A Mathematical Model of a Powerful Valve Motor in 3D Format in Rectangular Coordinates

Solutions of the Laplace equation for a rectangular parallelepiped in the forms of the first and second boundary problems are considered. The method of separation of Fourier variables is used, based on which an analytical calculation of electric machines is proposed. In the solution, the yoke, tooth layers, and the air gap of the active region are represented by a set of rectangular parallelepipeds with a width equal to the pole pitch. The accompanying Fourier constants (two for an elementary parallelepiped) are determined from the conditions of the magnetic field at the boundaries of the parallelepipeds: magnetic potentials and magnetic inductions are the same if magnetic sheets (MMF of windings) are located at the boundaries; a jump occurs in the magnetic potential equal to the magnetic sheet current. The proposed method is used to analytically calculate in rectangular coordinates a 150-kW valve motor with permanent magnets located in closed grooves of a rotary core.