a thin plate along with experimental validations. The distributed-parameter electroelastic model of the thin plate with the piezoceramic patch harvester is developed based on Kirchhoff’s plate theory for all-four-edges clamped (CCCC) boundary conditions. Closed-form steady-state response expressions for coupled electrical output and structural vibration are obtained under transverse point force excitation. Analytical electroelastic frequency response functions (FRFs) relating the voltage output and vibration response to force input are derived and generalized for different boundary conditions. Experimental validation and extensive theoretical analysis efforts are then presented with a case study employing a thin PZT-5A piezoceramic patch attached on the surface of a rectangular aluminum CCCC plate. The importance of positioning of the piezoceramic patch harvester is discussed through an analysis of dynamic strain distribution on the overall plate surface. The electroelastic model is validated by a comparison of analytical and experimental FRFs for a wide range of resistive electrical boundary conditions. Finally, power generation performance of the structurally integrated piezoceramic patch harvester from multiple vibration modes is investigated analytically and experimentally.

Energy harvesting from ambient low-frequency magnetic field using magneto-mechano-electric composite cantilever

A magneto-mechano-electric (MME) composite cantilever for energy harvesting from ambient low-frequency magnetic field has been investigated in this study. The MME composite cantilever is made of a piezoelectric bimorph with NdFeB magnets attached at its tip. The properties of the MME composite cantilever based energy harvester were theoretically predicted by using the equivalent circuit model. The experimental results show that the maximum power density for excitations at the short- and open-circuit resonance frequencies (<100 Hz) is 11.73 μW/Oe2 cm3, which is one order of magnitude higher than that of previously reported magnetoelectric energy harvester. The research has proved the potential application of the composite cantilever for harvesting ambient low-frequency magnetic field energy.

Research of Complex PZT Film Base on Shear Mode Energy Harvesting

The preparation of complex PZT with high d31 piezoelectric performance, which is used to the energy harvesting cantilever in vibration mode, is discussed in this paper. The Si/SiO2/Cr/Au/PT/PZT/PT structure base on (100) silicon crystallographic is growth through a PT transition layer before coating Sol-gel PZT film, which is in favor of the PZT film polarization processing in d31 shear mode. It is shown that the PZT film present the perovskite phase after optimize annealing at 700°C by XRD analysis. Piezoelectric properties test indicated that the PZT film has the coercive field at 23kV/cm and the remnant polarization is 60μC/cm2. The silicon-based cantilever with complex PZT film fabricated by MEMS technology is also given in the paper.

Wind energy harvesting with a piezoelectric harvester

An energy harvester comprising a cantilever attached to piezoelectric patches and a proof mass is developed for wind energy harvesting, from a cross wind-induced vibration of the cantilever, by the electromechanical coupling effect of piezoelectric materials. The vibration of the cantilever under the cross wind is induced by the air pressure owing to a vortex shedding phenomenon that occurs on the leeward side of the cantilever. To describe the energy harvesting process, a theoretical model considering the cross wind-induced vibration on the piezoelectric coupled cantilever energy harvester is developed, to calculate the charge and the voltage from the harvester. The influences of the length and location of the piezoelectric patches as well as the proof mass on the generated electric power are investigated. Results show that the total generated electric power can be as high as 2 W when the resonant frequency of the cantilever harvester is close to the vortex shedding frequency. Moreover, a value of total generated electric power up to 1.02 W can be practically realized for a cross wind with a variable wind velocity of 9–10 m s−1 by a harvester with a length of 1.2 m. This research facilitates an effective and compact wind energy harvesting device.

A Multimode Relayed Piezoelectric Cantilever for Effective Vibration Energy Harvesting

A piezoelectric cantilever with an eccentrically connected wire-mass relay is proposed for extensive energy harvesting from broadband vibration responses. The relay mass is chosen to be much greater than that of the cantilever. The vibration source is magnified by the relay as a bending-swinging-torsional excitation to drive the cantilever. Thus, multiple vibration modes of the cantilever are effectively employed to enhance energy harvesting. A prototype device was developed and characterized. The results show that the proposed structure can generate much more electricity over a broader bandwidth than conventional structures.

Enhanced energy harvesting using multiple piezoelectric elements: Theory and experiments

Power and bandwidth of piezoelectric harvesters can be increased by using multiple piezoelectric elements in one harvester. In this contribution, a novel energy harvesting cantilever array with magnetic tuning including three piezoelectric bimorphs is investigated theoretically and experimentally, with a good agreement between model and experiment. Other than harvester designs proposed before, this array is easy to manufacture and insensitive to manufacturing tolerances because its optimum operation frequency can be re-adjusted after fabrication. Using the superposition principle, the Butterworth-Van Dyke model and a mechanical lumped parameters model, the generated voltage and current are determined analytically. Formulas for calculating the power generated by array harvesters with an arbitrary number of piezoelectric elements connected in series or in parallel are derived. It is shown that optimum harvester design must take both the connected load and the operating frequency into account. Strategies for connecting multiple bimorphs to increase the maximum generated power and/or enhance the bandwidth compared to a single bimorph harvester are investigated. For bandwidth enhancement it is essential that individual rectifiers are used for the bimorphs. An example with three bimorphs shows that, depending on the chosen tuning strategy, the power is increased by about 340% or the bandwidth is increased by about 500%, compared to one single bimorph.

Analytical modeling and experimental verification of vibration-based piezoelectric bimorph beam with a tip-mass for power harvesting

Power harvesting techniques that convert vibration energy into electrical energy through piezoelectric transducers show strong potential for powering smart wireless sensor devices in applications of structural health monitoring. This paper presents an analytical model of the dynamic behavior of an electromechanical piezoelectric bimorph cantilever harvester connected with an AC–DC circuit based on the Euler–Bernoulli beam theory and Hamiltonian theorem. A new cantilevered piezoelectric bimorph structure is proposed in which the plug-type connection between support layer and tip-mass ensures that the gravity center of the tip-mass is collinear with the gravity center of the beam so that the brittle fracture of piezoelectric layers can also be avoided while vibrating with large amplitude. The tip-mass is equated by the inertial force and inertial moment acting at the end of the piezoelectric bimorph beam based on D'Alembert's principle. An AC–DC converting circuit soldered with the piezoelectric elements is also taken into account. A completely new analytic expression of the global behavior of the electromechanical piezoelectric bimorph harvesting system with AC–DC circuit under input base transverse excitation is derived. Moreover, an experimental energy harvester is fabricated and the theoretical analysis and experimental results of the piezoelectric harvester under the input base transverse displacement excitation are validated by using measurements of the absolute tip displacement, electric voltage response, electric current response and electric power harvesting.

Cantilever driving low frequency piezoelectric energy harvester using single crystal material 0.71Pb(Mg1/3Nb2/3)O3-0.29PbTiO3

We present a high performance piezoelectric energy harvester CANtilever Driving Low frequency Energy harvester (CANDLE) consisting of cantilever beam and cymbal transducers based on piezoelectric single crystal 0.71Pb(Mg1/3Nb2/3)O3-0.29PbTiO3. Electrical properties of CANDLE under different proof masses, excitation frequencies, and load resistances are studied systematically. Under an acceleration of 3.2g (g = 9.8 m/s2), a peak voltage of 38 V, a maximum power of 3.7 mW were measured at 102 Hz with a proof mass of 4.2 g. Low resonance frequency and high power output performance demonstrate the promise of the device in energy harvesting for wireless sensors and low-power electronics.

Experimental model validation for a nonlinear energy harvester incorporating a bump stop

In some practical applications, cantilever beam piezoelectric energy harvesters are subjected to large amplitude base excitations which induce nonlinear behaviour in the harvester that affects their performance. In this paper, a cantilever piezoelectric energy harvester model is developed which takes account of geometric nonlinearity arising through the inextensible beam condition and material nonlinearity arising in the piezoelectric layers of the harvester. The model is validated against experimental measurements for different base accelerations and load resistances, and an investigation into the nonlinear behaviour indicates that nonlinear softening is caused predominantly by material nonlinearity. To reduce the beam amplitude and the resulting bending stress in the cantilever harvester, a bump stop is incorporated into the harvester design and the influence of the bump stop is modelled. Comparisons of theoretical predictions with experimental measurements indicate that taking account of the nonlinear behaviour improves the prediction significantly in some cases. Parameter studies are also conducted to investigate how the stop location and initial gap size between the harvester and stop affect the performance of the nonlinear energy harvester.

Piezoelectric MEMS Energy Harvester for Low-Frequency Vibrations With Wideband Operation Range and Steadily Increased Output Power

A piezoelectric MEMS energy harvester (EH) with low resonant frequency and wide operation bandwidth was designed, microfabricated, and characterized. The MEMS piezoelectric energy harvesting cantilever consists of a silicon beam integrated with piezoelectric thin film (PZT) elements parallel-arranged on top and a silicon proof mass resulting in a low resonant frequency of 36 Hz. The whole chip was assembled onto a metal carrier with a limited spacer such that the operation frequency bandwidth can be widened to 17 Hz at the input acceleration of 1.0 g during frequency up-sweep. Load voltage and power generation for different numbers of PZT elements in series and in parallel connections were compared and discussed based on experimental and simulation results. Moreover, the EH device has a wideband and steadily increased power generation from 19.4 nW to 51.3 nW within the operation frequency bandwidth ranging from 30 Hz to 47 Hz at 1.0 g. Based on theoretical estimation, a potential output power of 0.53 μW could be harvested from low and irregular frequency vibrations by adjusting the PZT pattern and spacer thickness to achieve an optimal design.