Behavior of a thin flexible twisted web
Abstract
In an earlier IWEB paper, "A New Method for Analyzing the Deformation and Lateral Translation of a Moving Web" [5], a nonlinear PDE model, suitable for use with low-cost FEA software, was developed. That work considered only in-plane deformation of a flat web. For a twisted web, something more is needed. Attempts to run a straightforward three-dimensional model on a 3D version of the FEA software were unsuccessful. It seems that adding an extremely thin third dimension causes serious convergence difficulties for the solver. Furthermore, the number of nodes increases dramatically, causing run times to increase from minutes to hours. More sophisticated or special-purpose FEA codes might be able to cope with the problems. However, one of the goals of this work is to develop methods that will run fast on low-cost software. So, attention is focused on creating a two-dimensional solution based on concepts similar to those used in large-deflection plate theory. This paper describes such a model. It incorporates the following features. 1. It allows analysis of the effects of rollers that have both in-plane and out-of-plane misalignment, including large rotations. 2. Since the equations of equilibrium for the in-plane stresses are the same as those used in the [5], this model is a natural extension of that work. 3. It incorporates the normal entry and normal strain boundary conditions for the downstream roller and can, therefore, include the effects of nonuniform webs and rollers. 4. Nonlinear definitions of stress and strain incorporate the effects of large rotations.
Citation
Brown, J. L. (2007, June). Behavior of a thin flexible twisted web. Paper presented at the Ninth International Conference on Web Handling (IWEB), Stillwater, OK.