Electrical-mechanical Coupling Research Articles

Design and kinetic analysis of piezoelectric energy harvesters with self-adjusting resonant frequency

Vibration-based energy harvesters have been developed as power sources for wireless sensor networks. Because the vibration frequency of the environment is varied with surrounding conditions, how to design an adaptive energy harvester is a practical topic. This paper proposes a design for a piezoelectric energy harvester possessing the ability to self-adjust its resonant frequency in rotational environments. The effective length of a trapezoidal cantilever is extended by centrifugal force from a rotating wheel to vary its area moment of inertia. The analytical solution for the natural frequency of the piezoelectric energy harvester was derived from the parameter design process, which could specify a structure approaching resonance at any wheel rotating frequency. The kinetic equation and electrical damping induced by power generation were derived from a Lagrange method and a mechanical–electrical coupling model, respectively. An energy harvester with adequate parameters can generate power at a wide range of car speeds. The output power of an experimental prototype composed of piezoelectric thin films and connected to a 3.3 MΩ external resistor was approximately 70–140 μW at wheel speeds ranging from 200 to 700 RPM. These results demonstrate that the proposed piezoelectric energy harvester can be applied as a power source for the wireless tire pressure monitoring sensor.

Electret Length Optimization of Output Power for Double-End Fixed Beam Out-of-Plane Electret-Based Vibration Energy Harvesters

Thanks to miniaturization, it is now possible to imagine self-powered systems that can harvest energy from the environment to produce electrical energy. Out-of-plane electret-based vibration energy harvesters (E-EVHs) are an effective and inexpensive energy harvester type that has attracted much attention. Increasing the capacitance of variable capacitors is an effective way to improve the output power of E-EVHs. In this paper, firstly an accurate capacitance theoretical model of a double-ended fixed beam out-of-plane E-EVHs which has 97% reliability compared with FEM (COMSOL Multiphysics) results is presented. A comparison of capacitance between the double-ended fixed beam structure and a cantilever structure of the same size indicates that the double-ended fixed beam structure has greater capacitance and capacitance variation. We apply this theoretical capacitance model to the mechanical-electrical coupling model of double-ended fixed beam out-of-plane E-EVHs and study harvesters’ output performances for different electret lengths by numerical and experimental method, respectively. There exists an optimal electret length to harvest maximum power in our simulation results. Enhanced electrostatic forces with increasing the electret length emphasizes the soft spring effect, which widens the half power bandwidth and lowers the resonance frequency. Increasing the length of the electret can reduce the resistance of the optimum load. The experimental results show trend consistent with the numerical predictions. The maximum output power can reach 404 µW (134.66 µW/cm2/g) at the electret length of 40 mm when the external acceleration and the frequency were 5 m/s2 and 74 Hz, respectively. The maximum bandwidth reaches 2.5 Hz at the electret length of 60 mm. Therefore, the electret length should be placed between 40 mm and 60 mm, while ensuring a higher output power and also get a larger bandwidth in practical applications.

An investigation on the aggregate-shape embedded piezoelectric sensor for civil infrastructure health monitoring

In this paper, a new type of aggregate-shape embedded piezoelectric sensor for health monitoring of civil infrastructures was developed. The sensor was designed by using piezoelectric ceramic chip as the functional phase, and a new composite material as packaging phase. 3D printing technology was also used for packaging system design and sensor fabrication. The frequency independence, linearity, sensitivity, response rate, and service performance of the sensor were tested by frequency scanning and amplitude scanning. Experimental results show that within the vibration frequency range of common civil engineering structures, the new aggregate-shape embedded piezoelectric sensor has good mechanical and workability properties. Test results also show that the new embedded sensors have very good mechanical-electrical coupling performance, which builds a solid foundation for further application in the civil engineering infrastructures.

HOLE PROBLEMS IN A CIRCULAR PIEZOELECTRIC PLATE

Due to the unique electric-mechanical coupling effects, piezoelectric materials are widely used in sensors and actuators. Not only in smart structures but also in structural health monitoring, the developments of piezoelectric materials combined with the micro electro mechanical system (MEMS) techniques make our lives totally different. This paper provides a series of numerical simulations about the circular piezoelectric plate with a hole in the plate by using the special boundary element method (BEM). The Green’s functions of BEM are obtained from the derivation of extended Stroh formalism. By this formalism, the analytical closedform solutions of hole in an infinite piezoelectric medium under various loading conditions are obtained. The results demonstrate the coupling effects with different boundary conditions in the circular plate, which will satisfy the requirements of the designers who need to use the products with the hole in the piezoelectric circular plate.

Design Optimization of PZT-Based Piezoelectric Cantilever Beam by Using Computational Experiments

Piezoelectric energy harvesting is gaining huge research interest since it provides high power density and has real-life applicability. However, investigative research for the mechanical–electrical coupling phenomenon remains challenging. Many researchers depend on physical experiments to choose devices with the best performance which meet design objectives through case analysis; this involves high design costs. This study aims to develop a practical model using computer simulations and to propose an optimized design for a lead zirconate titanate (PZT)-based piezoelectric cantilever beam which is widely used in energy harvesting. In this study, the commercial finite element (FE) software is used to predict the voltage generated from vibrations of the PZT-based piezoelectric cantilever beam. Because the initial FE model differs from physical experiments, the model is calibrated by multi-objective optimization to increase the accuracy of the predictions. We collect data from physical experiments using the cantilever beam and use these experimental results in the calibration process. Since dynamic analysis in the FE analysis of the piezoelectric cantilever beam with a dense step size is considerably time-consuming, a surrogate model is employed for efficient optimization. Through the design optimization of the PZT-based piezoelectric cantilever beam, a high-performance piezoelectric device was developed. The sensitivity of the variables at the optimum design is analyzed to suggest a further improved device.

Density functional studies on wurtzite piezotronic transistors: influence of different semiconductors and metals on piezoelectric charge distribution and Schottky barrier

The mechanical–electrical coupling properties of piezoelectric semiconductors endow these materials with novel device applications in microelectromechanical systems, sensors, human–computer interfaces, etc. When an applied strain is exerted on a piezoelectric semiconductor, piezoelectric charges are generated at the surface or interface of the semiconductor, which can be utilized to control the electronic transport characteristics. This is the fundamental working mechanism of piezotronic devices, called the piezotronic effect. In the present report, a series of piezotronic transistors composed of different electrode metals and semiconductors is examined using density functional theory calculation. It is found that the influence of semiconductors on the piezotronic effect is larger than the impact of metals, and GaN and CdS are promising candidates for piezotronic and piezo-phototronic devices, respectively. The width of the piezoelectric charge distribution obtained in the present study can be used as a parameter in classical finite-element-method based simulations, which provide guidance on designing high-performance piezotronic devices.

Theoretical study on thermal and acoustic surface wave properties of Ga3PO7 crystal at high temperature

The high-temperature piezoelectric crystal Ga3PO7is a versatile functional material widely used in many electromechanical devices. As the Curie temperature of this crystal is as high as 1346 ℃, it can break through the current temperature limitations(1200 ℃) and then be used in extremely high-temperature condition. However, it is very difficult to explore its properties in such a high-temperature environment. Moreover, the relevant theoretical research has not been reported to date. Aiming at this problem, the density function theory combined with quasi harmonic approximation theory is used to investigate the structural, thermal and surface acoustic wave (SAW) properties of Ga3PO7. Firstly, the Gibbs energies of Ga3PO7 crystal with different stains are calculated, and the equilibrium structures of Ga3PO7 crystal at different temperatures (from 0 ℃ to 1200 ℃) are found according to minimal energy principle. Secondly, based on the result above, we optimize Ga3PO7 crystal at different temperatures, and then, the thermal and elastic properties of Ga3PO7 crystal within 0-1200 ℃ are calculated using CASTEP package based on the density functional theory in the generalized gradient approximation. The results show that its lattice constants increase almost linearly as temperature increases while its density decreases. Owing to anisotropy, its lattice constant along the c axis increases much more greatly than along the a axis. The coefficients of thermal expansion along the a and c axis are evaluated to be 1.6710-6 K-1 and 3.5810-6 K-1, respectively, and the volumetric heat capacity is evaluated to be 2.067 J/gK. These values all agree well with the experimental values. Finally, the elastic constants, bulk modulus and SAW properties of Ga3PO7 crystal at different temperatures (from 0 ℃ to 1200 ℃) are calculated. The results show that the bulk modulus can reach 175 GPa, and it changes very little as temperature increases. The fluctuation of elastic constants has slight influences on SAW velocity and the electric-mechanical coupling factor. When the propagation angle is 151, it possesses the stablest SAW properties and the largest electric-mechanical coupling factor which can reach 0.7%. The comprehensive analyses of the thermal, mechanical and SAW properties show that Y-cut Ga3PO7 possesses a greater potential application in high temperature environment.

Some aspects of coupled electrical-mechanical effects in dielectric materials

The propensity of electrically insulating materials to generate/store electrical charges leads to a panel of electromechanical phenomena that can be either exploited in applications relevant to electrical engineering, or represent limitations in the performance of insulating materials. The aim of this contribution is to describe various features of these electrical-mechanical coupling phenomena with focus on the field-induced strain measurement of charged polymers, on the charge distribution measurement by pulsed electroacoustic method and on the contribution of electromechanical effects in electrical ageing phenomena.

Electric field induced variation of temperature and entropy in dielectric elastomers

Dielectric elastomer is a kind of typical electro-active polymer material. Under external electric field it can produce large electrostriction deformation and possesses the advantages of high elastic energy density, super short response time, high efficiency, and so on. It is widely used in the artificial muscles, facial expressions, actuators, energy harvesters, sensors, robots and Braille display devices, and also shows huge application potential in the aerospace and intelligent bionic areas. We built the free energy of the dielectric elastomer electrical-mechanical coupling system and investigated its constitutive relation and stability behavior. Then we calculated the elastomer’s critical deformation suffering from the voltage. If electrical breakdown, electromechanical instability and snap-through instability can be avoided, the large electrostriction deformation can induce adiabatic temperature change and isothermal entropy change of the dielectric elastomer. We used the entropy-temperature or electric displacement-electric field plane to describe the temperature change and entropy change of dielectric elastomer undergoing large electrostriction deformation. With the influence of temperature, we developed a temperature and deformation coupling thermodynamical free energy model to calculate the electric field induced variation of temperature and entropy in dielectric elastomers. The results should offer great help in guiding the design and fabrication of excellent actuators featuring soft dielectric elastomers.

Cantilever Beam Based Piezoelectric Energy Harvester

Abstract With the application of wireless sensor networks become widespread, supply energy for these wireless sensors proves to be a significant issue. Moreover, for the ambient vibration lies everywhere, the vibration can supply energy for the wireless sensor via energy harvester. The piezoelectric energy harvester becomes the research focus for the simple structure and higher energy conversion efficiency. Due to the transcendental equation in distributed parameter model, the numerical method is become powerful complement for theoretical and experimental method. This paper uses ANSYS to analyze the single piezoelectric cantilever in static analysis, model analysis, harmonic response analysis and mechanical-electrical coupling analysis. It analyzes the natural frequency and voltage effect from four aspects which are length to thickness ratio, length to width ratio, the substrate thickness to piezoelectric thickness ratio and seismic mass. Test and measurement for piezoelectric energy harvester is conduct on the testing platform. Macro cantilever beam piezoelectric energy harvester are tested and measured

A Single-Inductor 0.35 µm CMOS Energy-Investing Piezoelectric Harvester

Because miniaturized systems store little energy, their lifespans are often short. Fortunately, vibrations are consistent and abundant in many applications, so ambient kinetic energy can be a viable source. Vibrations induce the charges in piezoelectric transducers to build electrostatic forces that damp vibrations and convert kinetic energy into the electrical domain. The shunting switches and switched-inductor circuit of bridge rectifiers in [1-2] increase this output energy by extending the damping (i.e., harvesting) duration within a vibration cycle. Because the output voltages of bridge rectifiers clamp and limit the electrical damping forces built, switched-inductor converters in [3-4], whose damping voltages can exceed their rectified outputs, draw more power from vibrations. Still, electrical-mechanical coupling factors in tiny transducers are low, so electrical damping forces (i.e., voltages) remain weak. Investing energy into the transducer can increase this force, but unlike in [5-6], which demand multiple inductors and high-voltage sources, the system presented here invests energy with only one inductor at low voltages.

Simulation and Test for the Lightning Damage of the Glass Fiber Composites

Theoretical deducing, simulated lightning test and finite element simulation are used to research the mechanism and state of lightning damage of the aircraft composites sandwich panels. It provides the basis for the design of the aircraft lightning protection. The three-dimensional finite element model of the composites panel is constructed through the thermal electrical-mechanical multi-Physics coupling field. According to the structure and the role process, the lightning effect of the aircraft composites is analysed to study the damage mechanism and the possible state of the composites panel that is struck by lightning. The impact current generator is used to carry out the simulated lightning test to observe the lightning effect of the composites panel. By comparing the results of the test and the simulation, the effectiveness and the correctness of the simulation are verified.

Simulation and measurement of the flip chip solder bumps with a Cu-plated plastic core

With the aim to miniaturize and to reduce the cost, the increasing demand, regarding to advanced 3D-packages as well as high performance applications, accelerates the development of 3D-silicon integrated circuits. The trend to smaller and lighter electronics has highlighted many efforts towards size reduction and increased performance in electronic products. The radio frequency (RF) performances are limited by parasitic effects due to the resistor–inductor–capacitor (RLC) network, between the wire bond connections from the dies to the lead frame. The use of flip-chip bonding technology for very fine pitch packaging allows high integration and limits parasitic inductances. Electromigration (EM) and thermomigration (TM) may have serious reliability issues for fine-pitch Pb-free solder bumps in the flip-chip technology used in consumer electronic products. A possibility to extend the reliability is the use of plastic ball in the solder bumps. Bumps containing a plastic solder balls have an excellent reliability. Using a plastic ball with a low Young modulus, the solder hardness is moderated and the stress on a ball is relaxed. Due to this, the stress does not concentrate on the solder joint which prolongs the lifetime. In this investigation, the thermal–electrical–mechanical coupling of electromigration on bumps containing a plastic solder is studied.

Regions of latest mechanical contraction correspond to regions of latest electrical activation: an electro-mechanical coupling study in patients undergoing cardiac resynchronization therapy

Background Numerous studies have shown that placing the left ventricular (LV) pacing lead in the latest contracting region (mechanically dyssynchronous) or the latest activated region (electrically dyssynchronous) of the LV improves patient response to Cardiac Resynchronization Therapy (CRT). However, no studies have examined electrical and mechanical dyssynchrony in the same patients to examine electrical-mechanical coupling. We hypothesized that the region of latest mechanical contraction would correspond to the region of latest electrical activation but the time between mechanical and electrical activation would vary between patients.

Enhanced Sliding Mode Control with CEMF Compensation for Tracking Control of a Piezoactuated Flexure-Based Mechanism

This paper proposes an enhanced sliding mode controller (SMC) for piezoelectric actuator based flexural mechanism (PABFM) to track desired motion trajectories. First, based on the variable structural control approach, the proposed controller is established to accommodate parameter uncertainties, nonlinearity, and unmodelled disturbances. Because the traditional sliding-mode control cannot deal with mismatched disturbances effectively, a hysteresis counterelectromotive force (CEMF) model is proposed to describe nonlinear hysteresis effect and electric-mechanical coupling of PABFM. as Similar to the CEMF voltage for a motor caused by a changing electromagnetic field due to a rotating armature, the CEMF voltage appears to PA due to polarization and molecule friction of piezomaterial. The CEMF model is identified using a charge system search (CSS). Then, the proposed SMC with CEMF compensation is studied to deal with the mismatched nonlinear disturbances. To check the consistency of the proposed SMC controller with CEMF compensation, the simulation results were compared with the experimental results. The real-time implementation validated the tracking error better than the traditional SMC.

Assessing the relationship between the inter-rod coupling and the efficiency of piezocomposite high-intensity focused ultrasound transducers

The electroacoustic conversion efficiency of the ultrasonic transducer is a critical performance index for high-power applications. The material properties, volume fraction (VF) and aspect ratio (AR) are typically regarded as the design parameters of the piezocomposite transducer. We hypothesized that the spacing between piezoelectric rods was also a dominant factor. Therefore, the inter-rod coupling effects on the efficiency of 1–3 piezocomposite ultrasonic transducers were investigated in this study. The efficiencies of six flat and three curved 1.0MHz PZT4 epoxy composite transducers with different geometric parameters were measured. Finite element transient analyses of the inter-rod electrical-mechanical coupling in the composites were carried out to explain the measured results. The experimental results showed that for 0.47 AR, the 79% VF transducers had lower efficiency than the 64% VF and 53% VF transducers. For 0.19 AR, the efficiency of the 59% VF transducer was not greater than the efficiency of the 39% VF transducer. Numerical analyses demonstrated that the positive peak voltage induced by the coupling of the side rods was more than twice the level induced by the coupling of the diagonal rods for any spacing. The diagonal coupling voltage peak did not change for spacings larger than 0.2mm. Moreover, for spacings of 0.05 and 0.1mm, the inter-rod coupling caused 24% and 20% waveform shifts of the driving voltage, respectively, while the 0.2mm spacing coupling caused a 14% reduction in the amplitude of the driving voltage. As a result, the asymmetry of the driving voltage degraded the efficiency of the composite transducers and became more severe when the spacing was decreased. We concluded that the efficiency loss induced by inter-rod coupling as a function of spacing should be considered when designing piezocomposite transducers.

Wave propagation in a periodic elastic-piezoelectric axial-bending coupled beam

The wave propagation in a periodic elastic-piezoelectric axial-bending coupled beam is investigated in this paper by considering the mechanical–electrical coupling behavior. The strain energy and kinetic energy of each sub-cell are first formulated to extract the dynamic stiffness matrices, and then the compatibility and continuity conditions at the interface between the adjacent cells are utilized to derive the transfer matrix that governs the propagation of the wave along the periodic piezoelectric beam. By employing the Lyapunov exponent method, the dynamic behaviors of the periodic beam structure are evaluated with different base beam materials, dimension ratios, piezoelectric constants and elastic stiffness. The results indicate that regardless of the length ratio, there exist certain frequency intervals, where the width and magnitude of the prominent stop band of the aluminum beam with periodic piezoelectric patches are always broader and larger than those of the steel base system. In addition, as the thickness ratio decreases, the location of the stop band tends to move toward a higher frequency. Numerical studies also demonstrate that different piezoelectric constants and elastic stiffness affect the characteristics of wave propagation in completely different fashions. The investigation in the present study provides basic guidelines to design periodic elastic-piezoelectric laminate structures in order to achieve desired filtering characteristics.

Toughening effect of ferroelectric ceramics induced by domain switching and dislocations

The multi-scale analysis of fracture toughness of ferroelectric ceramics under complicate mechanical–electrical coupling effect is carried out in this paper. The generalized stress intensity factor (SIF) arising from spontaneous strains and polarization transformation in switching domain zones is accurately obtained by using an extended Eshelby theory. Taking BaTiO3 ferroelectric ceramic for example, it is discovered that the crack propagation can be induced by domain switching arising from negative electrical field when the crack surface is parallel to the isotropic plane, and the obtained critical electric displacement intensity factor (EDIF) approximates closely to that obtained by the Green’s function method. Additionally, as pinning dislocations and slip dislocations can strongly influence properties of ferroelectric devices and induce the property degradation, it is necessary to investigate the dislocation toughening effects on fatigue and fracture mechanisms. The results show that the dislocation shielding and anti-shielding effects on mode II SIF, mode I SIF and EDIF are obviously different when a dislocation locates at a position near the crack tip. Through the calculation of the critical applied EDIF for crack propagation by using mechanical energy release rate (MERR) theory, it is discovered that the slip angles obviously influence fracture toughness, and the mode II SIF arising from dislocation has little influence on fracture toughness, however, the mode I SIF and EDIF arising from dislocation have great influences on fracture toughness.

Study of Screen‐Printed PZT Cantilevers Both Self‐Actuated and Self‐Read‐Out

Usually, resonating cantilevers come from silicon technology and are activated with pure bending mode. In this work, we suggest to combine high‐sensitive cantilever structure with both self‐actuated and self‐read‐out piezoelectric thick‐film for high electrical–mechanical coupling. This cantilever is realized through screen‐printing deposition associated with a sacrificial layer. It is composed of a PZT layer between two gold electrodes. Optimum performances of piezoelectric ceramics generally imply the use of mechanical pressure and very high sintering temperature that are not compatible with the screen‐printing process. Addition of eutectic composition Li2CO3‐Bi2O3‐CuO or borosilicate glass‐frit to PZT powder and application of isostatic pressure improve the sintering at a given temperature. Firing temperature of 850°C, 900°C, and 950°C is tested. Microstructural, electrical and mechanical characterizations are achieved. In addition to the bending mode, the in‐plane 31‐longitudinal vibration mode and the out‐of‐plane 33‐thickness resonance mode are revealed. Correlations between experimental results and modeling of the different vibration modes are established. The piezoelectric parameters of PZT cantilevers approach those of ceramics. Quality factors between 300 and 400 associated with the unusual 31‐longitudinal mode make screen‐printed PZT cantilevers good candidates for detection in liquid and gaseous media.

Mechanical and Electrical Coupling Vibration Characteristic Analysis of Power Train System for Electric Driven Vehicle

Determine the electrical and mechanical coupling modeling and analysis method of power train system for electric driven vehicle. Mechanical vibration mathematical model, rotation DQ axis mathematical model of PMSM and electrical-mechanical coupling model of Power-train System for a new energy vehicle are given. Numerical solution and parameter sensitivity analysis has been done. Consider the impact of temperature change, iron core magnetic saturation, motor torque fluctuations and load torque fluctuation on the system.