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research-article

Hopf bifurcation control for rolling mill multiple-modal-coupling vibration under nonlinear friction

[+] Author and Article Information
Lingqiang Zeng

School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China
zeng_l_q@163.com

Yong Zang

School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China
yzang@ustb.edu.cn

Zhiying Gao

School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China
gaozhiying@me.ustb.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4037138 History: Received June 06, 2016; Revised June 01, 2017

Abstract

Rolling mill system may lose its stability due to the change of lubrication conditions. Based on the rolling mill vertical-torsional-horizontal coupled dynamic model with nonlinear friction considered, the system stability domain is analyzed by Hopf bifurcation algebraic criterion. Subsequently, the Hopf bifurcation types at different bifurcation points are judged. In order to restrain the instability oscillation induced by the system Hopf bifurcation, a linear and nonlinear feedback controller is constructed, in which the uncoiling speed of the uncoiler is selected as the control variable, and variations of tensions at entry and exit as well as system vibration responses are chosen as feedback variables. On this basis, the linear control of the controller is studied using the Hopf bifurcation algebraic criterion. And the nonlinear control of the controller is studied according to the center manifold theorem and the normal form theory. The results show that the system stability domain can be expanded by reducing the linear gain coefficient. Through choosing an appropriate nonlinear gain coefficient, the occurring of the system sub-critical bifurcation can be suppressed. And system vibration amplitudes reduce as the increase of the nonlinear gain coefficient. Therefore, introducing the linear and nonlinear feedback controller into the system can improve system dynamic characteristics significantly. The production efficiency and the product quality can be guaranteed as well.

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