Study on the Nonlinear Dynamic Behavior of Rattling Vibration in Gear Systems

Abstract

To reveal the nonlinear dynamic behavior of gear rattling vibration caused by gear backlash, a 2-DOF oscillator model with spring and damping elements was established. Based on the theory of discontinuous dynamical systems, the phase plane of gear motion was divided into three parts: the domain of tooth surface meshing motion, the domain of free motion and the domain of tooth back meshing motion. Introducing the global mapping and local mapping dynamics method, the process of gear teeth from impact to meshing and then impact and meshing was accurately described. The influence of different restitution coefficients on gear impact-meshing motion was studied by numerical simulation. The results showed that the grazing bifurcation caused by gear backlash will lead to complex mapping structures of the system and even chaos. The restitution coefficient directly affects the impact-meshing behavior. The introduction of meshing stiffness and restitution coefficient can reasonably characterize the elastic deformation and energy loss during gear meshing, which provides a theoretical model for the application of the theory of discontinuous dynamical systems to a more complex multi-degree of freedom flexible contact gear transmission system.