Investigation on bifurcation and chaos control for a spur pair gear system with and without nonlinear suspension

A nonlinear dynamic model of a spur pair gear system is proposed, which considers gear backlash, static transmission error, meshing stiffness and so on. The dynamic behaviors of the system with and without nonlinear suspension are respectively investigated through Runge-Kutta numerical integration method, in which the damping coefficient and support stiffness are chosen as the control parameters. The motions of system are identified by using bifurcation diagram, phase portrait and Poincare map. The research results reveal that with the change of control parameters, the system undergoes different motion forms consisting of period-one, multi-period, quasi-period, even chaotic motions. Under nonlinear suspension, the system gets more complex dynamic responses than those under linear suspension, which reveals that the model with nonlinear suspension represents the practical gear system accurately. The study could provide some theoretical guide for analysis of bifurcation characteristics, chaos control and system parameter optimization.