Vibration stability and bifurcation analysis of two-stage spur gear systems supported by squeeze film dampers

The squeeze film dampers (SFDs) demonstrate superior efficacy in attenuating vibrations. In the present study, the oil-film forces of SFDs are computed utilizing the finite element method, adhering to the Galerkin principle. Taking into account the time-varying meshing stiffness (TVMS), static transmission error (STE), and tooth backlash, a nonlinear dynamic model for a two-stage spur gear system, bolstered by SFDs, is developed by the lumped parameter methodology and D'Alembert's principle. Based on the Gram-Schmidt QR decomposition, a strategy for calculating the Lyapunov exponent spectrum and Floquet characteristic multipliers of high-dimensional gear-rotor-SFD systems is proposed. By comparing with classical literature, the accuracy of the computational strategy is verified. Qualitative and quantitative assessments are conducted on the vibration stability of a two-stage spur gear system supported by rolling bearings and SFDs. The analysis evaluated the damping effect of SFDs in enhancing the vibration stability of gear systems and improving the periodic motion of the system. The study indicates that the application of SFDs can effectively reduce the occurrence of saddle-node bifurcations, Hopf bifurcations, and period-doubling bifurcations, and the chaotic and unstable vibration region is greatly narrowed and suppress nonlinear characteristics such as bistable responses and jump phenomena.