Bifurcation and chaos analysis of a spur gear pair system with fractal gear backlash

•The model of gear backlash with tooth surface microscopic features is adopted.•The bifurcation and chaos of the system with fractal backlash is discussed.•A relationship between gear dynamics and tooth surface microscopic features is built. The dynamic characteristics of a spur gear pair system with two kinds of gear backlash are studied, in which the modeling of gear backlash is emphasized. Meanwhile, the sliding friction force is derived. On this basis, a torsional dynamic model is established. Some simulation experiments are conducted using rotational velocity and initial gear backlash as variables. And the bifurcation and chaos of the system with fixed backlash and fractal backlash are compared. The results show that both two conditions exhibit a common pattern in motion state evolution, but the system with fractal backlash enters chaos at a higher rotational speed and a larger initial gear backlash. The system with fixed backlash exhibits more rich nonlinear dynamic behaviors. The dynamic model with fractal backlash deduced in this paper outlines a method of establishing an indirect relationship between bifurcation, chaos, and tooth surface microscopic features. The results provide fundamental support for designing and manufacturing the spur gear in the future.