Electromechanical Model Research Articles

Harnessing energy from hand-shaking vibration for electronics through a magnetic rolling pendulum bistable energy harvester

Converting the kinetic energy of human movement into electricity provides a solution for the power supply of portable electronics for communication, medical treatment, positioning, search-and-rescue, etc. Due to the characteristics of high sensitivity and snap-through, a magnetic rolling pendulum bistable energy harvester (MRP-BEH) based on magnetic-spring mechanism is proposed for scavenging energy from handshaking vibration. The harvester possessing the advantage of small damping exploits the rolling oscillation of a suspended magnet. By establishing the electromechanical model, numerical outcomes of the MRP-BEHs with different potential well depths are investigated through the response under constant and sweep frequency excitations. Particularly, the complex dynamic behaviors are characterized by basins of attraction and bifurcation diagrams. A prototype is fabricated, and experiments are undertaken under harmonic and handshaking excitations. Experimental results are consistent with numerical simulations, and excitation of 0.5 g witnesses a broadband frequency range from 5.18 Hz to 10.02 Hz for the harvester with proper system parameters. Regarding the excitation of handshaking, an instantaneous maximum power of 21.9 mW and an average power of 4.21 mW is achieved with matched load resistance. By boosting the output voltage with a transformer, the charging and discharging experiments of capacitors for powering various electronics demonstrate the broad application prospects of the harvester. This research, in a nutshell, broadens the methodology for achieving bistable oscillation and introduces a fresh perspective for designing high-efficiency energy harvesters attuned to human motion.

Electromechanical model for electro-ribbon actuators

The emerging field of soft actuators is anticipated to significantly impact areas that require enhanced adaptability and safe interaction including biomedical robotics. The electro-ribbon actuator, characterised by its compliance, lightweight, high efficiency, extensive scalability, and direct electrical control, emerges as a promising candidate for the future of soft robotics. Although the electro-ribbon actuator demonstrates efficient performance, a comprehensive understanding of its fundamental mechanics remains unexplored. To explain the impact of the actuation mechanism and the design parameters on the performance of the actuator, we have developed a mathematical model grounded in large deformation beam theory. As evidenced by our experimental results, this model accurately predicts the quasi-static behaviour of electro-ribbon actuators. Utilising this model, we establish a strategic road map for the development of electro-ribbon actuators with a range of passive stiffness tailored to achieve required output forces and displacement. This study provides a pivotal foundation for the model-based control and design optimisation of electro-ribbon actuators.

Numerical modelling of electromechanical coupling behaviors in HTS coil with implementation of H formulation in FE software

(Re)Ba2Cu3O7-x (REBCO) coated conductors (CCs) have attracted considerable concern because of their outstanding current carrying capacity in magnetic fields of high strengths. A huge electromagnetic force is generated in the superconducting coil when conducting large currents in strong magnetic field. Thus, management of stress and strain has become a key technical challenge for the stability and safety of superconducting coil during operation. To accurately predict the electro-magnetic and mechanical characteristics of superconducting coil in strong magnetic field, an electromechanical model on the basis of the H-formulation and arbitrary Lagrangian-Eulerian (ALE) method is proposed here with FE software. To verify the proposed model, the simulation outcomes of the coil during magnetization are compared with the experimental outcomes. The coupling effect of magnet at high field strengths is dependent on the position of the coil. To reduce the screening current effect, the overshoot method with plateau is found superior to the traditional overshoot method, and an increase in the stabilization time can decrease the maximum value of stress. Finally, the electromechanical behaviors of single winding coil and two-tapes co-winding coil are compared.

The Impact of Wheel Flat on Traction Drive System of Electric Locomotives

Wheel flat can seriously affect the wheel–rail contact performance and cause impact vibrations, which significantly threaten the safe operation of railway vehicles. It is crucial to accurately assess the effects of wheel flats on the wheel–rail contact performance and the vibration impact on the traction drive system. However, studies related to wheel flats have focused on the mechanical part and have yet to fully consider the electrical and mechanical parts of the entire traction drive system. Therefore, this paper first builds an electromechanical coupling model based on the electric traction drive system and the locomotive-track coupling dynamics model. Then, based on this model, the impact of the wheel flat on the electrical and mechanical parts of the traction drive system under different flat lengths, different flat depths, and different vehicle speeds was analyzed. The results indicate that with the increasing depth of the flat spot, the wheel–rail dynamic response, motor rotor speed, and motor torque exhibit more significant fluctuations. Additionally, as the locomotive speed increases, the impact of the flat on the wheel–rail contact performance intensifies. Wheel flats can excite the 1st bending mode of the wheelset, resulting in vibration shocks at 90 Hz.

Optimal position and dimensions of embedded normal piezoelectric transducers, higher order plate models and experimental approach

This study investigates the different optimal parameters of piezoelectric transducers polarized in the thickness direction. The studied parameters are regarding sensor and actuator embedding position in the thickness, sensor ratio and sensor dimensions. It involves a parametric study using MUL2 FE numerical tool, via coupled electro-mechanical two-dimensional models. The performance of the corresponding configuration was judged by the maximum output electric potential signal induced in the sensor due to the propagated Lamb Wave induced by the actuator. An experimental campaign was carried out on glass fiber/ polyester plates embedded with piezoelectric transducers to validate the different results.

A Timoshenko-Ehrenfest beam model for simulating Langevin transducer dynamics

The Langevin transducer is a widely used power ultrasonic device across both medical and industrial applications, from orthopaedic surgery to drilling and welding. It is a sandwich-type device which typically consists of piezoelectric ceramic rings between two metallic end-masses. The transducer is commonly operated at a particular resonant mode to deliver ultrasonic vibrations to a target structure of interest, and is generally modelled using approaches including the transfer matrix method and electromechanical equivalent circuit methods. Here, we propose a variational framework to study the dynamics of the Langevin transducer based on the Timoshenko-Ehrenfest beam theory and Hamilton's principle. The variational equation derived from this model is then discretized by the standard finite element method with spectral elements. To verify the proposed one-dimensional electromechanical model, the computed resonance frequencies, or natural frequencies, of the one-dimensional model are compared to those of a three-dimensional finite element model with respect to varying geometry parameters characterizing the transducer. The results of the reduced one-dimensional and full three-dimensional models are then compared to those measured through an experimental investigation consisting of laser Doppler vibrometry. This is undertaken for the first ten eigenfrequencies, including longitudinal and bending modes, where normalized amplitudes and vibration mode shapes are reported. The close correlation between modelling and experiment demonstrates that the proposed one-dimensional electromechanical model can deliver results consistent with the full three-dimensional model and from experiment, thus verifying a rapid and reliable method for studying the free vibrations and dynamics of the Langevin transducer which accounts for the axial vibrations of the piezoelectric ceramic stack in all cases.

An electro-mechanical contact model for particulate systems

This study presents an electro-mechanical contact model to investigate the electrical response within a particulate system under mechanical loading. The model considers the electrical resistance across particle-to-particle and particle-to-wall contacts by formulating bulk and contact resistances, separately. Hertz and Holm's models are utilised for the contact resistance in the overlapping region. The bulk resistance for a particle is estimated considering particle geometry transformations during the compression. The proposed electro-mechanical contact model is verified and validated against published analytical solutions and experimental data. Finally, the contact model is applied to simulate a high-pressure torsion test to investigate the influence of three different materials on the electrical conduction properties of the system after particle fragmentation. The intensity distributions of electric potential, current and resistance of the granular system are analysed at both particle and system scales. An electroactivity index is proposed for evaluating the contribution of each fragment sieve cut on the bulk electrical conduction behaviour.

Analytical approach to piezoelectric model synthesis with the use of Cauer's method for system design.

Piezoceramic materials have unique property which enables direct and bilateral conversion between mechanical and electrical energy. This ability facilitates significant miniaturisation of technology and opens many opportunities in design of new actuators and energy harvesters. Mathematical modelling of piezoelectric modules is notoriously hard due to complex constitutive equations defining mechanical and electrical energy conversion. The article presents research on a new synthesis method based on the Cauer's method. Mechanical damping is introduced with the use of Rayleigh's approximation. A discrete electromechanical model is formed based on the Mason's piezoelectric model. The proposed approach allows modelling of piezoelectric systems based on a set of characteristic frequencies. The method allows a more general approach to the problem of modelling new systems, as opposed to application-oriented methods seen in literature. A non-standard model analysis method using edge graphs and structural numbers is also verified as a potential alternative for matrix-based method. The authors compare their precision and computation requirements. The structural method of mechanical model analysis gave identical results as the reference matrix method. However, the non-classical algorithm took much longer to calculate and was using more memory. The electromechanical model analysis has shown an error of 5% in comparison to resonance frequencies taken from a reference plate specification. The calculated magnitude of displacement was well above the capability of a 3.5mm thick piezoelectric plate. The synthesis method presented in this paper allows synthesizing piezoelectric cascade models based on limited information in form of characteristic frequencies. Currently this method allows a coarse approximation of the real piezoelectric parameters with limited number of inputs. The additional method of analysis based on structural numbers offers a promising alternative to matrix calculations but requires a more thorough investigation of the computational power required to determine whether it can compete with existing algorithms.

A wide drive frequency matching method for harmonic suppression and voltage stabilization of ultrasonic motors.

To reduce harmonic components, balance system impedance, and stabilize driving voltage, an additional matching circuit is required for ultrasonic motors (USMs) driver. However, the performance of inductor or capacitor matching can be seriously weakened with changes in driving frequency. Therefore, this paper presents a simple and effective LC matching method against driving frequency adjustment for USMs. First, the driving scheme of the USM is proposed and the electromechanical coupling model is analyzed. Subsequently, the output characteristics of the full-bridge inverter are derived theoretically when the driving frequency deviates from the mechanical resonant frequency. Then, the impedance circular transform method is proposed, which can intuitively analyze the effect of matching parameters on the voltage amplitude. A matching objective function is established that can consider both the voltage stabilization and harmonic suppression. The matching parameters are solved using random weight particle swarm optimization. Simulations and experiments demonstrate that within the operating frequency of the USM, the proposed matching method can effectively prevent overvoltage and suppress harmonic components. Furthermore, compared with the existing resonant matching method, the proposed matching method can realize more stable driving capability at different frequencies. The proposed method could be useful for USMs' variable-frequency driver design.

Impacts of Electrode Resistance on Resonance Characteristics of Film Bulk Acoustic Resonators

In the actual manufacturing process of film bulk acoustic resonators (FBAR), metal leads are necessary to complete the electrical topological connection. However, the electrode resistance will significantly influence the characteristics of the resonator. In this paper, the influence of electrode resistance on resonance characteristics of FBAR is analyzed. To be specific, how different electrode resistances affect the quality factor, impedance value, and electromechanical coupling factor of the FBAR series-parallel resonance frequencies is studied by incorporating the electrode resistances into an overall equivalent electromechanical model (i.e., the Mason model) and the COMSOL finite element simulation method. The results show that the increase of electrode resistance will result in the decrease of the series resonant frequency, the impedance value increases significantly and the quality factor decreases significantly at series resonant, while the parallel resonant frequency does not change, the impedance value slightly increases and the quality factor slightly decreases at parallel resonant, and their electromechanical coupling factor slightly increases.

Theoretical modeling and experimental investigation of carbon fiber reinforced plastic-based piezoelectric actuator

Piezoelectric actuators based on non-metallic materials have drawn much attention in recent years. Carbon fiber reinforced plastic (CFRP) is one of the ideal materials for the development of lightweight, high power density piezoelectric actuators because of its low density, high stiffness. However, its anisotropic characteristics pose a challenge in actuator development. In this study, we designed a CFRP-based piezoelectric actuator, which utilizes hybrid modes of first-order longitudinal mode and second-order bending mode. The electromechanical coupling dynamic model for CFRP-based piezoelectric actuator was established a, based on the modal superposition method and energy method, and while taking into account the stress-strain relationships in anisotropic materials. The size of the actuator was calculated through the model and a prototype was processed for experimental research. The experimentally obtained results of frequencies and transient- as well as steady-state vibration characteristics demonstrated excellent agreement with the predictions of our mathematical modeling. Actuator performance evaluation results show that under a single-phase excitation voltage of 200 Vp-p, the CFRP-based actuator can reach maximum speed, thrust force, output power, thrust–weight ratio, power density, and efficiency of 617 mm s−1, 65 N, 1.14 W, 980.3 N kg−1, 223.5 W kg−1, and 10.4%, respectively. These results are satisfactory compared with actuators in other reports, especially the power density, which is nearly tripled. These results demonstrate the superior performance of the CFRP-based actuator and illustrate a new approach for developing lightweight and powerful actuators.

Synchronous control of tri-motor vibration system considering an adaptive back-stepping control strategy

In oil and gas drilling engineering, the anti-phase synchronization of two co-rotating rotors in a tri-motor vibration system is easy to implement owing to its inherent coupling characteristics, which can lead to the exciting force generated by the vibrating system being very small. Thus, an adaptive back-stepping control strategy is proposed to apply in a tri-motor vibrating system and improve the processing capacity of drilling fluid shaker screens. The algorithm developed in this paper is that a complex higher-order nonlinear system is simplified into lower-order subsystems by the adaptive back-stepping control theory, and then the adaptive law for varying load torque is derived by combining with the adaptive theory to regulate the velocity of motors in a closed loop. Firstly, a dynamical model to describe the tri-motor vibration system is established, and the dynamical equations of the vibrating system are derived based on the Lagrange equation. Then, the speed error controller and the phase difference error controller are designed by combining the adaptive back-stepping control algorithm with the master–slave control (MSC) structure. According to Barbalat’s lemma, the stability of the control system is analyzed to verify the feasibility of the control method. Finally, the dynamical equations of the vibrating system are used to establish an electromechanical coupling control model of a tri-motor driven planar system through the Runge–Kutta method, and it verified the reliability of the control strategy, the robustness, and the stability of the control system, respectively, and intuitively revealed the synchronization characteristics of tri-motor vibration control system. The results demonstrate the phase difference among the three motors can be accurately stabilized at zero by a phase synchronization control strategy based on the adaptive back-stepping control method, and the method is simple and fast-speed and the control system has better robustness.

Electric shovel trajectory tracking with inversion sliding mode based on Lyapunov functions

The harsh actual working environment and heavy weight of the electric shovel pose a great challenge to its trajectory tracking performance. Taking into account the strong robustness and anti-interference performance of the sliding mode control method and the global stability of the inversion control method, a Lyapunov-based inversion sliding mode trajectory tracking method is proposed in this paper, and its effectiveness is verified through numerical simulation based on the electromechanical coupling dynamic model of the electric shovel and the actual electric shovel tracking experiment. The results show that the trajectory tracking method can effectively realize the trajectory tracking of the electric shovel accompanied by tracking deviation within 0.3 m. The existence of the track slip phenomenon makes the electric shovel shake when steering, which also makes the actual operating velocity of the electric shovel fluctuate greatly. Meanwhile, the steering process of the electric shovel is accompanied by a regenerative braking steering mode.

Coupled models for designing and predicting performance of active sonar systems

Active sonar systems used to survey and image the seafloor typically transmit a pulse on a projector, receive echoes on an array of hydrophones, and condition and digitize the signals using on-board electronics. The quality of the data produced by these sensors is a function of the transducers, the electronics, and the environment. Simultaneous modeling of all these factors is necessary for accurate prediction of the system performance. Data products from these systems are often uncalibrated because absolute calibration is not required for their applications. However, modeling active sonar systems in their natural units within each domain provides clear benefits such as allowing system limitations to be accurately identified early during the design phase and easing validation of system performance in comparison with experimental data. This presentation will discuss the use of coupled multi-domain models in the design of two active sonar systems: the Sediment Volume Search Sonar and a multibeam echosounder architecture based on sigma-delta conversion. By coupling electro-mechanical transducer models and electrical hardware models with the Point-based Sonar Signal Model (PoSSM), it was possible to identify critical design parameters and sensitivities in the design of these sensors.

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.

Performance analysis of electromagnetic vibration energy harvester under square excitation

Harvesting energy from surrounding vibrations is an effective method for powering various low-power electronic devices. The energy output performance of vibration energy harvesters under some special excitations remains to be investigated. In this paper, a vibration energy harvester (VEH) system based on a rack and pinion mechanism and a bevel gear set is proposed, and a detailed electromechanical coupling modeling of the system under general excitation and square wave excitation is carried out. The energy output characteristics of the proposed system under square wave excitation are explored through simulation and experiment. When the energy output is the target, the priority of adjusting the constituent parameters in the equivalent mass parameter, equivalent damping parameter and equivalent stiffness parameter of the system can be obtained based on the simulation results. The experimental results under periodic square wave excitation force show that the maximum output power of the proposed system is 2.7 W at an amplitude of 4 kN and a frequency of 3 Hz. This is a 55 % increase in the maximum power compared to the sinusoidal excitation under the same conditions. It is demonstrated that the proposed system has great potential to power various low-power electronic devices.

Adaptive optimal fault-tolerant vibration control and sensitivity analysis of semi-active suspension based on a self-powered magneto-rheological damper

To reuse the energy dissipated by vehicle suspension, a semi-active suspension with a self-powered magneto-rheological damper is proposed. An electromechanical coupling model of self-powered semi-active suspension is established. The energy conversion efficiency is defined and investigated by changing the electrical parameters. By considering unmodeled dynamics and perturbation values, an adaptive optimal fault-tolerant control algorithm is proposed to ensure the vibration-isolation performance. The robust index of the adaptive optimal fault-tolerant control algorithm is constructed using the Lyapunov equation and evaluated by changing the key parameters. The sensitivity of the key parameters to the damping force is investigated using a grey relation analysis approach. Furthermore, multi-objective optimization between the vibration-isolation capability and energy harvesting is conducted. Via analysis, the proposed suspension can harvest more energy near the second resonance range. Compared to passive control and self-powered mode, the adaptive optimal control algorithm mitigates vibration more significantly in the time and frequency domains, respectively, under stochastic excitation. The robust index is most sensitive to inductance and the diameter of the magnetism cylinder. The length of the damping channel and the diameter of the magnetism cylinder influence the sensitivity of key parameters to the damping force most obviously.

Modelling and analysis of a novel E-shape piezoelectric vibration energy harvester with dynamic magnifier

An important issue in conventional harvesters is that the output performance is limited to small strains and narrow bandwidth. To address these issues, a novel E-shape harvester with dynamic magnifier is devised to magnify the base vibration and enhance electric energy in low-frequency complicated environment. In this study, a novel electromechanical coupling dynamic model is established by considering the characteristics of the E-shape structure. Meanwhile, the analytical expressions of the eigenfunction and resonance frequency of the developed model are presented. The effect of system parameters on the power output are investigated and discussed. Results indicate that the electric energy can be significantly enhanced and the vibration amplitude can be magnified using properly design structural parameters. The proposed harvester with dynamic magnifier is a simple and effective approach for enhancing energy harvesting near a target operating frequency.

Electromechanical coupling dynamics of dual-motor electric drive system of hybrid electric vehicles

In this study, to investigate the electromechanically coupled dynamics of a dual-motor electric drive system (DEDS) of hybrid electric vehicles under typical conditions. Considering the time-varying stiffness of gears, a dynamic model of the gear system and permanent magnet synchronous motor (PMSM) was developed, and a comprehensive electromechanical coupling dynamics model of DEDS applicable to coupling dynamics analysis was obtained. Based on this model, the impacts of the transmission error and electromechanical coupling effect on the dynamics of DEDS under steady-state and acceleration conditions were simulated and analyzed. This study demonstrates the significant impact of transmission errors on the dynamic load of high-speed gear pairs and the speed synchronization characteristics of the system. The study also reveals that the electromechanical coupling effect exacerbated the fluctuation of the gear dynamic load. During the speed change process, the electromechanical coupling effect did not introduce new resonance points. However, transmission errors tend to induce low-frequency resonance of the gear dynamic load and speed synchronization error (SSE). In addition, when the system is operated near the resonant speed, a large torsional vibration dominated by the resonant excitation frequency is generated, distinguished using the current signal to assess the resonance risk. The research results are important for the integrated design and condition monitoring of DEDS and offer valuable insights for enhancing the operational efficiency and reliability of the system.

Understanding wind turbine power converter reliability under realistic wind conditions

AbstractThe reliability of wind turbine power converters is crucial for analyzing wind energy project costs, and for estimating maintenance and downtime. The published literature in this field relies on evaluating the reliability effect of wind speed to estimate the converter lifetime. However, this paper demonstrates that wind turbulence intensity, which has not been widely considered in similar reliability analyses, shows a significant impact on converter lifetime. This paper uses 821 10‐min wind speed time series sampled at 1 Hz on the two most commonly deployed wind turbine converter topologies: the two‐level voltage source and the three‐level neutral point clamped. Electromechanical and thermal modelling, combined with statistical analysis shows that mean wind speed and turbulence intensity both impact the lifetime of both converter topologies. However, the paper estimates that the three‐level converter can operate 2.4 to 4.0 times longer than the two‐level converter depending on the operating wind speed and turbulence intensity.