The Jiles-Atherton (J-A) model is a commonly used physics-based model in describing the hysteresis characteristics of ferromagnetic materials. However, citations and interpretation of this model in literature have been non-uniform. Solution methods for solving numerically this model has not been studied adequately. In this paper, through analyzing the mathematical properties of equations and the physical mechanism of energy conservation, we point out some unreasonable descriptions of this model and develop a relatively more accurate, modified J-A model together with its numerical solution method. Our method employs a fixed point method to compute anhysteretic magnetization. We obtain the susceptibility value of the anhysteretic magnetization analytically and apply the 4th order Runge-Kutta method to the solution of total magnetization. Computational errors are estimated and then precisions of the solving method in describing various materials are verified. At last, through analyzing the effects of the accelerating method, iterative error and step size on the computational errors, we optimize the numerical method to achieve the effects of high precision and short computing time. From analysis, we determine the range of best values of some key parameters for fast and accurate computation.

Giant magnetostrictive materials (GMMs) have broad application prospects in the field of servo valves, but the giant magnetostrictive actuator (GMA) has problems such as large loss and severe heat generation, which affect the output effect and accuracy. To solve these problems, this paper designs a stacked giant magnetostrictive actuator (SGMA) and analyzes the magnetic circuit and magnetic field distribution of the SGMA. Based on the magnetic field analysis and the Jiles–Atherton model, we analyze the SGMA magnetization model, simplify the traditional model, and give a solution for the simplified model using the Runge–Kutta method. We analyze the eddy current loss of the SGMA, and according to Bessel’s equation and the Kelvin function, we calculate the relationship among eddy current loss, GMM rod radius, and magnetic field frequency. By analyzing the inherent hysteresis of GMMs, a hysteresis loss model of the SGMA is established in this paper. We also calculate the coil impedance and obtain the coil loss model. Based on the loss model, the SGMA cooling system is designed. Based on the above analysis, we design a SGMA prototype, set-up the corresponding experimental platform, and conduct the necessary experiments. The experimental results show that the SGMA responds well to different signals, but as frequency increases, attenuation, deformation, and hysteresis become more pronounced, which verifies the amplitude and phase changes caused by various losses in the theoretical analysis. The experiment also observes the temperature rise of the oil-cooled SGMA at different frequencies, indicating that the cooling system can effectively control the temperature change of the SGMA, which validates the foregoing analysis.

A comprehensive model is a basis for adequately understanding the energy conversion mechanism of magnetostrictive materials and guides the design of magnetostrictive devices. This paper established a fully coupled model that fully considered the piezomagnetic effect and the electromagnetic effect in its procedure of energy conversion. The proposed model can accurately predict the output voltage with different excitation levels and illustrate the interaction between physical fields. Based on the established model, we quantify the voltage contributed by the piezomagnetic effect and the electromagnetic effect. After a thorough analysis, we discovered that even though the voltage generation is always dominated by the piezomagnetic effect of the magnetostrictive material, the proportion from the electromagnetic effect will increase moderately with larger excitation levels. In addition, the magnetostrictive effect toward the output performance is also discussed, which proved to lead to a marginal impact on the voltage waveform.

Giant magnetostrictive actuators (GMA) are widely used in the field of servo valves, but the displacement of GMA is limited, which renders meeting the requirements of large flow direct-drive electro-hydraulic servo valves (DDV) difficult. In order to solve these problems, this study proposes a double-row bow-type micro-displacement amplifier (DBMA), used to increase output displacement of GMA to meet the requirements. This study, by static analysis, analyzes the force of a flexure hinge based on theoretical mechanics and material mechanics, derives the stiffness matrix of the flexure hinge by the influence coefficient method, establishes the pseudo-rigid model, and derives the amplification ratio of a DBMA. Also, by kinetic analysis, using Castigliano’s second theorem, a formula of equivalent stiffness and natural frequency of DBMA were derived and the influences of different parameters on them were analyzed, respectively. After that, we analyzed the amplifier using finite element method (FEM) simulation software and verified the model by manufacturing a prototype and building a test system. Theoretical calculations and experimental results showed that the amplification ratio of the DBMA fluctuated between 15.43 and 16.25. The natural frequency was about 305 Hz to 314 Hz and the response bandwidth was up to 300 Hz. The error among the theoretical, simulated, and experimental values was within 8%, supporting the accuracy of the model.

Giant magnetostrictive rotary actuators (GMRAs) can realize rotary motion in large scale and with high precision. A series of rectangular voltage signals organized in strict order exerted on GMRA helps its clamping mechanism and driving mechanism complete specific actions such as clamping, loosening, and actuating, thus leading to the stepping output of the rotor. In order to describe the overall performance of GMRA, an angular displacement model is established, which can be divided into four parts, namely, the current model, magnetic field model, output force model, and vibration model. The experimental results indicate that the established model agrees well with the actual performance of GMRA in operating conditions. After that, utilizing the established model, simulations are conducted to analyze the angular response of GMRA. According to the simulation results, the order of driving signals is optimized, making the maximum driving frequency rise from 160 Hz to 210 Hz, while the peak angular speed of GMRA reaches 70.77 mrad/s. The modeling and optimization methods proposed in this paper can be helpful for the structural optimization and controller design of GMRA as well.

The internal magnetic field characteristics of giant magnetostrictive actuators have an important influence on their output performance. Aiming at the deficiency of current scholars’ research, based on the electromagnetic theory and finite element method, this paper analyzes the magnetic field intensity on a giant magnetostrictive cylinder by using COMSOL Multiphysics software. Considering the inhomogeneity of magnetic field intensity along the radial direction of giant magnetostrictive cylinders, a new averaging method is introduced to calculate the magnetic field intensity in the axial section of the cylinder. The influence of the magnetic permeability of the displacement conversion mechanism (shell) and the size of the air gap inside the device on the magnetic field intensity of the giant magnetostrictive cylinder are analyzed. The prototype of the actuator is manufactured, and the correctness and accuracy of the simulation data are verified by experiments. In order to make the magnetic field on the cylinder strong and uniform, the displacement conversion mechanism and the shell should be made of low permeability and high permeability materials, respectively, and the air gap size should be reduced as much as possible under the condition of meeting the size requirement of the actuator pre-tightening force applying device.