The research on dynamic characteristics and dynamics of gear transmission system has been gradually developed from static analysis to dynamic analysis.The method of gear dynamics analysis is based on impact theory at first, and then gradually developed to vibration theory. In the research model, dynamic research of multi-stage gear system is carried out step by step through dynamic research of single-stage gear pair, and then to the transition of complex system including gear, drive shaft, bearing and box structure at the same time.
Before 1950s, meshing impact was used as the basis for describing and interpreting the dynamic excitation and response of gear shaft system. Gear shaft system was simplified as a simple single-degree-of-freedom system, and the dynamic behavior of gear shaft system was expressed by the single-degree-of-freedom system dynamic response under impact.Since 1950s, gear shafting has been regarded as an elastic mechanical vibration system. Based on the vibration theory, the dynamic behavior of the system under the action of meshing rigidity, transmission error and meshing impact has been analyzed, thus laying a foundation for gear dynamics and rotor dynamics.
1983, L.D. Mitchell and J.W. Daws 1983, L.D. Mitchell andJ.W.Daws discussed  the prediction method of gear box system vibration and coupling non-linear characteristics, preliminary study on theoretical modeling and vibration analysis of gear system, and predicted the vibration of gear system by theoretical and empirical methods. However, there is still a certain gap between theoretical calculation results and actual conditions, and the results are difficult to be applied in engineering practice.
Umezawa has carried out in-depth research on the dynamic characteristics of, made comprehensive and in-depth research on vibration analysis, dynamic modeling, computer simulation and so on of the system, and achieved a series of research results.Umezawa has also studied the influence of gear tooth stiffness on gear vibration by using the length of the shaft and the installation position of the gear on the shaft. It is considered that the shaft stiffness only affects the frequency of the vibration and the amplitude depends on the vibration performance of the gear on the overlap plane.