Bifurcation and chaos analysis of a gear pair system with multi-clearance

Abstract

In order to investigate the characteristics of bifurcation and chaos for a spur gear pair system, a three-degree-of-freedom nonlinear dynamic model with multi-clearance is established, in which time-varying meshing stiffness, static transmission error, gear backlash and bearing clearance are comprehensively taken into account. Through introducing a relative generalized coordinate, the dimensionless dynamic equations of motion of system are derived and then solved by using Runge-Kutta numerical integration method. And the bifurcation and chaos features of gear pair are systematically analyzed and discussed from bifurcation diagrams with meshing frequency, gear backlash, bearing clearance and damping ratio as control parameters under different loaded conditions. Meantime, with the help of Poincaré map and phase diagram, the motion forms of system are accurately identified. The analysis results reveal that as meshing frequency increases, the system shows various types of motion states which contain periodic motion, quasi-periodic motion and chaotic motion. Similarly, with the increasing of gear backlash, the system undergoes complex motion forms under lightly loaded condition, whereas it is only in period-one motion state under heavily loaded condition. Furthermore, the system motion state is gradually switched from chaos to periodic or quasi-periodic motion under lightly loaded condition when bearing clearance changes. However, under heavily loaded condition, the bearing clearance has a weak effect on dynamic behavior of the gear system. Apparently, the system tends to be more stable under heavily loaded condition than that under lightly loaded condition. In addition, the growing damping ratio can effectively suppress the chaotic behavior and control nonlinear vibration of gear system. The research results provide useful guidance for dynamic design and vibration control for gear set.