Electromechanical Coupling Model Research Articles

A distributed-parameter electromechanical coupling model for a piezoelectric energy harvester with variable curvature

Enabling technologies for harvesting ambient vibration energy have attracted considerable attention in research communities from different disciplines in the last decades. Among the various devices, straight cantilever-based energy harvesters have been widely investigated from the perspective of designs, modeling, simulation and experiments. In this study, we propose curved piezoelectric energy harvesters (PEHs) with variable curvature to further broaden application scenarios. Within the framework of the Euler–Bernoulli beam theory, we develop a distributed-parameter electromechanical coupling model for a curved segmented unimorph with variable curvature by Hamilton’s Principle and solve it using the Rayleigh–Ritz method. The convergence and accuracy of the model are validated by finite element simulation and experiments. Based on the proposed model, we perform a systematic parameter study and discuss the effects of the proof mass, Young’s modulus of the substrate, the thickness ratio of the substrate to the total thickness, the curvature of the substrate and the piezo patch on the mechanical and electrical responses of the structures. The theoretical model will help engineers to design and optimize new PEHs and serve as a benchmark solution for future research in this field.

A Coarse-Grained Methodology Identifies Intrinsic Mechanisms That Dissociate Interacting Protein Pairs.

We address the problem of triggering dissociation events between proteins that have formed a complex. We have collected a set of 25 non-redundant, functionally diverse protein complexes having high-resolution three-dimensional structures in both the unbound and bound forms. We unify elastic network models with perturbation response scanning (PRS) methodology as an efficient approach for predicting residues that have the propensity to trigger dissociation of an interacting protein pair, using the three-dimensional structures of the bound and unbound proteins as input. PRS reveals that while for a group of protein pairs, residues involved in the conformational shifts are confined to regions with large motions, there are others where they originate from parts of the protein unaffected structurally by binding. Strikingly, only a few of the complexes have interface residues responsible for dissociation. We find two main modes of response: In one mode, remote control of dissociation in which disruption of the electrostatic potential distribution along protein surfaces play the major role; in the alternative mode, mechanical control of dissociation by remote residues prevail. In the former, dissociation is triggered by changes in the local environment of the protein, e.g., pH or ionic strength, while in the latter, specific perturbations arriving at the controlling residues, e.g., via binding to a third interacting partner is required for decomplexation. We resolve the observations by relying on an electromechanical coupling model which reduces to the usual elastic network result in the limit of the lack of coupling. We validate the approach by illustrating the biological significance of top residues selected by PRS on select cases where we show that the residues whose perturbation leads to the observed conformational changes correspond to either functionally important or highly conserved residues in the complex.

Transient output performance of symmetrical V-shaped micro-piezoelectric energy harvester by using PZT-5H

Wireless sensors have been developed rapidly, while their energy supply components are relatively backward since the beginning of the twenty-first century. This paper proposes a symmetrical V-shaped micro-piezoelectric energy harvester (SV-MPEH) based on PZT-5H, which is used to supply energy to sensors that detect ambient temperature. Firstly, the finite element model and the electromechanical coupling model are established. Secondly, the SV-MPEH adopts parametric design to ensure steady-state output power. Then, the output performance of the SV-MPEH is simulated when the initial temperature is 373 K under the accelerations of 0.5 g, 1 g, and 1.5 g, respectively. Finally, three sets of steady-state output powers are obtained by using two access methods (Type I and Type II) of piezoelectric components. The simulation results indicate that the output power of the SV-MPEH is nearly 20% higher than that of conventional cantilever harvester under the same simulation parameters. In addition, the power density of the SV-MPEH shows a different upward trend through the two access methods (Type I and Type II) of piezoelectric sheets, and Type I exhibits a higher growth rate than Type II.

Piezoelectric Performance of a Symmetrical Ring-Shaped Piezoelectric Energy Harvester Using PZT-5H under a Temperature Gradient.

With the rapid development of microelectronics technology, low-power electronic sensors have been widely applied in many fields, such as Internet of Things, aerospace, and so on. In this paper, a symmetrical ring-shaped piezoelectric energy harvester (SR-PEH) is designed to provide energy for the sensor to detect the ambient temperature. The finite element method is used by utilizing software COMSOL 5.4, and the electromechanical coupling model of the piezoelectric cantilever is established. The output performance equations are proposed; the microelectromechanical system (MEMS) integration process of the SR-PEH, circuit, and sensor is stated; and the changing trend of the output power density is explained from an energy perspective. In the logarithmic coordinate system, the results indicate that the output voltage and output power are approximately linear with the temperature when the resistance is constant. In addition, the growth rate of the output voltage and output power decreases with an increase of resistance under the condition of constant temperature. In addition, with an increase of temperature, the growth rate of the output power is faster than that of the output voltage. Furthermore, resistance has a more dramatic effect on the output voltage, whereas temperature has a more significant effect on the output power. More importantly, the comparison with the conventional cantilever-shaped piezoelectric energy harvester (CC-PEH) shows that the SR-PEH can improve the output performance and broaden the frequency band.

Stability and Sommerfeld Effect of a Vibrating System With Two Vibrators Driven Separately by Induction Motors

The previous studies on the vibrating system with vibrators are mainly focused on existence and stability problems for the synchronous solutions of dynamical systems from the point of view of mathematics and mechanics, whereas the Sommerfeld effect and electromechanical coupling characteristics are less considered, especially less validated by experiment. In this article, we take a dynamical model with two rigid frames driven by two vibrators, for example, where vibrators are powered by induction motors separately. The synchronous and stable states of the system are studied first. Then, the Sommerfeld effect is further revealed to study what happened around the natural frequency of the system. Based on the average method, the criteria of synchronization of two vibrators and that of the stability are discussed in theory and numeric. Under the precondition of implementing synchronization, the Sommerfeld effect is given by establishing the electromechanical coupling model, in which the jump phenomena at the resonant point for the rotational velocities and the vibration amplitude of the system are explained. The synchronization and the coupling characteristics of the considered system are examined by the experiment. Finally, a type of vibrating centrifugal dehydrator has been successfully applied in engineering according to this article.

Electromechanical Coupling Modelling of High Speed EMUs with Rotor Field Oriented Control

According to the theory of vehicle system dynamics and rotor flux-oriented control (RFOC), an electromechanical coupling simulation model of transmission system of high-speed EMUs is established considering the effect of mechanical and electrical characteristics. Firstly, an EMUs multi-body system (MBS) model including is developed by Simpack software based on the structure and parameters of a high-speed EMUs, and a RFOC simulation model of traction transmission system is also built by the Simulink platform. Then two types of models are linked by Simpack co-simulation interface model. Consequently, the electromechanical coupling model of EMUs is developed. The computer simulation method is adopted to simulate the coupling system with RFOC. Simulation results indicate that the proposed model can effectively reveal the change of electrical performance of the high-speed EMUs, the coupling system has a good anti interference performance and robustness.

Research on piezoelectric vibration energy harvester with variable section circular beam

In order to reduce the natural frequency of the piezoelectric vibration energy harvester, improve performance of the piezoelectric vibration energy harvester, and meet the requirements of energy acquisition in the low-frequency vibration environment, a variable-section circular piezoelectric vibration energy harvester is presented. The dynamic model and electromechanical coupling model of variable-section circular piezoelectric vibration energy harvester are established. The main factors affecting the output performance of piezoelectric vibration energy harvester are analyzed. The structure parameters of piezoelectric vibration energy harvester are optimized by orthogonal experiment. An experimental platform is built to test output voltage and output power of piezoelectric vibration energy harvester. The experimental results show that when the number of energy harvester is 4 and the external load is 180KΩ, the parallel output power can reach 0.213mW, which can meet the requirements of micro-power device power supply.

Modeling and nonlinear analysis of stepped beam energy harvesting from galloping vibrations

Abstract This paper presents a nonlinear distributed-parameter model for harvesting energy from galloping oscillation. The stepped beam structure is beneficial to increase the stress and strain of the piezoelectric elements, thereby enhancing the power generation. The finite element analysis is used to verify the feasibility and effectiveness of the developed harvester. A nonlinear distributed-parameter model for the piezoelectric energy harvester with a stepped beam is developed. The instantaneous fluid force in the transverse direction is analyzed. Based on Euler-Bernoulli beam theory, a distributed-parameter model for undamped free vibration is derived, which can be used for the modal analysis. The electromechanical coupling model is established by using the piezoelectric effect theory. The forced vibration subjected to the galloping excitation load is analyzed by using the mode superposition method. The state vector and the fourth order Runge-Kutta algorithm are used to seek the numerical solution. The effects of the electrical load resistance, length, width and thickness of the piezoelectric beam, exposure area and mass of the bluff body on the output power are investigated. In order to find the optimal design of the energy harvester, optimization design is performed based on the established theoretical model. The particle swarm optimization algorithm is employed to search the optimal solution in multidimensional space. Finally, experimental work was carried out, the electrical output characteristics of the energy harvester prototypes were measured. The simulation results are validated with the experimental data. It is demonstrated that the optimal configuration of the energy harvester can improve the output power from galloping phenomenon effectively.

On the double resonance activation of electrostatically actuated microbeam based resonators

Abstract Electrostatically actuated microelectromechanical system (MEMS) devices have shown prominent potential in various applications. However, despite their low power consumption, they do require high input voltages to be actuated. This is even worse if these devices are driven around their mechanical resonant state. Assuming a double resonance excitation scheme, both electrically and mechanically, activates the system’s mechanical and electrical resonances simultaneously. This double resonance activation was recently verified experimentally to alleviate the problem of high actuating voltage/displacement near the resonant state. Therefore, in this work, an analytical electro-mechanical coupled model for a double-resonance-driven microbeam, assuming a classical nonlinear beam model combined with an RLC electric circuit model is first proposed and then numerically examined. Good match among the numerical simulations and the experimental data when the electrical resonance frequency band is sufficiently high is demonstrated. The suggested model can be used to further optimize certain MEMS designs and therefore fully benefit from this double resonance activation scheme in improving MEMS sensors and actuators.

Design and Research on a Nonlinear 2DOF Electromagnetic Energy Harvester With Velocity Amplification

In order to power the microelectronic devices of the Internet of Things in the low-frequency broadband vibration environment, a novel nonlinear 2DOF electromagnetic energy harvester was proposed based on the magnetic levitation structure and velocity amplification mechanism. The electromechanical coupling model was established and numerically simulated to analyze the generating characteristics. A prototype was fabricated and tested to verify the theoretical model. The influences of the key parameters, including the gap between the suspended magnet and the lower spring, excitation acceleration, spring stiffness, mass of copper cylinder, on the generating characteristics were studied. When it was subjected to a harmonic excitation with acceleration amplitude of 0.8g, the measured open-circuit voltage reached peaks of 3.13 V at 8 Hz and 2.93 V at 13.5 Hz, respectively. The optimal output power at 8 Hz was 10.18 mW with the matched load resistance of 250~Ω. Both the experimental and theoretical results demonstrated that this novel electromagnetic energy harvester had obvious advantages in increasing the output power and widening the bandwidth.

Performance evaluation of a bimodal standing-wave ultrasonic motor considering nonlinear electroelasticity: Modeling and experimental validation

• A nonlinear dynamical model was proposed for a typical SWUM. • The inherent nonlinearities of the stator and the contact nonlinearities are modeled. • Several important nonlinear characteristics are accurately predicted and clarified. This paper proposes a nonlinear whole-machine dynamic model for a typical bimodal standing wave ultrasonic motor considering nonlinear electroelasticity of piezoelectric vibrator under high excitation voltage. To capture the inherent nonlinearities of the piezoelectric element, nonlinear constitutive relations of piezoelectric element are adopted to derive the nonlinear electromechanical coupling model of the stator. The contact mechanism between the stator and the mover including stick-slip-separation dynamics and asperity contact mechanics is modeled based on a physical-based equivalent spring model and a modified Coulomb friction model. The measured nonlinear relationships between the excitation voltage and the amplitude response of the stator near resonant frequency are used along with analytical approximations for the nonlinear vibration responses by harmonic balance method to identify the critical nonlinear parameters. Finally, experiments are conducted to validate the proposed model, and the results show that the simulations agree well with the experimental results. In particular, nonlinear speed saturation phenomenon and the resonant frequency drift of the motor can be predicted and analyzed by the developed model when the motor is driven at a higher voltage, which are useful for the performance evaluation and working range choice of such motors under high-power input conditions.

Modeling and verification of piezoelectric wind energy harvesters enhanced by interaction between vortex-induced vibration and galloping

Previous works verified experimentally that interactions between vortex-induced vibration (VIV) and galloping may greatly improve the performance of piezoelectric wind energy harvesters (PWEHs) at low wind speeds. However, no mathematical model has been available to date to predict the responses or optimize the structures of PWEHs. In this paper, a distributed-parameter electromechanical coupling model of a VIV-galloping interactive PWEH was derived and was then experimentally validated using two harvester prototypes. For the first prototype, while the theoretical critical galloping speed is approximately 2.1 times the theoretical critical VIV speed, the experiments verified the proposed model’s prediction that this harvester involves full interaction between VIV and galloping because there is only one wind speed region (in the wind speed range of interest) that offers high electrical output. For the second prototype, whose theoretical galloping speed is about 2.3 times the critical VIV speed, the model indicates that there are two completely separate wind speed regions that have relatively high electrical outputs, implying that this is a harvester without the interaction between VIV and galloping, coinciding with the experimental results. For both prototypes, the model is accurate enough to predict the onset reduced speeds for the wind speed regions with high electrical outputs, and can be used to obtain the output voltage in the wind speed range of interest. The proposed model can thus be used to design VIV-galloping interactive PWEHs with enhanced performance in the collection of low speed airflows.

Nonlinear Dynamics and Performance Enhancement of Multi-stable Wideband Energy Harvesting: Theoretical Analysis

A new multi-stable wideband harvester is proposed to increase the power density of energy harvesting under wide-bandwidth and low-frequency operations. This harvester can possess with an arbitrary multi-stable state by combining the nonlinearities of stopper-engaged cantilevers and magnetic forces. The harvesting efficiency can be enhanced by interwell oscillations and the global amplitude of the harvester is restricted by the cantilever-stopper engagement. An electromechanical coupling model of the proposed harvester is established to describe its dynamic characteristics. To explore the influence of potential well configurations on a multi-stable energy harvesting, the proposed harvester with four typical potential well configurations is considered while its equivalent nonlinear restoring force can be experimentally identified. The dynamic characteristics of these four configurations at different levels of a harmonic excitation will be explored by both numerical and experimental methods. It is expected that a multiple-well potential with non-uniform depths and shallower outer wells is much more suitable for the proposed system when the external excitation exceeds a critical intensity.

Design and simulation of a novel ancient Chinese bow-type piezoelectric actuator

Piezoelectric materials are increasingly researched and used because of their ability to convert electrical energy and mechanical energy. Piezoelectric patches are usually applied with other structures to form piezoelectric actuators to expand the capability and use of piezoelectric patches. In this paper, a new piezoelectric actuator based on the ancient Chinese arch structure is proposed. The piezoelectric actuator is mainly composed of a bow device and several piezoelectric plates. Firstly, the electromechanical coupling model of the cantilever beam structure is established based on the finite element method. The action characteristics of the bow-type piezoelectric actuator are studied. Then static analysis of the cantilever beam with the bow-type piezoelectric actuator is applied. The effect of the bow-type piezoelectric actuator on the cantilever beam under different parameters is analysed and compared, including actuation voltages, locations and physical dimensions of the bow-type structure. Especially, the thickness of the device and the span of the bow device are optimized to better capability. The simulation results show that the thickness and the span of the bow-type device in the bow-type piezoelectric actuator affect the action of the piezoelectric actuator on the cantilever beam remarkably. Additionally, the bow-type piezoelectric actuator is easy to install, simple to manufacture, and can be reused. The research in this paper will provide a reference for the active control or energy harvesting of structural vibration.

Design and Analysis of a Magnetically Coupled Multi-Frequency Hybrid Energy Harvester.

The approach to improve the output power of piezoelectric energy harvester is one of the current research hotspots. In the case where some sources have two or more discrete vibration frequencies, this paper proposed three types of magnetically coupled multi-frequency hybrid energy harvesters (MHEHs) to capture vibration energy composed of two discrete frequencies. Electromechanical coupling models were established to analyze the magnetic forces, and to evaluate the power generation characteristics, which were verified by the experimental test. The optimal structure was selected through the comparison. With 2 m/s2 excitation acceleration, the optimal peak output power was 2.96 mW at 23.6 Hz and 4.76 mW at 32.8 Hz, respectively. The superiority of hybrid energy harvesting mechanism was demonstrated. The influences of initial center-to-center distances between two magnets and length of cantilever beam on output power were also studied. At last, the frequency sweep test was conducted. Both theoretical and experimental analyses indicated that the proposed MHEH produced more electric power over a larger operating bandwidth.

Design, analysis and experimental study of a T-shaped piezoelectric energy harvester with internal resonance

In this paper, a T-shaped piezoelectric energy harvester (TPEH) is proposed by taking advantages of internal resonance and multimodal techniques. The developed TPEH is composed of a clamped-sliding main beam and a branched vertical cantilever beam at the center. The sliding end of the clamped-sliding beam could move freely along the axial direction, and two piezoelectric patches are attached at both sides of the substrate near the sliding end. An electromechanical coupling model was established based on the extended Hamilton’s method. The simulation results are in good agreement with the experimental results. The simulation and experimental results indicate that the 1:3 internal resonance phenomenon of the TPEH occurs when the excitation frequencies are close to the first resonance of the TPEH. As a result, the energy conversion efficiency can be significantly increased through the high-frequency response at the low-frequency excitation. Meanwhile, the operational bandwidth is widened with the hardening nonlinear response of the proposed TPEH within the first resonance bandwidth. Finally, it was demonstrated that the proposed TPEH is able to harvest practical vibration energy with low-amplitude and low frequency.

Study on electromechanical performance of steering of the electric articulated tracked vehicles

Articulated tracked vehicles (ATVs) usually use hydraulic drive or mechanical drive modes. Electrically driven tracked vehicles have become a promising development direction for saving energy and meeting the environment requirements. In this study, based on the mechanical motion equation and the dynamic ATV equation, the electromechanical coupling model of the track vehicles is established by coupling the motor equation. The typical mechanical and electrical parameters in the ATV steering process are measured and compared with the numerical results to verify the correctness of the electromechanical coupling model. Experimental results indicate the main mechanical and electrical parameters of the ATV electro-mechanical system are changed at different articulated point deflection angles. The characteristic parameters of ATV include the change in current and voltage, the size of trajectory radius and the change of power under different deflection angles (10°, 15°, 20°, 25° and 30°), all of which are of great significance for the control of ATV. The current and voltage signals of ATV under specific trajectory can be calculated in reverse by the model, thereby providing a theoretical basis for the trajectory control of articulated vehicles. Therefore, this study provides a reference for the theoretical analysis of electromechanical performance, road driving performance and vehicle design of the electric ATV.

Electrodynamic response study on railgun launcher based on electromechanical coupling model

The electrodynamic behavior of a medium caliber railgun launcher has been studied based on an electromechanical coupling model, which uses a unified modeling method for both electromagnetic and electromechanical field. This model adopts a material equivalent method to simulating the sliding contact behavior for the in-bore armature. An embedded node encoding program during field meshing operation provides good load transfer accuracy between electromagnetic field and mechanical field. Dynamic properties of in-bore magnetic field are firstly simulated and a subsequent dynamic analysis is conducted by mapping element results from electromagnetic analysis step to structure analysis step. The electromechanical-elastic response of the barrel is studied under the excitation current. The numerical model has shown reliability compared to experimental results.

Uncertainty analysis of dielectric elastomer membranes under electromechanical loading

The uncertainty in modeling finite deformation membrane electromechanics is analyzed by comparing low and high fidelity models against data on the dielectric elastomer VHB 4910. Both models include electrically and mechanically induced stress during transverse deformation of the membranes. The low fidelity model approximates deformation to be homogeneous while the high fidelity model includes a more accurate kinematic assumption of inhomogeneous deformation. We illustrate the importance of model fidelity with regards to parameter uncertainty and the associated propagation of errors in predicting membrane forces and charges in realistic actuator configurations. Both the low and high fidelity models are shown to accurately predict membrane forces and charges under different applied displacements and voltages. However, there are significant differences in the estimation of the dielectric constant used to model the membrane electromechanics. Bayesian statistics are used to quantify the uncertainty of the modeling approaches in light of both force–displacement and charge–voltage measurements. We quantify the hyperelastic, electromechanical coupling, and dielectric model uncertainties self-consistently using all mechanical and electrical experiments conducted on the 3M elastomer VHB 4910. We conclude that the low fidelity model is useful for system dynamic and control applications yet is limited in self-consistent predictions of both forces and charges from applied displacements and voltages. In comparison, the high fidelity model provides a more accurate description of the electromechanical coupling and dielectric constitutive behavior, but requires more computational power due to finite element discretization. In addition, the high fidelity modeling illustrates that a deformation dependent dielectric constant is necessary to self-consistently simulate both force–displacement and charge–voltage data.

Influence Mechanism of Electromechanical Parameters on Transient Vibration of Electric Wheel System

<div class="section abstract"><div class="htmlview paragraph">Electric wheel systems of in-wheel motor driven vehicles consist of the motor controller, in-wheel motor and tire-suspension assembly. The coupling between the electromagnetic excitation and elastic structure gives rise to electromechanical dynamic issues. As for the structural layout of the electric wheel system, the driving motor is directly connected to the wheel without torsion dampers or transmission in the driveline, thus making the electric wheel structure a weak damping system. Moreover, the driving torque of electric wheel can change rapidly in various conditions of vehicle. As a result, the transient vibration problem becomes one of the key electromechanical dynamic issues in the electric wheel system. To investigate this problem, the electromechanical coupling model of the electric wheel system is established first. Then the transient responses of the electric wheel under abrupt changes of the driving torque are simulated. The results indicate that the tire mainly suffers from longitudinal shocks in the anti-phase rotational mode at 95 Hz and vibration in the in-phase rotational mode at 44Hz successively, while the motor vibrates in the in-phase rotational mode at 44Hz. As the electric wheel system is electromechanically coupled, the influence mechanism and rules of electromechanical parameters on the transient vibration are studied. The results show that the permanent magnet flux linkage increases damping ratio of the in-phase rotational mode in virtue of the electromagnetic stiffness and damping, thus further weakening transient vibration of motor. The anti-phase rotational mode is sensitive to tire’s stiffness. It is effective to optimize tire’s shock by adjusting tire’s stiffness. This paper reveals the electromechanical coupling mechanism of the electric wheel system, and provides reference for parameter design from the perspective of improvement in dynamic characteristics.</div></div>