Calculation of the Stationary Magnetic Field Taking Into Account the Error of Magnetization Characteri

Abstract

Bilateral methods for calculating the magnetic field characteristics of electrical systems containing ferromagnets and permanent magnets are considered. The methods are based on the application of the Lagrange multiplier method to the electromagnetic field equations in terms of the scalar potential. The study described in the article complements the results of the previous article of the authors devoted to a similar bilateral method based on the Pontryagin maximum principle. The approach based on the Lagrange multiplier method has the advantage that it is applicable for solving both dynamic and stationary problems with distributed parameters. The corresponding conjugate partial differential equations for different optimality criteria (for both uniform and standard metric) are obtained. The solution of the problem of calculation of bilateral estimates of the solution in the calculation of the static magnetic field in a ferromagnet placed in a third-party uniform magnetic field is considered. This method is also applicable for the calculation of the fields of permanent magnets, which requires taking into account the residual magnetization, the final width of the hysteresis loop. For this purpose, the corresponding ratios are given. It is assumed that the main source of error in the calculation is the approximate values of the magnetic permeability of the medium. The obtained results can also be used in solving direct and inverse problems for the system of ferromagnetic bodies and in test problems using other methods.