## 4 Experiments
The optimal assembly orientations of each component and the corresponding unbalance of the four-stage rotor were calculated according to Strategy-1, Strategy-2, and Strategy-3, respectively, as shown in Tables 12-14. \(\theta_{21}\), \(\theta_{22}\), \(\theta_{23}\), and \(\theta_{24}\) were the optimal assembly orientations of the front shaft, the LPC, the HPC, and the back shaft, respectively, without considering the distribution of the screw holes of each component. The mean value and standard deviations of the optimal results were provided in Table 15. Furthermore, the optimal assembly orientations where the screw hole exists were obtained by a secondary calculation. As shown in Table 16, the optimal assembly orientations achieved during six iterations were exactly same. This indicates that the measurement errors of each parameter had little influence on the optimal results, especially when considering the existence of the distributed screw holes of each component. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sequence** & \(\mathbf{\theta_{21}}\)[\({}^{\circ}\)] & \(\mathbf{\theta_{22}}\)[\({}^{\circ}\)] & \(\mathbf{\theta_{23}}\)[\({}^{\circ}\)] & \(\mathbf{\theta_{24}}\)[\({}^{\circ}\)] & **Unbalance [g-mm]** \\ \hline
1 & 0 & 140.80 & 45.20 & 30.17 & 402.15 \\
2 & 0 & 143.92 & 45.07 & 30.01 & 401.90 \\
3 & 0 & 141.99 & 45.00 & 30.00 & 402.46 \\
4 & 0 & 141.92 & 45.07 & 30.04 & 402.50 \\
5 & 0 & 141.97 & 45.02 & 30.01 & 401.53 \\
6 & 0 & 142.95 & 45.04 & 30.00 & 404.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: The optimal results were calculated according to Strategy-2. Figure 9: The setting of the initial unbalance of the four-stage rotor. The four-stage rotor was assembled according to the above three optimization results, and the unbalance of the assemblies was measured by a dynamic balancing machine further. The dynamic balancing machine was manufactured by Shanghai Shenzhong Co., Ltd. (Shanghai, China), and its minimum residual unbalance reaches 0.5 g\(\cdot\)mm/kg. The experimental device was shown in Figure 10, and the corresponding results of the experiments were shown in Table 17. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Strategy** & \(\mathbf{\theta_{21}}\) [\({}^{\circ}\)] & \(\mathbf{\theta_{22}}\) [\({}^{\circ}\)] & \(\mathbf{\theta_{25}}\) [\({}^{\circ}\)] & \(\mathbf{\theta_{24}}\) [\({}^{\circ}\)] & **Unbalance [g-mm]** \\ \hline
1 & 0 & 120(4 \(\times\) 30) & 105(7 \(\times\) 15) & 120(4 \(\times\) 30) & 189.68 \\
2 & 0 & 150(5 \(\times\) 30) & 60(4 \(\times\) 15) & 60(2 \(\times\) 30) & 403.07 \\
3 & 0 & 0 & 0 & 0 & 320.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: The optimal results with considering the distributed screw holes of each component. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sequence** & \(\mathbf{\theta_{21}}\) [\({}^{\circ}\)] & \(\mathbf{\theta_{22}}\) [\({}^{\circ}\)] & \(\mathbf{\theta_{23}}\) [\({}^{\circ}\)] & \(\mathbf{\theta_{24}}\) [\({}^{\circ}\)] & **Unbalance [g-mm]** \\ \hline
1 & 0 & 0 & 0 & 0 & 324.60 \\
2 & 0 & 0 & 0 & 0 & 328.13 \\
3 & 0 & 0 & 0 & 0 & 324.92 \\
4 & 0 & 0 & 0 & 0 & 324.90 \\
5 & 0 & 0 & 0 & 0 & 327.14 \\
6 & 0 & 0 & 0 & 0 & 329.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: The optimal results were calculated according to Strategy-3. Figure 10: Measurement of the unbalance of the four-stage rotor. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Strategy** & \(\mathbf{\theta_{21}}\) [\({}^{\circ}\)] & \(\mathbf{\theta_{22}}\) [\({}^{\circ}\)] & \(\mathbf{\theta_{23}}\) [\({}^{\circ}\)] & \(\mathbf{\theta_{24}}\) [\({}^{\circ}\)] & **Unbalance [g-mm]** \\ \hline
1 & 0 & 120(4 \(\times\) 30) & 105(7 \(\times\) 15) & 120(4 \(\times\) 30) & 184.6 \\
2 & 0 & 150(5 \(\times\) 30) & 60(4 \(\times\) 15) & 60(2 \(\times\) 30) & 404.1 \\
3 & 0 & 0 & 0 & 0 & 325.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: The results of three experiments.