Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic

doi:10.1088/1674-1056/24/7/074501

中国物理B ›› 2015, Vol. 24 ›› Issue (7): 74501-074501.doi: 10.1088/1674-1056/24/7/074501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic

刘爽^{a b}, 王兆龙^a, 赵双双^a, 李海滨^{a b}, 李建雄^{a b}

a Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China;
b National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao 066004, China

收稿日期:2014-12-05 修回日期:2015-01-07 出版日期:2015-07-05 发布日期:2015-07-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and the University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013).

Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic

Liu Shuang (刘爽)^{a b}, Wang Zhao-Long (王兆龙)^a, Zhao Shuang-Shuang (赵双双)^a, Li Hai-Bin (李海滨)^{a b}, Li Jian-Xiong (李建雄)^{a b}

a Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China;
b National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao 066004, China

Received:2014-12-05 Revised:2015-01-07 Online:2015-07-05 Published:2015-07-05
Contact: Wang Zhao-Long E-mail:zlwang1988@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and the University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013).

摘要/Abstract

摘要： Grazing bifurcation of a relative rotation system with backlash non-smooth characteristic is studied along with the change of the external excitation in this paper. Considering the oil film, backlash, time-varying stiffness and time-varying error, the dynamical equation of a relative rotation system with a backlash non-smooth characteristic is deduced by applying the elastic hydrodynamic lubrication (EHL) and the Grubin theories. In the process of relative rotation, the occurrence of backlash will lead to the change of dynamic behaviors of the system, and the system will transform from the meshing state to the impact state. Thus, the zero-time discontinuous mapping (ZDM) and the Poincare mapping are deduced to analyze the local dynamic characteristics of the system before as well as after the moment that the backlash appears (i.e., the grazing state). Meanwhile, the grazing bifurcation mechanism is analyzed theoretically by applying the impact and Floquet theories. Numerical simulations are also given, which confirm the analytical results.

关键词: relative rotation system, backlash, grazing bifurcation, zero-time discontinuous mapping

Abstract: Grazing bifurcation of a relative rotation system with backlash non-smooth characteristic is studied along with the change of the external excitation in this paper. Considering the oil film, backlash, time-varying stiffness and time-varying error, the dynamical equation of a relative rotation system with a backlash non-smooth characteristic is deduced by applying the elastic hydrodynamic lubrication (EHL) and the Grubin theories. In the process of relative rotation, the occurrence of backlash will lead to the change of dynamic behaviors of the system, and the system will transform from the meshing state to the impact state. Thus, the zero-time discontinuous mapping (ZDM) and the Poincare mapping are deduced to analyze the local dynamic characteristics of the system before as well as after the moment that the backlash appears (i.e., the grazing state). Meanwhile, the grazing bifurcation mechanism is analyzed theoretically by applying the impact and Floquet theories. Numerical simulations are also given, which confirm the analytical results.

Key words: relative rotation system, backlash, grazing bifurcation, zero-time discontinuous mapping

中图分类号: (Rotational dynamics)

45.20.dc

05.45.-a (Nonlinear dynamics and chaos)

刘爽, 王兆龙, 赵双双, 李海滨, 李建雄. Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic[J]. 中国物理B, 2015, 24(7): 74501-074501.

Liu Shuang (刘爽), Wang Zhao-Long (王兆龙), Zhao Shuang-Shuang (赵双双), Li Hai-Bin (李海滨), Li Jian-Xiong (李建雄). Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic[J]. Chin. Phys. B, 2015, 24(7): 74501-074501.

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Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic

Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic

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