Since the 1970s, scholars have done extensive and in-depth research on gear transmission system. Scholars began with the simple dynamics of spur gears. Through the lumped parameter method, the spur gear is simplified into a single degree of freedom or two degree of freedom dynamic model to study its natural characteristics and torsional vibration response. For example, Professor K. umezawa of Tokyo Institute of technology and others simplified a pair of helical cylindrical gears into a mass spring system through the centralized parameter method. The deformation of helical cylindrical gear is solved. Some characteristics of torsional vibration of helical cylindrical gears are obtained. In the following in-depth research, many important research results have been obtained in the dynamic modeling, calculation method and vibration analysis of cylindrical gear. Later, it was found that there are many nonlinear factors in the gear transmission system, such as gear meshing in and out impact, tooth surface friction and time-varying meshing stiffness. The nonlinearity of gear transmission system has become a research focus and continues to this day.
In the late 1970s, R.C. Azar and others studied the nonlinear problem of spur gear by considering the gear inertia with numerical method and introducing nonlinear factors such as time-varying stiffness, backlash and tooth surface friction. The research shows that for light load spur gear transmission system, when the meshing frequency of spur gear coincides with half of the natural frequency of power output shaft, the vibration response of the system is large due to the influence of backlash. With the deepening of people’s understanding of gear transmission system and the development of computer science and technology, the dynamic model of gear transmission system is becoming more and more perfect. In 1991, Japanese scholars N and others established a six degree of freedom nonlinear analysis model based on the single degree of freedom torsional vibration analysis model, considering the stiffness of the bearing, the stiffness of the shaft and the influence of power input and load, and analyzed the nonlinear dynamic response of spur gear transmission system.
At the same time, domestic scholars have also conducted in-depth research on the dynamics of gear transmission system. In 1991, Zhong Yifang of Huazhong University of technology studied the dynamic characteristics of involute helical cylindrical gear pair. In 1992, Liu Geng of Northwest University of technology studied the influence of various parameters of gear pair on the dynamic characteristics of internal helical gear and external helical gear. In terms of multiple degrees of freedom, Tang zengbao established an eight degree of freedom analysis model and equation for spur cylindrical gear. Assuming that the gear meshing stiffness changes into rectangular wave, the torsional vibration and transverse vibration of spur cylindrical gear are studied. At the same time, considering a variety of nonlinear factors, the dynamic differential equation of multi gear meshing is solved by combining the state space method and modal analysis method. Ma Hui of Chongqing University took the helical gear coupled three parallel axis rotor system as the research object, considered the geometric eccentricity, and coupled the gear system with the rotor system. The research results show that the geometric eccentricity of the gear has a great influence on the meshing force.
Scholars have studied the nonlinear problems of gear transmission system more and more deeply, considered the problems more and more comprehensively, and the calculation method of dynamic response of gear dynamic system is more and more advanced. Li Yinggang et al. Established the dynamic model of single degree of freedom gear pair system considering time-varying stiffness, backlash, damping and external excitation, solved it by incremental harmonic balance method, and verified the calculation results by fourth-order variable step Runge Kutta numerical method. The results show that the calculated results of the two methods agree well. At the same time, under the action of external excitation, it will cause nonlinear dynamic behaviors such as parameter resonance, multivalued solution and amplitude jump of gear system. In his doctoral dissertation, Zhang Jing of Chongqing University studied the simulation and experiment of gear transmission dynamics under different factors, and obtained many important conclusions by combining the theoretical research and experimental research of gear dynamics. In the aspect of fault diagnosis of gear transmission system, Xu Guang studied the typical faults of gear transmission system and carried out fault simulation test.