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齿轮传动系统共存吸引子的不连续分岔

金花 吕小红 张子豪 王昕

金花, 吕小红, 张子豪, 王昕. 齿轮传动系统共存吸引子的不连续分岔. 力学学报, 2023, 55(1): 203-212 doi: 10.6052/0459-1879-22-424
引用本文: 金花, 吕小红, 张子豪, 王昕. 齿轮传动系统共存吸引子的不连续分岔. 力学学报, 2023, 55(1): 203-212 doi: 10.6052/0459-1879-22-424
Jin Hua, Lü Xiaohong, Zhang Zihao, Wang Xin. Discontinuous bifurcations of coexisting attractors for a gear transmission system. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 203-212 doi: 10.6052/0459-1879-22-424
Citation: Jin Hua, Lü Xiaohong, Zhang Zihao, Wang Xin. Discontinuous bifurcations of coexisting attractors for a gear transmission system. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 203-212 doi: 10.6052/0459-1879-22-424

齿轮传动系统共存吸引子的不连续分岔

doi: 10.6052/0459-1879-22-424
基金项目: 国家自然科学基金 (12062008), 甘肃省科技计划 (20YF8WA043, 21JR7RA314, 21JR7RA316)和中央引导地方科技发展资金(22ZY1QA005)资助项目
详细信息
    通讯作者:

    吕小红, 教授, 主要研究方向为机械系统动力学. E-mail: lvxh@mail.lzjtu.cn

  • 中图分类号: O322, TH113.1

DISCONTINUOUS BIFURCATIONS OF COEXISTING ATTRACTORS FOR A GEAR TRANSMISSION SYSTEM

  • 摘要: 大量的多吸引子共存是引起齿轮传动系统具有丰富动力学行为的一个重要因素. 多吸引子共存时, 运动工况的变化以及不可避免的扰动都可能导致齿轮传动系统在不同运动行为之间跳跃变换, 对整个机器产生不良的影响. 目前, 一些隐藏的吸引子没有被发现, 共存吸引子的分岔演化规律没有被完全揭示. 考虑单自由度直齿圆柱齿轮传动系统, 构建由局部映射复合的Poincaré映射, 给出Jacobi矩阵特征值计算的半解析法. 应用数值仿真、延拓打靶法和Floquet特征乘子求解共存吸引子的稳定性与分岔, 应用胞映射法计算共存吸引子的吸引域, 讨论啮合频率、阻尼比和时变激励幅值对系统动力学的影响, 揭示齿轮传动系统倍周期型擦边分岔、亚临界倍周期分岔诱导的鞍结分岔和边界激变等不连续分岔行为. 倍周期分岔诱导的鞍结分岔引起相邻周期吸引子相互转迁的跳跃与迟滞, 使倍周期分岔呈现亚临界特性. 鞍结分岔是共存周期吸引子出现或消失的主要原因. 边界激变引起混沌吸引子及其吸引域突然消失, 对应周期吸引子的分岔终止.

     

  • 图  1  直齿轮副的力学模型

    Figure  1.  Mechanical model of a spur gear pair

    图  2  延拓打靶法计算的分岔图

    Figure  2.  Bifurcation diagram calculated by continuation shooting method

    图  3  相图、Poincaré映射和吸引域

    Figure  3.  Trajectories, Poincaré maps and basins of attraction

    图  4  两种方法计算的合成分岔图

    Figure  4.  Composite bifurcation diagram calculated by two methods

    图  5  相图和Poincaré映射

    Figure  5.  Trajectories and Poincaré maps

    图  6  Pa变化的分岔图和相图

    Figure  6.  Bifurcation diagram of displacement as a function of Pa and trajectories

    图  7  吸引域

    Figure  7.  Basins of attraction

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出版历程
  • 收稿日期:  2022-09-09
  • 录用日期:  2022-11-03
  • 网络出版日期:  2022-11-07
  • 刊出日期:  2023-01-18

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