Electromechanical Dynamic Model Research Articles

Output performance analysis of a piezoelectric micro nuclear battery powered by radioisotopes

Abstract This paper investigates the output performance (output voltage, electrical energy output, power output) of a piezoelectric micro nuclear battery powered by radioisotopes. The theoretical formulations are base on Euler-Bernoulli beam theory and include the effects of load nonlinearity due to radioactive source. By employing extended Hamilton’s principle, the nonlinear electromechanical Lagrange equations are derived then solved by using Runge-Kutta method to obtain the dynamic output response. The results based on present electromechanical dynamic model are validated through direct comparisons with the results in the open literatures. The effects of initial gap, length of the piezoelectric layer, thickness of the collector and load impedance on the output voltage, energy output and power output of the piezoelectric micro nuclear battery are discussed in detail.

Performance analysis of vertical stirred mill based on multi-coupling method

To improve vertical mill performance, a vertical stirred mill is used as the research object. Firstly, an electromechanical multi-body dynamic model (EMBD) of the vertical stirred mill is established, followed by the establishment of a discrete element method (DEM) analysis model of the grinding media, and then the DEM-EMBD coupling model is formed. The feasibility of the DEM-EMBD coupling model is verified through experiments. On this basis, the stress distribution state of the helical agitator is analysed based on the coupling method of the discrete element method and finite element method (DEM-EMBD-FEM). The DEM-EMBD coupling model can better reflect the dynamic characteristics of the vertical stirred mill by comparing it with the DEM model and the coupling method of discrete element method and computational fluid dynamics (DEM-CFD) respectively. Finally, the effects of vertical stirred mill structural parameters, operating parameters and grinding media size on mill performance are investigated by the DEM-EMBD and DEM-EMBD-FEM coupling models. The approach then provides insights into the structural design of vertical stirred mills, motor selection, and the welding process between the helical blades and screw.

Modelling and characterisation of a magnetically coupled piezoelectric beam for energy harvesting gear meshing motion

Gear transmission systems are crucial components for transmitting power and motion in a host of engineering applications. Recently, the potential to embed sensors into transmission components has attracted significant attention for accurate condition monitoring of system health. As a result, embedded sensors must operate in a safe and stable manner, whilst being able to provide a continuous power-supply and ensure operational autonomy. In this work, a magnetically coupled beam-type piezoelectric energy harvester is developed for energy harvesting of rotational centrifugal forces and individual gear meshing excitation events. A new coupled electromechanical dynamic model is developed to explain the working principle and response of the harvester when excited by a combination of gear meshing excitation events, a centrifugal force, and a magnetic force. Since gear meshing events are observed to lead to an increased hardening nonlinearity of the energy harvester, and a decrease in power output, a novel variable-section cantilever structure was developed. Our detailed theoretical analysis demonstrates that the novel variable stiffness structure improves both the power output and bandwidth, with excellent agreement with experimental measurements. This work provides new theoretical insights into the application of magnetically coupled piezoelectric energy harvesters for self-powered sensing systems for critical gear transmission systems.

Controlled synchronization of three co-rotating exciters based on a circular distribution in a vibratory system

In this article, an engineering problem of three co-rotating exciters with the circular distribution in a vibrating system is investigated. The dynamical model constructed by the motion differential equations is established. By introducing the small parameter averaged method in the dynamic equation, the synchronization and stability conditions of the electromechanical coupling dynamical model is derived. To illustrate the necessity of the controlling method, the self-synchronization of the vibrating system is firstly analyzed with the theory, numerical simulations and experiments. With the self-synchronization results, it is indicated that the ellipse trajectory which is needed in the industry can’t be realizefd by the self-synchronization motion of the vibrating system. And then, a fuzzy PID controlling method based on the master–slave controlling strategy is introduced in the vibrating system to realize the controlled synchronization. The Lyapunov stability criterion is given to certify the stability of the controlling system. Through some simulations and experiments, the effectiveness of controlled synchronization is illustrated in the discussion. Finally, the present work illuminates the feasibility and practicality for designing some new types of vibrating screens in the industry.

Energy harvesting from low-frequency vibrations of hanger using PVDF: An experimental study and performance analysis

Piezoelectric energy harvesters (PEH) are widely used to collect piezoelectric energy. However, adapting to different engineering application environments is difficult for traditional PEHs. To improve the engineering application value of PEH, a hanger piezoelectric energy harvester (HPEH) based on low frequency vibration of hanger is proposed in this paper. A dynamic electromechanical coupling model was established for hanger structure, and the effects of the external load resistance, the polyvinylidene fluoride (PVDF) piezoelectric film installation location, the stability of the PVDF piezoelectric film with different winding methods, and the external excitation amplitude on the energy output performance of the HPEH were studied. Results indicate that the optimal load resistance of the HPEH studied in this paper is 1.0 MΩ; the PVDF piezoelectric film location has a significant impact on the performance of the HPEH, and the output power is highest at hanger Lc/4; the PVDF piezoelectric films during ring winding is better than those in spiral winding for the same external cycle excitation; in the external excitation amplitude range of 2d–6d (d: hanger diameter), appropriately increasing the external excitation amplitude is conducive to improving the output voltage of the HPEH, with the root mean square voltage increasing by 95.11 % at external excitation amplitude A = 6d compared with that at the initial excitation amplitude. It provides an innovative solution for the field of cable structures and new energy sources, and the further research and application of this technology is expected to have a profound impact in the field of energy sustainability and engineering technology.

Electromechanical coupling dynamics for a novel non-resonant harmonic piezoelectric motor

Most of the traditional piezoelectric motors are driven by the resonance of piezoelectric ceramics and can achieve a large output torque. However, these motors also have the defects of high speed and difficulty to adjusting the speed when working. To overcome these issues, a novel non-resonant harmonic rotary piezoelectric motor operating at low speed is presented. Electromechanically coupled vibration has a great influence on the dynamic performance of the piezoelectric motor, which may lead to instability of the output performance of the motor. Therefore, the electromechanical coupling dynamic characteristics of the proposed non-resonant piezoelectric motor are studied in this paper. The working principle of the motor is illustrated, and the electromechanical dynamic model and nonlinear dynamic equations are established. Utilizing the dynamic equations, the coupled natural frequencies, amplitude-frequency characteristics, and dynamic responses of the motor are developed. Meanwhile, the influence of parameters on natural frequency and nonlinear response is analyzed. What's more, the natural frequencies of the system are tested by building an experimental platform. Results show the minimum coupled natural frequency of the motor is 11231 rad/s. The length of the piezoelectric stack, the length, and mass block of the harmonic rod have an important influence on the natural frequency of the proposed non-resonant harmonic piezoelectric motor. The nonlinear piezoelectric effect has a larger effect on the forced response amplitude when the excitation frequency is far away from resonance, but a smaller effect on the forced response amplitude when the excitation frequency is near resonance. What's more, the maximum error between the theoretical natural frequencies and the test frequencies is 3%, which verifies the correctness of the theoretical model.

Controlled synchronization of a vibrating screen driven by two motors based on improved sliding mode controlling method.

With a requirement of miniaturization in modern vibrating screens, the vibration synchronization method can no longer meet the process demand, so the controlled synchronization method is introduced in the vibrating screen to achieve zero phase error state and realize the purpose of increasing the amplitude. In this article, the controlled synchronization of a vibrating screen driven by two motors based on improved sliding mode controlling method is investigated. Firstly, according to the theory of mechanical dynamics, the motion state of the vibrating screen is simplified as the electromechanical coupling dynamical model of a vibrating system driven by two inductor motors. And then the synchronization conditions and stability criterion of the vibrating system are derived and numerically analyzed. Based on a master-slave controlling strategy, the controllers of two motors are respectively designed with Super-Twisting sliding mode control (ST-SMC) and backstepping second-order complementary sliding mode control (BSOCSMC), while the uncertainty is estimated by an adaptive radial basis function neural network (ARBFNN). In addition, Lyapunov stability analysis is performed on the two controllers to prove their stability theoretically. Finally, simulation analysis is conducted based on the dynamics model in this paper.

A high-performance rotational electromagnetic energy harvester based on magnetic plucking: Design, simulation, and experiment

Harvesting rotational energy to supply low-powered electronic devices can optimize the whole power supply system layout. In this paper, we propose a high-performance rotational electromagnetic energy harvester and construct an electro-mechanical dynamic model. The harvester consists of the halbach magnet array (HMA), a radially magnetized cylindrical rotatable magnet, and a copper coil, respectively. The proposed energy harvester is tested in a rotating platform and the correctness of the mathematical model is verified by experimental results. As one of the important components of the harvester, the magnetic field characteristics of the HMA are simulated by the finite element method (FEM) and compared with other magnet arrangements. Additionally, the effect on output when the HMA is rotated individually has also been analyzed. Numerical and experimental results indicate that the rotational energy harvester also has an optimal speed, and the corresponding maximum output power decreases significantly with the increase of the distance between magnets. Numerical results indicate that the maximum power output can be obtained as 516.05 mW at 520 rpm, which is a pretty remarkable result. To verify practical application capability, a rectifier-stable circuit is constructed to light 54 LEDs in experiments.

Dynamic modeling with quantifying dissipated power density and experimental validation of dielectric elastomer actuators

This paper proposes a dynamic electromechanical model for dielectric elastomer actuators (DEAs) with dissipative processes. Dielectric loss of elastomers, resistance of electrodes, actuator geometry, elastomer viscoelasticity and nonlinear electromechanical coupling are considered, and a new visco-hyperelastic constitutive model with frequency-dependent parameters is developed for large-strain elastomers. The dynamic responses of DEAs at different driving frequencies are experimentally measured and comprehensively compared with those predicted results. The relative errors over the time period of 0–50 s at 5 and 7 Hz are respectively 3.6% and 3.4%, demonstrating the effectiveness of the model. The proposed dynamic model can not only predict the frequency response of DEAs but also characterize the creep and hysteresis behavior with reasonable accuracy. The power density dissipated during dielectric elastomer actuation is calculated and analyzed. The results suggest that selecting low-resistance electrodes and elastomers with short dielectric relaxation time and low viscous loss is a feasible way to achieve high energy conversion efficiency for DEAs. This work can be helpful for the design and control of DEAs, paving the way for their practical applications.

Design and disturbance rejection control of a piezoelectric nanopositioning stage

The article covers structural design and disturbance rejection control of a flexure-based compliant piezoelectric nanopositioning stage. The stage is devised using four-bar amplification mechanisms, auxiliary guiding mechanisms, and a compound parallelogram mechanism. Static and dynamic models of compliant mechanisms are analyzed based on a compliance matrix method. A modified Prandtl-Ishlinskii (PI) model with dead zone operators is used to describe the asymmetric hysteresis. Then, a global electromechanical dynamic model is built and identified. A comprehensive disturbance rejection controller (CDRC) combining a robust H∞ control and a disturbance observer-based (DOB) control is proposed for high trajectory tracking accuracy and anti-disturbance performance. The trajectory tracking accuracy of the stage can be up to 3 nm in experiments. As amplitudes of reference signals increases, relative tracking errors gradually decrease. System instability and oscillation caused by strong external disturbances are also reduced. Experimental results prove the effectiveness of the developed CDRC.

Composite synchronization of three inductor motors with a circular distribution by a fuzzy proportional–integral–derivative method in a vibration system

Abstract. In this article, the composite synchronization of three inductor motors with a circular distribution by a fuzzy PID (proportional–integral–derivative) method in a vibration system is investigated. The composite synchronization motion is comprised of self-synchronization and controlled synchronization motions. In the self-synchronization section, the electromechanical coupling dynamical model of the vibration system is established by introducing an inductor motor model into the dynamic model. The responses of the vibrating system are calculated, and the synchronous condition and stability criterion are both derived. With the controlled synchronization section, a master–slave controlling strategy and fuzzy PID method are applied on the controlling model. The stability of the control system is proved by the Lyapunov stability theory. A series of simulations are employed to demonstrate the practicability of the designed method. Finally, some experiments are conducted to verify the effectiveness of the proposed control method in practical application. The proposed control method exhibits a superior ability to satisfy the control of multiple motors, to be accurate in targeting the rotational speed arrival, and to be strongly robust against uncertainties and disturbances. The composite synchronization theory introduces a novel concept to design and develop types of vibration equipment.

Electromechanical dynamic analysis for powertrain of off-grid switched-reluctance wind turbine hydrogen production system

Research on hydrogen production from wind power is important for improving wind energy utilization and hydrogen production efficiency; however, research on switched-reluctance hydrogen production from wind power has been relatively limited, and its system operation characteristics are unclear. Therefore, it is necessary to conduct research on the electromechanical coupling characteristics of switched-reluctance wind turbine hydrogen production systems (WTHPSs). An electromechanical dynamic model was established for the powertrain of an off-grid switched-reluctance WTHPS, including wind turbine, gear transmission system, switched-reluctance generator (SRG), and hydrogen production devices (HPDs). The model considers the detailed characteristics of the gear system, the nonlinear physical details of the HPD, and the electromagnetic characteristics of the generator. An improved control strategy was also developed for the SRG to reduce torque fluctuation. The steady- and transient-state electromechanical characteristics were simulated and analyzed, and the influences of the SRG control strategy and HPD switching on the system dynamic characteristics and hydrogen production rate were investigated. First, with respect to the improved SRG control strategy, the results show that SRG torque fluctuation can be reduced. The influence of the SRG electromagnetic torque on the transmission system gradually decreases from the high-speed stage to the low-speed stage. However, for a sudden decrease in wind speed, the SRG with the improved control strategy tracks the reference speed more slowly. Second, with respect to the hydrogen production rate, almost no difference can be observed between the two SRG control strategies. Single and multiple HPDs have a slight effect on the dynamic characteristics of the system when the HPDs can consume all the generated power. The production rate of HPDs in a parallel connection is higher than that with a single device at the same power, and the difference increases with an increase in power.

Multifrequency controlled synchronization of four inductor motors by the fixed frequency ratio method in a vibration system

In this article, multifrequency controlled synchronization of four inductor motors by the fixed frequency ratio method in a vibration system is investigated. The electromechanical coupling dynamical model of the vibrating system is established. The synchronous condition of the vibrating system is obtained with the small parameter method. Through the theoretical derivation and numerical simulation, multifrequency self-synchronization of four induction motors in the vibration system can’t be realized. To achieve the purpose of multifrequency synchronization motion, the method of multifrequency controlled synchronization is proposed, and a fuzzy PID controlling method is introduced. The stability of the controlling system is certified by the Lyapunov criterion. An arbitrariness of the proposed controlling method which is applied to the vibration system is presented. To certify the accuracy of the theory and simulation, a vibrating test bench is constructed. Some experiments are operated to validate the effectiveness and the proposed controlled synchronization method.

Design and Experimental Investigation of Three Degrees of Freedom Nanoscale Microsuspension Actuators

Nanoscale actuators are one of the key technologies in high-precision servo systems. For optical storage systems, the performance of the actuator determines the maximum storage capacity and read/write speed. This article introduces a three-degrees of freedom nanoscale microsuspension actuator. Compared with an actuator from a traditional optical storage system, the proposed actuator can hold dual objective lenses with large apertures, the load capacity of which is increased by 3.14 times. With dual objective lenses operating at the same time, the actuator can achieve a large range of layer jumps. Thanks to the four-sided magnetic circuit and the overall structure, the actuator has an operating bandwidth greater than 10 000 Hz for dynamic performance, can compensate systematic errors in nanoscale, and provides a radial tilt servo direction. We have derived the actuator a unified electromechanical dynamic model, an equivalent stiffness model, an equivalent damping model, and a magnetic circuit analysis model in detail. Compared with other analysis models of microsuspension actuator, the proposed models provide a theoretical guidance for the determination of each key parameter, and can effectively improve design efficiency. The theoretical models and design method of the actuator are also applicable to microactuators design and active vibration isolation design of other high-precision servo systems. The simulation and experimental results verify the good dynamic performance of the actuator and show the effectiveness of the principal analysis and design method.

Indirect Vector Control of Linear Induction Motors Using Space Vector Pulse Width Modulation

Vector control schemes have recently been used to drive linear induction motors (LIM) in high-performance applications. This trend promotes the development of precise and efficient control schemes for individual motors. This research aims to present a novel framework for speed and thrust force control of LIM using space vector pulse width modulation (SVPWM) inverters. The framework under consideration is developed in four stages. To begin, MATLAB Simulink was used to develop a detailed mathematical and electromechanical dynamic model. The research presents a modified SVPWM inverter control scheme. By tuning the proportional-integral (PI) controller with a transfer function, optimized values for the PI controller are derived. All the subsystems mentioned above are integrated to create a robust simulation of the LIM’s precise speed and thrust force control scheme. The reference speed values were chosen to evaluate the performance of the respective system, and the developed system’s response was verified using various data sets. For the low-speed range, a reference value of 10 m/s is used, while a reference value of 100 m/s is used for the high-speed range. The speed output response indicates that the motor reached reference speed in a matter of seconds, as the delay time is between 8 and 10 s. The maximum amplitude of thrust achieved is less than 400 N, demonstrating the controller’s capability to control a high-speed LIM with minimal thrust ripple. Due to the controlled speed range, the developed system is highly recommended for low-speed and high-speed and heavy-duty traction applications.

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.

Design parameters of a reluctance actuation system for stable operation conditions with applications of high‐precision motions in lithography machines

Recently, the reluctance actuator has attracted great attention to replace the Lorentz actuator in the next generation of wafer scanners in semi-conductor lithography machines. The reluctance actuator has a non-linear position-force characteristic, which may cause high oscillations and unstable operation. This study presents a linearisation technique by optimising the main parameters of the reluctance actuator to operate away from the saturation point. Also, in this study, the critical current is formulated for the stable dynamic behaviour of the reluctance actuator. Optimisation based on the Grey Wolf Optimiser is performed considering the high-precision motion requirements and physical constraints. The high-precision motion requirements include the desired work-space displacement, natural frequency, and maximum force. The electromechanical dynamic model of the reluctance actuator motion system is formulated to characterise the interaction among electrical, magnetic, and mechanical parts. The simulation results show that the optimal design of the reluctance actuator works in the linear region, and for stable dynamic behaviour, the input current is limited by the critical current. Finally, a feedforward controller is designed based on the approximation of the force–current relationship to improve the tracking performances of the reluctance actuator motion system. The simulation results in time and frequency domains show an improvement in tracking performances using the feedforward controller.

Disturbance mechanism of the solar array drive system on spacecraft

An electromechanical dynamic model of the solar array drive system (SADS) was proposed to analyze the disturbance characteristics, and verified by the experiment study in the laboratory. The factors which directly cause the SADS’s disturbance were differentiated based on the idea of reductionism, and corresponding disturbance characteristics were investigated. The other kinds of factors which do not cause disturbances but affect the disturbance characteristics of SADS, as well as their influence rules, were also analyzed. The results of the proposed model agree well with the experimental data, with an error of less than 10%. Disturbances of SADS occur when the rotational-motion acceleration and structural-vibration acceleration are not both equal to zero. The current subdivision of the drive controller, nonlinear magnetic field of the stepping motor, and the varying meshing parameters of the gear reducer can directly cause disturbances, which vary periodically and occur near excitation frequencies and high-order harmonic frequencies. The amplitude of the disturbance increases with a decrease in the number of current subdivisions, an increase in electromagnetic excitation and the fluctuation margin of gear-meshing parameters. The closed-loop current control, nonlinear friction between the brush and slip ring, the bending-torsional coupling of the solar array, and the gear clearance of the gear reducer do not cause the SADS’s disturbances but can affect their profile and spectrum distribution from different aspects, even introducing disturbance components in the non-driving directions.

Modeling and parametric study on DE-based vibro-impact energy harvesters for performance improvement

This paper develops a dynamic electromechanical coupling model to investigate the energy harvesting (EH) performance of the vibro-impact (VI) energy harvester comprising a cylindrical capsule, an internal free moving ball, and two dielectric elastomer (DE) membranes at both ends of the capsule. The developed model can describe the electromechanical properties of the collision between the ball and the membrane, which is verified by the existing experimental data. On this basis, the effect of system parameters, such as the mass and the radium of the ball, the internal radium and the length of the capsule, and the pre-stretch ratio of DEs, on the average power density of the energy harvester is also studied under diverse external stimuli including the inclined angle and the excitation frequency. The results show that at the small excitation frequency, the EH performance of the energy harvester can be improved by increasing the pre-stretch ratio of membranes and the mass of the ball and decreasing the radium of the ball and the internal radium of the capsule. The conclusions can help provide a guide for the optimal design of the energy harvester in the practical application so as to improve the EH performance.

Modelling and simulations for signal loss evaluation during sampling phase for thermoluminescence authenticity tests

<p class="Abstract"><span lang="EN-GB">In authenticity tests using the thermoluminescence (TL) method, the sampling phase is fundamental to collecting an appropriate amount of powder for analysis. The powder is usually obtained by drilling in hidden and pertinently selected areas of an artefact. During the drilling, a local temperature increase can occur, and, because thermoluminescence emission is dependent on the heating rate, the authenticity test result could be invalidated due to underestimation of the signal intensity. In this work, the percentage of signal intensity loss is investigated through the combination of a dynamic electro-mechanical model and a typical TL glow curve simulation. After first modelling the drilling procedure to estimate the maximum temperature reached, the optimal parameters that should be used during the sampling phase are checked by simulations together with an evaluation of the correlated signal losses.</span></p>