Axisymmetric wound roll models

Abstract

Axisymmetric wound roll models provide the greatest definition of wound roll internal stresses to date. Simple one dimensional models can provide the user with radial profiles of pressure and circumferential stress as a function of radius. These models later evolved into pseudo two dimensional models where for the first time the impact of web nonuniformities such as thickness and web length could be studied across the web width. These models are described as pseudo two dimensional models because they were a series of the earlier one dimensional models. As such the outputs were limited to the pressure and circumferential stress outputs of one dimensional models but could also be used to predict the shape of the wound roll. Axisymmetric models provide outputs of pressure, circumferential stress, axial stress, and shear stress as a function of radius and cross machine direction location throughout a wound roll. As such these models are capable of describing more types of roll defects than all previous winding models. This paper will focus on the development of a new two dimensional axisymmetric wound roll model based upon a pre-stress formulation. The roll defects that axisymmetric models can be used to analyze will also be discussed.