## 1 Introduction  
Gas turbines are widely used in transportation, energy, aviation, and national defense and are hailed as \"the crown jewels\" in the machinery manufacturing industry with the most market application prospects. The dynamic performance of the rotor directly affects the performance and life of the entire gas turbine. Therefore, the rotor design is important. The rod-fastened rotor (RFR) of a heavy-duty gas turbine is a typical disk-rod rotor, which has two structural forms: a central rod-fastened rotor and a circumferential rod-fastened rotor. The central rod-fastened rotor relies on a central tie rod to clamp the rotor together, while the circumferential rod-fastened rotor uses several circumferentially evenly distributed tie rods to clamp the rotor together. The contact interface and tie rods are the most distinctive features of the RFR. Compared with the integral rotor, the RFR has the advantages of low weight, ease of cooling, easy assembly, and flexible selection of disk material. By contrast with the integral rotor, the RFR mainly depends on the contact interface between the disks to transmit force and power. Therefore, the RFR cannot be simplified as an integral rotor to make a further study. A lot of work on the RFR has been reported, including the contact interface processing, the research of the mechanical model of the RFR, and the dynamic analysis of the RFR system. By experimental measurement, [PERSON] and [PERSON] [1] found that the height of micro-convex bodies on the rough surface is approximate to the Gaussian distribution. They assumed that the machined surface was a smooth surface covered by a certain density of equal-curvature spherical micro-convex bodies obeying Gaussian distribution. The micro-convex bodies did not affect each other, and the contact of each micro-convex body conforms to the Hertz contact formula. In the plane contact, the relational expression of the number of micro-convex bodies, the average contact area, the load, and the distance between the two planes are derived in the elastic range. It lays the foundation for studying the rough surface contact problem with the statistical parameter model, and the model is called the GW model. [PERSON]. [2] investigated the isotropic and heterogeneous rough surface contact problem, in which the radius of curvature of the micro-convex body is arbitrarily distributed. The results are consistent with the results of the GW model, extending the scope of application of the GW model. In the literature [3], based on the elastic contact theory and statistical parameter description, the calculation method of normal contact stiffness of rough surface considering the influence of surface waviness is given. [PERSON]. [4] proposed an elastoplastic contact model of a rough surface, including elastic, elastoplastic, and plastic deformation states. It compensates for the serious deviations caused by the GW model based on elastic deformation when it is subjected to large normal loads. In the literature [5,6], the GW model was modified by transforming the interaction between the micro-convex bodies into elastic deformations of the nominal contact surface, and the contact between the rough surface and the smooth plane was analyzed in the elastic and elastoplastic range. The results showed that with the increase of the normal load, the plastic deformation caused by the micro-convex body and the interaction between them became increasingly obvious, which must be fully considered. [PERSON] and [PERSON]. [7] proposed the fractal contact model based on the self-affine fractal features of the machined surface. That is the MB model. The fractal dimension and fractal roughness with an independent scale are used as the characterization parameters of the rough surface.