Using a two dimensional winding model to predict wound roll stresses that occur due to circumferential steps in core diameter or to cross-web caliper variation

Abstract

This paper describes a model for estimating the stresses throughout a wound roll as a function of both radius and width. Width direction stresses are influenced by non-uniform winding tensions created through stacking layers of film with cross-web caliper variation. The model computes the effects of cross-web non-uniformity by dividing the roll into an arbitrary number of cross-web segments, treating each as a separate wound roll with its own winding tension, and tension taper. In order to compute tension, segment diameters are first determined. For this, a special model based upon stacking thick walled cylinders with orthotropic properties is used. Computations of the wound-in pressure and tension are then computed from any existing model that allows the compressive roll modulus to be a function of pressure.