To the Calculation of Electric Machines by the Method of Separation of Variables Using Symbolic Calculations

Abstract

Electromagnetic calculations of electric machines are traditionally performed using numerical methods. However, the approximate nature of the results obtained during the numerical calculation makes it difficult to develop general theoretical and practical conclusions. In this regard, the issues of developing accurate analytical methods for calculating electromagnetic parameters and operating modes of electromechanical systems remain relevant. The article presents a mathematical model of the magnetic field of a magnetoelectric valve motor using the Fourier– Euler variable separation method. The field created by the rotor magnets and the current of the stator winding was assumed to be plane-parallel. The active region of the engine was divided into a set of geometrically homogeneous horizontal bands, at the boundaries of which the conditions of conjugation of their magnetic fields are fulfilled: scalar magnetic potentials and normal components of magnetic induction do not undergo a jump (rupture). In addition to permanent magnets and stator winding currents, magnetizations of ferromagnetic sections of its magnetic circuit were considered as sources of the magnetic field. The article presents the design scheme of the engine and the corresponding Fourier-Euler equations for scalar potentials and magnetic inductions. Based on them, a system of linear parametric equations with respect to unknown Fourier constants is obtained. To solve it in symbolic form, the SymPy library of the Python programming language was used. The obtained analytical expressions for Fourier constants can be used to study the dependencies of their values on the parameters of an electric machine.