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 ac-counts 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 develop-ment 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 concen-tration or singularity existing there, are also discussed