The effect of friction and inelastic deformation on chatter in sheet rolling

Abstract

Vibrations or chatter of a rolling mill often accompany the processing of thin sheet. The oscillation of the work rolls produces an unsteady squeezing motion of the sheet in the roll bite gap that induces additional inelastic deformation of the sheet. This report evaluates the effect of this inelastic deformation on the chatter motion. The inelastic deformation of the sheet caused by the chattering motion produces a dynamic contribution to the roll force. The primary goal of this study is to determine this force and corresponding spring and damping coefficients. The formulation uses an asymptotic method valid for thin sheets. The material is rate sensitive and friction at the roll-sheet interface is proportional to the relative slip between the sheet and rolls. The main results are analytical expressions for the spring and dampening coefficients. They depend on the reduction, entrance gauge, roll bite length (or roll diameter), roll-sheet friction, processing rate, and material behaviour. The spring coefficient also depends on the entrance tension and slip parameter (or roll speed). The theory examines a linear reduction and a roll bite gap made by circular rolls. The qualitative behaviour of the spring and damping coefficients is rather insensitive to the nature of the reduction. An interesting prediction is negative damping or spring coefficient for some operating conditions. Control systems can use the spring and damping coefficients to predict deviations in the system stiffness or damping due to changes in the operating state of the mill.