Modeling and analysis of a spur gear pair considering multi-state mesh with time-varying parameters and backlash

Backlash-induced variations may lead to teeth separation and back-side tooth mesh in lightly loaded geared drive. Effects of teeth separation and back-side tooth mesh are considered. The dynamic model of a spur gear pair under multi-state meshing conditions such as teeth separation, drive- and back-side tooth mesh is established based on the gear transmission principle and forces acting on teeth. Time-varying meshing stiffness, time-varying friction, load distribution, comprehensive transmission error and backlash are included in the model. Variations of the dynamic meshing force of the system under different meshing states are analyzed numerically. The dynamic meshing force affects the meshing state of the system significantly. Furthermore, the effects of load, backlash and comprehensive transmission error on meshing states and vibro-impact properties of the system are studied by defining three different Poincaré maps, where bifurcation diagrams, top Lyapunov exponent diagrams (TLE), phase portraits are used. Results indicate that the complicated phenomena such as drive-side impact, teeth separation and back-side impact gradually occur with the decrease of the load or the increase of the comprehensive error. However, these phenomena always exist with the increase in backlash. This study provides a theoretical reference for the optimization of gears.