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It is of great significance to research on methods for obtaining the initial magnetization curve, the important magnetic property of ferromagnetic materials. In the existing methods, a time-varying magnetic field is adopted as the excitation field. To obtain the initial magnetization curve, magnetic field and induced magnetic flux density in the specimen have to be measured step-by-step as the excitation field changes, and this is inefficient. Thus, a calculation method for initial magnetization curve based on time-space transformation is proposed in this paper. In this method, an elongated rod or a circular ring is used as the specimen. A spatially varying magnetic field generated by constant magnetization is utilized as the excitation field. The strength of the excitation field changes with the spatial positions of the specimen. Under the action of the excitation field, the magnetic field strength within the specimen is calculated by means of the responding magnetic field strength on the surface of the specimen according to the continuity of the tangential magnetic field strength. While, based on the Gauss' law for magnetism, the law of approach to saturation and the basic equation of magnetization curve in Rayleigh region, the induced magnetic flux density within the specimen can be calculated from the responding magnetic flux density on the surface of the specimen. After obtaining the magnetic field strength and magnetic flux density in the specimen, the initial magnetization curve can be obtained. To verify theoretically the correctness of the method, simulations are carried out with an elongated rod and a circular ring. In experiments, a spatially varying magnetic field generated by DC coils is applied on the specimen as the excitation field. The initial magnetization curve calculated from the magnetic field strength and magnetic flux density on the surface of the specimen is similar to the known initial magnetization curve. Experimental results also show that when adopting an elongated rod rather than a circular ring as the specimen, this calculation method for initial magnetization curve is simpler and the error in the results is smaller, which are different from those obtained by existing measurement methods for initial magnetization curve. In addition, in order to study the influence of the limiting factors in practical applications of the calculated results, further research is conducted based on the simulation data. Results show that when choosing a proper elongated rod as the specimen, the initial magnetization curve can be calculated from the magnetic field strength and magnetic flux density on the surface of the specimen under the constant magnetization, also the induced magnetic field flux in the specimen does not have to be measured by the encircling detecting coil which makes this method easy to operate. Namely, this method is feasible in practice. This paper may be a theoretical guidance for exploring new measurement methods for initial magnetization curve.
[1] Yu L L, Zeng Z M 2001 Practical Handbook of steel materials (Beijing: China Machine Press) p4 (in Chinese) [虞莲莲, 曾正明 2001 实用钢铁材料手册(北京: 机械工业出版社) 第4页]
[2] Si L Y, Lin H, Liu Z 2007 Proceedings of the CSEE 27 26 (in Chinese) [司利云, 林辉, 刘震 2007 中国电机工程学报 27 26]
[3] Zhang P, Liu L, Chen W M 2013 Acta Phys. Sin. 62 177501 (in Chinese) [章鹏, 刘琳, 陈伟民 2013 62 177501]
[4] Yuan J M, Wu X J 2011 Proceedings of SPIE: 2011 International Conference on Photonics, 3D-Imaging, and Visualization Guangzhou, China, October 28-30, 2011 p820511-1
[5] Guo Z Z, Hu X B 2013 Acta Phys. Sin. 62 057501 (in Chinese) [郭子政, 胡旭波 2013 62 057501]
[6] Kvasnica B, Fabo P 1996 Meas. Sci. Technol. 07 763
[7] Feng J, Zhang J F, Lu S X, Wang H Y, Ma R Z 2013 Chin. Phys. B 22 018103
[8] Hao K S, Huang S L, Zhao W, Wang S 2011 Chin. Phys. B 20 068104
[9] Matyuk V F, Osipov A A 2007 Russ. J. Nondestruct. Test 43 143
[10] Nakata T, Takahashi N, Fujiwara K, Nakano M, Ogura Y, Matsubara K 1992 IEEE T. Magn. 28 2456
[11] Jiles D (translated by Xiao C T) 2003 Introduction to magnetism and magnetic materials(Lan zhou: Lanzhou University Press) p39 (in Chinese) [吉利斯 D著(肖春涛译) 2003 磁学及磁性材料导论(兰州: 兰州大学出版社)第39页]
[12] Stupakov O 2006 J. Magn. Magn. Mater. 307 279
[13] Perevertov O 2005 Rev. Sci. Instrum. 76 104701
[14] Nguyen M, Maier M, Schinkoethe W 2014 IEEE Trans. Magn. 50 7400705
[15] Takahashi N, Miyagi D, Inoue F, Nakano M 2011 J. Appl. Phys. 109 07A330
[16] Xiao C H, He H H, Wu R G, Wang C R 1998 J. Huazhong Univ. of Sci. & Tech. 26 61 (in Chinese) [肖昌汉, 何华辉, 吴任国, 王长荣 1998 华中理工大学学报 26 61]
[17] Han X T, Wang Z, Ma X H, Wang G J 2007 Acta Phys. Sin. 56 1697 (in Chinese) [韩献堂, 王治, 马晓华, 王光建 2007 56 1697]
[18] Yuan J M 2012 Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese) [袁建明 2012 博士学位论文 (武汉: 华中科技大学)]
[19] Ke S, Zhang H, Ni Z J, Ye D P, Zhang G Z, Su L G 2003 Common Steel Magnetic Characteristics Quick Reference (Beijing: China Machine Press) p9 (in Chinese) [柯松, 张辉, 倪泽钧, 叶代平, 张国珍, 苏李广 2003 常用钢材磁特性曲线速查手册(北京: 机械工业出版社) 第9页]
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[1] Yu L L, Zeng Z M 2001 Practical Handbook of steel materials (Beijing: China Machine Press) p4 (in Chinese) [虞莲莲, 曾正明 2001 实用钢铁材料手册(北京: 机械工业出版社) 第4页]
[2] Si L Y, Lin H, Liu Z 2007 Proceedings of the CSEE 27 26 (in Chinese) [司利云, 林辉, 刘震 2007 中国电机工程学报 27 26]
[3] Zhang P, Liu L, Chen W M 2013 Acta Phys. Sin. 62 177501 (in Chinese) [章鹏, 刘琳, 陈伟民 2013 62 177501]
[4] Yuan J M, Wu X J 2011 Proceedings of SPIE: 2011 International Conference on Photonics, 3D-Imaging, and Visualization Guangzhou, China, October 28-30, 2011 p820511-1
[5] Guo Z Z, Hu X B 2013 Acta Phys. Sin. 62 057501 (in Chinese) [郭子政, 胡旭波 2013 62 057501]
[6] Kvasnica B, Fabo P 1996 Meas. Sci. Technol. 07 763
[7] Feng J, Zhang J F, Lu S X, Wang H Y, Ma R Z 2013 Chin. Phys. B 22 018103
[8] Hao K S, Huang S L, Zhao W, Wang S 2011 Chin. Phys. B 20 068104
[9] Matyuk V F, Osipov A A 2007 Russ. J. Nondestruct. Test 43 143
[10] Nakata T, Takahashi N, Fujiwara K, Nakano M, Ogura Y, Matsubara K 1992 IEEE T. Magn. 28 2456
[11] Jiles D (translated by Xiao C T) 2003 Introduction to magnetism and magnetic materials(Lan zhou: Lanzhou University Press) p39 (in Chinese) [吉利斯 D著(肖春涛译) 2003 磁学及磁性材料导论(兰州: 兰州大学出版社)第39页]
[12] Stupakov O 2006 J. Magn. Magn. Mater. 307 279
[13] Perevertov O 2005 Rev. Sci. Instrum. 76 104701
[14] Nguyen M, Maier M, Schinkoethe W 2014 IEEE Trans. Magn. 50 7400705
[15] Takahashi N, Miyagi D, Inoue F, Nakano M 2011 J. Appl. Phys. 109 07A330
[16] Xiao C H, He H H, Wu R G, Wang C R 1998 J. Huazhong Univ. of Sci. & Tech. 26 61 (in Chinese) [肖昌汉, 何华辉, 吴任国, 王长荣 1998 华中理工大学学报 26 61]
[17] Han X T, Wang Z, Ma X H, Wang G J 2007 Acta Phys. Sin. 56 1697 (in Chinese) [韩献堂, 王治, 马晓华, 王光建 2007 56 1697]
[18] Yuan J M 2012 Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese) [袁建明 2012 博士学位论文 (武汉: 华中科技大学)]
[19] Ke S, Zhang H, Ni Z J, Ye D P, Zhang G Z, Su L G 2003 Common Steel Magnetic Characteristics Quick Reference (Beijing: China Machine Press) p9 (in Chinese) [柯松, 张辉, 倪泽钧, 叶代平, 张国珍, 苏李广 2003 常用钢材磁特性曲线速查手册(北京: 机械工业出版社) 第9页]
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