Multi-status mating mechanism and incomplete bifurcation of an internal gear system with time-variant parameters and temperature

Tooth mismatch induced by backlash leads to the multi-status engagement of the internal meshing spur gear system (IMSGS), attenuating transmission accuracy and quality. This paper presents the nonlinear switching mechanism between different mating states of IMSGS considering time-variant parameters with temperature effect. Based on decomposing action, the mating status during gear operation are effectively divided into five states. A novel dynamic model of IMSGS with continuous switching behavior between multiple states is developed considering time-varying backlash, time-varying meshing stiffness (TVMS) and friction. An improved TVMS model incorporating the temperature stiffness and nonlinear Hertzian contact is established and analyzed. Switching behavior between engaging states is precisely identified via constructing five types of Poincaré mappings. The effects of engagement frequency, load factor and transmission error on the bifurcation and global dynamics of the multi-status switching behavior are discussed in detail. The relationship between multi-state mating behavior and coexisting attractors is revealed via the basin of attraction and incomplete bifurcation. Results show that bifurcation behavior due to parametric variations has a significant impact on the evolution of the switching behavior of engaging status. Incomplete bifurcation due to parameter and initial disturbances are the main reasons for the coexisting responses. The sieve attraction domain of coexisting behaviors has been widely observed. Incomplete bifurcation intensifies the complexity of the topology of the basin of attraction, and reduces the local and global dynamic stability of the system.