## 4 Experiment
### Vibration Test  
The vibration test device of rotary parts is shown in Figure 7, including vibration isolation platform, power system, experimental rotors, and acceleration sensors, etc. The power system provides the power source and the required speed of the rotor rotation. The acceleration sensors are arranged in two orthogonal directions of the rotor to measure the vibration amplitude. The experimental rotors are assembled by the direct assembly strategy and the double constraint optimization assembly strategy for vibration measurement. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rotor Parameter** & **First-Stage Rotor** & **Second-Stage Rotor** & **Third-Stage Rotor** \\ \hline Radius of top face/mm & 43 & 189 & 100 \\ Radius of bottom face & 189 & 100 & 66 \\ /mm & 310 & 500 & 330 \\ Geometric eccentricity & 0.0026 & 0.0011 & \(-\)0.0119 \\ error in X direction/mm & 0.0419 & 0.0051 & \(-\)0.0047 \\ Geometric eccentricity & 0.0021 & 0.0015 & 0.0003 \\ error in Z direction/mm & 2.3 & 3.1 & 0.9 \\ Lowest tilt point phase/\({}^{\circ}\) & 220 & 221 & 51 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Rotor geometric characteristics and parameter errors of rotary parts rotors. Figure 6: Test device diagram of rotor geometric parameters and mass parameters: (**a**) Precision air bearing turntable; (**b**) Experimental rotor. According to Equation (9), the coordinate of the rotor center and the mass centroid can be obtained from the parameter as shown in Tables 2 and 3. The rotor coaxiality and unbalance assembled by First assembly strategy and Third assembly strategy are shown in Table 4.  
The eligibility criteria of coaxiality is less than or equal to 0.05 mm and the eligibility criteria of unbalance is less than or equal to 800 g mm. It can be seen from Table 4 that the coaxiality and unbalance by the optimized assembly strategy are better than those by the direct assembly strategy. The coaxiality and unbalance by the third assembly strategy is the only one which can meet the assembly requirements. With the increase of rotor stages, the advantages of the optimized assembly strategy are more obvious. Taking the three-stage rotor as an example, the coaxiality by the third assembly strategy is reduced by 44.1%, and the unbalance is reduced by 78.4%, which shows the advantages of the third assembly strategy. The vibration amplitude of the rotary parts rotors which are assembled by the optimized assembly strategy is compared with the vibration amplitude assembled by the direct assembly strategy is shown in Figure 8. The vibration amplitude increases with the increase of the speed and then the amplitude of the rotor begins to decrease when the speed reaches the critical speed, which is consistent with the amplitude changing trend shown in Figure 4 and the correctness of the model is verified in this paper. The vibration amplitude of the rotary parts rotors by the third assembly strategy is 3.3 \(\upmu\)m, 3.1 \(\upmu\)m, 4.8 \(\upmu\)m, and 3.1 \(\upmu\)m less than the vibration amplitude using direct assembly strategy when the speed is 4000 rpm, 5000 rpm, 6000 rpm, and 7000 rpm, respectively. The average amplitude is reduced by 22.5%. Therefore, the double constraint optimal assembly strategy established in this paper can effectively suppress the rotary parts rotor vibration. We did five sets of repetitive experiments, when the speed is 4000 rpm, the vibration amplitudes of optimized assembly strategy are 8 \(\upmu\)m, 8.7 \(\upmu\)m, 7.1 \(\upmu\)m, 6.4 \(\upmu\)m, and 6.8 \(\upmu\)m. The mean is 7.4 \(\upmu\)m, the standard deviation is 0.84 \(\upmu\)m, the uncertainty introduced by measurement repeatability \(u(x_{1})=0.84\)\(\upmu\)m, the uncertainty introduced by the resolution of eddy current