## 1 Introduction  
As a new type of bearingless motor, a bearingless permanent magnet slice motor (BPMSM), not only inherits the advantages of wear-free, maintenance-free, long life, low noise and high precision, but also makes up for the shortcomings of a complex structure and high cost [1, 2, 3]. Nowadays, it has been widely applied in the medical industry, IC manufacturing, and aerospace. Researches on the optimization of BPMSMs has become a new hotspot in the fields of miniaturization, high-sealing performance, and ultra-cleanliness, which are of great significance. In contrast to conventional motors, the mechanical setup of BPMSMs offers much more freedom in terms of constructive design. However, the design leads to a nonlinear flux and current distribution, resulting in a nonlinear force and torque generation [4]. In [5, 6], the installation site of the rotor (internal rotor or external rotor) was changed to achieve optimal power between the bearing forces and motor torque. In [7], a bearingless slice motor with an external rotor design was introduced to realize linear force and torque generation behavior with the help of feedback control. For high-speed bearingless drive optimization, the number of rotor poles and stator slots as well as the winding arrangement were analyzed in [8; 9]. With the increasing demands for canned pumps and chambers in the semiconductor manufacturing industry, bearingless slice motors with wide air gaps were proposed in [10; 11]. To achieve a compact and lightweight design, symmetric sets of Halbach magnet arrays are often used in BPMSM structural designs [12; 13]. Considering feasibility and efficiency, optimization relying on the performance measurements of laboratory prototypes always focuses on qualitative analyses. Systematic research with comprehensive considerations on BPMSM structural parameters, including the arrangement of stators and rotors, the winding configurations, the number of turns of the winding, and the structural style of the permanent magnets (PMs), face challenges from the point of view of system costs and the need for a high-purity experimental environment based on laboratory prototypes. With the development of finite element analysis software, such as Ansoft and Ansys, the transient state union simulation technique has been adopted to analyze different motor structures, explore the general rule of the optimization of PMs and windings, and establish a general method for the static and dynamic analyses of the BPMSM. Some typical simulation methods have been utilized in the field of bearingless motor optimization over the past few decades [14; 15; 16; 17; 18]. Recently, vibration suppression methods along the axial and radial directions for BPMSMs were proposed in [19; 20] using simulations. In addition, research on the material properties of bearingless motor parts, especially the rotor, were verified through simulations in [21; 22]. As an alternative approach, electrical machine performance optimization through advanced control algorithms [23; 24; 25] can also realize improvements without high system costs for prototype development in physical modifications. The aforementioned studies focused on the specific mechanical structural optimization of BPMSMs without improvements to the overall performance. Moreover, the mechanical structural parameter optimization of BPMSMs is a nonlinear, multivariable, multi-objective, and strongly-coupled comprehensive problem. As a preliminary study of BPMSMs, this paper presents the sensitivity evaluation index of candidate mechanical structural parameters for specific performance based on a virtual prototype developed in Ansoft Maxwell. The dominant structural parameters are selected to be optimized by performing orthogonal tests. Finally, based on the regression model and a genetic algorithm (GA), a multi-structural optimization method for BPMSMs is proposed. The optimization results are verified through simulation experiments.