Choy et al established the dynamic model of the transmission system by using the transfer matrix method and the dynamic model of the box by using the finite element method. Then, taking the inner and outer rings of the bearing as the coupling interface between the box and the transmission system, the dynamic response of the coupling system was analyzed in time domain and frequency domain respectively. Gao Weijin and others studied the vibration transmission characteristics of the gear shaft bearing box under different excitation conditions, and found that the output shaft bearing did not play a role in attenuating the vibration in the dynamic response transmission process. Therefore, the bearing should be replaced because of its poor matching with the system. Beta य़ EB et al. Meshed the flange and spoke of the gear with three-dimensional solid element, and modeled the gear with slicing method and Pasternak elastic foundation. The effects of different flange and spoke structures on the dynamic response of the gear were studied.
Abousleiman et al. Meshed the ring gear and planet carrier of the planetary gear train with three-dimensional solid elements, and studied the influence of the flexibility of the ring gear and planet carrier on the dynamic response of the gear. Zhang Jun et al. Established the dynamic model of planetary gear train with ring gear flexibility by using dynamic substructure method, and analyzed the influence of ring gear flexibility on the natural frequency and vibration mode of the system. In order to obtain accurate dynamic response of planetary gear transmission system, he Chaoxia et al.  established a dynamic model of 2K-H Planetary transmission system coupled with box vibration by using dynamic substructure method, and found that box flexibility greatly reduced the dynamic meshing force and bearing reaction force of planetary transmission system. Helsen et al. Established the rigid flexible coupling model of the wind turbine gearbox by using the dynamic substructure method, and compared the simulation results with the multi rigid body model and the pure torsion model established by the lumped parameter method, and pointed out that the box flexibility should be considered when modeling the gear system. Ambarisha A pair of helical gear pair dynamics model of coupling box was established by using full finite element box (with more degrees of freedom) and polycondensation finite element box (with less degrees of freedom) respectively. The simulation results show that the difference of dynamic response obtained by using different box models at resonance and non resonance speeds is very small, which indicates that the modal polycondensation method (Craig Bampton) is used Methods) effective.
Abbes et al. Meshed the box with elastic plate element, established the coupling dynamic model of gear shaft bearing box with a pair of gears, and calculated its natural frequency. The effectiveness of the dynamic substructure method was verified by comparing with the natural frequency calculated by the full finite model. Guo et al. Meshed the box with three-dimensional solid elements, and established the coupling dynamic model of gear shaft bearing box with a pair of gears. The natural frequency and working noise of the modeling object were tested experimentally. Qian Lulu and others analyzed the inherent characteristics of single-stage gear transmission system with dynamic substructure method, finite element method and experimental method respectively, which verified the effectiveness of dynamic substructure method applied to gear system. The research on dynamic model of gear system based on dynamic substructure method also includes the work of Ou Weilin et al., Zhu caichao et al., Chang Lehao et al., Ren Yafeng et al., Liu Lan et al.