# Research status of gear transmission system dynamics in China

Domestic scholars have also done related work in the development of gear transmission system. Zhu Qin and Xie Longbai established the dynamic model of gear transmission system by using transfer matrix method, and studied the bending coupling vibration characteristics of gear rotor system model with multiple parallel shafts. Xia boqian et al. Summarized the coupling model of bending torsion coupling vibration of gear rotor bearing system, and established a more precise and reasonable coupling model by considering the influence of the instantaneous position of gear meshing line on the dynamic meshing force of gear pair. Changshan et al. Comprehensively introduced the research progress of dynamic model of gear transmission system at home and abroad. Li Ming et al reviewed the development of gear pair dynamic modeling and gear rotor bearing system dynamic model, and reviewed the research status of bending torsional coupling vibration and nonlinear dynamics of gear rotor bearing system in the first 20 years. Wang Chao and Qin Wenjie analyzed the meshing process of a pair of gears by means of geometric parameterization and dynamic finite element method. Song Xueping, et al. Studied the coupling vibration characteristics of gear shaft system in rotor system, and gave an approximate solution method of gear time-varying meshing stiffness.

Based on the analysis method of nonlinear system, Shen Yongjun et al. Summarized the research situation of nonlinear dynamic model of gear transmission system, including the research based on numerical method, analytical method, experimental method, and considering gear fault and friction coefficient of gear surface, and predicted the future research hotspot and direction. Lin Tengjiao et al. Used the 3D impact / dynamic contact finite element method to calculate the time-varying meshing stiffness and meshing impact excitation of gear teeth, and studied the internal dynamic excitation caused by tooth stiffness excitation, error excitation and meshing impact excitation, and the impact of external excitation caused by impact acceleration on the impact characteristics of the system. Cui Yahui et al. Established a complex dynamic vibration model of multi-stage gear rotor bearing system. The model considered the effects of time-varying meshing stiffness, static transmission error, unbalance mass, bearing stiffness and elastic shaft. The angle between the meshing line and the horizontal line was taken as the reference angle, and the dynamic meshing force of the multi-stage gear system was calculated by using the reference angle.

For high-speed gear rotor system, Dou Wei et al. Established a nonlinear vibration model considering the coupling of bending and torsion. Through numerical simulation, the vibration characteristics of the gear rotor system were obtained, and the effects of eccentricity and time-varying meshing stiffness on the vibration characteristics of the system were studied. Cui Li et al. Established a nonlinear dynamic model of the flexible rotor system of gear rolling bearing, which takes into account the backlash, radial bearing backlash, time-varying meshing stiffness and time-varying bearing stiffness. Huang Guanhua and others used the finite element method to solve the time-varying meshing stiffness of the gear pair of the high-speed train gear transmission system. Considering the elasticity between the components of gear rotor system, Zhang Tao et al. Proposed a dynamic characteristic analysis method based on contact finite element theory to simulate the continuous meshing process of gear pair. By analyzing the parameters such as dynamic transmission error, dynamic contact force and center offset difference, the coupling relationship between various vibration and meshing characteristics in the system was obtained.

Wang Zhidong et al. Established the subsystems of the gear transmission system, combined with the relationship between the subsystems, obtained the dynamic model of the whole gearbox coupling system, analyzed the vibration characteristics of the system, and revealed the influence of external excitation and internal excitation such as bearing stiffness on the vibration characteristics of the system. Wang Yilong et al. Designed a new type of damping ring, established a bending torsional coupling dynamic model of a rotor gear transmission system with damping ring by using the lumped parameter method, solved the vibration equation of the system numerically by using Runge Kutta method, and analyzed the damping effect of the new damping ring. Wang Jing et al. Established a nonlinear mathematical vibration model of rolling bearing bevel gear with 7 degrees of freedom, and analyzed the nonlinear dynamic behavior of the system.

In conclusion, gear transmission system dynamics modeling has made great progress, from the initial linear system to the present nonlinear system, from single degree of freedom model to multi degree of freedom model, from simple gear pair model to high-precision finite element model. More and more parameters are considered in the model. From the initial time-varying stiffness and backlash to tooth surface friction, mass eccentricity, bearing clearance, motor, load, etc., the gear transmission system model is constantly developing and improving. 