## 4 Simulation Analysis
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Bearing Parameters** & \begin{tabular}{c} **Two-Layer Nested** \\ **Two-Pole Crossover** \\ \end{tabular} & \begin{tabular}{c} **Four-Layer Nested** \\ **Four-Pole Crossover** \\ \end{tabular} & \
\begin{tabular}{c} **Six-Layer Nested** \\ **Six-Pole Crossover** \\ \end{tabular} &
\begin{tabular}{c} **Eight-Layer Nested** \\ **Eight-Pole Crossover** \\ \end{tabular} \\ \hline \hline Center shaft diameter & 110 & 110 & 110 & 110 \\ (mm) & 234 & 362 & 490 & 618 \\ Magnet thickness (mm) & 30 & 30 & 30 & 30 \\ Magnet length (mm) & 28 & 28 & 28 & 28 \\ Axial length (mm) & 113 & 185 & 257 & 329 \\ Permanent magnet & N48 & N48 & N48 & N48 \\ grades & 1.4 T & 1.4 T & 1.4 T & 1.4 T \\ Residual magnetism & 88 & 416 & 1044 & 2096 \\ Number of unit cells & 22 & 104 & 261 & 524 \\ Ring gap (mm) & 2 & 2 & 2 & 2 \\ Axial displacement (mm) & 2–30 & 2–30 & 2–30 & 2–30 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic parameters of bearings with different structures. decreases with the increase of axial displacement. This is because as the axial displacement of the bearing increases, the attraction and repulsion between the permanent magnets increase, limiting the further increase of the axial displacement. However, as the axial displacement continues to increase, the outermost layer of permanent magnets will gradually leave the working surface, resulting in a reduction in the working area and a decrease in the number of layers of permanent magnets that interact. This ultimately leads to a decrease in its axial bearing capacity. In addition, the images indicate that the maximum bearing capacity of the theoretical model is greater than that of the simulation model. This discrepancy arises from the construction of the equivalent magnetic circuit model, where the leakage flux from the outermost layer and the air gap is neglected. Additionally, the shaft material is treated as an ideal magnetic conductor, and its magnetic resistance is not considered. Consequently, the results of the theoretical analysis are higher than those obtained from the simulations. Moreover, in the theoretical model, the axial length of the permanent magnet bearing is calculated based on the combined length of four layers of permanent magnet rings, without accounting for the length of the unit cell. This leads to a difference in the axial displacement associated with the maximum bearing capacity of the two models. For the single structure bearing, the errors between the theoretical and simulation models are 0.7%, 3.5%, 1.2%, and 2%, respectively. According to the simulation results, the unit cell bearing capacity and unit magnet block bearing capacity for different structures of the permanent magnet thrust bearing are shown in Table 2. As the number of nested and cross layers in the bearing increases, both the unit cell and the unit magnet block bearing capacity also increase. This trend can be attributed to the higher ratio of the number of magnet layers to the working surface in the multilayer structure, which leads to a more efficient utilization of the magnetic field. Figure 11: Carrying capacity of permanent magnet thrust bearing with different structures. The increased magnet utilization in the multilayer cross-nested structure enhances the overall bearing capacity, as reflected in the higher unit cell and unit magnet block bearing capacities. These results validate the advantages of the multilayer cross-nested structure in improving the bearing's load-carrying performance. By effectively using the available magnetic flux and optimizing the distribution of magnetic forces, the proposed structure significantly enhances the bearing's overall efficiency and capacity.