Dynamic modeling and vibration transmission analysis of the two-stage gearbox with simultaneous consideration of shaft flexibility and instantaneous gear meshing stiffness

For a two-stage gear transmission system, the coupled vibration response and vibration transmission law are not clear due to the mutual influence of two internal excitations. In this paper, a dynamic model of a two-stage gear transmission system that can simultaneously consider shaft flexibility and instantaneous gear meshing stiffness is proposed. Firstly, the flexible shaft is modelled with rigid element method. Secondly, a quick influence coefficient method is proposed to evaluate the instantaneous meshing stiffness of normal and broken teeth. Thirdly, the coupling dynamics model of gear-shaft-bearing-pedestal is developed by combining the radial contact force models of bearing and pedestal. The accuracy of the quick influence coefficient method is verified by comparison with finite element method and literature methods, and the correctness of the coupling dynamic model is verified by experimental results. Then the transmission laws of coupled vibration and fault excitation are revealed by the defined vibration transmission path, power flow and vibration contribution index. The results show that the power flow is maximum at the gear element position, and the vibration attenuates sharply when passing through the bearing interface. Besides, the fault residual signal is utilized to select the fault-sensitive measuring point, which provides a theoretical reference for the fault monitoring of the complex gear transmission system.