星型齿轮传动系统定常与奇怪吸引子的共存现象

Coexistence of Trivial and Strange Attractors in Star Gear Systems

建立了具有间隙的星型齿轮传动系统的非线性动力学模型 ,并用数值方法对非线性微分方程组进行了求解。研究了系统中定常吸引子和奇怪吸引子的共存问题。针对两种典型的系统参数 ,以不同的初值条件分别得到了共存的周期吸引子和奇怪吸引子、准周期吸引子和奇怪吸引子 ,分析和比较了各吸引子的动态特性。通过分析各齿轮副的动态啮合力 ,判别了各齿轮副啮合过程中出现的无冲击状态、单边冲击状态、双边冲击状态。并讨论了各吸引子所对应的星轮载荷分布均匀性。

The present studies on the coexistence of multiple attractors of gear systems are mainly based on the single-DOF dynamic system model which takes a gear pair as examining objective. This paper establishes a dynamic model of star gear systems with backlashes and develops a numerical method to solve the nonlinear governing differential equations. Then it studies the coexistence of multiple attractors of a four-DOF star gear system under different initial values. The coexistent situations of both periodic and strange attractors and both quasi-periodic and strange attractors have been identified and investigated. By comparing various dynamic behaviors of the attractors with each other, the meshing situations of no impact, single-sided impact and double-sided impact between gear pairs are identified by analyzing the dynamic meshing forces. Furthermore, the attractors corresponding to the situations of both load balance and unbalance among the star gears are also observed and demonstrated.