Stability Analysis of a Nonlinear Coupled Vibration Model in a Tandem Cold Rolling Mill

Xing Lu,Jie Sun,Dianhua Zhang,Zhenhua Wang,Guangtao Li

doi:10.1155/2019/4358631

Abstract

Mill chatter in tandem cold rolling mill is a major rejection to the quality and production of the strips. In most mill vibration models, either the roll mass is usually limited to vibrate in vertical direction and vertical-horizontal directions, or the multiple rolls system is simplified to a single mass system. However, the torsional chatter is also a typical type of mill chatter, and the presence of intermediate roll and backup roll will affect the overall vibration of the mill structure system. In this paper, a newly cold rolling mill vibration model coupled with the dynamic rolling processing model and nonlinear vibration model is proposed with the consideration of dynamic coupling and nonlinear characteristics of the rolling process, multiroll equilibrium, and roll movement in both vertical-horizontal-torsional directions. By using Hopf bifurcation theorem and Routh–Hurwitz determinant, the existence of the Hopf bifurcation point of the mill vibration system and bifurcation characteristics are analyzed. At last, the influence of different rolling conditions on the stability of the coupled mill system is investigated, and these results can also be used to design an optimum rolling schedule and determine the appearance of mill chatter under certain rolling conditions.

Highlights

With the optimization and upgrading in the steel industry, the urgent demands for high strip quality and strip yield have become more stringent
Researchers tend to consider that mill chatter is a typical self-excited vibration [1,2,3], which consists of third-octave mode chatter (150–250 Hz), fifth-octave mode chatter (500–700 Hz), and torsional chatter
The backup roll was set as a mass point, and a connector was used to represent the displacement of the backup roll and mill stand housing

Summary

Introduction

With the optimization and upgrading in the steel industry, the urgent demands for high strip quality and strip yield have become more stringent. Erefore, a further multiroll and nonlinear verticalhorizontal-torsional coupled vibration model of the universal crown control mill (UCM mill) needs to be proposed and analyzed Based on this proposed rolling mill vibration model, the bifurcation phenomenon and stability of the mill system is analyzed to illustrate the dynamic characteristics of the UCM mill more comprehensively. Assuming the thickness fluctuation and tension variation are caused by roll gap vibration as separated disturbances, the deviation of the rolling force in the x direction can be written as dPx zPx zhin dhin zPx zhout dhout zPx zTb zPx zTf dTf. Based on equation (17), the deviation of the rolling force in the x direction can be expressed as wTb 2 dhin wTfdyw whin 2.

Dynamic Nonlinear Vibration Model of the UCM Mill

Vr zhn

Analysis of Vibration Stability of the Roll System

Stable Range Analysis of Other Rolling Parameters

Findings

Conclusion