Finding an analytical solution for the cylinder's fluxmetric demagnetizing factor using spherical harmonics

Abstract

The work examines an analytical solution for calculating the fluxmetric demagnetizing factor of cylindrical magnets at large values of magnetic susceptibility and an arbitrary value of elongation. The application of the analytical solution for calculating the demagnetizing factor significantly simplifies the modeling and calculation of magnetic characteristics of cylindrical technical objects. A simplified analytical model of the scalar potential of the magnetic field of a cylinder with infinite magnetic favorability, inductively magnetized in a uniform magnetic field, was constructed using an approximate representation of the distribution of fictitious magnetic charges on its surface. The method of spherical harmonic analysis for the magnetic field was used, which made it possible to obtain an analytical representation of the demagnetization field in the central cross section of the cylinder. Limitation of the harmonic series of this representation by seven first harmonics is proposed, and an additional amplitude factor is applied to correct the contribution of the first harmonic to the demagnetization field. This made it possible to compensate for the distortion of the magnetic field near the ends of the cylinder and bring the simplified analytical model closer to the target mathematical model with a uniform demagnetization magnetic field. The reliability of the results of calculating the fluxmetric demagnetizing factor according to the derived formula was evaluated by comparing them with the known results obtained using the numerical method of calculation and according to empirical formulas. It is shown that the proposed approach makes it possible to obtain reliable results of calculating the fluxmetric demagnetizing factor with a deviation of up to 5 % at infinite favorability in the range of cylinder elongation values from 0.01 to 500.