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本文引用格式:周杜,乐源,李高磊,吴鑫.两自由度齿轮传动系统全局动力学研究[J].动力学与控制学报,2019,17(6):514~519;   Zhou Du,Yue Yuan,Li Gaolei,Wu Xin.Study on global dynamic characteristic of two degrees of freedom gear transmission system[J].Journal of Dynamics and Control,2019,17(6):514-519.
两自由度齿轮传动系统全局动力学研究    点此下载全文
周杜  乐源  李高磊  吴鑫
西南交通大学 力学与工程学院, 成都 610031,西南交通大学 力学与工程学院, 成都 610031,西南交通大学 力学与工程学院, 成都 610031,西南交通大学 力学与工程学院, 成都 610031
基金项目:国家自然科学基金资助项目(11672249,11732014)
DOI:10.6052/1672-6553-2019-003
摘要:
      齿侧间隙的存在,使齿轮传动系统存在着丰富的非线性动力学行为.考虑两自由度齿轮传动系统的动力学模型,利用数值方法分析系统的分岔和混沌动力学行为.通过简单胞映射方法对非线性齿轮系统进行全局分析,得到系统的吸引子,吸引域等全局特性.结果显示:随着激振频率的变化,系统存在多个周期解共存以及周期解与混沌运动共存现象.最后利用系统的相轨线图与庞加莱截面图进行对比分析,在不同的初值条件下,系统呈现出不同的周期运动或混沌运动.利用简单胞映射方法的数值计算结果可以实现在不良参数条件下,通过合理控制系统的初值条件而获得理想的系统响应.
关键词:间隙,齿轮传动系统,分岔,混沌,简单胞映射,全局分析
Study on global dynamic characteristic of two degrees of freedom gear transmission system    Download Fulltext
Zhou Du  Yue Yuan  Li Gaolei  Wu Xin
Fund Project:
Abstract:
      The existence of tooth side backlash in gear transmission system induces rich nonlinear dynamical behaviors. Considering the nonlinear dynamic model of a two-degrees-of-freedom gear transmission system, the bifurcation and chaos of the system were analyzed by using the simple cell mapping method. Firstly, the global characteristics of the nonlinear gear system were analyzed, and the attractor and attracting domain were obtained. The results show that, with changing excitation frequency, the system exhibits coexistence of multi periodic solutions and coexistence of periodic and chaotic motions. Furthermore, the phase diagram of the trajectory of the system was compared with that of the Poincaré section. It is shown that, under different initial conditions, the system presents different periodic or chaotic motions. Therefore, based on the numerical results by the simple cell mapping method, ideal system responses, such as periodic motions, can be realized by reasonably selecting the initial conditions, when certain parameters make the system undergoes complicated responses.
Keywords:backlash,gear transmission system,bifurcation,chaos,simple cell mapping,global analysis
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