## 4 Conclusions  
According to the results, the following conclusions can be drawn:  
1. When the rotation angle of the shaft segment with the contact surface is small, EFS of the contact surface is almost constant. When the rotation angle is large, EFS of the contact surface changes almost exponentially with the rotation angle. In the rotor dynamics analysis, the vibration angle is very small, so it is correct to ignore the influence of the rotation angle on EFS of the contact interface.
2. The greater the RMS of the height distribution of the micro-convex body \(\sigma\), the smaller EFS of the contact interface. That is to say, the rougher the surface, the lower EFS of the contact surface. Therefore, EFS of the contact surface can be increased by reducing the surface roughness. The average radius of the curvature of the top of the micro-convex body \(\beta_{0}\) has almost no effect on the equivalent flexural stiffness of the contact surface.
3. When the preload is small, EFS of the shaft segment with the contact interface increases rapidly with the increase of preload. When the preload increases further, the increasing speed of EFS of the shaft segment with the contact interface gradually becomes slow. When the preload reaches a certain value, EFS of the shaft segment with the contact interface tends to be consistent with the flexural stiffness of the corresponding integral shaft segment.
4. The preload affects the contact stiffness of the contact interface of disks, which in turn affects the natural frequency of each order of the rotor system. The greater preload makes the natural frequency of the RFR closer to the natural frequency of the corresponding integral rotor within a certain range of preload. The preload affects the displacement and load transmission of the shaft segment of the rotor, which slightly reduces the flexural stiffness of the rotor and makes each order's natural frequency decrease to a certain extent.
5. During the process of vibration of the rotor system, the coordinated deformation of the tie rods enhances the local bending stiffness of the rod-fastened shaft segment of the rotor. The coordinated deformation of the tie rods increases the first-order and third-order natural frequencies of the RFR, while decreases the second-order natural frequency of RFR. When the preload is relatively small, the effect is larger.
6. With the increasing number of tie rods and the installation radius of the tie rods, the first-order and third-order natural frequencies increase monotonously, while the second-order natural frequency decreases monotonously. The effect of the number of tie rods and the installation radius of the tie rods on the first-order and second-order natural frequencies is larger than the effect on the third-order natural frequency. The effect of the tie rod radius on the natural frequencies of the rotor system is very small and almost negligible.  
Conceptualization, L.Y. and H.X.; methodology, H.X.; validation, H.X.; formal analysis, H.X.; investigation, H.X.; data curation, H.X.; writing--original draft preparation, H.X.; writing--review and editing, H.X. and T.X.; project administration, L.Y.; funding acquisition, L.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China [Grant No.11872288], the National Science and Technology Major Project [Grant No. J2019-IV-0021-0089], and the Natural Science Foundation of Shaanxi Provincial [Grant No.2019 JM-219].  
**Conflicts of Interest:** The authors declared no conflict of interest with respect to the research, authorship, and publication of this article.