## 1 Introduction
[1] proposed a pure torsional dynamic model of planetary gear wear based on Archard's equation to evaluate gear wear and analyzed the influence of gear wear on planetary gear dynamic parameters and vibration response. [PERSON] et al. [2] established a computational model of planetary gear transmission and studied the influence of surface wear on the dynamic characteristics of a typical planetary gear transmission. Many scholars have conducted further research on issues such as tooth surface wear. [PERSON] et al. [3] combined the torsional dynamics model with the surface wear model to study the interaction between surface wear and dynamic response of planetary gear sets. [PERSON] et al. [4] proposed a stiffness model based on the three-segment tooth profile equation to calculate the meshing stiffness under healthy wear conditions and established the meshing relative displacement function considering the influence of back backlash and wear thickness. [PERSON] et al. [5] coupled the Archard wear model with a nonlinear dynamics model and proposed a new solar wheel RUL dynamic evaluation method to accurately evaluate the remaining service life of gears with worn surfaces. Planetary gear transmission is widely used in various fields due to its advantages of compact structure, light weight, large carrying capacity, large transmission ratio and high transmission efficiency [6]. The strong impact inside the gearbox will cause vibration damage, and the dynamics and vibration characteristics of planetary gears have been paid more and more attention [7; 8; 9]. [PERSON] et al. [10] studied the influence of dynamics on the gear stress, that is, the change in the wheel rim thickness and the number of planets. [PERSON] et al. [11] used  
Figure 1: Planetary transmission with large coincidence tooth profile and coplanar teeth. (**a**) Large coincidence tooth profile. (**b**) Model of coplanar gear planetary array. the lumped parameter model and finite element model to study the complex nonlinear dynamic behavior of a positive planetary gear. In order to obtain an accurate vibration response prediction and understand the coupled vibration mechanism in planetary gear systems, [PERSON] et al. [12] proposed a comprehensive, fully coupled, dynamic modeling method using virtual equivalent shaft elements to improve the reliability of planetary gear systems. The structure of planetary gears determines their functional strength. In order to optimize the superiority of the structure, many scholars have conducted a lot of research on this. [PERSON] et al. [13] proposed a multi-objective selection of the structural scheme and parameters of a dual carrier planetary gear system, considering the use of a dual carrier planetary gear system with three and four outer shafts. The torque method was used to select among all possible structural schemes of the discussed planetary gear system. [PERSON] et al. [14] studied the kinematic principles and structural symmetry of coaxial and noncoaxial transmission of linked planetary gear trains, extended the composite structure based on linked planetary gear trains, and conducted a calculation method for the reduction ratio of the extended structure. [PERSON] et al. [15] studied the influence of the pressure angle on the meshing stiffness of the meshing gear and the dynamic model of the planetary gear group in view of the planetary gear structure. [PERSON] et al. [16] designed an automatic transmission with improved planetary gear using the lever method and carried out kinematics and dynamics analysis. With the development of optimization methods for planetary gear structure, an optimization method based on graph theory has been proposed. Many scholars began to study this. [PERSON] et al. [17] used graph theory to analyze the kinematics, static force and power flow of planetary gear systems. [PERSON] et al.