Establishment of the integrated safety domain for spur gear pair and its safety characteristics in the domain

In order to reveal the evolutionary mechanism of the safety characteristics for the gear transmission system, the integrated safety domain is established and the safety characteristics of the spur gear pair in it are researched according to our previous research results. An integrated safety domain including 8 safety grades of the spur gear pair considered its multi-state meshing characteristics is established. Single and double drive-side meshing, tooth disengagement, single and double back-side contacting and the tooth surface contact fatigue, tooth surface plastic deformation and tooth root bending fatigue under drive-side meshing and back-side contacting are included in the established integrated safety domain. The calculated multi-initial values bifurcation diagrams, the calculated safety characteristic transition curves and the constructed bifurcation & safety dendrogram are used in combination to investigate the transition process of the system motion and its safety characteristics. Phase portraits, Poincaré maps and safe basins are used in combination to investigate the transition mechanism of the system motion and its safety characteristics. The influences of load on the system safety characteristics in three different safety domains are analyzed comparatively when the multi-state meshing characteristic of spur gear pair is considered. The influences of the meshing frequency and the fluctuation amplitude of meshing stiffness on the safety characteristics of the system in the established integrated safety domain are investigated. The transition mechanism of the system safety characteristics and the range of three sensitive parameters are obtained. The identification method of the safety characteristic considering the integrated safety domains and the fractal degree of the safety basin is introduced. The study is helpful in the selection of system parameters for mitigation and design against fatigue or improving safety. It is also helpful for grading safety early warning of the gear transmission system and the corresponding safety protection measures or adjusting system parameters can be taken according to actual engineering requirements.