## 5 Conclusions  
In this paper, the vibration characteristics of compressor stator blades with inner and outer ring structures considering contact friction are studied by combining experimental and numerical methods. Firstly, the main components of a compressor stator blade vibration test system with inner and outer rings are introduced. Then, the function of each part of the experimental system is introduced. The main flow of the experimental measurement and experimental conditions are explained. The numerical analysis model and the method corresponding to the experimental platform are given. The nonlinear vibration characteristics of the compressor stator blades are studied in numerical and experimental studies.  
When the excitation force of the blade surface is 1 N, the maximum amplitudes of the measuring point at the bottom of the outlet side of the test blade are about 27 um at 20 N and 30 N normal loads, and 17.8 um at a 10 N normal load. The corresponding numerical results are 26 um and 18.5 um. When the excitation force changes to 2 N, the amplitude measurement results corresponding to the normal loads of 10 N, 20 N, 30 N and 40 N are 32 um, 40 um, 53.4 um and 53.7 um, respectively. The corresponding numerical results are 33 um, 39 um, 52.3 um and 52.3 um. However, when the fixed normal load is 20 N and the blade exciting force is changed, the maximum amplitude is 27 um at 1 N, 40 um at 2 N, about 50 um at 3 N and 61 um at 4 N. The corresponding numerical results are 26 um, 39 um, 52 um and 63 um. The trend of the experimental measurement and numerical results is consistent and the error is small. A comparative analysis of the data reveals this phenomenon. The nonlinear vibration characteristics of the blade are affected by both the exciting force and the normal load of the contact surface. There is a certain macro-slip on the contact surface between the blade and the outer holding ring when the normal load is relatively small. The state of the whole contact surface is characterized by nonlinear vibration. At this time, the relative motion of the contact surface consumes the vibration energy, so the amplitude will be slightly reduced. When the normal load increases, the relative motion of the blade contact surface weakens or even ceases to slip. So, the contact surface develops fretting slip or even becomes viscous, and the vibration characteristics are also similar to linear vibration characteristics. However, when the normal load is fixed and the excitation force changes, the change trend is just the opposite.  
In actual compressor equipment, the assembly structure of the stator blade ring and the load characteristics of the blade will be more complicated, so the analysis of the vibration characteristics of the blade becomes more difficult. The research in this paper provides a numerical calculation model and a test measurement method that are helpful for the design of and vibration safety research on compressor stator blades. Of course, depending on the test ideas in this paper, test measurements of complex loads and larger blades can be further carried out. This research is also of great value in that more abundant nonlinear vibration data on compressor stator blades can be obtained.  
Methodology, J.M.; Validation, J.M.; Formal analysis, Z.L.; Investigation, Z.L.; Resources, Y.X. and D.Z.; Data curation, J.M.; Software: Z.L.; Writing--original draft: J.M.; Writing--review & editing, D.Z.; Project administration: Y.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Science and Technology Major Project (J2019-IV-0022-0090) and the Fundamental Research Funds for the Central Universities (xtr072021002).