Chatter dynamics in sheet rolling

Abstract

Two and four degree of freedom (DOF) systems describing chatter in sheet rolling are investigated. In the two DOF case, this includes studying the nonlinear behavior that arises due to the deformation at the work-backup roll interface. The force displacement relation between two cylindrical rolls being pressed together is inherently nonlinear due to the changing contact area. The investigation also includes the additional plastic deformation of the sheet in the roll-bite that is present during chatter. As the work rolls vibrate the gap widens and narrows inducing additional plastic deformation of the sheet. For the two DOF case, one mode of vibration is a motion of the work roll-sheet mass center. The other mode is a squeezing motion of the sheet in the bite by the work rolls. The natural frequencies seem to correspond with fifth octave chatter. The nonlinear theory predicts a small shift in the vibrational frequency. The role of inter-stand tension in triggering instability is also discussed. The four DOF system extends the research of Yarita et al. by providing analytic expressions for the natural frequencies. It appears that this system is capable of predicting third octave chatter, in addition to fifth octave chatter.