In this paper, an approach for a two-and-half-dimensional (2.5D) finite element method (FEM)-based analysis, or quasi-three-dimensional (3D) FEM analysis, of an axial flux machine is discussed. By cutting the 3D model laterally and thereby creating cylindrical surface cuts, the 3D model can be split into several cylindrical surfaces. Transforming those cylindrical cuts into planes leads to a layer-based two-dimensional (2D) model with different radii for each layer. By integrating over all lateral surface cuts, the results for the entire axial flux machine can be determined. In comparison to the simulation of a full 3D FEM model, the simulation of the proposed 2.5D model is much faster. To validate the approach, the two main types of axial flux machines are simulated with both 3D-FEM-based model and 2.5D-FEM-based approach, and the results are presented in this paper.

This is the first of a series of papers on novel methods for the calculation of eddy current losses in permanent magnets (PMs) and the shortcomings of previously conducted analyses. Eddy current losses in PMs and their mitigation are significant factors when designing inverter-fed electric drives. Especially with the need for drives with high power density, a trend toward increased rotational speeds and, therefore, higher fundamental frequencies and inverter switching frequencies are observable. Higher harmonic frequency components of concentrated windings and fractional slot windings are widely taken into account when designing rare sintered earth magnets for permanent magnet synchronous machines (PMSMs). However, inverter-related losses are rarely simulated in Finite Element Method (FEM) co-simulations and can contribute as a major factor to the power losses in PMSMs. In the worst case, this neglection can lead to the thermal demagnetization of the permanent magnets. Segmentation provides an effective measure to limit eddy current losses. However, not every kind of segmentation proves effective in a drive application. Depending on the frequency behavior of the magnetic flux in a permanent magnet, segmentation can increase eddy current losses within the magnet compared to a non-segmented magnet. This behavior is due to the reaction to the flux caused by the eddy currents within the magnet. The reaction of the eddy currents is often neglected [1, 2], and, in other cases, the vicinity of ferromagnetic material is neglected in analytical calculations [3] but proves crucial for the exact calculation of higher frequency losses [4, 5]. In this paper, an analytical solution to calculate harmonic eddy current losses in permanent magnets, including the reaction flux with homogeneous excitation, is given.

This is the second of a series of papers on new methods for the calculation of eddy current losses in permanent magnets (PMs) and the shortcomings of previous analyses. Our first paper extended Ruoho’s work on harmonic field distributions to the reaction field of eddy currents within permanent magnets. The approach was based on the methods of the harmonic complex AC calculation. In this paper, the models presented in our previous paper are further extended to allow a harmonic calculation of eddy current losses in permanent magnets for homogeneous fields, including the effects of eddy current losses in an adjacent ferromagnetic material, leakage flux factors, and non-constant inductance.