Study on safety characteristics of the spur gear pair considering time-varying backlash in the established multi-level safety domains

Multi-state meshing characteristics induced by backlash and contact ratio in the gear pair are an unsolved puzzle about its relationship to safety characteristics of the gear transmission system. A nonlinear dynamics model of spur gear pair considering time-varying backlash, multi-state meshing, contact ratio and other time-varying parameters is improved. The time-varying backlash comprehensively determined by static backlash, tooth elastic deformation, thermal deformation and oil film thickness is calculated to identify the multi-state meshing of the system. The safety characteristics of the system are classified into nine safety levels according to the influence of meshing states on operation stability. Nine safety domains corresponding to the safety levels are established, respectively. An algorithm is proposed to calculate the safe basin of the gear transmission system in established safety domains. The evolution of safety characteristics in established safety domains is investigated from a local and global perspective by safe basin, nonlinear analysis methods, bifurcation and safety dendrograms and statistical methods. The results show that the value of backlash is affected by meshing states and working conditions of the system. Time-varying backlash is important in identifying multi-state meshing and establishing multi-level safety domains. The safety levels of system responses can be judged by established multi-level safety domains, and the safety characteristics of the system are affected by system parameters, motions and bifurcations. It provides a theoretical basis for the prediction of meshing states and the design of system parameters.