六辊UC轧机轧制过程混沌、分形特性探索和定量判据动力学分析

Chaotic Character in the Rolling Process of a 6 High UC Mill and Dynamic Analysis of Its Quantitative Criterion

研究了六辊ＵＣ轧机的轧制过程，对其数据进行了分析处理，给出带材的平均厚度、二次板形控制量、板凸度和四次板形控制量随时间变化的趋势图、混沌相图和递次振幅图。首次发现带材板形指标板凸度具有混沌倍分叉特性及线性变换后的迭代模型：ｘｎ＋１＝ｒｘｎｅｘｐ（１－ｘ２ｎ）。对该迭代模型倍分叉图进行Ｆｅｉｇｅｎｂａｕｍ数和李雅普诺夫指数图计算。由此对该过程出现的“轧不精原理”的混沌与分维机制给出了定量判据。提出了该轧制过程板形特征具有混沌特性的新观点，为该混沌特性的控制与利用给出了理论依据和提高轧制精度的一种新思想。

The rolling process of a 6 high UC mill has been studied. The results of data analysis can be expressed in terms of strip average thickness, secondary flatness controlling value (crown) and quatery flatness controlling value, and can be ploted into following graphies: the tendency plots of their varying with time, their phase space plots and successive amplitude plots. And it is found that the linearly transfered model of crown: x n +1 = rx n exp(1- x 2 n ) has a chaotic double bifurcation character. Then from those plots the Feigenbaum number and Lyapunov exponent of this iterative model could be determined. Thereafter a quantitative criterion for judging the chaotic and fractal characters of the “none accurate rolling theory” are worked out. So it is clarified that the strip flatness has chaotic characteristics. Taken this as a theoretical basis, controlling the chaotic character could be a new way to enhance the accuracy of the rolling process.