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Modification and Numerical Method for the Jiles-Atherton Hysteresis Model

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

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)

Abstract

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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

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 3 , March 2017 , pp. 763 - 781
Copyright
Copyright © Global-Science Press 2017 

Footnotes

Communicated by Bo Li

References

[1] Clerk, A. E., Ferromagnetic Material, North-Holland Publishing Company, Amsterdam, 1980.Google Scholar
[2] Olabi, A. G. and Grunwald, A., Design and application of magnetostrictive materials, Mater. Des., 22 (2008), 469–483.CrossRefGoogle Scholar
[3] Lu, Q. G., Chen, D. F., Wei, G. Q. and Ding, J. J., Development of giant magnetostrictive materials and its application in the field of precision actuators, J. Hubei Univ. Technol., 21 (2006), 92–94.Google Scholar
[4] Stoner, E. C. and Wohlfarth, E. P.. A mechanism of magnetic hysteresis in heterogeneous alloys, Philos. Trans. R. Soc. London, 24 (1948), 599–642.Google Scholar
[5] Jiles, D. C. and Atherton, D. L., Theory of ferromagnetic hysteresis, J. Appl. Phys., 55 (1984), 2115–2120.Google Scholar
[6] Jiles, D. C. and Atherton, D. L., Ferromagnetic hysteresis, IEEE Trans. Magn., 19 (1983), 2183–2185.Google Scholar
[7] Smith, R. C., Dapino, M. J. and Seelecke, S., Free energy model for hysteresis in magnetostrictive transducers, J. Appl. Phys., 93 (2003), 458–466.Google Scholar
[8] Preisach, F., Uber die magnetische nachwrikung, Z. Phys., 94 (1935), 277–302.Google Scholar
[9] Cincotti, S., Marchesi, M. and Serri, A.. A neural network model of parametric non-linear hysteretic inductors, IEEE Trans. Magn., 34 (1998), 3040–3043.CrossRefGoogle Scholar
[10] Jiles, D. C., Frequency dependence of hysteresis curves in conducting magnetic materials, J. Appl. Phys., 76 (1994), 5849–5855.Google Scholar
[11] Li, Z., Li, Q. M., Li, C. Y., Sun, Q. Q. and Lou, J., Queries on the J-A modelling theory of the magnetization process in ferromagnets and proposed correction method, P. CSEE, 31 (2011), 124–131.Google Scholar
[12] Hamimid, M., Feliachi, M. and Mimoune, S. M., Modified Jiles-Atherton model and parameters identification using false position method, Physica B: Condens. Matter, 405 (2010), 1947–1950.Google Scholar
[13] Malczyk, R. and Izydorczyk, J.. The frequency-dependent Jiles-Atherton hysteresis model, Physica B: Condens. Matter, 463 (2015), 68–75.Google Scholar
[14] Benabou, A., Leite, J. V., Clenet, S., Siman, C. and Sadowski, N., Minor loops modelling with a modified Jiles-Atherton model and comparison with the Preisach model, J. Magn. Magn. Mater., 320 (2008), e1034–e1038.CrossRefGoogle Scholar
[15] Chwastek, K., Frequency behaviour of the modified Jiles-Atherton model, Physica B: Condens. Matter, 403 (2008), 2484–2487.Google Scholar
[16] Szewczyk, R., Bienkowski, A., Salach, J., Extended Jiles-Atherton model for modelling the magnetic characteristics of isotropic materials, J. Magn. Magn. Mater., 320 (2008), e1049–e1052.Google Scholar
[17] Tan, X. and Baras, J.S., Modeling and control of hysteresis in magnetostrictive actuators, Automatica, 40 (2004), 1469–1480.Google Scholar
[18] Calkins, F. T., Smith, R. C. and Flatau, A. B., Energy-based hysteresis model for magnetostrictive transducers, IEEE Trans. Magn., 36 (2000), 429–439.Google Scholar
[19] Liu, H. F., Jia, Z. Y., Wang, F. J. and Zong, F. C., Parameter identification of displacement model for giant magnetostrictive actuator, J. Mechanical Engineering, 47 (2011), 115–120.Google Scholar
[20] Wang, B. W., Cao, S. Y. and Huang, W. M., Magnetostrictive Materials and Devices, Metallurgical Industry Press, Beijing, 2008.Google Scholar
[21] Wang, L. J., The curve of magnetic hysteresis loop of the polynomial fitting ferromagnetic material, Phys. Exp. Coll., 19 (2006), 58–61.Google Scholar
[22] Guan, Z. and Lu, J. F., Fundamentals of Numerical Analysis (2nd Edition), Higher Education Press, Beijing, 2010.Google Scholar
[23] Wang, Z. L., Gong, C. and He, Q., Master of Science in MATLAB Calculation (2nd Edition), Publishing House of Electronics Industry, Beijing, 2009.Google Scholar