Three-Dimensional Polycrystal Magnetic Field Analysis of Thin Steel

The 3-D polycrystal magnetic field analysis method by means of coordinate transformation is proposed. The local coordinates are fixed in each crystal grain and the global coordinates are defined in the polycrystal steel. Though it is assumed that each crystal grain has the same magnetized characteristics as those of a single crystal grain, the crystal grain shape and its orientations of alpha, beta, and gamma angles are taken into account. When the proposed model is applied to the real grain oriented (GO) steel with 56 crystal grains in 80-mm × 80-mm, and with 0.35-mm thickness, the calculation results are compared with the grain orientations measured by X-ray diffraction. The GO steel has a higher degree of
(110)[001]
texture with about 3% silicon. The calculated results of higher magnetic flux density part and lower magnetic flux density part in the real GO steel are explained by the alpha angle distribution. The calculated inclination angle distribution and the measured alpha angle distribution seem to be in good agreement. The calculated normal component of the magnetic flux density reflects the beta angle distribution of the real GO steel. It is concluded that the proposed 3-D polycrystal magnetic field analysis is appropriate.