## 3 Numerical Simulations and Discussion
### Accuracy of SDA and TODA
#### 3.2.1 Results
Figure 10: The maximum identification errors of each rotor unbalance in h1.4 based on SDA using #10 point as one of the required measuring points: (**a**) relative error for the rotor unbalance amplitude; (**b**) absolute error for the rotor unbalance angle. Figure 9: Identification error changed with rotating frequency based on TODA using #20 point as one of the required measuring points in the simulation of 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 Figure 10, for SDA, the maximum relative errors of the rotor unbalance for #1-#4 discs are 5%/5.0000001199\({}^{\circ}\), 5%/5.000020523\({}^{\circ}\), 5.000039\(\circ\)/5.00022366\({}^{\circ}\), and 5%/5.000170751\({}^{\circ}\), respectively, which are almost equal to the setting errors (5%/5\({}^{\circ}\)) of the inputted unbalance responses. According to Figure 11, for TODA, the maximum relative errors of rotor unbalance for each disc also almost equal the setting error. They are 5%/5\({}^{\circ}\), 5%/5.00002\({}^{\circ}\), 5.00006%/5.00008\({}^{\circ}\), and 5%/5.00005\({}^{\circ}\), respectively. Similar results can be found in the second kind of calculation simulation example for g1.1, h1.1, h4.4, and g1.4, according to Table A2 and Figures A5-A8 in Appendix B. However, according to Figures 12 and 13, which show the maximum identification errors of each rotor unbalance for g4.4, for TODA, the maximum identification errors of rotor unbalance for #3 and #4 discs are 134.9012142%/16.8563\({}^{\circ}\) and 1350.530732%/26.69523\({}^{\circ}\), respectively, although the errors for #1 and #2 discs are almost equal the setting error 5%/5\({}^{\circ}\). Whereas, for SDA, the maximum identification errors for the rotor unbalance for #1-#4 discs are 5%/5\({}^{\circ}\), 5.00001%/5.00014\({}^{\circ}\), 5.0039%/5.00404\({}^{\circ}\), and 5.17322%/2.65779\({}^{\circ}\), respectively. Only the rotor unbalance angle of #4 disc is a bit bigger than the setting error of 5%. The others are almost equal to the input setting error of 5%/5\({}^{\circ}\). Figure 11: The maximum identification error for each rotor unbalance in h1.4 based on TODA using #10 point as one of the required measuring points (the other measuring points are at the location of the two bearings and the four discs): (**a**) relative error for the rotor unbalance amplitude; (**b**) absolute error for the rotor unbalance angle. Figure 12: The maximum identification error for each rotor unbalance in g4.4 based on SDA using #20 point as one of the required measuring points: (**a**) relative error for the rotor unbalance amplitude; (**b**) absolute error for the rotor unbalance angle. Hence, the rotor unbalance identification errors for #3 and #4 discs from 1 to 2001 Hz are as shown in Figure 14. The maximum error occurs at the beginning. The maximum identification error for rotor unbalance for #3 disc is at 1 Hz. For #4 disc, the maximum identification errors of rotor unbalance amplitude and angle are at 1 Hz and 2 Hz, respectively. However, when the rotating frequency becomes high, the identification errors are almost equal the input setting error of 5%/25\({}^{\circ}\).