Analytical Model of a Bearingless Motors With Conformal Mapping Method

This paper presents an analytical framework for modeling the air-gap magnetic field, suspension force, and Maxwell stress tensor (MST) in bearingless permanent magnet synchronous motors (BPMSMs), with the goal of improving both suspension performance evaluation and early-stage design efficiency. By leveraging Schwarz-Christoffel conformal mappings, we derive closed-form solutions for the magnetic field in the air gap without assuming infinite slot depth. The model naturally accommodates slot-depth effects and captures spatial harmonics critical to MST and force evaluation. The analytical solution is embedded within a multi-objective optimization loop, reducing the time of a single evaluation from hours to under one minute. Furthermore, we propose a unified visualization method combining MST contours, radial force fields, and error-angle loci, which enables intuitive interpretation of suspension stability. The analytical results show strong agreement with finite element analysis (FEA), confirming the model's validity. The proposed method significantly reduces computational effort while maintaining accuracy, making it suitable for design space exploration. Future work will address magnetic saturation and rotor slotting to further enhance model fidelity.