Parametric model of electric machines based on exponential Fourier approximations of magnetic air gap flux density and inductance

Abstract

Purpose This study aims to present a parametric model of a novel electrical machine, based on a slotless air gap winding, allowing for fast and precise magnetic circuit calculations. Design/methodology/approach Approximations of Fourier coefficients through an exponential function deliver the required nonlinear air gap flux density and inductance. Accordingly, major machine characteristics, such as back-EMF and torque, can be calculated analytically with high speed and precision. A physical model of the electrical machine with air gap windings is given. It is based on a finite element analysis of the air gap magnetic flux density and inductance. The air gap height and the permanent magnetic height are considered as magnetic circuit parameters. Findings In total, 11 Fourier coefficient matrixes with 65 sampling points each were generated. From each, matrix a two-dimensional surface function was approximated by using exponentials. Optimal parameters were calculated by the least-squares method. Comparison with the finite element model demonstrates a very low error of the analytical approximation for all Fourier coefficients considered. Finally, the dynamics of an electrical machine, modeled using the preceding magnetic flux density approximation, are analyzed in MATLAB Simulink. Required approximations of the phase self-inductance and mutual inductance were given. Accordingly, the effects of the two magnetic circuit parameters on the dynamics of electrical machine current as well as the electrical machine torque are explained. Originality/value The presented model offers high accuracy comparable to FE-models, needing only very limited computational complexity.