## 4 Results and Discussion  
### Blade Vibration under Different Normal Loads  
The experimental objects were the compressor stator blade and the contacted outer holding ring. Regarding the fixed blade surface excitation force, the vibration test of the changing normal force on the contact interface was carried out first. The test was divided into two groups. In one of the groups, the exciting force was 1 N and the normal loads were 10 N, 20 N and 30 N, respectively. The excitation force of the other group of working conditions was 2 N, and the normal forces on the contact interface were 10 N, 20 N, 30 N and 40 N, respectively. In the experiment, the vibration response of 10% of the height of the outlet side for the test model blade was measured. After the measurement data were processed, they were compared with the numerical calculation value of the corresponding working condition. Figures 9-11 gives the test results under different normal loads when the exciting force is 1 N. It can be seen from the figure that the basic change trend of the test data is roughly consistent with the numerical results. The numerical analysis results show that the first-order vibration frequency of test model is roughly 28 Hz, and the resonance range of the experimental measurement data is also in this frequency range. When the excitation force of the blade surface is 1 N, the maximum amplitude of the measuring point at the bottom of the outlet side of the test blade is about 27 \(\upmu\)m. Additionally, there is little difference between the measured amplitude of 20 N and 30 N normal loads. The corresponding numerical result is 26 \(\upmu\)m. While the interface normal force is 10 N, the maximum amplitude for the test stator blade is 17.8 \(\upmu\)m. The corresponding numerical result is 18.5 \(\upmu\)m. The relative error between the numerical values and experiments is small. Since the law is not obvious when the exciting force is small, the test results of the exciting force of 2 N are further given in Figures 12-15, which were also tested under different normal loads. It is not difficult to find that the test data of these working conditions correspond well with the numerical results. The resonance frequency of the numerical simulation and the resonance range measured in the experiment basically coincide, and the overall variation trend is similar. When the exciting force of the blade surface is 2 N, the maximum amplitudes of the measuring point at the bottom of the outlet side of the test blade are about 53.4 \(\upmu\)m and 53.7 \(\upmu\)m, which correspond to the measured results of the normal loads of 30 N and 40 N. The corresponding numerical result is 52.3 \(\upmu\)m. When the normal loads are 10 N and 20 N, the maximum amplitudes of the test blades are 32 \(\upmu\)m and 40 \(\upmu\)m. The corresponding numerical results are 33 \(\upmu\)m and 39 \(\upmu\)m. The relative error of the numerical value and the test is still very small, basically within 5%. Figure 9: Response curve under 10 N normal load with 1 N exciting force. Figure 11: Response curve under 30 N normal load with 1 N exciting force. Figure 12: Response curve under 10 N normal load with 2 N exciting force. Figure 10: Response curve under 20 N normal load with 1 N exciting force. Figure 14: Response curve under 30 N normal load with 2 N exciting force. Figure 13: Response curve under 20 N normal load with 2 N exciting force. Figure 15: Response curve under 40 N normal load with 2 N exciting force. The above two test conditions are analyzed here. It can be seen that when the excitation force of blade surface is fixed, the variation amplitude increases with the normal force at the interface increases gradually. An explanation is given here that there is a certain macro-slip in the contact interface between test model blade and the contacted holding ring while normal force is relatively small. The state of the test model interface is characterized by nonlinear vibration.