Unimorph Piezoelectric Cantilever Research Articles

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.

A miniature piezoelectric pump with high performance

The high performance and miniaturization of the piezoelectric pump are essential for its application. A single-chamber piezoelectric pump with a circular unimorph piezoelectric actuator and cantilever check valves is proposed in this work, which has good output performance and smaller overall size. The working principle of the piezoelectric pump was described, and the theoretical working characteristics of the cantilever check valve were analyzed in detail. The corresponding experimental prototype was made for the output performance assessment. The experimental results show that the pump has good self-suck ability under well-assembled process conditions, which provides a guarantee for the high flow rate and the output pressure of the piezoelectric pump. The maximum flow rate of 4.5 ml/min is obtained when the pump is driven by an offset sinusoidal voltage of 180Vpp at 50 Hz; the maximum output pressure of the pump reaches 52 kPa under 180Vpp at 150 Hz. In addition, at 70 Hz, 180Vpp, the comprehensive performance of the piezoelectric pump is better, with a flow rate above 3 ml/min and an output pressure over 35 kPa. The proposed piezoelectric pump has the characteristics of simple structure, high performance, small size, and low cost, which can be applied in microelectronic cooling, biomedical, and other fields.

Piezoelectric unimorph and bimorph cantilever configurations: Design guidelines and strain assessment

Multi-stable configurations of piezoelectric harvester are quite successful in achieving the two important goals, the broadband frequency response and large orbit oscillations exhibiting periodic, multi-periodic, and chaotic solutions. However, in the quest of achieving large amplitude broadband frequency response, assessment of induced strain levels considering the limits on the strain in piezoelectric material has received minimal attention. In this context, the investigation presents analytical formulation for the assessment of induced strain and voltage(s) in piezoelectric unimorph and bimorph cantilevers. The formulation quantifies not only the induced voltages in individual piezoelectric layers of a bimorph, but also the equivalent voltages in parallel and series connection modes, respectively. Also, while computing the induced voltage in the first piezoelectric layer, the contribution from the induced voltage of second piezoelectric layer to the acting bending moment is captured in the formulation. The formulations are validated through the experiments and results from the literature. Further, we have applied two practically useful normalization schemes, the - and -normalizations to the analytical expressions. Using the two normalization schemes, influences of variation of substrate and adhesive layer thicknesses, elastic moduli of layers, and substrate-to-composite length fraction are visualized and discussed. Based on the results, summarized guidelines for design and selection of geometric and material parameters are presented, which may also be applicable for other sensing and actuation applications. At last, practically suitable ranges and optimum values for the normalized design variables are proposed.

Energy harvesting efficiency of unimorph piezoelectric acoustic black hole cantilever shunted by resistive and inductive circuits

A unimorph piezoelectric cantilever equipped with an Acoustic Black Hole (ABH) termination is designed for broadband energy harvesting. The ABH termination, with its tapered region, induces a focusing of the flexural vibrations which can be used to increase the efficiency of an energy harvesting device. A modal-based analytical model is presented, providing an explicit form of the electro-mechanical coupling for each beam eigenmode. Closed-form expressions for the coupled mechanical response and electrical outputs are obtained, allowing one to draw out a complete parametric study to optimize the device. The optimization procedure is conducted following two steps: first, optimal location and dimensions of a single piezoelectric patch are achieved by maximizing the modal electro-mechanical coupling factor (MEMCF) for each structural mode. Thanks to the proposed analytical approach, it is clearly shown that by putting the piezoelectric patch at the maximum of the strain field in the tapered termination, and by adjusting its length in accordance with the focalization created by the ABH effect, the ABH cantilever produces much higher MEMCFs over a wide frequency range and thus outperforms those of a uniform beam. Second, optimization of the shunted circuit is comprehensively performed for a circuit with only resistance, or both resistance and inductance, in series or in parallel. Analytical results show that the key design rule resides in matching the time scale of the circuit with that of the forcing frequency. Addition of the inductance allows enhancing the performance, but on a narrow frequency band. Finally, broadband advantages can be further obtained by considering multiple piezoelectric patches, in which the optimum is obtained when the shunted circuit in each patch is tuned targeting an eigenmode of the ABH beam.

Analysis of Energy Harvesting Enhancement in Piezoelectric Unimorph Cantilevers.

Environmental energy harvesting is a major operation in research and industries. Currently, researchers have started analyzing small-scale energy scavengers for the supply of energy in low-power electrical appliances. One area of interest is the use of piezoelectric materials, especially in the presence of mechanical vibrations. This study analyzed a unimorph cantilever beam in different modes by evaluating the effects of various parameters, such as geometry, piezoelectric material, lengths of layers, and the proof mass to the energy harvesting process. The finite element method was employed for analysis. The proposed model was designed and simulated in COMSOL Multiphysics, and the output parameters, i.e., natural frequencies and the output voltage, were then evaluated. The results suggested a considerable effect of geometrical and physical parameters on the energy harvesters and could lead to designing devices with a higher functional efficiency.

Electromechanical simulation and analysis of perovskite piezoelectric ‎unimorph cantilever nanogenerator with interdigitated electrodes in ‎vibration energy harvesting application

This paper addresses a unimorph cantilevered piezoelectric nanogenerator having high ‎output power through vibrational energy harvesting that is simulated using finite element ‎method (FEM). The simulations are done for three types of perovskite piezoelectric ‎materials including PZT, PMN-PT and MAPbI3. The interdigitated electrodes were ‎exploited‏ ‏to obtain longitudinal vibration mode using d33 mode of piezoelectric layer during ‎the bending of nanogenerator structure. The presented structure consists of a piezoelectric ‎nanolayer with gold interdigitated electrodes on it, which is placed on a flexible PET ‎polymeric substrate. To encapsulate the piezoelectric layer, an SU-8 epoxy is placed over ‎the surface. The poling process is also simulated by applying high voltage through IDs to ‎piezoelectric layer. Generally, the electric potential distribution of the piezoelectric layer ‎must be performed by applying mechanical loadings. Then the output voltage, ‎power for free vibrations and base excitation (0.25-2g) of the nanogenerator at resonance ‎frequency are investigated. The resonance frequency of the PZT, PMN-PT, and MAPbI3 were ‎calculated to be 549 Hz, 560.5 Hz and 631 Hz, respectively. We found that PZT ‎piezoelectric materials yields maximum output voltage and electrical power values of 91.69 ‎V and 350 mW which shows better performance in vibrational energy harvesting ‎application. In comparison, the results of the simulation implied a good agreement with ‎other experimental studies. The unimorph piezoelectric energy harvester system generates ‎high voltage and output power in response to sub-kilohertz ambient vibration‎.‎‎

Modeling of a Symmetric Five-Bar Displacement Amplification Compliant Mechanism for Energy Harvesting.

This paper presents an analytical model to determine a closed form mathematical representation for the output displacement of a displacement amplification compliant mechanism used for energy harvesting. A symmetric five-bar compliant mechanism with right-circular and corner-filleted flexure hinges was mathematically modeled and its displacement was determined using the Castigliano energy theorem. The stresses within the flexure joints, the weakest points in the mechanism body, were calculated. The mathematical model expresses both the displacement amplification and the stresses as functions of the design parameters and the load caused by the harvester. The developed model can be used to optimize the mechanism dimensions for maximum harvested power, while minimizing its structural stresses. The mechanism was also modeled numerically using finite element methods; both the analytical and numerical models were verified experimentally. The mathematical model of the mechanism was integrated with a model representing a piezoelectric energy harvester to calculate the open-circuit voltage. As a proof of concept, experiments were performed using an unimorph piezoelectric cantilever at low-frequency (less than 1 Hz) harmonic excitation inputs. The measured open-circuit voltage was found to be in agreement with that calculated using the proposed model, when integrated with the model representing the piezoelectric beam. The power generated by the piezoelectric harvester, equipped with the proposed displacement amplification mechanism, was more than a hundred times that without amplification.

Modeling and simulation of a gauge shaped beam coupled with macro fiber composite for energy harvesting application

This paper presents a novel unimorph piezoelectric cantilever with non-conventional geometry named as gauge shaped beam to investigate stress, Eigen frequencies and electric potential for improved vibration energy scavenging. The harvester is made of macro fiber composite (MFC) as the active piezoelectric layer bonded to a brass substrate. Complete transversely isotropic elastic and piezoelectric properties are assigned to the composite structure in a three-dimensional finite element model using COMSOL Multiphysics. Dynamic behaviour of the proposed structure was simulated and the results obtained were compared with traditional rectangular geometry. The results proved that the gauge shaped beam has a higher stress distribution around the gauge length, enhanced electric potential and lower resonance frequencies than the conventional rectangular structure which makes it better for the design of piezoelectric based vibration energy harvesters.

Modelling and analysis of a piezoelectric unimorph cantilever for energy harvesting application

ABSTRACT Piezoelectric energy generator with an unimorph cantilever working in 31-mode can convert external mechanical stimuli into electrical energy. Its potential application includes wireless sensor network and integrated electronic devices. In this work, an unimorph cantilever subjected to an external mechanical excitation is discussed. Analytical expressions relating generated electric charge, the open voltage and generated energy to the applied mechanical excitation are derived based on the constitutive equations of piezoelectric material. The dependence of charge, voltage and energy sensitivities on elastic modulus ratio and thickness ratio of the elastic substrate and piezoelectric layer under different conditions are also examined. The primary focus of this work is to investigate some geometrical parameters in order to improve the generated energy of the desired piezoelectric energy harvester by developing a model. Such model is also in a good agreement with the experiment results.

Energy harvesting performance of unimorph piezoelectric cantilever generator using interdigitated electrode lead zirconate titanate laminate

An unimorph piezoelectric cantilever generator with an interdigitated electrode (IDE) was developed for application to vibration energy harvesters driven in longitudinal mode. Lead zirconate titanate (PZT) thick film was fabricated by lamination of 10 sheets printed with Ag IDE; the laminated film was subsequently cofired at 850 °C for 2 h. Compared with a conventional IDE PZT thick film, the approximately 270 ㎛-thick cofired IDE PZT laminate revealed a significantly increased capacitance due to reduction of transition area. The use of multilayered IDE could result in the enhancement of energy harvesting performance for unimorph piezoelectric cantilever generator using PZT laminate. Optimized bending resonance frequency was obtained at 78 Hz for the unimorph piezoelectric cantilever generator with tip mass of 2.3 g driven in longitudinal vibration mode. Its energy harvesting performance was characterized as having a high power density of 26.7 mW/cm3 across the resistive load of 80 kΩ, corresponding to a normalized power factor of 6.7 mW/G2·cm3.

Precise, Long-Time Displacement Self-Sensing of Piezoelectric Cantilever Actuators Based on Charge Measurement Using the Sawyer–Tower Circuit**Supported by the National Natural Science Foundation of China under Grant No 11521202.

Previous studies show that near linearity exists between displacement and charge of piezoelectric actuators, while studies under higher fields are lacking and long-time displacement self-sensing is still a challenge. Here we indicate that precise, long-time displacement self-sensing can be accomplished using the Sawyer–Tower circuit, where a high-impedance electrometer and a non-leaky capacitor are used to measure the charge. Calibrating the results on a piezoelectric unimorph cantilever shows that the displacement resolution of charge self-sensing is ∼3 nm, much better than that of ∼40nm for the calibrating laser sensor. Testing results under a unipolar field up to 2 kV/mm with different periods indicate that a direct proportional relationship holds between charge and displacement with the maximum error of 4.65%. The self-sensing time can be over 20 min or even longer if a higher-impedance electrometer is used.

Performance of non-uniform cantilever based piezoelectric energy harvester

Cantilever based piezoelectric energy harvesters (PEHs) have been optimized in terms of shape, size, material properties and damping to improve their electrical outputs. In most of the PEHs, a cantilever beam with width of rectangular, triangular and trapezoidal shapes, respectively, have been analyzed in optimizing the power output. In this paper, we investigate the influence of non-uniform beams with linearly and quartic varying widths. To analyze the model, we first modify the electromechanical formulation of uni-morph piezoelectric cantilever beam with uniform section to include the non-uniform variation of beam width. Subsequently, we obtain the voltage, current and the power output versus frequencies at different external loads for uniform and non-uniform beams with varying tapering parameters. Based on the analysis, we found that the diverging beam with tapering parameter of 0.6 can produce an enhanced power output by 3833% as compared to that of uniform beam. Since, the frequency also changes due to change in the tapering parameter of non-uniform beam, such significant changes in the output are also demonstrated for designing a wide band PEH based on an array of uniform and non-uniform beams. Finally, we also performed numerical study of PEHs of unimorph as well as coupled beams with uniform and non-uniform sections.

Modeling and simulation for low-frequency vibration energy harvesting based on piezoelectric unimorph cantilever beam

In order to solve the problem of sustainable energy supply for low-power electronic products used in low-frequency vibration environment, the mathematic model was established based on the theory of piezoelectricity and Euler-Bernoulli beam. Also, the effects of different parameters of PZT unimorph beams such as the length, width, and tip mass on generating capacity were studied by FEM. The results show that the energy harvester with PZT unimorph beam and tip mass is suitable for low-frequency vibration environment. Increasing the length or reducing the width of the beam can significantly lower the first-order modal frequency of energy harvester when other conditions remain the same. Within certain range, the first-order modal frequency of the beam also gradually reduced as the tip mass increasing. When the size of the PZT unimorph beam is 60x60x0.33mm, the tip mass is 8.92g and an exciting force of 0.01N is applied to it along z axis, an output of 8.1V can be obtained. Meanwhile, the PZT unimorph beam is under the first vibration mode and the resonant frequency is 16.296Hz.

Fabrication and energy harvesting characteristics of unimorph piezoelectric cantilever generators with interdigitated electrode lead zirconate titanate laminates

Interdigitated electrode (IDE) unimorph piezoelectric cantilever generators (UPCGs) were fabricated and their energy harvesting characteristics were investigated. A hard lead zirconate titanate (PZT) material with a high mechanical quality factor (Qm) of 1280 was used for the active piezoelectric film of the IDE UPCGs. Two different laminated IDE UPCGs were prepared; one has Ag/Pd interdigitated electrode (IDE) formed only on the top and bottom PZT sheets (D-IDE), while the other has Ag/Pd IDE on all of the PZT sheets (M-IDE). Cofiring was conducted at 1050 °C for 2 h for PZT laminates with IDEs. The fabricated IDE UPCGs exhibited power densities of 50.4 µW/cm3 for the D-IDE and 820 µW/cm3 for the M-IDE. The UPCG with the M-IDE exhibited a higher performance than that with the D-IDE. Specifically, a significantly enhanced normalized power factor of 670 µW/(g2·cm3) was found at 118 Hz across 100 kΩ.

Optimization of unequal-active-and-passive-area piezoelectric unimorph cantilevers with collisions for ultra-thin keyboard design

The purpose of this study is to optimize the design of piezoelectric unimorph cantilevers, for ultra-thin keyboard design, so that the first resonant frequency is located in the sensitive frequency range and the first resonant amplitude is above the perception threshold of human hands for vibratory stimulus. The piezoelectric unimorphs used in this study have unequal active and passive areas. Simulations and experiments were first compared to find the effects of the dimensions on the first resonant frequency and displacement frequency response without collisions. A finite element model with collisions based on the verified boundary conditions was then built. Both the experiment data and simulation data was combined to build a regression model to predict the first resonant frequency with collisions for ultra-thin keyboard design. This study can help designers quickly design a vibrotactile device, in the early design stage.

Power enhancement of broadband piezoelectric energy harvesting using a proof mass and nonlinearities in curvature and inertia

This paper investigates the mechanical behavior of a unimorph piezoelectric cantilever beam with a tip mass subjected to a harmonic base excitation for energy harvesting. The energy harvester is modeled as an in-extensional beam with Euler–Bernoulli assumptions. The curvature and the inertia terms are assumed to be nonlinear due to large amplitude vibrations. The governing equations of motion are derived using the Euler–Lagrange equations. The reduced-order model equations (ROMs) are obtained based on the Galerkin method. A parametric study is performed to reveal the influence of different parameters such as proof mass, damping ratio and external resistance load on the scavenged power from the nonlinear energy harvester. It is shown that the addition of a sufficient large tip mass, significantly increases the power and the voltage. The effect of the tip mass on the Fast Fourier Transform (FFT) of the tip displacement and generated voltage is studied, and it is shown that in the presence of the tip mass two frequencies of the system are excited in contrast to the no tip mass case in which one frequency is excited. Furthermore, it is observed that the second excited frequency is three times of the first one, and due to the small amplitude ratios of the tip displacement of the second frequency to the first frequency, the second frequency can be neglected. Energy conservation is examined in the absence of the mechanical damping, and it is shown that energy harvesting annihilates the vibrations. In addition, the effect of the external resistance load on the average power is discussed in the presence and absence of the tip mass and the optimum value of the resistance load is obtained for each system. Some results obtained from MATLAB software were validated by using FE analysis with commercial software COMSOL, and a good accordance was shown between the results obtained from mentioned methods.

Parameter identification of partially covered piezoelectric cantilever power scavenger based on the coupled distributed parameter solution

ABSTRACTAmong the various techniques of power scavenging, piezoelectric energy harvesting usually has more power density. Although piezoceramics are usually more efficient than other piezoelectric materials, since they are very brittle and fragile, researchers are looking for alternative materials. Recently Cellulose Electro-active paper (EAPap) has been recognized as a smart material with piezoelectric behavior that can be used in energy scavenging systems. The majority of researches in energy harvesting area, use unimorph piezoelectric cantilever beams. This paper presents an analytical solution based on distributed parameter model for partially covered pieoelectric cantilever energy harvester. The purpose of the paper is to describe the changes in generated power with damping and the load resistance using analytical calculations. The analytical data are verified using experiment on a vibrating cantilever substrate that is partially covered by EAPap films. The results are very close to each other. Also asymptotic trends of the voltage, current and power outputs are investigated and expressions are obtained for the extreme conditions of the load resistance. These new findings provide guidelines for identification and manipulation of effective parameters in order to achieve the efficient performance in different ambient source conditions.

Optimal design of a unimorph piezoelectric cantilever devoted to energy harvesting to supply animal tracking devices

This paper presents the mechanical structure optimization of a piezoelectric energy harvesters devoted to supply embedded animal tracking devices. The harvester mechanical structure being a bilayer unimorph piezoelectric cantilever is composed of two elements: a piezoelectric layer and a non-piezoelectric layer (i.e, active and passive layers). The suggestion of this paper is to find the optimal ratio between their two thicknesses in order to maximize the output recuperated voltage at the electrodes. For that, from the model that links the mechanical excitation moment and the output electrical charge, a gradient-based optimization is carried-out. Comparison with existing mechanical piezoelectric harvester structure is made and which clearly demonstrates that the proposed structure permits to gain up to five-times in terms of the output charge and a significant gain in terms of output electrical power for the same condition.

Modeling and Analysis the Effect of PZT Area on Square Shaped Substrate for Power Enhancement in MEMS Piezoelectric Energy Harvester

Modeling and analysis of a MEMS piezoelectric (PZT-Lead Zirconate Titanate) unimorph cantilever with different substrates are presented in this paper. Stainless steel and Silicon [Formula: see text] are considered as substrate. The design is intended for energy harvesting from ambient vibrations. The cantilever model is based on Euler–Bernoulli beam theory. The generated voltage and power, the current density, resonance frequencies and tip displacement for different geometry (single layer and array structure) have been analyzed using finite element method. Variation of output power and resonant frequency for array structure with array elements connected in parallel have been studied. Strain distribution is studied for external vibrations with different frequencies. The geometry of the piezoelectric layer as well as the substrate has been optimized for maximum power output. The variation of generated power output with frequency and load has also been presented. Finally, several models are introduced and compared with traditional array MEMS energy harvester.

Modeling and simulation of a deformed smart structure using piezoelectric patch

PurposeSafety improvement and cost reduction have a strong influence on the way to achieve maintenance operations of complex structures, in particular in air transportation, in civil engineering and others. In this case, piezoelectric ceramics such as sensors and actuators have been used. The advantages of piezoelectric materials include high achievable bandwidth, reliability, compactness, lightness and ease of implementation, thus making them well-suited to be used as actuators and sensors in the case of onboard structures. In this context, this study based around the examination of health and deformation of smart structures, taking into consideration the mechanical and piezoelectric behaviour of sensors and actuators, mechanical contact as well as the initial conditions and the imposed boundary conditions. This paper aims to present an approach for modeling of an intelligent structure by the finite element method. This structure is of aluminum type beam with elastic behaviur where piezoelectric rectangular pellets discreetly spread on the surface of the beam are instrumented. The numerical results were computed and compared to the experimental tests available in the literature and the results show the effectiveness of these piezoelectric (PZT) elements, depending on their positions, and to control the deformed structure, good agreement has been found between the experimental data and numerical predictions.Design/methodology/approachNumerical modeling by finite elements model for the measurement of the deformation and the change in shape of a clamped-free structure composed of both elastic and piezoelectric materials have been given by using the Ansys® software. The numerical results were valid by comparisons with analytical and experimental results find in the literature.FindingsThe numerical results showing a good correlation and agree very well. It was also concluded that the actuator and the sensor will be better placed at the housing because it is the position or the actuator that has the greatest impact and where the sensor gives the greatest signal. They are said to be co-located as glues one below the other on either side of the beam.Originality/valueThese materials have an inverse piezoelectric effect allowing them to control the form and present any noise or vibration at any time or position on the structure. The study presented in this paper targets the modeling of a PZT beam device for deform generation by transforming electrical energy into usable load. In this paper, a unimorph piezoelectric cantilever with traditional geometry is investigated for micromanipulation by using the software Ansys®.