## 4 Results and Discussion  
### Nonlinear Vibration Results of Different Models  
The nonlinear vibration of compressor stator under the action of normal load and exciting force was simulated with iterative calculation. For the analysis of the model, the vibration response characteristics of the blades were analyzed by changing the normal load and assuming that the exciting force remained unchanged. The circumferential flow force and axial flow force of the blade surface were set as 40 N and 16 N, respectively. The vibration amplitude of the outlet node of the 50% blade height was extracted. Figure 9 shows the vibration response curves with a series of different normal loads under corresponding working conditions. Figure 8: Mesh of rotor and stationary blades. Figure 9: Response normalization amplitude curves under different normal loads with 40 N exciting force. (**a**) Circumferential amplitude curve. (**b**) Axial amplitude curve. Since the blades were subjected to airflow forces in two directions, the results given here include circumferential and axial vibration responses. It is worth pointing out that the vibration response curves of several results with high normal load in Figure 9 are overlapped, which made it impossible to distinguish in detail. The reasons will be analyzed in detail later. In order to facilitate comparison, the amplitude was normalized. The maximum amplitudes calculated from the resonant frequencies in a series of working conditions were taken as the reference to normalize the axial and circumferential curves. Firstly, it is not difficult to see that when excitation force remains constant, the vibration response of the compressor stator blade increases with the increase of normal load, and the vibration response no longer changes when the normal load increases to a certain extent. This phenomenon can be observed for both axial and circumferential amplitude. In addition, the resonant frequencies of various calculation conditions are roughly in the same position. At the same time, the ratio of blade amplitude magnitude of circumferential and axial is roughly consistent with the ratio of excitation force given in the corresponding direction. As for the phenomenon of blade vibration response no longer changing significantly under the normal load of a large contact surface, we can provide the following explanations. Under dry friction damping, the normal load of blade contact surface changes the motion state of the blade contact surface. When the normal load is small, the friction motion of the contact surface between the blade and the outer ring is in a macroscopic slip state. In this case, the friction damping effectively dissipates the vibration energy, thus reducing the common amplitude value of the blade. With the increase of normal load, tangential stiffness of contact surface increases, friction motion converts into fretting slip state and the vibration energy dissipated by friction damping is very small. When the normal load reaches a certain level, the contact surface can be approximated as no longer having relative motion and the blade and outer ring are approximately seen as a whole. At this time, the change of normal load no longer affects the amplitude of blade vibration response. The stator blade vibration response curve obtained in this paper can be compared with that in [27]. In this reference, the vibration response of the blade disk was analyzed using the Mindlin contact friction model. Similar rules appear in the process of numerical analysis. When the normal load and excitation force change, the motion state of the contact surface also changes between macroscopic slip and micro slip. This shows that the research of this paper is reasonable. In order to further analyze the changing characteristics of the contact surface, in the iterative calculation, the variation of the equivalent stiffness coefficient of the contact surface with the normal load of the contact surface under resonant frequency was extracted.