Single- and multi-stand chatter models in tandem rolling mills

Many different modes of chatter and their possible causes have been identified after years of research, yet no clear and definite theory of their mechanics has been established. One of the most important reasons for this can be attributed to the fact that only oversimplified models with a single input and a single output were historically used to formulate chatter in rolling. Such a situation has hindered a complete analysis of the underlying mechanisms. In this paper, a state-space representation of single- and multi-stand chatter models will be proposed in a rigorous and comprehensive mathematical form for stability analysis of the various chatter mechanisms. First, a dynamic model of the rolling process that utilizes homogeneous deformation theory will be established that includes the material strain-hardening and work roll flattening effects. By coupling this dynamic rolling process model with a structural model for mill stands, a single-stand chatter model in a state-space representation will be proposed. Based on the single-stand chatter model, a multi-stand chatter model will be formulated by incorporating the inter-stand tension variations and the time delay effect of the strip transportation. A simulation program will also be presented for the study of the dynamic rolling process in the time domain and for verifying the results from stability analysis.