## 4 Simulation Analysis  
Finite element simulation is an important means of performance verification at the product design stage. In order to verify the load-carrying characteristics of the proposed modular multi-unit cell permanent magnet thrust bearing, four types of structures were developed based on the concepts of modularity and generalization. These included a two-layer nested two-pole crossover, a four-layer nested four-pole crossover, a six-layer nested six-pole crossover, and an eight-layer nested eight-pole crossover bearing. All models were constructed using commercial finite element software, and their bearing characteristics were analyzed. The different models utilize a generalized and modular unit cell structure, varying only in the number and arrangement of unit cells. This approach aimed to demonstrate the load-bearing characteristics of different layer nested and pole crossover configurations. The simulation models of the different structures are illustrated in Figure 10. The red block indicates the rotor and the blue color indicates the stator. Since the magnetic permeability of adiabatic materials and air in Ansoft/Maxwell 2023R1 software is almost identical, the basic structure of the bearing was simplified during  
Figure 10: Simulation models of bearings with different structures. the modeling process. The rotor and stator seats were excluded, and only the rotor and stator chokes, block mounting baskets, and permanent magnet blocks were retained. The four structural bearing models were then created by adjusting the number of permanent magnet blocks and their arrangement based on the number of layers in the rotor and stator. For the simulation, the motion domain settings of the permanent magnet thrust bearing were as follows: The rotor was assigned a motion domain, with the bearing speed set to 180 rpm. The axial displacement of the rotor was set to range from 2 mm to 30 mm, with a step size of 1 mm. The basic parameters of the bearings are outlined in Table 1. Given these parameters, the neutral axis diameter of bearings with different structures was consistent, and the performance characteristics of the permanent magnets were identical. The air gap between the permanent magnet rings was set at 2 mm. Additionally, the quantity of permanent magnets and unit cells varied among different structural configurations. The maximum diameter of the bearing was related to the number of nested layers, while the axial length was determined by the number of cross layers in the bearing. These parameters for different bearing structures are also summarized in Table 1. This modeling and simulation approach enabled the evaluation of various structural configurations and their corresponding bearing characteristics, such as load capacity, stiffness, and displacement response. Based on Ansoft/Maxwell software, simulation verification of bearings with different structures was carried out to analyze the bearing performance in the interval of axial displacement of 2-30 mm and the maximum bearing capacity of each layer was superimposed by Equation (16), to find out the maximum axial bearing capacity of the bearing as a whole. \[F=\sum_{1}^{k}F_{k}+\sum_{1}^{l}F_{l} \tag{16}\]  
where \(F\) is the maximum total bearing capacity of the bearing, \(k\) and \(l\) denote the number of layers of the rotor and stator, respectively, and \(F_{k}\) and \(F_{l}\) are the bearing capacity of the \(k\)th layer of the rotor and the \(l\)th layer of the stator, respectively. The bearing capacity of permanent magnet thrust bearings with different structures is shown in the Figure 11 by comparing the finite element simulation results with the theoretical model. Overall, the axial bearing capacity of the bearing first increases and then