## 5 Experimental Research  
In order to further verify the effectiveness of the proposed method for the dynamic balance correction of the AMB rotor, the dynamic balance correction experiment was carried out on the AMB rotor test rig. The test rig includes a controller, power amplifier, magnetic bearing rotor system, fiber optical sensor frequency converter and host computer, as shown in Figure 11.  
The square wave signal of the fiber optical sensor is introduced into the acquisition system. As shown in Figure 12, the rising edge of the square wave is the zero phase of the vibration displacement vector. Since the marker is located at the center of the starting shot hole, the zero phase of the vibration displacement vector and the counterweight vector are unified.  
Figure 11: AMB rotor test rig.  
Figure 10: Comparison diagram of two dynamic balance correction axis trajectories.  
The AMB rotor is driven to 70 Hz and the initial vibration displacement vectors \(D_{a0}\) and \(D_{b0}\) are calculated. The test weight mass \(M_{A}\) and \(M_{B}\) are added successively at the end \(A\) and \(B\), and the specific values are shown in Equation (18). The vibration displacement vector of the two test weights is obtained.  
\[\begin{array}{l}M_{A}=0.48\times 10^{-3}\ \mathrm{kg}\angle-22.5^{\circ}\\ M_{B}=0.48\times 10^{-3}\ \mathrm{kg}\angle+135^{\circ}\end{array} \tag{18}\]  
The initial vibration displacement vector and the vibration displacement vector of the two test weights are shown in Table 3.  
According to Equations (16) and (17), the influence coefficient and final counterweight are calculated, and the dynamic balance of the rotor is corrected.  
Figure 13a,b show the axis trajectories at both ends \(A\) and \(B\) before dynamic balance, respectively. Figure 13c,d respectively show these axis trajectories after dynamic balance.  
As can be seen from the figure, the collected signal contains not only the displacement signal at the rotational speed frequency, but also the disturbance signal generated by the hardware system. In order to make it easier to observe, the displacement signal obtained by ANF tracking is used to draw the axis trajectory which only includes the displacement signal at the rotational speed frequency; this is shown in Figure 14.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(x_{a}\) & \(D_{a0}\) & \(D_{a1}\) & \(D_{a2}\) \\ \hline Amplitude (\(\upmu\)m) & 5.3 & 3.8 & 4.0 \\ Phase (\({}^{\circ}\)) & 71.2 & 60.6 & 76.7 \\ \hline \(x_{b}\) & \(D_{b0}\) & \(D_{b1}\) & \(D_{b2}\) \\ \hline Amplitude (\(\upmu\)m) & 13.7 & 13.8 & 12.4 \\ Phase (\({}^{\circ}\)) & \(-\)39.5 & \(-\)176.7 & 171.8 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Vibration displacement vector.  
Figure 12: Schematic diagram of vibration displacement vector phase calculation.  
Figure 15 shows the displacement spectrum of each end of the rotor before and after dynamic balance. It can be seen from the figure that at the speed of 4200 r/min, the displacement amplitudes of the \(x_{a}\), \(x_{b}\), \(y_{a}\) and \(y_{b}\) ends of the rotor decreased by 56.6%, 62.8%, 49.2% and 63.7%, respectively, after dynamic balance.  
Figure 14: Rotor axis trajectory of ANF tracking signal.  
Figure 13: Comparison diagram of rotor axis trajectory before and after dynamic balance.  
We can drive the rotor to 100 Hz and then decelerate freely. Figure 15(a) is a comparison diagram of the displacement before and after dynamic balance with the decrease in rotational speed. Figure 15(b) is a spectrum analysis diagram. It can be observed from the figure that the vibration amplitude of the rotor decreases at different rotational speeds, and the higher the rotational speed is, the more significant the decrease in the displacement amplitude will be.