## 4 Results and Discussion
### Nonlinear Vibration Results of Different Models
Here, because the range of normal load and equivalent stiffness coefficient varied by a large order of magnitude, logarithmic coordinates were adopted for the convenience of analysis. The following Figure 10 shows the variation trend of the equivalent stiffness  
under a series of different normal contact loads under corresponding working conditions in Figure 11 and the amplitude curve is normalized here. Figure 11: Response normalization amplitude curves under different normal loads with 4 N exciting force. (**a**) Circumferential amplitude curve. (**b**) Axial amplitude curve. Figure 10: The equivalent stiffness coefficients of different normal loads at the resonant frequency of 40 N excitation force. Of course, the normal load of the contact surface set by a small airflow force amplitude cannot be too large, otherwise the contact surface is in an approximate stick state. From the analysis figure, we can first find a similar trend with the 40 N excitation force level; that is, the vibration response increases with the increase of normal load. However, it still increases to a point where it does not change. The reason for this is similar to the previous analysis, except that because the excitation force is small, the normal load required for the state transition of the contact surface is also very small. In addition, the resonance frequency is in the same position as previously calculated. Again, the equivalent contact stiffness curve is given here in Figure 12. It can be seen that the contact surface of the model still has a frictional state change under the lower excitation force level. However, the excitation force corresponding to the normal load is different. Logarithmic coordinates were used again because the range of equivalent stiffness coefficients was too large. The analysis of this part is similar to the previous analysis, and will not be repeated in the paper. Previously, the nonlinear vibration response characteristics of the model contact surface under different excitation force levels were analyzed. Another case is studied here; that is, the normal contact surface load was constant, and then the amplitude of the excited force was changed. The process analyzed is similar to the previous one. Using the same numerical model, the normal load of the contact surface was assumed to be 30 N. Then, the displacement amplitude of the 50% high outlet side of the stator blade was extracted by changing the excitation force of a series of blades. The ratio between the axial and circumferential flow forces of the model and the excitation force was still maintained during the analysis. The following Figure 13 shows the curve of the blade vibration response. It can be seen that under the same normal load on the contact surface, the amplitude of the blade vibration response increases with the increase of airflow excitation force. This trend is easy to understand, because a larger airflow excitation force contains more vibration energy, which corresponds to a larger vibration amplitude. However, the contact characteristic of the contact surface is a nonlinear characteristic, which can be identified by careful analysis of the figure here. When the excitation force is small, the amplitude changes of the axial and circumferential vibration response and the magnitude changes of the excitation force basically show linear growth. However, when the exciting force increases to a certain order of magnitude, it is not difficult to see that the increasing magnitude of the exciting force is no longer linearly correlated with the increasing magnitude of the vibration amplitude. This indicates that the contact surface has nonlinear characteristics. It is reminiscent of the  
Figure 12: The equivalent stiffness coefficients of different normal loads at the resonant frequency of 4 N excitation force. previous analysis showing that the contact surface changes from fretting slip to macroscopic slip when the exciting force increases to a certain level.