Dynamic response characteristics of variable hyperbolic circular-arc-tooth-trace cylindrical gear transmission system considering wear effect

To illustrate the impact of tooth surface wear on the dynamic response of the cylindrical gear transmission system with variable hyperboloid circular-arc-tooth-trace (VH-CATT), a nonlinear dynamic model of VH-CATT cylindrical gear that considers wear effect was developed in this article. Firstly, according to the analysis conducted through the finite element method, the time-varying meshing stiffness of VH-CATT cylindrical gear is calculated, and the time-varying meshing stiffness considering wear is characterized by introducing wear fault characteristics. Then, the load ratio is introduced to represent the relationship between the error amplitude and the excitation load. By using the error amplitude as the bifurcation parameter, this parameter describes how the excitation load affects the dynamic characteristics of the VH-CATT cylindrical gear. Finally, the bifurcation diagram and maximum Lyapunov exponent of the VH-CATT cylindrical gear transmission system under various wear depths are computed using the fourth-order Runge-Kutta method. At the same time, the response state of the VH-CATT cylindrical gear is verified by phase diagram, Poincaré mapping and time history diagram. The findings indicate that the vibration amplitude of the VH-CATT cylindrical gear system increases as the error amplitude increases. The vibration phenomenon of VH-CATT cylindrical gear transmission system with wear fault is more obvious, and the system enters the bifurcation and chaos effect state in advance. Therefore, the wear of the tooth surface will lead to the decrease of the gear meshing stiffness, which will lead to the increase of the vibration amplitude of the system, resulting in the phenomenon that the dynamic response state of the system is advanced. The research results will provide a theoretical basis for high-quality VH-CATT cylindrical gear transmission and gear nonlinear dynamics research.