转速波动对冷轧扭转颤振稳定性的影响

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摘要

考虑冷轧薄板工艺中，冷轧机的主传动系统的转速波动诱发的非线性扭振效应。运用最大Lyapunov指数、双参分布、图胞映射等方法，研究非线性扭转颤振系统的单参分岔、双参分岔、混沌以及多初值条件的吸引子流形转迁等非线性动力行为和特征；通过分析双参分岔，获得系统在双参数匹配变化时的稳定运动区间；通过分析多初值条件下吸引子运动流形边界变化，获得吸引子、吸引域的分布图。数值仿真的结果明确了转速波动激励下的系统扭转振动的发展趋势和系统稳定与不稳定运动的切换条件和参数匹配区间，这为工程实践中避开混沌运动区间和轧制工艺参数优选提供了理论依据。

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	赵武
	刘志伟
	黄丹

关键词 ：扭振, 转速波动, 分岔, 最大Lyapunov指数, 吸引子, 双参分岔

Abstract：The nonlinear torsional vibration in cold rolling is usually induced by the speed fluctuation disturbance of its transmission system.Based on the methods of maximum Lyapunov exponent, double-parameter distribution and graph-cell mapping, nonlinear dynamic behaviors and characteristics of the self excited torsional chatter such as single-bifurcation, double-bifurcation, chaos and attractor manifold transition under multiple initial conditions were studied, and the stable motion interval of the system was obtained by the double-parameter bifurcation analysis.The boundary changing of the attractor motion manifold under the condition of multiple initial values, was analysed to obtain the distribution maps of the attractor and attraction domain.The simulation results make clear the development trends of torsional chatter characteristics under speed fluctuation excitation, as well as the switching conditions and parameter matching range of stable or unstable motions.The results provide a theoretical basis for avoiding chaotic motion intervals and optimizing rolling process parameters in engineering practice.

Key words： torsional vibration rotating speed fluctuation bifurcation maximum Lyapunov exponent attractor double-parameter bifurcation

收稿日期: 2020-02-10 出版日期: 2021-09-28

引用本文:

赵武，刘志伟，黄丹. 转速波动对冷轧扭转颤振稳定性的影响[J]. 振动与冲击, 2021, 40(18): 228-236.
ZHAO Wu, LIU Zhiwei, HUANG Dan. Effect of rotating speed fluctuation on the stability of torsional chatter in cold rolling. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(18): 228-236.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2021/V40/I18/228

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