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Bifurcation and chaos analysis of spur gear pair in two-parameter plane

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Abstract

A developed algorithm is designed based on the simple cell mapping method and escape time algorithm to examine every state cell and the dynamic characteristics of the multi-parameter coupling in torsion-vibration gear system. Two different types of bifurcation caused by the intersection of the period-doubling bifurcation curves are researched by analyzing the distribution map and the bifurcation diagram of system’s dynamic characteristic in the parameter plane, \(\omega -F\). The occurrence processes of periodic bubbles and saltatory periodic bifurcation are studied. The stationary solution and its phase trajectory of the fractal of the periodic motion attractor boundary are researched too. The sufficient condition of the fractal structure of the periodic attractor domain is achieved. Homoclinic or heteroclinic trajectory in phase space is found caused by the intersection of the different periodic motion trajectories in non-smooth system.

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Acknowledgments

This investigation was financially supported by the National Natural Science Foundation of China (Grant No. 51365025, 11462012), by Innovative Research Group Foundation of Gansu Province of China (1308RJIA006) and by Research Fund for the Doctoral Program of Higher Education of Chana (20126204110001).

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Authors and Affiliations

  1. School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Xiang-Feng Gou, Ling-Yun Zhu & Dai-Lin Chen

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  1. Xiang-Feng Gou
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  2. Ling-Yun Zhu
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Correspondence to Xiang-Feng Gou.

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Gou, XF., Zhu, LY. & Chen, DL. Bifurcation and chaos analysis of spur gear pair in two-parameter plane. Nonlinear Dyn 79, 2225–2235 (2015). https://doi.org/10.1007/s11071-014-1807-1

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