齿轮系统倍周期分岔和混沌层次结构的研究

RESEARCH ON PERIOD-DOUBLING BIFURCATION AND CHAOS HIBERARCHY IN GEAR SYSTEM

针对考虑间隙和时变啮合刚度的强非线性齿轮系统动力学模型,讨论了混乱带中倍周期分岔现象及混沌的层次结构问题。利用频谱分析法对周期运动和混沌运动进行判断,并对嵌于不同混乱带中的周期轨道进行区分。运用分频采样法求解强非线性齿轮系统主倍周期分岔序列与混沌带合并序列,以及混沌带中周期窗口和混沌窗口共存的层次结构问题。通过分析揭示了强非线性齿轮系统存在着复杂的分岔结构和普适规律,并为深入研究机械系统非线性动力学行为的性态提供参考。

Based on the dynamic model of strongly nonlinear gear system with clearance and time-variable mesh stiffness, the period-doubling bifurcation phenomena are researched, and the problem of hiberarchy in chaotic zones is discussed. By using the frequency analysis method the periodic motions and chaotic motions are judged, and the periodic orbits embedded in different chaotic bands are distinguished. The first perioddoubling bifurcation sequence and merged sequence of chaotic bands are obtained by means of the stroboscopic sampling method. The chaos hiberarchy problem in the coexistence area of period-window and chaos-window are also researched. Results show that complex bifurcation structure and some commonly suited rules are existed in the strongly nonlinear gear system. These conclusions can provide some references for deeply researching the characters of nonlinear dynamic behaviors in mechanical systems.