## 3 Simulation  
To study the vibration suppression effect of this dynamic analysis model of unbalanced vibration response model based on centroid stacking transformation, the dynamic simulation analysis of three-stage rotors stacking assembly is carried out. The finite element method was used for analysis. This method simplifies the rotor system into discrete rigid, elastic shaft segments, and bearings with stiffness and damping. The simulation model shows the division of the three-stage rotor, and the position of the drive end and the non-drive end is shown in Figure 2. The simulation parameters of rotary parts rotors are shown in Table 1. Besides, elastic supports are applied at the front and back rear respectively after the rotor is assembled. The stiffness of the drive end is \(8\times 10^{6}\) N/m, and the stiffness of the non-drive end is \(1.2\times 10^{7}\) N/m. Figure 3 shows the simulation results of vibration amplitude at the drive end of the rotor system. The vibration amplitude of the drive end is simulated and analyzed after the assembly of the rotor system under the working speed of the rotary parts. Taking the vibration response of the drive end as an example, the vibration amplitude is \(17.55\)\(\upmu\)m when the second and third stage rotors are assembled by the direct assembly strategy. The vibration amplitude is \(3.8\)\(\upmu\)m when the second stage rotor assembly phase angle is \(170^{\circ}\) and the third stage rotor assembly phase angle is \(188^{\circ}\) which is assembled by the optimization assembly strategy. The results show that the vibration amplitude is reduced by \(78.3\%\) through the adjustment of assembly phase. In all, it can be seen that the vibration amplitude of rotary parts rotor system can be changed, and the vibration suppression of rotor system can be realized by adjusting the assembly phase of each stage of the rotor. \begin{table}
\begin{tabular}{c c c c} \hline
**Rotor Parameter** & **First-Stage Rotor** & **Second-Stage Rotor** & **Third-Stage Rotor** \\ \hline Mass weight/g & 27,400 & 20,000 & 5800 \\ Height/mm & 310 & 500 & 330 \\ Geometric eccentricity & 0.001 & 0.001 & 0.001 \\ error in X direction/mm & & & \\ \hline Geometric eccentricity & 0.002 & 0.002 & 0.002 \\ error in Y direction/mm & & & \\ Geometric eccentricity & 0.002 & 0.002 & 0.002 \\ error in Z direction/mm & & & \\ Perpendicularity/mm & 0.001 & 0.001 & 0.001 \\ Mass eccentricity error in X & 0.002 & 0.002 & 0.002 \\ direction/mm & & & \\ Mass eccentricity error in Y & 0.001 & 0.001 & 0.001 \\ direction/mm & & & \\ Mass eccentricity error in Z & 0.001 & 0.001 & 0.001 \\ direction/mm & & & \\ Lowest tilt point phase/\({}^{\circ}\) & 0 & 0 & 0 \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters of rotary parts rotors. Figure 2: Simulation model of rotor vibration. To suppress the vibration and make the geometric errors, mass characteristics of the assembled rotary parts rotor meet the eligibility criteria which is obtained from the assembly workshop, this paper carries out three assembly strategies: Direct Assembly, Minimize Vibration Assembly, Optimal Assembly with Double Constraints. Figure 4 shows the results of coaxiality, unbalance, and vibration amplitude under three assembly strategies. It can be seen from Figure 4 that the coaxiality and unbalance of the first assembly method exceeds the eligibility criteria, and the vibration amplitude is the largest of the three assembly methods, which is 17.55 \(\upmu\)m. The unbalance of the second assembly method is lower than the standard line, and the vibration is the smallest of the three assembly methods, but the coaxiality is not constrained, which is far more than the eligibility criteria.