Cold Strip Shape Estimation Using Plate Vibration Analysis

Abstract

In cold strip mills, strip is usually rolled under longitudinal high tension, where the strip wavy shape is not visible directly because of the longitudinal elastic deformation.
To detect the strip shape indirectly during rolling, the strip vibration principle has been applied, and various kinds of shape meters have been developed so far. To clarify the measuring principle of these shape meters precisely, the authors carried out the analysis for the strip vibration by solving the differential equation strictly. Here transverse tension distribution which corresponds to the implicit strip shape is perturbed, and the state of strip vibration can be figured out by using perturbation method. As a result, the relation between the strip vibration and its shape is clarified. It is concluded that the strip shape can be estimated through the measured vibration amplitude distribution by applying some restricted outer force onto the strip.