# Continuous Rotor Dynamics of Multi-Disc and Multi-Span
## 3 Numerical Simulations and Discussion
### Calculated Unbalance Response
#### 3.3.2 Discussion  
(1) Accuracy  
From the above, the three unbalance response curves calculated by CRDAM, FEM and Ricatti are well coincident when the frequency is away from the critical frequency, but they are different when the frequency is near the critical frequency. At the critical frequency, the peak value of the amplitude of unbalance response curve appears and the amplitude decreases or increases rapidly near the critical frequency. When the peak values are different, the three unbalance response curves are not well coincident. When the same order critical frequencies are different, their coincidence becomes worse. The severity of the inconsistency of the unbalanced response is positively correlated with the difference of the critical frequency calculated the three methods. However, the three unbalance response curves calculated by three methods are well coincident when the frequency is smaller than the low order frequency (first, second, third and fourth order). Even near the lower critical frequency, the three unbalance response curves calculated by the three methods coincide well. The reason is that the low order frequencies and the unbalance response amplitude calculated by the three methods are almost equal. To intuitively evaluate the coincidence of the three unbalance response curves calculated by the three methods, Figures 17 and 18 are obtained using the computational example h5.5 and h1.5, respectively. In Figures 17 and 18, the red curve represents the error of CRDAM to FEM and the black curve represents the error of CRDAM to FEM. The relative error is used to describe the amplitude error of unbalance responses and the absolute error is used to describe the angle error. According to Figure 17a-c, the red curve is below the black curve from 0 Hz to 300 Hz, which means that the error of FEM to CRDAM is smaller than the error of Ricatti to CRDAM. The unbalance response obtained by CRDAM is closer to the unbalance response obtained by FEM than the unbalance response obtained by Ricatti. The errors are smaller when the frequency is away from the first, second, third, fourth and fifth critical frequency than when near these critical frequency. The error of FEM to CRDAM is small even when the frequency is near these critical frequency. The similar results can also be obtained from Figure 18a-c. According to Figure 17e, the red curve is close to the black curve when the frequency is smaller than the sixth order critical frequency. When the frequency is higher than the sixth order critical frequency, most parts of the red curve is above the black curve, but there are some parts of the red curve and black curve are coincident and there are some parts of the red curve is above the black curve. Hence, it can also be inferred that the unbalance response obtained by CRDAM is closer to the unbalance response obtained by FEM than the unbalance response obtained by Ricatti. Moreover, the errors are bigger when the frequency is near the sixth order critical frequency than when the frequency is away from the sixth order critical frequency. The similar results can also be obtained from Figure 18d-h.  
From the above, the unbalance responses calculated by the CRDAM, FEM and Ricatti are different. The unbalance response obtained by CRDAM is closer to the unbalance response obtained by FEM than the unbalance response obtained by Ricatti, especially when the frequency is smaller than the low order frequencies. Their differences are small when the frequency is away from the critical frequency and the differences are big when near these critical frequencies. When the frequency is smaller than the low order frequency, their differences are small too. Figure 17: Relative error of #2 point’s unbalance response amplitude and absolute error of #2 point’s unbalance response angle: (**a**) 0–150 Hz; (**b**) 150–220 Hz; (**c**) 220–300 Hz; (**d**) 300–500 Hz.