## 6 Experimental Results
### Acceleration Control of the AMB Rigid Rotor System  
Figure 13(a) shows the rotor vibration of AMBs--the AMB rigid rotor system operating at 45,000 rpm. This figure depicts the vibration responses along the radial directions (AX, BX, BY, and AY) and the axial direction (\(Z\)) during the acceleration, steady-state operation, and deceleration stages. During the acceleration phase, the rotor may experience significant unbalanced forces and inertial forces, leading to an increase in the radial vibration amplitude, which stabilizes after reaching a peak. When the motor enters the constant-speed operation state (4500 rpm), the rotor typically achieves a stable condition with smaller radial vibration amplitudes, and fluctuation data indicate that the amplitude varies within a narrow range. During the deceleration phase, the rotor may again undergo changes in unbalanced and inertial forces, causing an increase in the radial vibration amplitude until the speed decreases from 4500 rpm to 0. The rotor vibration is expressed in volts, with the maximum (\(U_{max}\)), minimum (\(U_{min}\)), and average (\(U_{avg}\)) values annotated for each direction. A consistent scale of 2 V/div is applied for all signals. The magnetic levitation system employs sinusoidal currents in three-phase windings to generate the electromagnetic forces required for rotor suspension and stabilization. During the operation, the alternating force contributions from the phase windings result in periodic imbalances, which manifest as vibrations in the radial directions. These vibrations are more pronounced due to the dynamic nature of the electromagnetic forces. Contrarily, the axial vibration remains subdued, as the system consistently counteracts the gravitational load. The error between the rotor vibration and the neutral point is presented in Figure 13(b). Figure 13(a) illustrates the amplitude magnitudes of the radial four degrees of freedom (AX, AY, BX, and BY) and the axial direction (\(Z\)) during the acceleration to 4500 rpm, stabilization, and subsequent deceleration of the AMB high-speed motor. Figure 13(b) presents the maximum vibration values for each degree of freedom during acceleration, constant speed, and deceleration, providing a comprehensive understanding of the vibration behavior of the AMB high-speed motor under different operating conditions. Through the real-time monitoring and analysis of fluctuation data, the control system can achieve more precise adjustments, ensuring the stability and reliability of the motor across various operational states. The 2D vibration plots provide a clear visualization of the rotor's anisotropic vibrational characteristics, emphasizing the varying dynamic responses along different radial directions. In Figure 14(a), the data indicate a notable discrepancy in the maximum vibration amplitudes, with AY reaching a peak value of 0.93 V compared to 0.38 V for AX. This disparity underscores the significant dynamic instability along the AY axis, potentially arising from uneven electromagnetic force distributions and transient imbalances during the rotor operation. Similarly, Figure 14(b) demonstrates a relatively balanced relationship between the maximum vibration amplitudes, with BX peaking at 0.81 V and BY at 0.76 V.  
Figure 16 illustrates 3D vibration plots, providing a comprehensive visualization of the rotor's dynamic behavior during operation. In both plots, the rotor speed is used as the horizontal axis (x-axis). In Figure 15(a), AX and AY serve as the vertical (\(y\)-axis) and depth (\(z\)-axis) coordinates, respectively, showing the rotor's vibration response during the acceleration, steady-state operation, and deceleration phases. This plot highlights the transient instabilities during the rotor's startup phase, characterized by pronounced oscillations in both AX and AY. As the rotor speed increases, the vibrations gradually stabilize, reflecting the steady-state operation.