Multi-state meshing characteristics and global nonlinear dynamics of a spur gear system considering local tooth breakage

The meshing state of a gear pair is significantly complex due to the presence of non-integer contact ratio and backlash, especially when there is a local tooth breakage (LTB). This paper presents the multi-state meshing behavior and global nonlinear dynamic characteristic of a spur gear pair with LTB. In order to obtain an accurate meshing state, a time-varying contact ratio considering LTB is calculated, and then nine meshing states and their boundary conditions are extracted. Later, a multi-state meshing nonlinear dynamic model incorporating the effect of LTB is developed. The time-varying meshing stiffness and load distribution coefficient considering LTB are calculated and analyzed in the time domain. Bifurcation and chaos characteristics of multi-state meshing behavior changing with meshing frequency under multi-initial values are studied. The global bifurcation of coexistence behavior is revealed based on the bifurcation dendrogram and basin of attraction. The result shows that LTB not only increases the dynamic meshing force but also changes the dynamic behavior if multi-state meshing occurs. Bifurcation and chaos induce multi-state meshing behavior. A special multi-initial bifurcation phenomenon, incomplete bifurcation, is found to be the primary factor contributing to the coexistence of attractors and parallel branches. This study provides a more accurate model for multi-state meshing and multi-initial bifurcation of a spur gear pair with LTB.