Magnetostrictive Model Research Articles

A nonlinear dynamic hysteresis model with magnetic–prestress–thermal coupling effect and dynamic electromagnetic losses of a giant magnetostrictive actuator

Compared with traditional actuators, the giant magnetostrictive actuator has the merits of fast response, high accuracy, and high reliability and has been widely applied. However, its performance is affected by the electromagnetic loss and the temperature, prestress, and magnetic coupling effect. In order to accurately analyze its performance, it is necessary to establish a nonlinear dynamic model including the electromagnetic loss and the magnetic–prestress–thermal coupling effect. First, based on the field separation approach, the magnetic fields generated by the eddy current loss and the anomalous loss are obtained and added to the Jiles–Atherton model. Second, the magnetostrictive model is given with the magnetic–prestress–thermal coupling effect. Finally, assuming the transmission of the giant magnetostrictive actuator as a mass–spring–damper system, a nonlinear dynamic hysteresis model with magnetic–prestress–thermal coupling effect and dynamic electromagnetic losses of a giant magnetostrictive actuator is developed. Based on this model, the output displacement curves of the giant magnetostrictive actuators under different driving currents and frequencies are given. The comparison with the experimental results shows that this model agrees well with the experiment.

Vibration characteristics of a single‐phase four‐column auto‐transformer core excited by geomagnetically induced currents

AbstractDuring geomagnetic storms, geomagnetically induced currents (GICs) occur in the power grid. GIC is a quasi‐direct current, which is represented by using a fixed DC current, the authors propose an approach that combines field‐circuit‐coupled and weakly coupled magneto‐mechanical models to investigate the magnetostriction characteristics of single‐phase, four‐column autotransformer cores excited by GICs. A non‐linear magnetostrictive constitutive model that considers the impact of stress and magnetisation intensity on ferromagnetic materials is introduced. The model reveals that the strain in the core initially increases as the magnetisation intensity increases; however, when the core begins to saturate, the magnetostrictive strain weakens as the magnetisation intensity increases. Moreover, the results of multiphysics finite‐element modelling are experimentally verified using a direct current bias platform. The results show that when excited by GICs, there is an enhancement in the vibration of the iron core, and the harmonic content of the vibration acceleration increases considerably, with the odd harmonics most significantly increasing in amplitude. The conclusion drawn is that GICs can exacerbate transformer vibration and significantly increase the content of harmonics, especially odd harmonics.

Modeling and simulation of magnetostrictive actuators based on ΔE effect Preisach model

Based on the classical Preisach model, combined with the magneto-mechanical coupling effect of Giant magnetostrictive materials (GMM), this paper introduces the Everett function to optimize the classical Preisach hysteresis model and improve its accuracy. By importing dynamic parameters, the dynamic Preisach hysteresis model is established. Combined with the constitutive model of GMM, a dynamic Preisach hysteretic nonlinear magnetostrictive actuator model based on the ΔE effect is established. Then, the finite element simulation is carried out by Comsol software and compared with the theoretical model simulation. The results show that the error between the magnetostrictive strain of the established hysteresis model and the finite element simulation results is less than 100 ppm, which verifies the accuracy of the proposed model. Finally, the curves of magnetic field intensity, magnetic induction intensity, magnetization, magnetostrictive strain and ΔE effect of GMA are obtained by using this model.

Non-linear modeling of a bi-layer magnetostrictive cantilever considering [formula omitted]E effect

Magnetostrictive cantilever beams are reliable and straightforward energy harvesting devices for powering wireless sensors using environmental vibrations. However, despite their widespread use, a comprehensive analytical model encompassing both mechanical and electromagnetic main features is still lacking. The mechanical-to-magnetic coupling of a magnetostrictive beam, with its various working conditions and nonlinear characteristics, can be effectively approximated by the Euler–Bernoulli (E–B) equation with damping (viscous and Kelvin–Voigt) coupled with a non-linear magnetostrictive model. In this study, we propose a practical and convenient model for a general concept device designed to convert vibrations into electrical energy. The model is thoroughly compared with experimental measurements aimed to prove the goodness of the approach rather than energy harvesting highest performance.

An improved stress-dependent magnetostriction model of silicon steel based on simplified multi-scale and Jiles–Atherton theory

Due to the magnetic domain movement and energy change under magnetic field and stress applied, the macroscopic magnetic properties and magnetostriction properties of non-oriented (NO) silicon steel are influenced. To present this effect of the magnetic domains’ motion mechanism, a stress-dependent magnetostriction must be modeled. This paper proposes an improved stress-dependent magnetostriction model (I-SDM model) for NO silicon steel based on a simplified multi-scale model. Firstly, the stress-dependent expression of the anhysteretic magnetization, obtained by assuming a six-domain structure and considering the volume fraction of magnetic domain energy, is introduced into the inverse Jiles–Atherton (JA) model. In this way, the stress-dependent hysteresis model is constructed. Then, coupling with the improved quadratic domain rotation model that considers pinning effects, the I-SDM model for NO silicon steel is built. Finally, with the parameters obtained from experimental results, the proposed model under varying stresses is simulated and compared with other models. It shows that the proposed model has the highest simulated accuracy for both λ-H loop and λ-B loop with stress applied.

Efficient Modeling of Magneto-Elastic Media Using the Feedback Preisach Model

Magnetic materials demonstrating relatively high magnetostriction are currently being widely employed in various applications. Actuators, energy harvesting and vibration damping are examples of such applications. Several magnetostriction models, which vary in quantitative accuracy, efficiency and identification approaches, have been previously suggested. This paper presents an efficient approach for modeling magneto-elastic media by employing a single scalar feedback Preisach-type model. Identification procedure of the proposed model and its experimental testing are presented. Testing and comparison results have demonstrated the overall good qualitative and quantitative accuracy of the proposed model. Details of the proposed approach, its implementation and experimental testing are given in the paper.

Modeling magnetostriction of grain-oriented sheet steels based on magnetization process and domain motion

Grain-oriented (GO) sheet steels are preferred for magnetic cores in large power transformers because of their low core loss and high permeability. However, GO sheet steels exhibit more complex magnetostriction than non-oriented (NO) materials, causing undesirable vibrations and acoustic noises in the transformer core, especially under certain operating conditions, such as DC bias and magnetic saturation. This paper proposes a magnetostriction model of GO sheet steels based on an improved understanding of the magnetization process and domain motion. Incorporating the positive and negative magnetostriction components attributed to domain wall motion and rotation, the proposed model can accurately reproduce the butterfly loops in a wide range of magnetization along the rolling direction (RD) of GO material. Its effectiveness and accuracy are verified by the experimental measurements.

Isotropic micromagnetic field model of ferromagnetic stress effects

We model magnetoelastic transducer processes including virgin field DH∼, virgin prestress DσH∼ and post stress DHσ∼ using the isotropic micromagnetic field model of ferromagnetic hysteresis and magnetostriction up to the coercive field. Magnetostriction of Fe94Ni3Cr2Mo1 steel has been precisely measured for DσH∼ with a thermally isolated yoke in order to compute microscopic Brown and macroscopic Villari stress fields. Magnetization M and field H were quasistatically measured with a Hall probe and differential Faraday induction coil. Prestress DσH reveals Brown field advanced virgin susceptibility and Villari field induced stress asymmetry. Post stress DHσ∼ reveals symmetric Brown field, stress asymmetry due to negative domain walls and cyclic creep due to Villari stress sensitivity dM/dσ, hyperbolic domain coupling and Néel viscosity.

Nonlinear dynamic characteristics of two-dimensional micro-positioning workbench based on giant magnetostrictive actuators

Studying the nonlinear dynamic characteristics of multi-field coupling of the giant magnetostrictive actuator (GMA) is one of the main ways to improve its output performance. Because of the problem that its multi-field coupling nonlinear dynamic characteristics are difficult to accurately describe, the multi-field coupled nonlinear dynamic model of GMA and two-dimensional micro-positioning workbench is established according to the Jiles–Atherton hysteresis model, magnetostrictive model, hysteresis nonlinear magnetic equation and the structural dynamics principle of GMA, respectively. The influence of equivalent damping coefficient, equivalent stiffness, and equivalent mass on the dynamic characteristics of each model is analyzed, and finally, the constructed model and the obtained law are experimentally verified. The results show that the displacement curve calculated by the model is consistent with the experimentally measured displacement curve, the influence of the equivalent damping coefficient, equivalent stiffness, and equivalent mass on the dynamic characteristics of the model measured by the experiment is consistent with the simulation analysis results, and the maximum error of the output displacement is 1.779 um, which verifies the correctness of the model. The research results provide a theoretical basis for improving the dynamic characteristics of GMA and improving the output performance of two-dimensional micro-positioning workbenches.

Magnetic Circuit Optimization and Physical Modeling of Giant Magnetostrictive Actuator

Due to the excellent performance, giant magnetostrictive actuator is used in the active vibration isolation control system. However, its hysteresis nonlinear dynamic model is too complex for engineering practical applications, so it is necessary to establish an accurate and easy-to-use model. Based on Simulink/Simcape, a magnetic circuit model and a nonlinear dynamic physical model of the giant magnetostrictive actuator are developed. In the optimization of the magnetic circuit, the uniform distribution and the magnetic energy utilization of the giant magnetostrictive actuator are taken as the optimization objective, and the design criteria of the magnetic circuit are given. The hysteresis performance between the current and the magnetization is analyzed by simulating the magnetic circuit model. From the perspective of energy conservation, a linear magnetostrictive model which can reflect the effects of the frequency doubling and preload is established. Finally, the accuracy of the nonlinear dynamic physical model for the giant magnetostrictive actuator is verified by an experiment. The results show that the physical model agrees well with the experiment results not only under the quasistatic operating conditions but also under dynamic operating conditions. The error of the output displacement of the GMA under step response is less than 0.6 μm.

Characterization of Terfenol-D and Comparison With Predictions of a Thermodynamically Consistent Two-Input, Two-Output Model of Hysteresis

Since its discovery more than forty years ago, Terfenol-D has promised much but has not yet been fully exploited in applications.The main reason for this is that it shows significant hysteresis and other nonlinearities, such as saturation, which need to be modeled correctly in order to maximize the application potential. In this article, we focus on the characterization of a Terfenol-D sample with the intention of developing a predictive two-input (magnetic field and stress) and two-output (magnetic flux density and strain) model of magnetostriction that exhibits hysteresis and saturation and is compatible with the laws of thermodynamics. Compatibility with thermodynamics is essential to ensure that numerical simulations do not exhibit unphysical behavior. The model is based on the Preisach hysteresis operator and its storage function and may be interpreted as a two-input, two-output neural net with elementary hysteresis operators as the neurons. In order to estimate the parameters, it is necessary to collect data over a wide range of magnetic fields (-300 kA/m to 300 kA/m) and compressive stresses (up to 60 MPa). Using the rate-independent memory evolution properties of the Preisach operator, we split the parameter estimation problem into three numerically well-conditioned, linear least squares problems with constraints. We show that the model is able to fit experimental data for strain and magnetization over a wide range of magnetic fields and stress.

Tuning the Performance of Acoustically Actuated Magnetoelectric Antenna via Magnetic and Mechanical Stimuli

Magnetoelectric (ME) antenna operates at the acoustic wave resonance rather than EM wave resonance, thus it shows significant superiority for developing compact antennas and antenna arrays. The simulation of ME antenna involves the nonlinear coupling of Electrostatics, Solid Mechanics, and Magnetic physics, making it difficult to model such devices. This paper proposes a fully multi-field coupled model for the ME antenna, in which the nonlinear magnetostrictive model is taken into account. The nonlinear magnetization is solved and then AC and DC simulations are performed by coupling different physics. The effects of magnetic bias and pre-stress on the converse magnetoelectric (CME) coupling and near-field radiation are discussed for the first time, to regulate the performance of the ME antenna with fixed dimensions. The results indicate that the magnetic bias and pre-stress can change the resonance frequency, CME coefficient, and near-field radiation of ME antenna. Particularly, it should be noted that pre-stress has the opposite effect in the low and high regions of the bias field. The near-field radiation is significantly enhanced by applying a proper magnetic bias or pre-stress. This simulation may facilitate the understanding of nonlinear CME behavior and provide a basis for designing nonlinear active and tunable ME antenna.

Enhanced near-field radiation of acoustic-actuated antennas using embedded magnetoelectric composites

Acoustic-actuated antennas operate at the acoustic wave resonance rather than electromagnetic (EM) wave resonance and thus show a significant superiority for the miniaturization of antennas. This paper designs a new acoustic-actuated antenna using embedded magnetoelectric (ME) composites, to improve the radiations of ME antennas through the enhanced strain transfer at the interfaces between different phases. The performance of the ME antenna is examined through a multiphysics finite element method with considering the nonlinear magnetostrictive model. Then, three optimum schemes are proposed for the improvement of the ME antenna, which are also verified by the simulation results. It has been demonstrated that the EM radiations of the embedded ME composite are effectively improved by changing its sizes or configuration. Due to the magnetic flux and stress concentration effects, the maximum |E| and |H| radiations are respectively enhanced by 88 % and 97 % via using a trapezoidal magnetostrictive layer. The effects of magnetic bias and pre-stress indicate that near-field radiations of the ME antennas with fixed dimensions can be enhanced by external multi-physics fields. This simulation may facilitate the understanding of nonlinear CME behavior as well as provide a basis for the design of tunable ME antennas.

Magnetostriction property modeling of silicon steel considering stress-induced and magnetocrystalline anisotropy

This paper proposed an improved magnetostriction model for correlation of anisotropy in non-oriented (NO) silicon steel based on the free energy, which considers stress-induced and magnetocrystalline anisotropy. Firstly, the free energy model, which includes stress-induced anisotropy energy, the energy of magnetic field, and the anisotropic energy of magnetic crystals, is incorporated into the anhysteretic magnetization parameter Man. Then, to obtain the magnetic field and proposed model parameters related to stress-induced and magnetocrystalline anisotropy, the magnetostrictive strain loops at different magnetization directions of NO silicon steel are measured. Finally, based on the parameters obtained from experimental data of the proposed model, magnetostrictive strain loops under varying magnetization directions are simulated. This improved magnetostriction model can be applied to the calculation of the vector magnetostriction of the motor core.

A simplified magnetostrictive model under rotational magnetization in an electrical steel sheet taking the pinning hysteresis effect into account

A large number of experimental observations show that under two-dimensional (2-D) rotational magnetization, there is a complicated relationship between the magnetostrictive strain and magnetic flux density. In this paper, the magnetostrictive characteristics in a non-oriented electrical steel sheet under 2-D magnetization are measured and modelled based on the experimental system developed by the laboratory. The in-plane magnetostrictive strain tensor under the 2-D magnetization is expressed as nonlinear superposition of dynamic magnetostrictive strain in the rolling direction (RD) and transverse direction (TD), respectively. The magnetostriction’s first derivative with respect to magnetization depicts the pinning effect and the interaction among magnetic domains which result in the hysteresis behaviour. And based on the particle swarm optimization (PSO), the model parameters are identified. The validity of the proposed model is verified by comparing the calculation results with the experimental ones. Studies have shown that the magnetostrictive properties in an electrical steel sheet have strong hysteresis behaviour under the 2-D magnetization, and the model proposed here can well characterize these characteristics.

A dynamic magnetostrictive model based on the Jiles–Atherton hysteresis model and field separation approach

PurposeThe purpose of this paper is to combine the Jiles-Atherton (J-A) hysteresis model with the field separation approach to realize the accurate simulation of dynamic magnetostrictive characteristics of silicon steel sheet.Design/methodology/approachFirst, the energy loss of silicon steel sheet is divided into hysteresis loss Why, classical eddy current loss Wed and anomalous loss Wan according to the statistical theory of losses. The Why is calculated by static J-A hysteresis model, Wed and Wan are calculated by the analytical formulae. Then, based on the field separation approach, the dynamic magnetic field is derived. Finally, a new dynamic magnetostrictive model is proposed by means of the quadratic domain rotation model.FindingsComparison of simulation and experimental results verifies that the proposed model has high accuracy and strong universality.Originality/valueThe proposed method improves the existing method’s problem of relying on too much experimental data, and the method ensures the calculation accuracy, parameter identification accuracy and engineering practicability. Consequently, the presented work greatly facilitates further explorations and studies on simulation of dynamic magnetostrictive characteristics of silicon steel sheet.

The Vector Electromagnetic Vibration of Magnetically Controlled Reactor Considering the Vector Hysteretic Magnetostriction Effect

Magnetically controlled reactors (MCRs) are widely used as reactive power compensation equipment owing to their favorable properties of smoothly adjusting their inductance value through dc bias. However, the dc bias and the rotational magnetization at corner and T-joint areas make the cores of MCRs saturated, resulting in high magnetostriction and vibration. Thus, the electromagnetic vibration analysis of MCRs must consider the vector hysteretic magnetostriction effect. In this article, a vector hysteretic magnetostriction model of silicon steel is proposed by combining the quadratic domain rotation model with the vector inverse Jiles–Atherton model firstly. Then, based on the measured magnetization and magnetostrictive characteristics curves of silicon steel, the model’s parameters are optimized by velocity controllable particle swarm optimization (VCPSO). Finally, the vector hysteretic magnetostriction model is combined with the finite element method (FEM) to simulate the vector vibration characteristics of MCR under dc bias. The simulation results show that the vector property of electromagnetic vibration and magnetic field at the T-joint area is higher than that at other areas. And the MCR vibration test results are consistent with the simulation results, which verify the accuracy of the proposed model in simulating electromagnetic vibration.

Parameter optimization of magnetostrictive bistable vibration harvester with displacement amplifier

The vibration harvester can transform the ambient vibration energy into electrical energy for the use of microelectronic equipment. Currently, the introduction of bistable structure in magnetostrictive harvester makes the system have two equilibrium states, thus the output capacity of the system is improved. In order to further improve the working ability and its ability to harvest vibration of magnetostrictive bistable harvester with displacement amplification mechanism, the identification of the key parameters of the magnetostrictive bistable vibration harvester's mathematical model are first proposed in the paper. The accurate values of system damping, electromechanical coupling factor, piezomagnetic coefficient and permeability are obtained. On this basis, bistable structure and displacement amplification mechanism in the harvester are optimized, including the repulsive permanent magnets distance in the bistable structure, mass ratio and stiffness ratio between the bistable structure and the displacement amplification mechanism. Finally, the working ability of the optimized prototype is tested through experiments. The results show that the output voltage and electrical power of the optimized prototype are increased by 2∼4 times and 4∼15 times compared with the unoptimized prototype. Under the excitation amplitude of 7.84 m/s2, the voltage of the optimized prototype reaches 2.96 V, and the electrical power reaches146.032 mW.

Stress-dependent nonlinear magnetoelectric effect in press-fit composites: A numerical and experimental study

Magnetoelectric (ME) composites have posed an immense research interest over the past few decades. Their multifunctional capabilities enable a wide array of applications like field and pressure sensors, energy harvesters, gyrators, etc. The voltage developed under applied magnetic fields in these composites is governed strongly by the stress and magnetization state of the magnetostrictive phase, which needs to be characterized effectively. Towards this end, magnetostriction measurements are carried out under applied stresses in Nickel to understand its magnetomechanical response. A three-dimensional magnetostrictive constitutive model is used to predict the magnetostrictive behavior, which is later implemented in COMSOL Multiphysics® using the external material module. The FE solutions obtained are validated against analytical solutions. The model is subsequently used to obtain FE solutions for the magnetoelectric response of press-fit composites subjected to general magneto-thermo-mechanical loading. Experiments are performed on the press-fit composite to validate the voltage response predicted by the developed model, which shows a good agreement. The developed FE model is used to conduct a parametric study to quantify the effect of external loading conditions, the shape of inclusion, and the field orientation with an effort to optimize the ME response in press-fit ME composites.

A Preisach-Based Magnetostriction Model for Highly Grain-Oriented Electrical Steel Under Rotating Magnetic Field

An accurate estimation for the magnetostrictive effect in highly grain-oriented electrical steel sheet (HGO-ESS) is helpful for determining the deformation and vibration originating from magnetostriction during the design stages of electrical equipment such as the motor and power transformer. In this paper, a Preisach-based magnetostriction model for HGO-ESS is proposed to simulate the normal and shear magnetostriction properties under alternating and rotating magnetic fields. In the model, the Everett function databases are constructed and identified by using a set of measured symmetric magnetostriction butterfly loops under different rotating magnetic field conditions. The measurement butterfly loops are measured by a round-type two-dimensional single strain tester (R-2-D-SST). Finally, the simulation data and measurement data under different rotational magnetization conditions are compared to verify the effectiveness of the proposed model.