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 actuator (GMA) may be a promising candidate actuator to drive an electronic controlled injector as giant magnetostrictive material (GMM) has excellent performances as large output, fast response and high operating stability etc. To meet the driving requirement of the injector, the GMA should produce maximal shortening displacement when energized. An unbiased GMA with a ‘T’ shaped output rod is designed to reach the target. Furthermore, an open-hold-fall type driving voltage is exerted on the actuator coil to accelerate the response speed of the coil current. The actuator displacement is modeled from establishing the sub-models of coil current, magnetic field within GMM rod, magnetization and magnetostrictive strain sequentially. Two modifications are done to make the model more accurate. Firstly, consider the model fails to compute the transient-state response precisely, a dead-zone and delay links are embedded into the coil current sub-model. Secondly, as the magnetization and magnetostrictive strain sub-models just influence the change rule of the transient-state response the linear magnetostrictive strain-magnetic field sub-model is introduced. From experimental results, the modified model with linear magnetostrictive stain expression can predict the actuator displacement quite effectively.

The Jiles-Atherton model was widely used in the description of the system with hysteresis, and the solution for the model was important for real-time and high-precision control. The secant method was used for solving anhysteretic magnetization and its initial values were optimized for faster convergence. Then, the Fourth Order Runge-Kutta method was employed to solve magnetization and the required computation cycles were supplied for stable results. Based on the solving method, the effect of the nonzero initial magnetic field on the magnetization was discussed, including the commonly used linear model of the square of magnetization under the medium initial value. From computations, the proposed secant iteration method, with supplied optimal initial values, greatly reduced the iterative steps compared to the fixed-point iteration. Combined with the Fourth Order Runge-Kutta method under more than three cycles of calculations, stable hysteresis results with controllable precisions were acquired. Adjusting the initial magnetic field changed the result of the magnetization, which was helpless to promote the amplitude or improve the symmetry of magnetization. Furthermore, the linear model of the square of magnetization was unacceptable for huge computational errors. The proposed numerical solving method can supply fast and high-precision solutions for the Jiles-Atherton model and provide a basis for the application scope of typical linear assumption.

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.

Purpose: 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.Design/methodology/approach: 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.Findings: 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.Originality/value: 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.