## 1 Introduction
So far, some scholars have studied the calculation methods of mesh stiffness of gear teeth with different faults, and some achievements have been made. [PERSON] et al. [11] established a gear stiffness analysis model with tooth fault, in which the influence of sparking and broken teeth was considered. [PERSON] et al. [12; 13] calculated the mesh stiffness of the tooth root cracked gear by considering the precise tooth root transition curve. Based on [PERSON] [14], [PERSON] et al. [15] established an improved analytical model for the calculation of TVMS of the cracked tooth root gear. [PERSON] et al. [7] established a new model and analyzed the influence of crack on the gear mesh stiffness when gear teeth root cracks appeared in the planetary gearbox. [PERSON] et al. [16] proposed a new analytical model for calculating the mesh stiffness of cracked gear teeth, which is non-uniformly distributed along the tooth width. [PERSON] et al. [17] proposed two better calculation expressions for the rigidity of the analytic grid of spur gears with root cracks. The dynamic response signals obtained by dynamic simulation are very clean signals, which are of great significance for analyzing and understanding fault characteristics and vibration mechanisms. Some scholars have done some research in this problem. [PERSON] [18] established a system dynamics model of planetary gear with tooth root crack and flexible ring rim. [PERSON] [19] and [PERSON] [20] considered the influence of the transfer path and established a planetary gear dynamics model of 21 degrees of freedom (DOF). Combined with the above mesh stiffness solution method, they solved the dynamic response in normal state and crack state. [PERSON] [21; 22] established a dynamic simulation model in the healthy state and damage state for the two-stage composite planetary gear train. [PERSON] et al. [23] also established an analytical expression for calculating the gear mesh stiffness and built a six-DOF gear dynamics model considering the mesh stiffness and sliding friction factors. To sum up, most of the literature decompose the mesh stiffness of gears into compression stiffness, bending stiffness, shear stiffness, and Hertz contact stiffness. Then these kinds of stiffness are synthesized, and the total stiffness is obtained. In these studies, especially for planetary gears, a few scholars consider the deformation stiffness of the gear body, and a few scholars consider the influence of tooth root transition on the stiffness solution. However, in the process of solving the stiffness of planetary gear, few scholars consider the influence factors of the fillet transition part of the tooth root and gear body at the same time. Therefore, in order to make up for this defect, on the one hand, the influence factors of the root fillet transition parts should be considered, and on the other hand, the influence of the gear body deformation should also be considered. On this basis, the formulas for calculating the mesh stiffness of gear teeth under healthy and fault conditions are derived respectively. The structure of this paper is as follows: In Section 2, the gear meshing stiffness is evaluated. The meshing stiffness of healthy gears and cracked gears are resolved in Sections 2.1 and 2.2, respectively. In Section 3, a dynamic model with eight degrees of freedom is established. In Section 4, the simulation and experimental results are analyzed and discussed, and finally, conclusions are given in Section 5.