Fully nonlinear solution to the stresses inside wound rolls

Abstract

The Hakiel approach has been the accepted method for calculating stresses in wound rolls. It determines the stress in rolls by summing the stress induced by wraps of film applied to the roll surface. This approach is called linear superposition and it is strictly valid only for linear differential equations. The radial properties of film in a roll make the equations highly nonlinear and this presents a problem. Test results have supported the general accuracy of the Hakiel method. The method described here obtains a fully nonlinear solution for the stresses which occur during winding and any roll deformation that may occur afterward. The subsequent roll deformation can be a result of air leaking out or plastic deformation of the film both in the stack and in-plane directions. Only the case involving air leaking is presented. It reproduces the Hakiel approach for linearized conditions and differs to varying degree for the nonlinear cases. The approach presented here is more suitable for highly nonlinear cases and for making roll-aging calculations.