Stress Field in Finite Width Axisymmetric Wound Rolls

A model is developed for predicting the stress field within a wound roll of web material, in which the radial, circumferential, transverse, and shear stresses can vary in both the roll’s radial and cross-web (transverse) directions. As has been the case in previous wound roll stress analyses based on one-dimensional models, the present approach accounts for the anisotropic and nonlinear material properties of the layered web material, and the incremental manner in which the roll is wound. In addition, the present development accounts for arbitrary cross-sectional geometry and material of the core, and the presence of nonuniform tension across the web’s width during winding. The solution is developed through an axisymmetric, two-dimensional, finite element analysis which couples individual models of the core and layered web region substructures. The core’s stiffness matrix at the core-web interface provides a mixed boundary condition for the web region’s first layer. In several parameter studies, variations of the stress components in the roll’s radial and cross-width directions are discussed and compared with predictions of the simpler companion one-dimensional model. The character of the stress field at the web region’s free edges and along the core-web interface, and the possibility of stress concentration or singularity existing there, are also discussed.