Modeling of a 4kW Axial Flux Machine - Measurements and 2D/3D Modeling

Licentiate thesis, 2025

Axial Flux Machines (AFMs) are emerging as promising alternatives to traditional Radial Flux Machines (RFMs) offering advantages in power density, compactness, and efficiency, especially for Electric Vehicles and other high-performance applications. This study investigates the modeling and analysis of AFMs using both Three-Dimensional (3D) and Two-Dimensional (2D) simulation approaches. A physical AFM was investigated and modeled with the 3D Finite Element Method (FEM), establishing a benchmark for accurate electromagnetic analysis. The 3D model was parameterized and transformed into an equivalent 2D model, with an extruded 2D model developed to enhance the comparison between the two approaches. A key focus of this work is the analysis of end leakage flux and end-turn leakage inductance, with results quantifying the 2D models’ computational efficiency versus their inability to capture the edge effects that are accurately represented in the much more time-demanding 3D models.

The study found that a medium mesh density and 120 time-steps per electrical period of the fundamental voltage provide an ideal compromise between computational accuracy and efficiency. Although the 2D model cannot fully replicate the geometric complexities of the 3D model, it proves to be an effective approximation in specific applications where detailed edge effects are less critical. Several 3D and 2D models with varying core and magnet lengths were compared. Furthermore, a narrow core and magnet length model was analyzed across five sizes from full 3D to 2D. Results indicate that rotor magnet leakage becomes significant, necessitating a 3D model when a magnetically leading rotor core surrounds the magnets in the radial direction. Similarly, winding end leakage effects require 3D modeling when the stator core’s radial thickness is small compared to the extent of the coil ends. For the investigated double stator single rotor machine, the recommended ratio of the length of the magnet in the radial direction to the radius of the computational plane should be greater than 0.5. Further, it is found with FEM that the end-turn leakage inductances in the d- and q-directions are 33% and 25% of the total d- and q-axis inductance, respectively. The 11% difference of power between 3D and 2D at higher speeds is due to the leakage inductance. Two analytical methods suggested in literature for calculation of end-turn leakage inductance, one for RFMs, and one for AFMs are modified and analyzed. It is found that both methods fail to capture the end-turn inductance well, with the best guess yielding a 60% lower value compared to FEM simulations.

This work advances modeling methodologies for AFMs by offering insights into refining mesh density and time-steps, identifying the limitations of 2D models, and offering detailed insights into electromagnetic phenomena like end leakage flux. Failing to refine the mesh density and time-steps can result in reduced precision of simulation results in key parameters, such as flux density and torque, and may fail to capture critical phenomena like end leakage flux. The findings contribute to improving AFM design and simulation techniques, identifying areas for further enhancement in 2D modeling to balance computational efficiency and accuracy.