Modeling of edge rolls defects

Based upon Hakiel's nonlinear orthotropic model for wound rolls, a model has been developed which takes into account widthwise variations in web properties. The model includes widthwise variations in the elastic modulus in the machine direction and it includes the effect of slack edges which is modeled as a widthwise variation in initial strain. Both variations can typically be found in paper and they are possible causes of soft outer edges on wound rolls. The variations are included by modifying the outer boundary condition in Hakiel's model. Calculations show that in-roll pressure decreases towards the edge if there is a slack edge or the elastic modulus has a lower value at the edge than elsewhere. This is consistent with empirical observations