Effects of concave rollers, curved-axis rollers and web camber on the deformation and translation of a moving web

Abstract

A new method of analysis is applied to three problems that have resisted detailed solution. These are:

1. Concave roller

2. Curved-axis roller

3. Cambered web (Curvature of the relaxed web along its longitudinal axis)

In the first two of these, the primary interest is the stress/strain field near the downstream roller. In the third, the primary interest is the lateral translation. In all cases it is useful to have information on the stress field throughout the span to evaluate the potential for damage and wrinkling.

For each case, the normal strain and normal entry rules are used to develop downstream boundary conditions that can be used with a nonlinear version of the theory of elasticity for two-dimensional plane stress. A finite-element partial differential equation solver is used to develop steady-state solutions that include stress/strain fields and displacements throughout the spans.

Along with specific numerical examples, there is a discussion of implications for such things as wrinkling, spreading, lateral translation and overstressing.

A major advantage of the new method is that it provides a new way of looking at problems that will facilitate other approaches to modeling. This is illustrated by developing a beam theory model for cambered webs.