Abstract:

By defining the system parameters as parameter variables and forming the parameter space, the nonlinear global dynamics of the gear transmission system under the coupling of parameter space and state space are studied in detail in this work. The correlative relationship between multiple parameters, multiple initial values and multiple stable behaviors is also obtained. Firstly, a method for calculating and identifying the multi-stable behavior of a nonlinear system under the coupling of two spaces is designed. Secondly, based on the designed method and combined with phase diagram, Poincaré map, bifurcation diagram, top Lyapunov exponent and basin of attraction, the existence and distribution of multi-stable behavior for the gear transmission system in different parameter planes are investigated numerically to better understand the motion mechanism of the system. In addition, the distribution characteristic of multi-stable behavior in the state plane is also studied on the base of the cell-to-cell mapping method. The multi-stable behavior and bifurcation that may be hidden in the parametric plane and the state plane are fully revealed. The formation mechanism of multi-stable behavior is analyzed as well. The results show that there are a large number of multiple stable behaviors which are banded distribution in the parametric planes of the gear system under the coupling of two spaces. Two different erosion phenomena, such as internal erosion and boundary erosion, are clearly observed in the state plane. The sensitivity of bifurcation points or bifurcation curves to initial values leads to the occurrence of multi-stable behavior. When the amplitude of backlash or error fluctuation changes in a small range, the global dynamic characteristics of the gear system are less affected by the backlash or error disturbance. However, the global dynamic characteristics are greatly affected by the meshing frequency. Global dynamic characteristics of the gear system become rich and complex under two-space coupling.

Key words: gear vibration, multi-stable behavior, parameter correlation, basin of attraction, nonlinear dynamics