# Dynamic Characteristics Analysis of a Rod Fastening Rotor System Considering Contact Roughness
## 1 Introduction  
Rod fastening rotors have become one of the main structures of gas turbines due to their advantage of convenient maintenance and good performance [1; 2; 3; 4]. The rotor system includes rods, discs, shafts and supports, where the phenomena of contact and friction usually happen in the discs. Therefore, contact stiffness plays an important role in the dynamic characteristics of the rotor system. It is of significance to understand the mechanical characteristics of the rod fastening rotor system in advance. Up to now, three kinds of methods for describing the contact stiffness of the joint's interface are widely used, including the equivalent method [5; 6], corrected matrix [7; 8] and virtual material method [9; 10]. The so-called equivalent stiffness method means that the contact behavior is described by the linear spring and viscous damping. [PERSON] et al. [11; 12] obtained the response of the bolted beam through a transient excitation test, from which the mechanical interface parameters are identified. After that, the dynamic equation of the system was further established by assembling the contact element and the whole component in [11; 12]. [PERSON] et al. [13] used a nonlinear spring to describe the nonlinear characteristic of the interface, where the stiffness of the nonlinear spring was determined by the foundation excitation test. In reference [14], the contact mechanism of the interface is seen as the combination of a hinge and angular spring. According to the finite element method, [PERSON] et al. [15] gave the change law of contact stiffness with different bolt loosening. As for the corrected stiffness matrix and virtual material, lots of researchers have made great endeavors on them. [PERSON] et al. [7] investigated the mechanism related to non-continuity in the disc joints. By modification of the stiffness of the beam element, [PERSON] et al. [16; 17] and [PERSON] et al. [18] discussed several important factors, such as disc contact and normal preload. [PERSON] et al. [19] regarded the joint's interface of the rod fastening rotor as a virtual material with stiffness and obtained the equivalent stiffness through the finite element analysis. [PERSON] et al. [20] set up a finite element model of a rotor system with disccontact, where the thin-layer element theory was adopted. [PERSON] (2017) presented the two- and three-dimensional contact elements. When analyzing the contact stiffness, the rough interfaces are mainly focused. The most favorable model for this purpose is the Greenwood-Williamson statistical model [PERSON] (2017). According to the boundary element method, [PERSON] et al. [PERSON] et al. (2018) calculated the contact stiffness of the elastomer with a fractal rough surface. [PERSON] et al. [PERSON] et al. (2018) studied the two-dimensional contact of the interface based on the Weierstrass Mandelbrot (W-M) function and obtained the elastic contact stiffness. [PERSON] et al. [PERSON] et al. (2018, 2019) established the fractal model for contact interface and W-M fractal function. Meanwhile, the analytical expressions of contact load and contact area under elastic-plastic conditions were determined in references [PERSON] et al. (2018, 2019). By utilizing the numerical simulation, [PERSON] et al. [PERSON] et al. (2019) studied the mechanical mechanism of the isotropic fractal interface in the elastic-plastic condition. [PERSON] et al. [PERSON] et al. (2019) discussed disc contact by using the isotropic fractal interface when both elastic contact and plastic contact are considered. [PERSON] et al. [PERSON] et al. (2019) observed the relationship between the grade of the asperity and the contact load and the contact stiffness of the interface. Aiming at a rod-fastened rotor system, [PERSON] et al. [PERSON] et al. (2019) investigated how surface roughness affects joint stiffness. [PERSON] et al. [PERSON] et al. (2019) carried out research on interface stiffness based on the fractal-curve description of the topology.