Electromechanical Model Research Articles

Nonlinear piezoelectric energy harvesting induced through the Duffing oscillator.

In this paper, nonlinear piezoelectric energy harvesting induced by a Duffing oscillator is studied, and the bifurcation trees of period-1 motions to chaos for such a piezoelectric energy-harvesting system are obtained analytically. Distributed-parameter electromechanical modeling of a piezoelectric energy harvester is presented first, and the electromechanically coupled circuit equation excited by infinitely many vibration modes is developed. The governing electromechanical equations are reduced to ordinary differential equations in modal coordinates, and eventually an infinite set of algebraic equations is obtained for the complex modal vibration responses and the complex voltage responses of the energy harvester beam. One single mode case is considered in this paper, and periodic motions with bifurcation trees are obtained through an implicit discrete mapping method. The frequency-amplitude characteristics of periodic motions are obtained for the nonlinear piezoelectric energy-harvesting systems, which provide a better understanding of where and how to achieve the best energy harvesting. This study describes about how the nonlinear oscillator induces piezoelectric energy harvesting through a beam system. The nonlinear piezoelectric energy harvesting is presented through a nonlinear oscillator. Due to the nonlinear oscillator, chaotic piezoelectric energy-harvesting states can get more energy compared to the linear piezoelectric energy-harvesting system.

Sardinia as a 100% renewable power system: A frequency stability study

This paper investigates a real complex power system supplied by a 100% renewable generation, focusing on the primary frequency regulation. The grid and the power production park are represented by means of an electro-mechanical model in a free open-source environment. The lack of synchronous generators in the grid, due to the conventional power plants shutdowns, requires higher performances from renewable power plants (RPPs) in terms of synchronization and inertial response. Doubly fed induction generators (DFIGs) are identified as the promising power plants able to lessen inertial issues. DFIG system control is investigated in the present paper, according to the recent studies in the literature, implementing a new strategy of control in case of avoiding maximum power point tracker (MPPT) operation. The 100% renewable 112-bus Sardinia islanded power system is the case study of this paper. Four scenarios were selected to show the primary frequency response in the most critical under and upper frequency events among the year. The simulations revealed that the most severe frequency nadir in the simulation reached a decrease of 0.37 Hz. DFIGs control system appeared robust in terms of inertial response and capability of reaching new stable operating point.

Effect of Metallization on Quality Factor and Noise Characteristics in Fused Silica Dual-Shell Gyroscopes

Metal coating of Fused Silica (FS) Micro-machined Hemispherical Resonator Gyroscopes (micro-HRGs) is necessary to allow for capacitive actuation and detection of motion. Metallization provides electrical conductivity, but reduces the quality factor of resonators. Both effects contribute to sensitivity and noise characteristics of the sensor. In this paper, we considered the metal coating material and thickness, linking the design and fabrication parameters to the gyroscope’s noise performance. We designed and fabricated FS Dual-Shell Gyroscopes (DSGs), a version of micro-HRG, and used it as a test vehicle to study the trade-offs between metallization, quality factor, conductivity, and noise characteristics. We developed an analytical electromechanical model to optimize metal-coating and predict gyroscope performance. The results have been confirmed experimentally. [2022-0052]

Switched electromechanical dynamics for transient phase control of brushed DC servomotor.

Robotic tasks often exceed the scope of steady-state or periodic behavior, which necessitates generally-applicable models of actuators intended to generate transient or aperiodic motion. However, existing electromechanical models of servomotors typically omit consideration of the switching power converter circuits required for directional, speed, or torque control. In this study, a multi-domain framework is established for switched electromechanical dynamics in servomotor systems for their analysis and control in general aperiodic tasks including transient phases. The switched electromechanical dynamics is derived from the individual models of the internal DC motor, gear train, and H-bridge circuit. The coupled models comprehensively integrate all possible distinct switching configurations of on-state, off-state, and dead time. A combination of cycle averaging with piecewise analytical solutions of the non-smooth dynamics is introduced to handle different temporal scales from high-frequency electrical to low-frequency mechanical variables. System parameters were estimated from experimental data using a dual-servomotor test platform. The model was validated for predictive accuracy against measured data in two distinct tasks-dynamic braking of a pendulum system and sinusoidal trajectory following. The model was also used to formulate the servomotor power consumption, which was implemented for optimal control demonstration and energy analysis. In particular, the servomotor power consumption model provided true optimality (minimization) when compared with the squared rotor torque and the positive rotor mechanical power that are commonly used as proxy models. While the focus of this work is on permanent-magnet, armature-controlled brushed DC servomotors, the approach is applicable to general electromechanical systems with switching-based control.

Characterization for the key parameters of 1-3 piezoelectric composite in thickness vibration mode

1-3 piezoelectric composite has been widely used in underwater acoustic and ultrasonic transducer, and its thickness vibration mode is most commonly used by transducer. The resonance frequency and the conductance are two key parameters of this mode, because they determine the working frequency of transducer and electrical match, respectively. In order to characterize these parameters, the electromechanical equivalent model of thickness vibration mode was established to obtain the admittance equation, and then the key parameters were calculated. Meanwhile, 1-3 piezoelectric composite samples with different structural parameters were prepared and tested, and the theoretical model was verified. Finally, the theoretical model was used to characterize the variation of resonance frequency and conductance with the structural parameters to guide the design of 1-3 piezoelectric composite.

Extended Simplified Electro-Mechanical Model of a Variable-Speed Wind Turbine for Grid Integration Studies: Emulation and Validation on a Microgrid Lab

The energy transition towards renewable energies is crucial for the sustainable development of a society based on hydrocarbons. The current level of penetration and growth of wind energy in electric power systems is evident and many researchers have presented new methods for simulating and representing the electrical and mechanical characteristics of variable-speed wind turbines. However, complete mathematical models developed and implemented, for example, in MATLAB/Simulink® software, require significant computational efforts that could make grid studies impractical when its scale tends to increase. To contribute to facing this issue, this paper proposes an extended simplified model for a variable-speed wind turbine that considers the dynamic behavior of its mechanical system and includes an approximate representation of the power electronic converter. This approach broadens the scope of studies related to grid frequency control and power quality (fast-frequency response, primary frequency control, and voltage control, among others), considerably reducing the computational burden. Several validations of the proposed simplified model are presented, including comparisons with a doubly fed induction generator-based wind turbine model (phasor type) from the MATLAB/Simulink® library, and laboratory experiments under controlled conditions. The results show a good fit of the proposed simplified model to the MATLAB/Simulink® model, with minimal delays about 3% of the wind turbine inertia constant. Moreover, with the proposal, the computational time is reduced by up to 80% compared to a detailed model. This time reduction is achieved without penalizing the numerical accuracy and the estimation quality of the real behavior of the variable-speed wind turbine.

Event-driven MEMS vibration sensor: Integration of triboelectric nanogenerator and low-frequency switch

Triboelectric-nano-generator (TENG) is able to produce a very small current and a large voltage compared to piezoelectric or electromagnetic generators. The large voltages from the TENGs are suitable for operating MEMS devices without external AC or DC generators. Producing micro-sized TENG using MEMS fabrication process enables integration of them with MEMS sensors and actuators. This combination is useful because the required voltage for driving MEMS is obtained from the motion of the event that is being measured. In this work, an event-driven vibration sensor is introduced which actuates a switch as the frequency or amplitude of the vibration exceeds a desired threshold. Using CMOS micromachining, a 1.5 mm × 1.5 mm TENG in contact-separation (CS) mode is fabricated to convert ambient vibrations to a voltage generated between a conductive aluminum layer and a dielectric Polyimide layer. The large generated voltage between the electrodes can operate a low-frequency electrostatic MEMS switch. Two events are able to produce the resonant dynamic pull-in needed to close the switch. Event one is when the input amplitude exceeds the dynamic pull-in threshold which is called acceleration sensitive mode. Event two is when the frequency of the vibration exceeds a specified threshold. An electromechanical model for the MEMS switch part of the vibration sensor is also presented. Results show that MEMS-TENG is able to supply the MEMS switch in the frequency sensitive and acceleration sensitive modes with a good signal-to-noise-ratio, sensitivity, and accuracy.

Impact of electrode conductivity on mass sensitivity of piezoelectric resonators at high temperatures

Abstract. High-temperature stable piezoelectric Ca3TaGa3Si2O14 and La3Ga5SiO14 resonators with keyhole-shaped Pt electrodes are coated with metal oxide films such as TiO2−δ and SnO2 that overlap the Pt electrodes. The resonators are exposed to reducing atmospheres in order to increase the electrical conductivity of the oxide film and then act as extended oxide electrodes. The resulting increase in the effective electrode radius causes an increase in the mass sensitivity of the resonators and, thereby, resonance frequency shifts. In other words, the effective mass of the Pt electrode becomes higher. An electrical circuit model is presented to describe the increase in the effective electrode radius of the resonator, which is used to calculate the related resonance frequency shift. Additionally, an electromechanical model is presented, which subdivides the resonator into two coupled oscillators. One is representing the resonator volume underneath the Pt electrode and the other underneath the oxide electrode at increased electrical conductivity. The model reflects how the oxide electrodes affect the resonance frequency. Furthermore, the impact of increasing oxide electrode conductivity on the resonance frequency is discussed with respect to the application of oxide electrodes and for gas sensing.

Self-sensing method for semi-active structural identification by removing piecewise bias from piezoelectric voltage

Structural system identification (SSI) that uses many actuators and sensors will be more accessible as a sensing technology if the number of these devices decreases. Recently, a semi-active SSI using a piezoelectric transducer and a unique semi-active input generation circuit was proposed. The semi-active SSI outperforms conventional SSIs with low energy consumption. If the semi-active input and its vibration response are estimated from the voltage generated by a piezoelectric transducer, some sensors will become redundant. Conventional self-sensing methods estimate structural vibrations without using vibration sensors. The semi-active SSI in combination with the self-sensing method will be more accessible than current technologies from the perspectives of a lower energy consumption and fewer number of devices. However, the following two problems exist: (1) A semi-active input generation circuit cannot introduce conventional hardware-based self-sensing methods with additional electric circuits because the electrical components in the additional circuits degrade the performance of the piezoelectric transducer. (2) Software-based self-sensing methods, such as the Kalman filter, cannot be used in system identification scenarios because the electromechanical parameters and models are unknown. To overcome these drawbacks, a novel software-based self-sensing method that does not require electromechanical models is proposed in this paper, and the effectiveness of the proposed method is thoroughly investigated using both simulations and experiments. The identification performance of the proposed method using the estimated input and output is the same as that using directly measured data. The proposed method can especially contribute to the predictive maintenance of structures in isolated environments. • A self-sensing method for piezoelectric semi-active control is proposed. • The elongation and inflow charge of the transducer is estimated from the piezoelectric voltage. • The proposed self-sensing method does not use additional circuits. • The structural system identification is implemented using estimated data.

The jetting process and spreading characteristics of the power-law fluids for material jetting process

Materials jetting, known as one of the 3D printing technologies, is widely applied in microelectronics packaging, biology and ceramic 3D printing due to its ability to print multi-materials by drop-on-demand. However, most of the materials are power-law fluids in 3D printing applications, the generation of satellites during the jetting process and droplet spreading characteristics are unclear and they have a great effect on the quality of the printout. In this paper, a common electromechanical and fluid-solid coupling model of the jet dispenser and observation platform of the jetting process are established. This modeling method is also suitable for other needle-driven jet dispensers. A commercial UV resin is adopted to study the jetting process of power-law fluid. To reveal the mechanism of satellite generation, the effects of input signals (rising time and falling time) on the dynamic characteristics of the needle and the jetting process are analyzed. On the basis thereof, the effectiveness of the optimal control parameters is demonstrated to eliminate satellites. In addition, the simulation and experimental results show that the falling time and fluid pressure can be controlled to adjust the spreading diameter and height of the droplet. Subsequently, the minimum line width of 0.276 mm is successfully printed with a nozzle of 0.07 mm.

Influence Factors of Inherent Characteristics of F5 Cold-Rolling Mill’s Main Drive System

This paper is focused on the inherent characteristics of the main drive system of the F5 cold-rolling mill in a steel plant. First, the main transmission mechanical structure was simplified to a five-inertia torsional vibration model. Secondly, the coupled torsional vibration model of strip and roll was established. The electromechanical coupling model of the motor control system and the motor rotor was established again. Finally, the AMESim software was used to calculate the natural frequency of the main drive system under various coupling conditions, and the influence mechanism of rolling parameters and motor control system parameters on the natural frequency of the main drive system was obtained, and an example of torsional vibration suppression is given by adjusting the control parameters. This study provides a profound theoretical basis for the on-site adjustment of process parameters and electrical control parameters to suppress torsional vibration.

Scavenging energy from aeroelastic vibrations for hybrid stall control in a fixed-wing micro aerial vehicle

Scavenging energy from aeroelastic vibrations was considered for a self-powered hybrid passive-active stall control system intended to improve the aerodynamic performance of fixed-wing micro aerial vehicles without exhausting available batteries. It was found that the passive component of the system generates intense streamwise vortices, which give rise to vortex-induced vibrations. Measured frequency response functions indicated accelerations in a wing prototype up to 0.1 g at relatively low frequencies, when it was operated at simulated flight conditions in a wind tunnel. Aiming to use this resource for additional power, a piezoelectric energy harvesting device was installed inside the wing and tuned for resonant response. Two electromechanical modeling approaches for the piezoelectric harvester were investigated, namely, an analytical model and finite elements simulations. A comparison with experimental results has shown that the latter approach is better equipped to deal with advanced designs, yielding accurate predictions in the present study. Extracted power and generated voltage were quantified as a function of the electric loading resistance. The reported data demonstrated that the proof of concept was achieved, so that a lightweight, low-consumption actuator for the active component of the stall control system can be powered by the energy of structural vibrations.

Excitation control of variable speed pumped storage unit for electromechanical transient modeling

In this paper, a new excitation control of variable speed pumped storage unit (VSPS) for electromechanical transient modeling is presented. Compared with the traditional VSPS excitation control based on current source, the inner loop control of rotor current is retained. The new VSPS excitation control model considers the rotor flux dynamics and represents it as a second-order system. The effectiveness of the proposed excitation control model is verified by the comparison between electromagnetic transient simulation and electromechanical transient simulation. The electromechanical transient simulation of VSPS based on current source and VSPS based on voltage source is compared to verify the necessity of considering rotor flux dynamics. The proposed VSPS excitation control model reflects the characteristics of controllable voltage source and can provide more accurate reactive power and voltage simulation results in transient stability analysis.

A generalized electromechanical coupled model of standing-wave linear ultrasonic motors and its nonlinear version

For the systematization of research on standing-wave linear ultrasonic motors (SWLUMs), this work develops a generalized electromechanical coupled model for characterizing SWLUMs. The proposed model focuses on dealing with modeling the generalized two-stage energy conversion in SWLUMs. The first-stage energy conversion is modeled by a four-terminal equivalent circuit model, which with a phase shifter and a couple of electromechanical transformers based on the electromechanical analogy method. The second-stage energy conversion is modeled by a physics-based, friction-driven system, involving contact nonlinearities between the stator and the mover. Furthermore, the effectiveness of this model and its further extension considering nonlinear vibrations of piezoelectric transducer (stator) are exemplified and discussed by a classical SWLUM with V-configuration stator, thereby indicating that the presented generalized model is valuable and pragmatic in simulating and characterizing SWLUMs both in electrical and mechanical domains.

Influence of material grading and compositional platinum profile on the functionally graded piezoelectric bridge structure

Bridge transducers are square or rectangular cymbals that have been proven to be a promising design for piezoelectric energy harvesting in the presence of high-impact loads. This study investigates the effect of compositionally graded platinum and material exponents on the performance metrics of a flex tensional bridge structure. A functionally graded piezoelectric material is created here by incorporating a compositionally graded Pb[ZrxTi1−x]O3/platinum material (Pb[ZrxTi1−x]O3/platinum) with a polymer of -(C2H2F2)n-. The multiphysics bridge structured model is solved using finite element analysis. The biokinetic energy is generated by footsteps with loads that are 1.5–3 times the body weight, and thus an impact load of 1500 N is considered in this study. The performance metrics in terms of voltage and power are scrutinised using the electromechanical model in order to attain maximum output at optimal settings. The optimal grading exponent values are determined by the platinum concentration as well as other functional factors. It is discovered that the power law-driven grading index improves bridge functionally graded piezoelectric material performance regardless of changes in other operating parameters. Although platinum impairs Pb[ZrxTi1−x]O3/platinum performance but synergising the composite material with the grading index enhances the performance metrics percentage of functionally graded piezoelectric material over the respective Pb[ZrxTi1−x]O3/platinum material. This research establishes the relevance of synergism on the electromechanical features and performance of bridge transducers, and is applicable to any bonded piezoelectric device, whether it is an energy harvester, actuator or sensor.

Output characteristics analysis of pendulum type triboelectric nanogenerators considering nonlinear electromechanical coupling effects

In this study, output characteristics analysis of pendulum type triboelectric nanogenerators (P-TENG) considering nonlinear electromechanical coupling effects is conducted. Based on the analysis of power generation mechanism, an equivalent capacitance model is proposed. Combined with the energy principle and equivalent circuit method, an electromechanical coupling model considering the nonlinear variation of pendulum angle is established. Using the harmonic balance method (HBM) and alternated frequency/time domain technique, the steady-state output of the P-TENG is solved analytically, and the stability of the results is determined. Numerical integration and dynamic tests are used to verify the accuracy of HBM results. By comparing the changes in the P-TENG output performance with and without the nonlinear effect, it is shown that the model proposed in this study can effectively avoid the underestimation of the operation bandwidth (a relative increment of 83%) and significantly improve the accuracy of the P-TENG performance estimation. Based on these results, the influence of the design parameters (including excitation amplitude, damping ratio, gap length, and electrode angle) on the dynamic output characteristics of the system is discussed. The output performance of the P-TENG can be improved by increasing the excitation amplitude, reducing the damping ratio, and minimizing the electrode angle. In the actual design, the gap length and friction amplitude should be comprehensively considered to maintain the P-TENG output performance in a better state. Various fitting models have been proposed to model the relationship between the design parameters and output performance. The fitting coefficients obtained from the parameter influence discussion can be used as the basis for the P-TENG output performance design.

An electro-mechanical dynamic model for flexoelectric energy harvesters

Flexoelectricity is a universal electro-mechanical coupling effect that occurs in dielectrics of all symmetric groups and becomes dominant at the micro- and nano-scales. It plays an important role in evaluating micro-electro-mechanical systems (MEMS) such as energy harvesters which convert vibrational energy to electric energy. At finer length scales, micro-inertia effects significantly contribute to the behavior of flexoelectric materials due to the mechanical dispersion. Hence, to properly characterize the vibrational behavior of MEMS, a reliable theoretical approach is required accounting for all possible phenomena that affect the output of the system such as voltage or power density. In this work, we present a consistent (dynamic) model and associated computational framework for flexoelectric structures to study the characteristics of the vibrational behavior of energy harvesters showing the dominance of the flexoelectric effect at micro- and nano-scales. In this context, we quantify the impact of the micro-inertia length scale and the flexoelectric dynamic parameter on both frequency and time responses of energy harvesters.

Enhancing Lithium-Ion Battery Aging Simulations By Coupling a High-Resolution, 3D, Grain-Scale Electromechanical Model to a Single Particle Model

One of the main goals in modeling lithium-ion batteries is to improve/predict longevity and resilience of new chemistries. Unfortunately, this requires simulation of thousands of charge/discharge cycles, which can be rather time consuming depending on the fidelity of the simulation. The purpose of this talk is to discuss a new modeling framework that couples a high-resolution, continuous damage model (CDM) to a single particle model (SPM) resulting in a good combination of speed and fidelity.In previous work, a 3D, continuum-level chemo-mechanical model was developed to investigate cracking within a single cathode particle comprised of hundreds to thousands of randomly oriented grains. The CDM predicted that particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. Essentially, when neighboring grains were misaligned, they expanded different rates relative to one another leading to high stresses and ultimately the formation of intraparticle cracks. The model predicted that small particles with large grains develop significantly less damage than larger particles with small grains. Finally, the model predicted most of the chemo-mechanical damage accumulates in the first charge after formation. This chemo-mechanical “damage saturation” effect indicated that initial particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced. This led to a need for simulating fatigue-like mechanism that degrade the battery over longer time scales.In order to reach the time scales, need to resolve fatigue-like degradation, the CDM needs to be complemented by a faster model. Therefore, recent efforts have been focused on using results from the CDM to inform parameters within the SPM. These parameters are homogenization factors that are associated with diffusion, particle radius, and/or exchange current density. By coupling the CDM to the SPM, the aging simulation is broken up into two domains: short-term and long-term degradation. The short-term degradation occurs over a single cycle and is handled by the CDM due of its high fidelity, but relatively expensive computational cost. Such mechanism include break-in crack caused by mismatches in grain orientation. The long-term degradation occurs over tens of cycles and is handled by the SPM due it’s computational efficiency. Most of the fatigue-like mechanism fall into this category.The eventual goal of this modeling framework is to upscale to a psudo-2D model allowing for full electrode simulation, which are informed by high-fidelity grain-scale simulations. Figure 1

Critical Damping in Travel Curves of Piezoelectrically Actuated Fast Mechanical Switches for Hybrid Circuit Breakers

Piezoelectrically actuated fast mechanical switches provide a low-loss conduction path in hybrid circuit breakers for protecting medium-voltage direct-current systems. As the desired actuation speed approaches the driving limit of a piezoelectric actuator, excessive vibration starts to dominate its underdamped travel curves, resulting in insulation failures and delayed switching in the fast mechanical switch. To improve the underdamped travel curves into critically damped travel curves, several switching motion control schemes with active damping filters are proposed in this paper. The switching motion controllers are based on an electromechanical model of a fast mechanical switch with experimentally identified parameters. According to hardware implementation tests, the proposed closed-loop control schemes optimized the switch travel curves with a 56% reduction in the undershoot and a 75% reduction in the settling time. Equipped with the critically damped travel curves, the piezoelectrically actuated fast mechanical switch is better suited for sequential submodule operations to reduce the interruption time, the peak current and the fault energy to be absorbed in hybrid circuit breakers.

Metamaterial based piezoelectric acoustic energy harvesting: Electromechanical coupled modeling and experimental validation

Piezoelectric energy harvesting technology utilizing acoustic metamaterials investigated by experiment and simulation improves the sound energy density and conversion efficiency. A fully coupled electromechanical model in both the mechanical and electric domains is crucial for accurate prediction and optimization of acoustic metamaterial based on sound energy harvesting. Based on the Kirchhoff thin plate theory, constitutive laws of isotropic aluminum substrate and transversely isotropic piezoelectric bimorph, the electromechanical coupled governing equation in the mechanical domain is deduced for a two-dimensional acoustic metamaterial based piezoelectric energy harvester. Each piezoelectric layer is represented as a current source in series with its internal capacitance for derivation of the electromechanical coupled governing equation in the electrical domain via Gauss’s law and Kirchhoff’s laws. With generalized boundary conditions, modal analysis is performed using the Galerkin method and Kelvin-Kirchhoff condition. The general transient response and frequency response functions are obtained under the excitation of sound waves and the reaction forces of the silicone rubbers. The time-history, power spectrum and phase portrait of the measured harvested voltage at 90 fixed frequencies agree well with the model predictions. The theoretical maximal harvested power is 3.09 mW, with the optimal resistance of 28180 Ω and inductance of 0.28H connected in parallel. Near the resonant frequency, the utilization rate of converting sound energy into electrical power is maximized. The proposed electromechanical coupled model can be used as a basis for further topology design and optimization and underlying physics for experimental study.