Stability of the coupled vibrations of work roll and strip in cold rolling process

Undesirable vibrations that occurred in cold rolling mills, widely known as chatter, are studied in this article by considering the interaction of three types of vibrations, namely, the longitudinal vibration of the rolled strip and the torsional and vertical vibrations of the upper work roll. The dynamic component of rolling force is determined using the quasi-static model under the assumption that the changes in roll gap and strip tension produce the variation of rolling force. The coupled vibrations of the work roll and rolled strip are mathematically governed by a set of 3-degree-of-freedom non-linear equations. Under chatter conditions, a new variable is introduced to represent the motion of the quasi-neutral point. A stability criterion for the motion of the quasi-neutral point is developed by studying the eigenvalues of the corresponding characteristic equation of the linearized parts of the non-linear equations. The chatter stability can then be examined by evaluating the determinants of five matrices. Numerical examples are given to show the stable and unstable vibrations in the cold rolling process. The unstable vibration would lead to skidding phenomenon and even break the rolled strip. The results presented in this article provide new insights into the dynamic interaction of the coupled vibrations and the dynamics of the rolling process.