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The purpose of this paper is to find the method for determining the displacement of the active element in a giant magnetostrictive transducer.

The giant magnetostrictive transducer with the active element made of Terfenol-D has been considered. A structure with an axisymmetrical transducer has been proposed. In the proposed model the coupling of magnetic and mechanical field has been taken into account. Maxwell’s equations for electromagnetics and Navier’s equations for mechanical systems are formulated in weak form and coupled using a nonlinear magneto-mechanical constitutive law for Terfenol-D. In order to obtain the distribution of the magnetic and mechanical fields the finite element method was used. The elaborated nonlinear magnetostrictive model has been implemented by using a finite element weak formulation with COMSOL Multiphysics.

The elaborated model for the giant magnetostrictive transducer allows to take into account the magneto-mechanical coupling as well as the material’s nonlinearity. The calculation results of the strain distributions caused by magnetostrictive forces have been presented. The output displacement of a transducer vs supply current for different compressive preload stresses has been calculated and measured. The simulation and measurements results are in close agreement.

Taking advantage of the geometrical structure of the prototype of the giant magnetostrictive transducer the computations are performed in an axial-symmetric domain with cylindrical coordinates (r, z, ϑ). The axisymmetric formulation describes the giant magnetostrictive transducers (GMT) without significant loss of accuracy. This approach leads to smaller numerical models and reduced computational time.

The elaborated magneto-mechanical model can be used to the design and optimize the structure of GMT.

The paper offers the magneto-mechanical model of the giant magnetostrictive transducer. The elaborated model can predict behavior of the magnetostrictive materials it can be used as a tool for the design process of the giant magnetostrictive transducer.

The 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.

First, 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.

Comparison of simulation and experimental results verifies that the proposed model has high accuracy and strong universality.

The 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 modeling of magnetostrictive effects is a topic of intensive research. The authors' goal is the precise modeling and numerical simulation of the magnetic field and resulting mechanical vibrations caused by magnetostriction along the joint regions of electric transformers.

The authors apply the finite element (FE) method to efficiently solve the arising coupled system of partial differential equations describing magnetostriction. Hereby, they fully take the anisotropic behavior of the material into account, both in the computation of the nonlinear electromagnetic field as well as the induced magnetostrictive strains. To support their material models, the authors measure the magnetic as well as the mechanical hysteresis curves of the grain-oriented electrical steel sheets with different orientations (w.r.t the rolling direction). From these curves they then extract for each orientation the corresponding commutation curve, so that the hysteretic behavior is simplified to a nonlinear one.

The numerical simulations show strong differences both in the magnetic field as well as mechanical vibrations when comparing this newly developed anisotropic model to an isotropic one, which just uses measured curves in rolling direction of the steel sheets. Therefore, a realistic modeling of the magnetostrictive behavior, especially for grain-oriented electrical steel as used in transformers, needs to take into account the anisotropic material behavior.

The authors have developed an enhanced material model for describing magnetostrictive effects along the joint regions of electric transformers, which fully considers the anisotropic material behavior. This model has been integrated into a FE scheme to numerically simulate the mechanical vibrations in transformer cores caused by magnetostriction.

Magnetostrictive alloys are widely used in actuator and sensor applications. The purpose of this paper is to developed a realistic physical model and a numerical computational scheme for their precise computation.

The main step in the physical modeling is the decomposition of the mechanical strain and the magnetic induction into a reversible and an irreversible part. For the efficient solution of the arising coupled nonlinear partial differential equations the authors apply the finite element method.

It can be demonstrated, that the hysteresis operators can be fitted by appropriate measurements. Therewith, the developed physical model and numerical simulation scheme is applicable for the design of magnetostrictive actuators and sensors.

The decomposition of the mechanical strain and the magnetic induction into a reversible and an irreversible part. The reversible part is described by the linear magnetostrictive constitutive equations, where the entries of the coupling tensor depend on the magnetization. The irreversible part of the magnetic induction is modeled by a Preisach hysteresis operator, and the irreversible part of the mechanical strain by a polynomial function depending on the magnetization.

Owing to the excellent performance, giant magnetostrictive materials (GMMs) are widely used in many engineering fields. The dynamic Jiles–Atherton (J-A) model, derived from physical mechanism, is often used to describe the hysteresis characteristics of GMM. However, this model, despite cited by many different literature studies, seems not to possess unique expressions, which may cause great trouble to the subsequent application. This paper aims to provide the rational expressions of the dynamic J-A model and propose a numerical computation scheme to obtain the model results with high accuracy and fast speed.

This paper analyzes different published papers and provides a reasonable form of the dynamic J-A model based on functional properties and physical explanations. Then, a numerical computation scheme, combining the Newton method and the explicit Adams method, is designed to solve the modified model. In addition, the error source and transmission path of the numerical solution are investigated, and the influence of model parameters on the calculation error is explored. Finally, some attempts are made to study the influence of numerical scheme parameters on the accuracy and time of the computation process. Subsequently, an optimization procedure is proposed.

A rational form of the dynamic J-A model is concluded in this paper. Using the proposed numerical calculation scheme, the maximum calculation error, while computing the modified model, can remain below 2 A/m under different model parameter combinations, and the computation time is always less than 0.5 s. After optimization, the calculation speed can be enhanced with the computation accuracy guaranteed.

To the best of the authors’ knowledge, this paper is the first one trying to provide a rational form of the dynamic J-A model among different citations. No other research studies focus on designing a detailed computation scheme targeting the fast and accurate calculation of this model as well. And the performance of the proposed calculation method is validated in different conditions.

The purpose of this paper is to improve the modeling accuracy of the magnetostrictive hysteretic characteristics by introducing hysteresis energy instead of pinning energy in the assembled domain structure model (ADSM).

First, the magnetostrictive characteristics and the domain movement process in an electrical steel sheet are measured and observed. The reasons for the influence of stress on magnetostriction are discussed on the mesoscopic level. Second, the ADSM model using the hysteresis energy is investigated to estimate the influence of external stress. Finally, the simulation results of the modified ADSM model are compared with the experimental data under the same calculation conditions.

The results show that the improved model not only explains the cause of hysteresis clearly from the perspective of the magnetic moment but also improves the modeling ability of magnetostrictive hysteretic.

The magnetostriction in electrical steel lags behind the external magnetic field, and it is significant for reducing core vibration to estimate the magnetostrictive hysteretic property accurately. This paper proposes an effective approach to model the hysteretic characterization of magnetostriction.

This paper aims to investigate a novel giant magnetostrictive (GM) force sensor using Terfenol-D rod.

First of all, principle of GM force sensor based on positive magnetostriction of Terfenol-D is presented. Then, design procedure of the GM force sensor is stated. Magnetic properties such as B-H curve and permeability of Terfenol-D are measured by a novel experimental setup and the results are used in analytical model, sensitivity estimation and numerical simulations. Then, an analytical model is presented and a numerical simulation using CST Studio Suite 2011 software is done. So as a result of numerical simulations, optimum geometry of the GM force sensor is obtained related to the condition in which the GM force sensor has highest sensitivity. After that, the sensor is fabricated using the simulation results and is tested by means of an experimental setup. Characteristic curve of the GM force sensor in several conditions is measured and the optimum operational condition is obtained considering highest sensitivity condition of the sensor. Also operational diagrams of the GM force sensor is plotted in loading and unloading conditions. Characteristics of the GM force sensor in optimum condition are presented.

It was found that the GM force sensor has maximum sensitivity and maximum linearity in 0.8A current, which can be known as optimum condition of application. In this sensor, maximum sensitivity is 0.51 mV/N (while current is 0.8A), which is highest among older investigations.

At last, theoretical, numerical and experimental results are compared and the criteria for magnetostrictive sensor design are presented.

The paper aims to analyze the behavior of the Galfenol rods under bending conditions that are employed in a vibration energy harvester by illustrating the spatial variations in stress and magnetic field.

This paper describes a 3‐D static finite element model of magnetostrictive materials, considering magnetic and elastic boundary value problems that are bidirectionally coupled through stress and field dependent variables. The finite element method is applied to a small vibration‐driven generator of magnetostrictive type employing Iron‐Gallium alloy (Galfenol).

The 3‐D static finite element modeling presented here highlights the spatial variations in magnetic field and relative permeability due to the corresponding stress distribution in the Galfenol rods subjected to transverse load. The numerical calculations show that about 1.1 T change in magnetic flux density is achieved which demonstrates the effectiveness of the inspected vibration‐driven generator in voltage generation and energy harvesting. The model predictions agree with the experimental results and are coherent with the magnetostriction phenomenon.

This paper fulfils the behavior analysis of Galfenol rods under transverse load that includes both compression and tension. The compressive and tensile stresses contributions to change in magnetic flux densities in the Galfenol rods were calculated by which the effectiveness of the inspected vibration‐driven generator in voltage generation and energy harvesting is demonstrated.

This paper aims to investigate the magnetostrictive phenomenon in a single electrical steel sheet, which may cause vibration and noise in the cores of transformers and induction motors. A measurement system of magnetostriction is created and the principal strain of magnetostriction is modeled. Furthermore, the magnetostriction property along arbitrary alternating magnetization directions is modeled.

A measurement system with a triaxial strain gauge is developed to obtain the magnetostrictive waveform, and the principal strain is computed in terms of the in-plane strain formula. A three-layer feed-forward neural network model is proposed to model the measured magnetostriction property of the electrical steel sheet.

The principal strain of magnetostriction of the non-oriented electrical steel has strong anisotropy. The proposed estimation model can be effectively used to model the anisotropic magnetostriction with an acceptable prediction time.

This paper develops the neural network combined with fast Fourier transform (FFT) to model the principal strain property of magnetostriction under alternating magnetizations, and its validation has been verified.

This paper proposes a robust modeling method of a giant magnetostrictive actuator which has a rate‐dependent nonlinear property.

It is known in statistics that the Least Wilcoxon learning method developed using Wilcoxon norm is robust against outliers. Thus, it is used in the paper to determine the consequence parameters of the fuzzy rules to reduce the sensitiveness to the outliers in the input‐output data. The proposed method partitions the input space adaptively according to the distribution of samples and the partition is irrelative to the dimension of the input data set.

The proposed modeling method can effectively construct a unique dynamic model that describes the rate‐dependent hysteresis in a given frequency range with respect to different single‐frequency and multi‐frequency input signals no matter whether there exist outliers in the training set or not. Simulation results demonstrate that the proposed method is effective and insensitive against the outliers.

The main contributions of this paper are: first, an intelligent modeling method is proposed to deal with the rate‐dependent hysteresis presented in the giant magnetostrictive actuator and the modeling precision can fulfill the requirement of engineering, such as the online modeling issue in the active vibration control; and second, the proposed method can handle the outliers in the input‐output data effectively.