A calculation method for initial magnetization curve under constant magnetization based on time-space transformation
Authors: Deng Dong-Ge  , Wu Xin-Jun  ,   School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Published: December 2020

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.