## 3 Numerical Simulations and Discussion
### Adjustment Point
#### 3.3.2 Discussion  
In the third kind of numerical simulation, the highest sensor resolution (0.1 nm) at present is considered. In the simulation of g1.4 and g4.4, when #20 point, which is near #1 disc, is used as one of the required measuring points, the identification accuracy for the rotor unbalance for #1 disc (at location of #21 point) is high. Similarly, #2 disc at #41 point, #3 disc at #61 point, and #4 disc at #81 point can obtain high identification accuracy for rotor unbalance as #40, #60, and #80 points are used respectively. In the simulation of h1.4 and h4.4, #1 disc at #11 point, #2 disc at #21 point, #3 disc at #31 point, and #4 disc at #41 point can obtain a high identification accuracy for rotor unbalance as #10, #20, #30, and #40 points are used, respectively.  
From the above, to obtain good identification results, there should be a measuring point near the disc, for which the rotor unbalance should be identified. The measuring point near the disc determines the identification error for the rotor unbalance and it should be near the disc the unbalance of which is to be identified. Hence, the measuring point is called an adjustment point.  
By applying the proposed adjustment point, the identification errors for rotor unbalance for #3 and #4 discs in the first and second kind of simulations are reduced and Figures 19 and 20 are obtained. According to Figure 19, the maximum identification error is almost equal to zero. It is 0.003589%/0.00193\({}^{\circ}\) for #3 disc and 2.04046\(\times\)10\({}^{-4}\)%/5.84276\(\times\)10\({}^{-5\circ}\) for #4 disc, while they are 123.71543%/21.8563\({}^{\circ}\) and 1281.45771%/21.69524\({}^{\circ}\), respectively, before the application of the adjustment point. According to Figure 20, the ultimate error is 5.0006%/5.00193\({}^{\circ}\) for #3 disc and 4.99979%/5.00377\({}^{\circ}\) for #4 disc. They are almost equal to the setting error of 5%/5\({}^{\circ}\), while they are 134.9012142%/16.8563\({}^{\circ}\) and 1350.530732%/26.69523\({}^{\circ}\), respectively, before the application of the adjustment point. Therefore, there should be a sensor mounted near each disc if the unbalances of all the discs are to be identified.  
It was established that SDA has a much better identification accuracy than TODA. The reason is that the unbalance responses in both the \(x\) and \(y\) directions are involved in TODA and the unbalance response in only one direction is needed for SDA. This means that the measured errors of unbalance responses in both the \(x\) and \(y\) directions will contribute to the identification error of TODA. Moreover, they are combined by division in TODA. When the measured errors in the two directions are not the same and the error, whose value is smaller, happens to be the denominator, a high identification error occurs. Based on the simulation results, the value of the denominator is smaller in most cases, but the value of the denominator can be bigger, in which case the identification error of SDA is bigger than that of TODA, according to Figures A9, A17 and A20. Moreover, according to Figures A9, A17 and A20, similar results for SDA and TODA can be obtained when the comprehensive effect of the response measuring errors in the \(x\) and \(y\) directions is equal to that in the \(x\) or \(y\) direction. It is indicated that the identification result of TODA is greatly affected by the measured error for the unbalance response due to the unbalance responses in both the \(x\) and \(y\) directions being required. In practical engineering, it is difficult to obtain completely consistent measurement errors for each unbalance response. The measured errors for unbalance responses in the \(x\) direction are different from those in the \(y\) direction. This may lead to big identification errors for TODA. Hence, SDA is better than TODA from the perspective of engineering applications.