In 1991, Ozguven analyzed the non-linear dynamic characteristics of spur gear with six-degree-of-freedom non-linear bending-torsion coupling model, based on the single-degree-of-freedom torsional vibration model to analyze the dynamic characteristics of spur gear, taking into account the stiffness of shaft and bearing as well as the influence of dynamic and load elements; afterwards, Ozguven established the non-linear dynamic model of spur gear drive with the consideration of the influence of shaft and bearing support stiffness.The nonlinearity of the system is studied.Tsuta studied the dynamic characteristics of helical gear drive considering the stiffness of shaft and bearing.Neriya established a dynamic analysis model of helical gear drive pair with eight degrees of freedom, considering the stiffness of shaft and bearing, and solved the dynamic response of the system under static transmission error.

In 1991, Kahraman considered the time-varying meshing stiffness and the non-linearity of backlash in spur gear drive, analyzed the response of non-linear Time-Varying Vibration System with bending-torsion coupling model of three degrees of freedom; afterwards, he established the corresponding linear dynamic model of helical gear pair, and focused on analyzing the influence of axial vibration on the dynamic characteristics of gear pair.In 1996, Velex et al. studied the influence of gear tooth manufacturing error and installation error on gear pair vibration and noise. It was shown that the amplitude and phase of gear tooth profile error had a great influence on gear pair vibration. Moreover, the influence of gear tooth pitch error, pressure angle error, installation eccentricity and tooth orientation error on system dynamic characteristics was also significant.

With the development of modern computing technology and testing technology, abundant achievements have been made in gear system dynamics theory based on modern vibration theory, which also makes great progress in multi-stage gear system dynamics research.The researchers applied transfer matrix method, finite element method and modal analysis method to the dynamic analysis of multi-stage gear system.

1996In 2003, K.Umezawa established a three-dimensional helical gear pair vibration model. For the first time, the combined effects of transverse bending vibration, torsional vibration, axial vibration and torsional oscillation of gear were considered. The bearing stiffness, damping and stiffness and damping of meshing pairs were identified by experimental method. Then, the theoretical model was simulated and calculated by computer to predict the vibration table of gear shaft system.Now it provides theoretical basis, but its dynamic experiment is mainly static single-degree-of-freedom experiment, which results in certain errors.

In 1997, Tordion et al. studied the stability characteristics of dynamic parameters of two-stage gear drive system with time-varying meshing stiffness.Choy applies modal analysis to dynamic analysis of multi-stage gear drive system, uses multi-mass-rotor-bearing discrete model to simulate gear shaft, uses transfer matrix method to analyze its transverse and torsional vibration, couples them through gear meshing, and further analyses mass imbalance and vibration of gear box and coupling of multi-stage gear drive.