Piezoelectric Cantilever Research Articles

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

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

Parametric Analysis of Nonlinear Bi-Stable Piezoelectric Energy Harvester Based on Multi-Scale Method

Given the geometric nonlinearity of the piezoelectric cantilever beam, this study establishes a distributed parameter model of the nonlinear bi-stable cantilever piezoelectric energy harvester, following the generalized Hamilton variational principle. The analytical expressions of the dynamic response were obtained for the energy harvesting system using Galerkin modal decomposition and the multi-scale method. The investigation focuses on how the performance of the energy harvesting system is influenced by the gap distance between magnets, external excited amplitude, mechanical damping ratio and external load resistance. The calculation results were compared with those obtained neglecting the geometric nonlinearity of the beam. The results show that the system responses contain jump and multiple solutions. The consideration of the geometrical nonlinearity significantly amplified the peak displacement and peak output power of the intra-well and inter-well motions. There is an evident hardening effect of the inter-well motion frequency response curve. By reasonable adjusting the parameters, it is possible to improve the output power of the piezoelectric energy harvesting system and broaden the operating frequency of the system.

Needle selector failure detection based on piezoelectric sensor and driver co-location characteristics

Aiming at the problem of the malfunction of knitting machines caused by the unstable operation of the piezoelectric needle selector during the jacquard process, a state detection scheme for the piezoelectric needle selector that integrates the sensor and drive function co-located is proposed. The motion state of bimorph piezoelectric cantilever beam and its bi-directional piezoelectric effect in the jacquard process of piezoelectric needle selector are analyzed. Electrical and dynamic models were established for the electrical characteristics inside the bimorph piezoelectric cantilever beam and the dynamic characteristics of the cutter head and baffle of the needle selector. The signal detection circuit is designed to realize the real-time detection of the piezoelectric needle selector state by analyzing the time domain and frequency domain characteristics of the electrical signal. The results show that in the normal working state of the piezoelectric needle selector, the internal electric signal of the piezoelectric driver has two characteristic frequencies, which are between 155 and 180 and between 1630 and 1670 Hz, and the time for the piece to swing to the limit position is relatively long under abnormal working conditions.

Vortex-induced piezoelectric cantilever beam vibration for ocean wave energy harvesting via airflow from the orifice of oscillation water column chamber

Micro piezoelectric generators have attracted immense interest to convert mechanical vibrations into electric energy for ultralow power wireless sensors. Herein, an ocean wave vortex-induced vibration piezoelectric energy harvester(Wavee-VIVPEH) is proposed to extract wave energy. The renewable and sustainable ocean environment energy harvesting device consists of an oscillating water column(OWC) air chamber, wind tunnel, and piezoelectric energy converter. A fixed bluff body in the vent tunnel induces airflow vortexes and excites the piezoelectric cantilever vibration converting up the ultralow frequency of ocean waves. The novel Wave-VIVPEH is a complex multi-physics system requiring feasible methodologies to enhance its performance. The theoretical models are derived to systematically investigate and optimize the operation. The flume and wind tunnel experiments and the related fluid-solid electric coupling simulations are carried out to verify the concept's feasibility. The aerodynamic kinetic performance in the OWC chamber is characterized by the models. The instantaneous maximum exhalation airspeed reaches 16.55 m/s with the air pressure of 349.97 Pa and the wave period of T = 2.5 s. In this wave condition, the results are well agreed with the simulation values of wind speed of 17.96 m/s, and air pressure of 382.55 Pa. The output power characteristics of the piezoelectric energy harvester are analyzed for the distance of the vortex wake between the piezoelectric cantilever beam and the bluff body. With the bluff body diameter of 25 mm and distance of d/dD= 4, the theoretical results on the maximum peak voltage and output power are 10.46 V, 3.26 mW agree with the simulation optimized values of the maximum peak voltage of 10.85 V and the output power of 3.55 mW. When the wind speed is 15 m/s, the theoretical voltage of 8.62 V approaches the experimental result of 8.47 V. Especially, the comparisons of the theoretical power and voltage to experimental and simulational results indicate that the ingenious Wave-VIVPEH has great potential in ocean wave energy harvesting applications to supply power for intelligent buoys.

Preliminary investigation on the energy harvesting of vortex-induced vibration with the use of magnet

The utilization of natural resources as renewable energy is thriving as its innovation brings clean energy, environmentally friendly and also cut down costs. Hence, the purpose of this study is to propose a technique to enhance the output voltage of piezoelectric as an energy harvesting device by applying nonlinear magnetic forces from a phenomenon called vortex induced vibration (VIV). This harvester device is designed with a presence of two magnets that placed at the bottom of a circular cylinder and on the lower base. The mechanical conversion energy that is studied is the vibration from circular cylinder’s oscillation through a phenomenon called Vortex Induced Vibration by using piezoelectric transducer. A VIV-based energy harvester has been fabricated and carried out in water flow to observe the optimum output voltage that can be generated. Three different lengths of piezoelectric cantilever plates and two magnet distances are tested to investigate the influence of system’s stiffness and the repulsive force to the harvested energy. From the experiment, it is observed that a lower stiffness of the system provides higher harvested voltage. In addition, the presence of magnets shows a greater output voltage due to the action of nonlinear magnetic forces where the position between two magnets able to shift the synchronization region thus, showing a greatly wider synchronization region and increasing the performance of VIV-based energy harvesting system.

High piezoelectricity in epitaxial BiFeO3 microcantilevers

The large switchable ferroelectric polarization and lead-free composition of BiFeO3 make it a promising candidate as an active material in numerous applications, in particular, in micro-electro-mechanical systems (MEMS) when BiFeO3 is integrated in a thin film form on a silicon substrate. Here, 200-nm-thick Mn-doped BiFeO3 thin films have been epitaxially grown on a SrRuO3/SrTiO3/Si substrate and patterned into microcantilevers as prototype device structures for piezoelectric actuation. The devices demonstrate excellent ferroelectric response with a remanent polarization of 55 μC/cm2. The epitaxial BiFeO3 MEMS exhibit very high piezoelectric response with transverse piezoelectric coefficient d31 reaching 83 pm/V. The BiFeO3 cantilevers show larger electromechanical performance (the ratio of curvature/electric field) than that of state-of-art piezoelectric cantilevers, including well-known PZT (Pb(Zr,Ti)O3) and the hyper-active PMN–PT (Pb(Mg1/3Nb2/3)O3-PbTiO3). In addition, the piezoelectricity in BiFeO3 MEMS is found to depend on the ferroelectric polarization direction, which could originate from the flexoelectric effect and be exploited to further enhance the electromechanical performance of the devices. These results could potentially lead to a replacement of lead-based piezoelectrics by BiFeO3 in many microdevices.

Low-Power Wearable Breath Monitoring Device With Humidity- and Ammonia-Sensing Functions (May 2022)

This article presents a wearable breath-monitoring device integrated with humidity- and ammonia-sensing functions. The breath-monitoring device was constructed using a piezoelectric cantilever array and hollow flexible polydimethylsiloxane (PDMS) membrane. Important parameters of breath, such as the respiratory rate and tidal volume, can be detected without actuated energy. The Nafion-based capacitive humidity sensor and ZnO nanoparticle-based resistance ammonia sensor were compactly integrated into the housing ring of a breath monitoring device. The fabricated humidity sensor demonstrated a faster response in the sensing range below 75% compared with a commercial product. The sensitivity of the fabricated ammonia sensor reached 0.16 ppm/mV and the sensor exhibited an approximately fourfold shorter response time compared with the commercial product. Two applications were tested for the developed device prototype. One was monitoring the humidity and ammonia of the environmental air along with breath parameters while breathing. The other was to examine the amount of breath air exhaled from the body of the subject. The total power consumed by the developed prototype device was approximately 46 mW, which is significantly lower than that of existing commercial products. This compact and lightweight prototype device demonstrates significant potential for wearable applications.

A high-resolution MEMS magnetoresistive sensor utilizing magnetic tunnel junction motion modulation driven by the piezoelectric resonator

High-sensitivity MEMS magnetoresistive (MR) sensors have attracted ever-increasing attention due to their ability to detect weak magnetic fields, but the resolution is severely limited by the 1/f noise. This paper reports a MEMS MR sensor that can effectively suppress the 1/f noise by modulating the magnetic field signal to the higher frequency region utilizing magnetic tunnel junction vertical motion modulation based on the MEMS piezoelectric cantilever resonator. The magnetic sensitivity can be increased to 2283.3%/mT with a high magnetic gain of 39.3 by integrating the structure-optimized fixed magnetic flux concentrators. The signal-to-noise ratio of the MEMS MR sensor can be improved by three orders of magnitude and the 160 pT/√Hz resolution can be reached. These results make the MEMS MR sensor based on the MTJ motion modulation a competitive candidate in the pico-Tesla magnetic detection.

Environmental vibration energy collection technology based on piezoelectric and electromagnetic model

In this paper, the vibration model of the piezoelectric cantilever, the piezoelectric and electromagnetic output model are established. The simulation analysis of the cantilever vibration is performed using Comsol Multiphysics software. The effects of structural parameters, including cantilever length, cantilever thickness, piezoelectric layer length, piezoelectric layer thickness, coil size and position, on the resonance frequency and output voltage were analyzed. A cantilever vibration energy collection device is designed. The feasibility and accuracy of theoretical analysis were verified through the experiment, and the resonance frequency and the output voltage of the experiment basically agree with the theoretical calculation value.

A Cantilever-Based Piezoelectric MEMS for Arbitrary XY Path Generation.

This work pertains to the design of a cantilever-based piezoelectric MEMS device that is capable of generating arbitrary paths of its tip. The conceived device consists of a pair of rigidly coupled piezoelectric bimorph cantilevers, and a theoretical model is developed for the analytical evaluation of the proper voltage distribution to be supplied to the inner and outer electrodes of each piezoelectric actuator, in order to drive the tip along any desired trajectory. Such a device could be appealing in some microsurgical operations, i.e., the unclogging of arteries, endoluminal treatment of obstructive lesions, but also as a 2D micropositioning stage, etc. Theoretical predictions of voltage versus time that allow several pathways such as circles, ellipses, spirals, etc., to be accomplished have been verified with multiphysics FEM simulations and the numerical outcomes seem to corroborate the proposed model.

Wind Energy Potential Ranking of Meteorological Stations of Iran and Its Energy Extraction by Piezoelectric Element

Piezoelectrics have been used in several recent works to extract energy from the environment. This study examines the average wind speed across Iran and evaluates the amount of extracted voltage from vortex-induced vibrations with the piezoelectric cantilever beam (Euler–Bernoulli beam). This study aims to compute the maximum extracted voltage from polyvinylidene fluoride piezoelectric cantilever beam at the resonance from vortex-induced vibration to supply wireless network sensors, self-powered systems, and actuators. This simulation is proposed for the first-ranked meteorological station at its mean velocity over six years (2015–2020), and the finite element method is used for this numerical computation. The wind data of 76 meteorological stations in Iran over the mentioned period at the elevation of 10 m are collected every three hours and analyzed. Based on the statistical data, it is indicated that Zabol, Siri Island, and Aligudarz stations had recorded the maximum mean wind speed over the period at 6.42, 4.73, and 4.42 m/s, respectively, and then energy harvesting at the mean wind speed of top-ranked station (Zabol) is simulated. The prevailing wind directions are also studied with WRPLOT view software, and the wind vector field of 15 top-ranked stations is plotted. For energy harvesting simulation, periodic vortex shedding behind the bluff body, known as vortex-induced vibration, is considered numerically (finite element method). The piezoelectric cantilever beam is at a millimeter-scale and has a natural frequency of 630 Hz in its mode shapes to experience resonance phenomenon, which leads to maximum extracted voltage. The maximum extracted voltages for three piezoelectric cantilever beams with the natural frequency of 630 Hz with the wind speed of 6 m/s are 1.17, 1.52, and 0.043 mV, which are suitable for remote sensing, supplying self-power electronic devices, wireless networks, actuators, charging batteries, and setting up smart homes or cities. To achieve this, several energy harvesters with various dimensions should be placed in different orientations to utilize most of the blown wind.

Vortex-based aggregation of micron particles in liquid using low-frequency vibration of a piezoelectric actuator

In this letter, we proposed a control method for microparticles aggregation by utilizing liquid vortices. The piezoelectric cantilever beam, equipped with a probe, caused fluid flow through low-frequency vibration and formed vortexes at the end of the probe to gather microparticles. The particle image velocimetry tests and the flow field simulation results revealed that the forming region of the liquid vortexes was consistent with the microparticle aggregation region. The control method proposed here has the merits of simple structures, no damage to the controlled objects and large control ranges.

A Piezoelectric Heterostructure Scavenging Mechanical Energy from Human Foot Strikes.

This paper presents a piezoelectric heterostructure for extracting mechanical energy from human foot strikes based on the impact of a moving block on the tips of the piezoelectric unimorph cantilevers. The use of the magnetic springs allows low-frequency and high-amplitude movements of the device. The piezoelectric unimorph cantilevers deform under a human foot strike on the pedal, and the piezoelectric elements in d31-mode produce output voltages. An analysis was conducted, and the working principle was stated. A prototype was fabricated to validate the feasibility of the proposed design. The experimental results show that the generated RMS voltage increases with human walking (running) speed. At the walking speed of 6 km/h, an average power of 36.26 μW is produced across a matching resistive load of 4 MΩ with an initial separating distance of 9 mm. Improvements of the device are possible, allowing an increase in the average power by increasing the number of piezoelectric unimorph cantilevers and using the piezoelectric materials with higher piezoelectric constants.

Duffing-type digitally programmable nonlinear synthetic inductance for piezoelectric structures

Piezoelectric shunt damping techniques using linear circuits (e.g. resistive-inductive) and switching circuits (e.g. synchronized switch on inductor) have been extremely well studied for suppressing resonant vibrations in flexible structures. Both analog circuits and synthetic impedance circuits with digital control have been explored for linear concepts. In a parallel body of work, from the domain of mechanical methods of vibration attenuation, it is also known that leveraging nonlinearities (e.g. stiffness nonlinearity) can enhance the frequency bandwidth and offer amplitude-dependent suppression over a range of frequencies. However, the existing piezoelectric shunt damping techniques have been mostly limited to linear or switching nonlinear circuits, with the exception of a few nonlinear capacitance efforts. This work aims to introduce cubic inductance to emulate Duffing-type hardening nonlinearity in the shunt circuit with precise digital programming and tuning capability. Experiments are performed on a piezoelectric bimorph cantilever under base excitation for concept demonstration and model validation. First, linear frequency response functions of the cantilever are obtained for the short- and open-circuit conditions, and for linear resistive-inductive synthetic shunt damping, to confirm the standard linear behavior and electromechanical model parameters. Then, cubic inductance is introduced to the circuit and nonlinear experiments (up- and down-frequency sweep) are conducted. Cantilever tip to base motion transmissibility frequency response is measured along with piezoelectric voltage to base motion counterpart for a range of base excitation amplitudes. The distortion of the frequency response curves with increased base acceleration levels is observed. The nonlinear cubic coefficient is then varied to alter the manifestation of nonlinear frequency response at a given base excitation level, demonstrating the ease of tuning and triggering the nonlinear behavior on demand by means of the digitally-controlled synthetic impedance shunt. Nonlinear electromechanical model simulations are also validated against the experiments, yielding a very good agreement.

Piezoelectric Energy Harvesting from Low-Frequency Vibrations Based on Magnetic Plucking and Indirect Impacts

This work proposes a mono-axial piezoelectric energy harvester based on the innovative combination of magnetic plucking and indirect impacts, e.g., impacts happening on the package of the harvester. The harvester exploits a permanent magnet placed on a non-magnetic mass, free to move within a predefined bounded region located in front of a piezoelectric bimorph cantilever equipped with a magnet as the tip mass. When the harvester is subjected to a low-frequency external acceleration, the moving mass induces an abrupt deflection and release of the cantilever by means of magnetic coupling, followed by impacts of the same mass against the harvester package. The combined effect of magnetic plucking and indirect impacts induces a frequency up-conversion. A prototype has been designed, fabricated, fastened to the wrist of a person by means of a wristband, and experimentally tested for different motion levels. By setting the magnets in a repulsive configuration, after 50 s of consecutive impacts induced by shaking, an energy of 253.41 μJ has been stored: this value is seven times higher compared to the case of harvester subjected to indirect impacts only, i.e., without magnetic coupling. This confirms that the combination of magnetic plucking and indirect impacts triggers the effective scavenging of electrical energy even from low-frequency non-periodical mechanical movements, such as human motion, while preserving the reliability of piezoelectric components.

Wearable Exoskeleton System for Energy Harvesting and Angle Sensing Based on a Piezoelectric Cantilever Generator Array.

Wearable exoskeletons are developing rapidly due to their superiority in improving human ability and efficiency. The construction of a multifunctional exoskeleton system relies on an efficient continuous energy supply and various high-performance sensors. Here, a magnetic-driven piezoelectric cantilever generator (MPCG) array is designed for energy harvesting and angle sensing of joint motions. Combining theoretical derivation and experimental characterization, it is found that the nonlinear magnetic force acting on the cantilever structure will cause the phenomenon of frequency upconversion, which greatly improves the output of the MPCG. The experiment successfully proves the feasibility of using the MPCG array as an energy-harvesting module to collect energy from human joint motions and power an RH/temp sensor. Furthermore, the MPCG array can also be used to sense the rotation angle and angular velocity. By integrating with a wireless data acquisition and transmission module and supporting software, a wearable joint rehabilitation monitoring and assessment system is built, which can measure the activities of the joint in real time and evaluate the flexion degree. The demonstrated wearable exoskeleton system for joint motion energy harvesting and joint angle sensing is of great value for the construction of a multifunctional exoskeleton system and wearable smart rehabilitation equipment.

Experimental investigation on performance improvement of cantilever piezoelectric energy harvesters via escapement mechanism from extremely Low-Frequency excitations

In this paper, we first design a frequency tuning device that enables the piezoelectric cantilever to operate under extremely low-frequency (below 2 Hz) excitations. Our design is mainly composed of three sections: coil spring for energy conversion and storage, escapement mechanism for frequency tuning, and piezoelectric cantilever for power generation. The prototype is capable of converting random excitation into regulated high-frequency oscillations, rendering the PEH to perform continuous high output voltage and attain low matched impedance. In experiments, this device successfully tuned the 0.75 Hz excitation into a 12.15 Hz oscillation, which is 0.68 Hz lower than the resonant frequency of the PEH. With this frequency tuning design, the performance of the PEH is less dependent on the external excitation. The instantaneous output power from the PEH on the frequency tuning device is 38.12 μW under 1 Hz excitation, which is 91 % of the output power of the same PEH vibrating under 0.35 g acceleration, 13.2 Hz harmonic excitation. Our design can be of great significance when harnessing energy from extremely low-frequency excitation such as ocean waves.

Tunable Piezoelectric Vibration Energy Harvester With Supercapacitors for WSN in an Industrial Environment

This article presents the design strategy and experimental validation of a battery-free power supply for wireless sensor nodes (WSN) on an industrial study case. The power supply is based on the principle of vibration energy harvesting (VEH). The general architecture of the linear generator with electronic is presented. It is composed of commercially available components as a MIDE PPA 1014 piezoelectric cantilever beam and a LTC3588 circuit to extract and shape the electrical energy. The energy source comes from mechanical vibrations measured on the industrial environment in operation. A tunable mechanism of the resonance frequency is added in order to have a wider range of use than the natural range of a linear harvester. To adapt the VEH according with the source, it resonant frequency range can be tuned with a dedicated tip-mass. Then a fine adjustment within a range of about 20 Hz is set using both a moving clamping device and a temporarily wired electronic device working as a maximum power point finder (MPPF). To achieve a long lifetime, the storage is done using balanced supercapacitors. Two operational demonstrators are shown. The test benches as well as numerous experimental tests are presented. Shaped according to the industrial environment (49.0 Hz @ 2.7 m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), the VEH is capable of delivering continuously 100mA@3.3V with 200 mA peaks. When the power harvested ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 2.9$ </tex-math></inline-formula> mW) is upper than the sensor average power, it offers the capability to store 17.5 J at 18.5 V. As a result, from this work, a WSN can successfully operate over a significantly long period of time despite fluctuations in the vibration source.

Topological optimization of a variable cross-section cantilever-based piezoelectric wind energy harvester

Wind energy is a typical foreseeable renewable energy source. This study constructs and optimizes a variable cross-section cantilever-based piezoelectric energy harvester for low-speed wind energy harvesting. The Galerkin approach is usually used to discretize the continuum model and then get the ordinary differential equations. However, this method is more suitable for calculating uniformity than the variable cross-sectional beam model. To solve this problem, we proposed an improved piecewise Galerkin approach for discretizing the continuum model with a variable cross section. By modifying the boundary expressions and modal functions between segments, it can improve both computation speed and accuracy. COMSOL simulations demonstrate that natural frequencies calculated via the improved method are more accurate than those of the traditional Galerkin method. The method of multiple scales is applied to determine the output power and critical wind velocity. A distinctive numerical approach is presented for shape optimization by combining the analytical calculation method with the particle swarm optimization (PSO) technique for low-speed wind energy harvesting. Additionally, the logic function is chosen to produce the optimal shape’s fitting expression for engineering applications. With all the improvements, the output power of a variable cross-section beam-based harvester reaches as much as 3.668 times that of a uniform beam model, demonstrating the importance of structural optimization for this type of energy harvesters. Finally, experiments are set up to verify the optimization procedure. Actually, it builds an analytical framework for the adaptive selection of variable-section piezoelectric cantilever wind-induced vibration energy harvesters.

Vibration energy harvesting via piezoelectric bimorph plates: An analytical model

Vibration energy harvesting using piezoelectric cantilevers has been widely studied during the past decade. As an alternative to piezoelectric cantilevers, plate-like energy harvesters can be much more effective in marine, aerospace, and automotive applications. This work presents an exact two-dimensional model that can be used for analyzing thin, moderately thick, and thick piezoelectric bimorph plate vibration harvesters. The model allows to consider for the substrate layer both homogenous materials, and those with varying properties along the thickness direction. For the latter case, porous materials with various porosity distributions are herein considered, and the piezoelectric layers are assumed to be wired in both parallel and series configurations. Rayleigh damping assumptions are also used to model the structural damping of the harvesting system. Using Hamilton’s principle and Gauss’s law, the energy harvesting model is established based on the first-order and the third-order shear deformation theories. Applying an analytical procedure to the electromechanical governing equations, closed-form steady-state response expressions, which relate the voltage output and the vibration response of the harvester to harmonic input force, are derived. Finally, the proposed model is validated, and the power generation performance of the plate harvester is discussed through conducting extensive parametric studies, covering the effect of design parameters, such as the applied electric load, porosity characteristics, electrical configuration, and geometrical parameters.