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Two-dimensional behavior of a thin web on a roller

Brown, Jerry
A web on a roller is usually modeled as a one-dimensional belt in a state of pure circumferential stress. However, most of the important problems in lateral web behavior involve shear stress and cross web stress. Furthermore, these stresses, as well as machine direction stress, are often nonuniform. Some work has been done for particular cases using continuum mechanics software. But there are no two-dimensional models that capture the relevant physical principles in a way that can provide a general basis for calculation and insight. Some of the issues that might be addressed with such a model are:
Localized loss of traction due to nonuniform stress
The amount of spreading that can be supported on a concave or curved roller
Strain transport into the next span
Interaction of spans due to loss of traction on part of the roller
In this paper, the two-dimensional equations of equilibrium for a thin web on a roller are developed from first principles, taking into account cylindrical roller geometry and the effects of friction between the web and roller. The questions listed above are explored by experiment and FEA analysis. A method is developed for determining the conditions that must be met at the entry to a roller to insure that entry span stresses - machine direction, cross web or shear - do not cause slipping. Conditions for both nonuniform webs and nonuniform rollers are treated.