Evolutionary mechanism of safety performance for spur gear pair based on meshing safety domain

Abstract

Drive-side teeth engaging, tooth disengagement and back-side teeth contacting are three meshing states of the spur gear pair. The influence of different meshing states on system safety is different. The safety performances of the system are classified into three safety levels, i.e., safe, quasi-safe and unsafe according to the influence of the meshing state. Three safety domains corresponding to three safety levels are established, respectively. The evolutionary mechanism of the system meshing safety performance is researched in the established safety domain. Multi-initial values bifurcation diagrams and the corresponding top Lyapunov exponents (TLE) of the spur gear pair considered the multiple meshing states are numerically calculated by the 4-order Runge–Kutta method in the C program. The bifurcation & safety dendrograms are constructed to analyze the transition process of the safety performance and the transition mechanism from safe to unsafe. The global integrity measure and integrity factor of the co-existing attraction domains in the safety basins are calculated to identify properly the erosion due to the meshing frequency and damping. It is determined that the safety performance of the system is changed by two patterns. One is the combined action of the bifurcation and varying with the relative displacement amplitude caused by the motion sensitive parameters. The other is one-to-two bifurcation caused by the sensitive parameters of the meshing state. The results provide a theoretical basis for the prediction and control of the meshing state and unsafe performance of the gear pair.