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

Arch-shaped axially magnetized bodies tend to appear frequently in electrical machine analysis such as in the overhang parts of the classical radial-flux machines as well as in the main parts of the axial-flux machines. The calculation of the 3-D fields originating from these bodies is demanding. The 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 the 3-D FEA. In this article, a new analytical technique is proposed to speed up the computation by a factor of 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 the 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.