Analysis of safety characteristics by nonlinear dynamics and safety basin methods for the spur gear pair in the established teeth contact safety domain

Abstract

The safe operation of gear pairs is the basic safety guarantee of the machine. The safety of the gear pair may be destroyed due to transfinite of kinematic variables and system parameters. In order to reveal its evolutionary mechanism, the safety characteristics of the spur gear pair are researched under the established safety domain. A nonlinear dynamics model of the spur gear pair considered multi-state meshing is introduced. The comprehensive teeth contact safety domain of the spur gear pair to prevent tooth surface contact fatigue, tooth surface plastic deformation and tooth root bending fatigue is established. A method of judging safety characteristics of the system is given. The safety basins, phase portraits and Poincaré mappings are computed to reveal the distribution of the coexistence attractors and judge the safety characteristics of the system motions under the established safety domain in the state space. Multi-initial values bifurcation diagrams and the corresponding top Lypunov exponents (TLE) via the change of the backlash, the fluctuation coefficient of the comprehensive transmission error and the external load are used to catch the motions in the studied state space and study their transition. Bifurcation & safety dendrograms are constructed to study the evolutionary processes of the system safety characteristics. System parameters are divided into two types according to their influence on the erosion and bifurcation of the system safety basins. Two patterns to change the system safety characteristics from safe to unsafe are found. The sensitive parameters of meshing state change the safety characteristics by one-to-two bifurcation. The sensitive parameters of dynamic characteristics mainly affect the safety characteristics by changing the amplitude of kinematic variables and the dynamic response of the tooth disengagement or back-side teeth contacting state. The study is helpful in the selection of system parameters for mitigation and design against fatigue.