## 3 Numerical Simulations and Discussion
### Adjustment Point
#### 3.3.1 Results
When #40 point, which is close to #2 disc, is used, the maximum identification error for rotor unbalance for #2 disc becomes the smallest. It is 1.64 \(\times\) 10\({}^{4}\)%\(\angle\)140.73\({}^{\circ}\). When #60 point, which is beside #3 disc, is used, #3 disc's rotor unbalance identification error, which is 6.03 \(\times\) 10\({}^{4}\)%\(\angle\)179.57\({}^{\circ}\), is the second smallest. When #80 point, which is beside #4 disc, is used, #4 disc's rotor unbalance identification error is 2.68 \(\times\) 10\({}^{15}\)%\(\angle\)179.95\({}^{\circ}\). Although it is the biggest among the obtained maximum identification errors of the four discs, it is the smallest error for #4 disc, which can be obtained by changing the measuring point from #20 to #40. From the perspective of the column in the matrix, when the measuring point is changed from #20 to #40, the maximum identification error for rotor unbalance for #1 disc becomes bigger. The maximum identification errors of rotor unbalance for #2, #3, and #4 discs are also changed apparently. As #20 point is applied, #1 disc acquires the best recognition accuracy, while #2 disc has the best recognition accuracy as #40 point is applied, #3 disc has the best recognition accuracy of unbalance amplitude as #60 point is applied, and #4 disc has the best recognition accuracy as #80 point is applied. \[SDA\_M1_{g14}=\left[ \begin{array}{ccc}\framebox{10.84}&376.18&14934.67&22570.13 \\ 400.78&42.54&7251.41&4823.78\\ 382.89&254.72&257.54&3203.79\\ 1153.90&475.79&1148.01&9.82\\ \end{array} \right] \tag{24}\]  
\[SDA\_M2_{g14}=\left[ \begin{array}{ccc}\framebox{2.12}&152.05&179.19&170.46 \\ 83.28&8.60&178.20&173.14\\ 132.99&51.14&\framebox{57.41}&173.82\\ 121.58&141.59&139.37&16.25\\ \end{array} \right] \tag{25}\]\[TODA\_M1_{g14}=\left[ \begin{array}{ccc}\hline 4.22\times 10^{2}&1.54\times 10^{5}&1.04 \times 10^{7}&7.39\times 10^{18}\\ \hline 4.97\times 10^{4}&1.46\times 10^{4}&3.45\times 10^{6}&9.50\times 10^{17}\\ 3.66\times 10^{4}&6.58\times 10^{4}&6.03\times 10^{4}&1.37\times 10^{17}\\ 9.14\times 10^{5}&1.94\times 10^{6}&3.89\times 10^{6}&2.68\times 10^{15}\\ \end{array} \right] \tag{26}\]  
\[TODA\_M2_{g14}=\left[ \begin{array}{ccc}\hline 170.38&179.83&178.53&179.98\\ \hline 178.23&140.73&179.01&180.00\\ 179.27&179.76&179.57&179.99\\ 179.75&179.67&179.67&179.95\\ \end{array} \right] \tag{27}\]  
where \(SDA\_M1_{g14}\) and \(SDA\_M2_{g14}\) are the matrix of the maximum identification error for rotor unbalance amplitude and the angle of #1 to #4 discs under different adjustment point conditions using SDA; \(TODA\_M1_{g14}\) and \(TODA\_M2_{g14}\) are the matrix of the maximum identification error for rotor unbalance amplitude and the angle of #1 to #4 discs under different adjustment point conditions using TODA. According to the number of AFPs of rotor unbalance obtained by SDA in Figures 15-18, the results are as follows:  
1. The numbers of AFPs of rotor unbalance amplitude for #1-#4 discs are 1001, 979, 744, and 762, respectively, according to Figure 15a. For the rotor unbalance angle, there are 1001, 990, 629, and 612 AFPs, respectively, according to Figure 15b. This indicates that the identification results for rotor unbalance for #1 disc are best when #20 point is used as one of the required measuring points. 2. According to Figure 16, there are 994, 999, 824, and 929 AFPs, respectively, for the rotor unbalance amplitude of #1 disc, #2 disc, #3 disc, and #4 disc, and 988, 1001, 835, and 787 AFPs, respectively, for the rotor unbalance angle. This indicates that the identification results for rotor unbalance for #2 disc are best when #40 point is used as one of the required measuring points. 3. According to Figure 17, the numbers of AFPs of rotor unbalance amplitude are 980, 987, 995, and 988, respectively, and the numbers of rotor unbalance angles are 974, 995, 995, and 960 respectively. This indicates that the identification results for rotor unbalance for #3 disc are best when #60 point is used as one of the required measuring points.