## 1 Introduction  
Spiral bevel gears are widely applied in complex surface conjugate gear meshes within space transmission systems. Its advantages include a compact structure, large torque capacity, and high efficiency. However, factors such as time-varying stiffness, nonlinear contact, and friction during the meshing process lead to vibration and noise in the transmission system, affecting its operational stability and lifespan. Therefore, studying the dynamic characteristics of spiral bevel gear transmission systems is a crucial approach to enhancing their design and manufacturing levels. [PERSON] et al. [1] established a transient mixed lubrication model and a two-degrees-of-freedom torsional dynamic model for spiral bevel gears, considering time-varying contact parameters and defects on the meshing path. [PERSON] et al. [2] proposed an analysis model that accurately and effectively calculates the nonlinear excitation and loading meshing characteristics of spiral bevel gears. [PERSON] [3] presented a formula describing the mechanical power loss of gear meshing under the conditions of coupling the equations of six-degrees-of-freedom motion and thermal mixed elastohydrodynamic lubrication and study the dynamic characteristics under the conditions of interaction between gear dynamics and tribology. [PERSON] et al. [4] proposed a numerical calculation model for time-varying meshing stiffness considering gear cracks and compared this model with the finite element method. The model allows for faster calculation of time-varying meshing stiffness in spiral bevel gears. [PERSON] et al. [5] proposed an interface characteristic model for a gear system considering the roughness of wheel teeth, affecting oil film distribution, contact damping, and friction. They investigated the dynamic characteristics of the gear system under different roughness and input torque conditions. [PERSON] et al. [6] proposed a new calculation model for meshing power loss in planetary gearsets, considering gear surface roughness based on the elastohydrodynamic lubrication method. In the process of studying the impact of gear surface roughness on dynamics, it is crucial to accurately establish gear models with different surface roughness. Investigating how to accurately establish spiral level gear models with different surface roughness is the foundation of this research. [PERSON] [7] proposed generating Gaussian friction surfaces using known spectral density functions. [PERSON] [8] proposed simulating rough surfaces through time series. [PERSON] et al. [9] substituted multiple surface parameter variables into the W m function to describe the height distribution of spatial surfaces. [PERSON] et al. [10], based on fractal geometry theory, proposed an anisotropic three-dimensional fractal rough surface model. They established a six-degrees-of-freedom model to explore the impact of fractal parameters on gear dynamics. [PERSON] et al. [11] proposed a novel semi-finite element predictive model to address the accurate dimensions, directions, and positions of dynamic meshing impact under high-speed and heavy-load conditions in spiral level gear transmission. [PERSON] et al. [12] proposed a 12-degrees-of-freedom dynamic model and investigated the nonlinear dynamic behavior of a central bevel gear system considering internal and external excitations. When considering the relationship between tooth surface friction and dynamics, the selection of the friction coefficient needs to be studied, focusing on the choice of the friction coefficient [13; 14; 15]. [PERSON] et al. [16] analyzed the surface roughness of ground and superfinishing tooth surfaces. Simultaneously, the study investigated the impact of the smoothness of the processed tooth surface on the dynamic characteristics of the gear pair, finding that the low surface roughness of superfinished wheel teeth significantly improves the gear dynamics.