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Modification and Numerical Method for the Jiles-Atherton Hysteresis Model

Part of: Numerical analysis: Ordinary differential equations Qualitative theory Applications to specific types of physical systems

Published online by Cambridge University Press:  07 February 2017

Guangming Xue ,
Peilin Zhang ,
Zhongbo He ,
Dongwei Li ,
Zhaoshu Yang  and
Zhenglong Zhao
Guangming Xue*
Affiliation:
Vehicle and Electrical Engineering Department, Ordnance Engineering College, Shijiazhuang 050003, P.R. China
Peilin Zhang*
Affiliation:
Vehicle and Electrical Engineering Department, Ordnance Engineering College, Shijiazhuang 050003, P.R. China
Zhongbo He*
Affiliation:
Vehicle and Electrical Engineering Department, Ordnance Engineering College, Shijiazhuang 050003, P.R. China
Dongwei Li*
Affiliation:
Vehicle and Electrical Engineering Department, Ordnance Engineering College, Shijiazhuang 050003, P.R. China
Zhaoshu Yang*
Affiliation:
Vehicle and Electrical Engineering Department, Ordnance Engineering College, Shijiazhuang 050003, P.R. China
Zhenglong Zhao*
Affiliation:
Vehicle and Electrical Engineering Department, Ordnance Engineering College, Shijiazhuang 050003, P.R. China
*
*Corresponding author. Email addresses:yy0youxia@163.com (G. Xue), zpl@163.com (P. Zhang), hzb_hcl_xq@sina.com (Z. He), 12ldw@163.com (D. Li), yangzhaoshu@sina.cn (Z. Yang), 498836250@qq.com (Z. Zhao)
*Corresponding author. Email addresses:yy0youxia@163.com (G. Xue), zpl@163.com (P. Zhang), hzb_hcl_xq@sina.com (Z. He), 12ldw@163.com (D. Li), yangzhaoshu@sina.cn (Z. Yang), 498836250@qq.com (Z. Zhao)
*Corresponding author. Email addresses:yy0youxia@163.com (G. Xue), zpl@163.com (P. Zhang), hzb_hcl_xq@sina.com (Z. He), 12ldw@163.com (D. Li), yangzhaoshu@sina.cn (Z. Yang), 498836250@qq.com (Z. Zhao)
*Corresponding author. Email addresses:yy0youxia@163.com (G. Xue), zpl@163.com (P. Zhang), hzb_hcl_xq@sina.com (Z. He), 12ldw@163.com (D. Li), yangzhaoshu@sina.cn (Z. Yang), 498836250@qq.com (Z. Zhao)
*Corresponding author. Email addresses:yy0youxia@163.com (G. Xue), zpl@163.com (P. Zhang), hzb_hcl_xq@sina.com (Z. He), 12ldw@163.com (D. Li), yangzhaoshu@sina.cn (Z. Yang), 498836250@qq.com (Z. Zhao)
*Corresponding author. Email addresses:yy0youxia@163.com (G. Xue), zpl@163.com (P. Zhang), hzb_hcl_xq@sina.com (Z. He), 12ldw@163.com (D. Li), yangzhaoshu@sina.cn (Z. Yang), 498836250@qq.com (Z. Zhao)
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Abstract

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.

Keywords

Modified J-A modelnumerical solution methoderror estimationoptimization

MSC classification

Secondary: 65L06: Multistep, Runge-Kutta and extrapolation methods 34C55: Hysteresis 39B12: Iteration theory, iterative and composite equations 82D40: Magnetic materials
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 3 , March 2017 , pp. 763 - 781
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Bo Li

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