# Meshing stiffness analysis of time-varying Gears Considering Different spalling shapes

With the rapid development of wind power technology in recent years, improving the working performance of wind turbine is gradually paid attention to. Wind turbine is in extreme working environment for a long time. As an important part of fan gearbox, gear will be more prone to failure. As one of the most common faults in gearbox, spalling will affect meshing stiffness between gear pairs Variable characteristics are the main cause of noise between gears. Therefore, accurate calculation of time-varying meshing stiffness of gear pairs under different spalling faults is an important basis for dynamic analysis of gear system.

Experts at home and abroad have done a lot of research on the establishment of time-varying meshing stiffness equation under spalling fault. Tian introduced the shear energy into the energy method for calculating the time-varying meshing stiffness of gear teeth, derived the formulas in detail, and verified the effectiveness of the proposed method. Zhao Shubin and others took a pair of spur gears as the research object, and established the time-varying meshing stiffness equation under the tooth spalling fault by using the potential energy method, By analyzing the influence of different spalling parameters on the time-varying meshing stiffness, it is concluded that the spalling width has the greatest influence on the time-varying meshing stiffness, and the thickness has the least influence. Tan Tianran takes the spur gear as the research object, calculates the time-varying meshing stiffness under the tooth surface wear, tooth root crack and other faults by using the potential energy method, and carries on the contrast verification by using the finite element method; Zheng Hongling takes the spur gear as the research object A. Saxena et al. Took spur gear as the research object, and studied the influence of spalling shape on the time-varying meshing stiffness; marques, et al Based on ISO maximum meshing stiffness criterion per unit length and approximate parabola variation law of meshing stiffness per unit length of single tooth, etc.  established a calculation model of helical gear meshing stiffness, and the analysis shows that the method can accurately calculate the meshing stiffness of helical gears In this paper, a time-varying meshing stiffness calculation method considering gear pair tooth profile modification and tooth profile modification is proposed On the basis of reference , et al.  proposed an improved method for calculating the time-varying meshing stiffness of helical gears based on the slicing method, and verified the effectiveness of the method, and discussed the influence of helix angle, gear width and friction coefficient on the time-varying meshing stiffness According to the spalling fault of tooth surface, the dynamic equation is established, and the influence of different spalling length, width and position on time-varying meshing stiffness and tooth root contact stress is analyzed by numerical method and finite element method respectively In this paper, the influence of different helix angle and modulus on the time-varying meshing stiffness of helical gears is studied, and a pair of dynamic models of helical gears are established to study the influence of cracks on the system Liu et al. Proposed a new method to calculate the contact line of helical gear, and proved the rationality of the proposed contact line method; Liu Wen et al. Proposed a new algorithm for correcting the time-varying meshing stiffness of helical gears, which was verified by the finite element method, and analyzed the influence of different helical gear parameters on the time-varying meshing stiffness.

On the basis of the research results, taking the helical gear in planetary gear transmission system as the research object, according to the meshing characteristics of helical gear pair, the expression of contact line of helical gear pair is established, and its expression is introduced into the time-varying meshing stiffness equation of helical gear pair with spalling fault established by potential energy method, and the time-varying meshing of helical gear pair is obtained through slicing method and integration idea Compared with the meshing stiffness obtained by finite element method and empirical formula, the accuracy of solving the time-varying meshing stiffness of helical gears in this paper is verified, and the influence of different spalling length, width, axial position and radial position (from tooth root to tooth top) and different spalling shape on the time-varying meshing stiffness is analyzed. 