关键词: 非线性齿轮系统, 分岔, 数值模拟, 稳定性, 周期解结构

Abstract: Based on nonlinear dynamic model of single freedom gear system with clearance, the structure of multi-periodic solution in state space is researched by using of the quasi-fixed-point trace (QFPT) method, and the periodic solution’s structure which how to change with the parameters of damping ratio and frequency is discussed. The stability and bifurcation of periodic motion are researched by the Predict-correct method. Results show that the QFPT method can be used to solve the multi periodic solution structure of nonlinear dynamic system effectively and provide a good foundation for researching the problems of the stability and bifurcation of periodic motion. The discussions of stability and bifurcation are help to more deeply research the road of leading to chaos.

Key words: Bifurcation, Nonlinear gear system, Numerical simulation, Periodic solution’s structure, Stability