Tension allocation in three dimensional wound roll

Abstract

Much consideration has been given to the relationship between web line tension and the stresses they induce in three dimensional wound rolls. Three dimensional wound rolls are distinctive because their radial and circumferential stresses are not uniform across their width. The non-uniformity results from numerous factors including Cross Machine Direction variations in the core stiffness, web thickness, or web line tension. Whatever the source, ultimately they produce variations in the radius across the width. In order to maintain material continuity, the incoming layer must therefore conform to a winding roll that is non-uniform in radius across its width. This is accomplished when the applied web line tension allocates across the width in proportion to the rail's local radius, as it converts into the outside layer's circumferential stress. The tension concentrates in high regions and disperses in the low regions. The model presented herein combines axisymmetric finite element analysis with a radius based tension allocation algorithm in order to simulate the actual stresses in a three dimensional roll. The circumferential stresses across the width are iteratively made to sum to the web line tension boundary condition. Comparison with experimental data from three dimensional rolls shows the model captures the essence of the roll behavior. It thus confirms the existence of the radius dependent tension allocation.