Generalized and Reduced Analytical Formulation for Ultra-Fast 3-D Field and Vector Potential Calculation From Arch-Shaped Axially Magnetized Bodies in Electrical Machines

Abstract

Arch-shaped axially magnetized bodies tend to appear frequently in electrical machine analysis such as in overhang parts of classical radial-flux machines as well as in main parts of axial-flux machines. The calculation of 3-D fields originating from these bodies is demanding. 3-D FEA suffers from high computational burden as well as no knowledge of the field origin. Analytic techniques involve the use of elliptic integrals and complex numbers for numerical evaluation, which makes them significantly slower than 3-D FEA.In this paper, a new analytical technique is proposed to speed up the computation by factor 20 for the global magnetic field created by a generic magnetized body, by removing complex numbers and reducing the analytic equations significantly without any loss of precision. As a result, it can compete with conventional 3-D FEA. In addition, integral methods may contribute to the wider use of parallel processing techniques. The original expressions for the vector potential are also provided, which has its own benefits and applications. Finally, the showcased magnetized body is assessed against 3-D FEA and discussed in terms of practical applications.

The Magnetic Field from Cylindrical Arc Coils and Magnets: A Compendium with New Analytic Solutions for Radial Magnetization and Azimuthal Current

“…To form a compact expression 𝜐(𝜈) is defined in-lieu of a conditional statement for the cases ( 67) and (68). Of interesting note, the summation of 𝛽 (1) is independent of azimuthal source terms, and the summation of 𝛿 (1) only contains radial source terms within the argument of the regularized beta function.…”