2-D Analytical Electromagnetic Modeling for Slotless Tubular Surface Magnet Machines Considering End-Effect

In this article, an analytical model using separation of variables method (SVM) is derived to predict magnetic field quantity distribution of a Slotless Tubular Surface Permanent Magnet Machine (STSPMM) considering the end-effect and the ferromagnetic permeability. In modeling the end-effect, previous researches have shortcomings in terms of accuracy, formulation complexity and computational burden. In order to model the end-effect, instead of taking into account the infinite space of the two sides of the machine, a finite distance is considered to ensure that the leakage flux density decays to a negligible value. With this assumption, in longitudinal direction, the SVM is formulated with Fourier series rather than Fourier integral. This is important since a series solution can be approximated using a finite number of eigenfunctions whereas an integral form requires continuous spectral analysis in an infinite frequency domain. In addition, proximity of ferromagnetic parts to the air-space is modeled using composite domain eigen-solutions, which reduce the computational and formulation complexity. In the end, a 12-pole 3-phase case-study is evaluated and compared with Finite Element Method (FEM).