Regenerative chatter in cold rolling

A dynamic model of the rolling process that includes the material strain-hardening and work roll flattening effects was developed based on homogeneous deformation theory. By coupling this new dynamic rolling process model with a structural model for a mill stand, a single-stand chatter model expressed through a state-space representation was constructed. Based on the single-stand chatter model, a multi-stand chatter model was formulated by incorporating the inter-stand tension variations and the strip thickness variation time delay effect caused by strip transportation between stands. In essence, the resulting model is a state-space representation of a set of delay differential equations whose coefficients are a function of the rolling process and mill structure parameters.;With the established chatter models, stability analyses were conducted with respect to various chatter mechanisms including the model matching, single- and multi-stand negative damping and regenerative effects. Stability criteria were established for each of the chatter mechanism, based on the Routh criterion for model matching, the general stability criterion associated with negative damping, and the integral criterion corresponding to regeneration. As a result, stability charts were constructed to illustrate stable regions in different rolling process parameter spaces. It was found that if the process parameters of either an upstream or downstream stand are fixed, then, optimal ranges of friction, inter-stand tensions and inter-stand distances that assure the chievement of a maximal rolling speed and prevent the onset of chatter in the sense of the multi-stand negative damping effect exist. It was also found that the interaction between the stands, through the time delay effect significantly reduces the stability of the rolling process in a tandem mill. In analogy to metal cutting, the stability chart of regenerative chatter in rolling has a characteristic lobed shape appearance.;SIMULINK simulation programs in the Matlab environment were created for a tandem mill. The characteristics of rolling chatter were explored in the time domain using models of increasing complexity in the sense of model matching, single- and multi-stand negative damping and regenerative effects. Furthermore, the stability charts created by stability analyses were verified through simulations. The effects of inter-stand tension variations and of the delay effect of the strip thickness variation during regeneration were explained.