## 3 Numerical Simulations and Discussion
### Adjustment Point  
#### 3.3.1 Results  
In the third kind of simulation of g1.4, the matrix of the maximum identified error for rotor unbalance for each disc was obtained with Equations (24)-(27). The numbers of AFPs were also obtained. They are shown in Figures 15-18. The simulations were conducted by using simulated unbalance responses as input data to SDA and TODA and by changing one measuring point which was close to the identified disc. The #20, #40, #60, and #80 points were used for the respective changes. The other \(m+n\) measuring points were at the discs and bearings. The simulated unbalance responses were calculated by means of the CRDAM contaminating the sensor resolution at 0.1 nm. In Equations (24)-(27), the four element values in a row of the matrix are the maximum identification errors of unbalance for #1-#4 discs, respectively, when using the same measuring point. The four elements in a column are the maximum identification errors of unbalance for the same disc when the measuring points #20, #40, #60, and #80 were applied, respectively. By comparing the biggest identification error obtained under different adjustment point conditions when the rotating frequency is changed from 1 to 2001 Hz, it is easy to find that the adjustment point plays a critical role in improving the identification accuracy for SDA and TODA. The details are as follows:  
Figure 14: Identification error changed with rotating frequency based on TODA using #20 point as one of the required measuring points in the simulation for g.4.4: (**a**) rotor unbalance amplitude of #3 disc; (**b**) rotor unbalance angle of #3 disc; (**c**) rotor unbalance amplitude of #4 disc; (**d**) rotor unbalance angle of #4 disc. According to Equations (24) and (25), for SDA, when #20 point, which is near #1 disc, is used as one of the required measuring points, the maximum identification error for rotor unbalance for #1 disc is the smallest among that of the four discs. The maximum identification error for rotor unbalance is 10.84%\(\angle\)2.12\({}^{\circ}\), while for #2-4 discs, their maximum errors are much bigger. 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 42.54%\(\angle\)8.60\({}^{\circ}\). When #60 point, which is beside #3 disc, is used, #3 disc's rotor unbalance identification error, which is 257.24%\(\angle\)57.41\({}^{\circ}\), is the second smallest and is close to the smallest error of 254.72%\(\angle\)51.14\({}^{\circ}\). When #80 point, which is beside #4 disc, is used, #4 disc's rotor unbalance identification error, which is 9.82%\(\angle\)16.25\({}^{\circ}\), is much smaller than the others. 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, while the maximum identification error for rotor unbalance for #4 disc becomes smaller. The maximum identification errors for rotor unbalance for #2 and #3 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 as #80 point is applied, and #4 disc has the best recognition accuracy as #80 point is applied. 2. As for TODA, similar results can be obtained, although the values of maximum identification errors are much bigger than the maximum identification errors for SDA, according to Equations (26) and (27). When #20 point, which is near #1 disc, is used as one of the required measuring points, the maximum identification error for rotor unbalance for #1 disc is the smallest among that of the four discs. The maximum identification error for rotor unbalance is 4.22 \(\times\) 10\({}^{2}\)%\(\angle\)170.38\({}^{\circ}\), while for #2-4 disc, their maximum errors are much bigger.