## 5 Experimental Validation  
Experimental verification technology is one of the key technologies for permanent magnet thrust bearings. To verify the accuracy of the theoretical derivations and finite element simulations, a test bed for permanent magnet thrust bearings was constructed based on the application scenario of permanent magnet thrust bearings in ship spindle propulsion. The experimental platform, shown in Figure 12, mainly consists of the following components: a four-layer nested four-pole crossover permanent magnet thrust bearing, a motorized pusher that controls the displacement of the bearing rotor, a rotor-driven rotating motor, and sensors for force, displacement, and torque. In the experiment design, a motor rotates the rotor at 180 r/min to simulate the rotational speed of a ship's diesel engine propulsion system. Meanwhile, an electric actuator moves the bearing rotor to a specified displacement to mimic the reaction force of the ship's propeller propulsion. The displacement range is from 2 mm to 25 mm, with a step size of 1 mm. Sensors for force, displacement, and torque continuously monitor the status of the experimental platform in real-time. This experimental setup is crucial for verifying the correctness of theoretical and simulation results and provides valuable data for evaluating the performance of permanent magnet thrust bearings in practical applications. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Carrying Capacity** & **Two-Layer Nested** & **Four-Layer Nested** & **Six-Layer Nested** & **Eight-Layer Nested** \\
**Indicators** & **Two-Pole Crossover** & **Four-Pole Crossover** & **Six-Pole Crossover** & **Eight-Pole Crossover** \\ \hline Unit cell (kN) & 0.308 & 0.486 & 0.524 & 0.551 \\ Unit magnet block (kN) & 0.077 & 0.121 & 0.131 & 0.138 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Indicators of the load-carrying capacity of bearings of different structures. Figure 12: Permanent magnet thrust bearing test bed and bearing prototype. According to the experiments conducted on the constructed four-layer nested four-pole crossover permanent magnet thrust bearing prototype and bearing test bed, different displacements were achieved by controlling the electric actuator, and the axial bearing capacity was recorded. By differentiating the bearing capacity with respect to displacement, the experimental rigidity of the permanent magnet thrust bearing can be derived. The theoretical, simulation, and experimental values of the bearing capacity of the permanent magnet thrust bearing are shown in Figure 13. The bearing capacity of the permanent magnet thrust bearing first increases and then decreases, with an effective working range of 2-15 mm. In the theoretical calculation, the maximum bearing capacity of the permanent magnet thrust bearing is 52.30 kN, which occurs at an axial displacement of 12 mm. In the finite element simulation, the maximum bearing capacity is 50.52 kN, corresponding to an axial displacement of 17 mm. In the experimental results, the maximum bearing capacity of the permanent magnet thrust bearing prototype is 48.45 kN. The error compared to the theoretical value is 7.3%, and the error compared to the simulation solution is 4%. The sources of error can be summarized in three areas. The first is an error in the equivalent magnetic circuit model at the time of construction. In the construction of the equivalent magnetic circuit model, the magnetic leakage of the outermost layer and the air gap part is neglected, and at the same time, the material of the central axis is approximated as a benign magnetically conductive material, and its magnetoresistance is neglected, so the results of the theoretical analysis may be larger than the experimental results.