Stability Analysis of Chatter in Tandem Rolling Mills—Part 1: Single and Multi Stand Negative Damping Effect

Abstract

Many different modes of chatter in rolling and their possible causes have been identified after years of research, yet no clear and definite theory of their mechanics has been fully established and accepted. In this twopart paper, stability of tandem mills is investigated. In Part 1, statespace models of singleand multistand chatter are formulated in a rigorous and comprehensive mathematical form. Then, the stability of the rolling system is investigated in the sense of the singleand multistand negative damping effects. First, a singlestand chatter model in statespace representation is proposed by coupling a dynamic rolling process model with a structural model for the mill stand. Subsequently, a multistand chatter model is developed by incorporating the interstand tension variations and the time delay effect of the strip transportation based on the singlestand chatter model. Stability criteria are proposed and stability analyses are performed to create corresponding stability charts in terms of the singleand multistand negative damping mechanism through numerical simulations. Particularly, the effect of friction conditions on chatter is examined and an explanation is given for the existence of an optimum friction condition. In Part 2, the regenerative effect and resulting instabilities are examined. Suitable stability criteria for each mechanism are established and stability charts are demonstrated in terms of relevant rolling process parameters.