含间隙和时变啮合刚度齿轮传动系统的分岔和混沌

齿侧间隙和时变啮合刚度的存在,使齿轮传动系统中存在着丰富的非线性动力学行为。基于Poincare映射,建立了两自由度齿轮传动系统的数学模型,并通过数值仿真,说明了齿轮传动系统中存在着倍周期分岔、Hopf分岔和混沌等复杂的非线性现象。分析了系统参数对齿轮动力学行为的影响,进而为消除齿侧间隙和时变啮合刚度引起的非线性动力学行为指明了方向,为齿轮传动系统的优化设计奠定了基础。

Bifurcation and chaos of the gear system with backlash and time-varying mesh stiffness

Owing to the gear backlash and time-varying mesh stiffness, the gear system had various nonlinear dynamic behaviors. Based on Poincare map, establishes a two-degree freedom nonlinear model of the gear system, and by numerical simulation, the results show that the gear system exists period-doubling bifurcation、 Hopf bifurcation and chaos etc complicated nonlinear phenomena. Analyzes the system parameters impact on gear dynamic behaviors, then points out the direction of eliminating the nonlinear dynamic behaviors for gear backlash and time-varying mesh stiffness, and lays the foundation for optimizing the gear system.