Two-dimensional behavior of a thin web on a roller

Abstract

This paper presents a continuation of work described at the 2009 IWEB conference in a paper titled, "Two-dimensional Behavior of a Thin Web on a Roller" [1]. In that paper (which will be referred to as Part I), linear two-dimensional equations of equilibrium for a thin web on a roller were developed, taking into account cylindrical roller geometry and the effects of friction between the web and roller.

The 2009 paper focused primarily on behavior as the web enters onto a roller. A steady state condition necessary for existence of a stick zone at the entrance was defined. This is particularly useful for predicting slipping on concave and curved-axis spreader rollers.

In Part 2, the following issues are considered.

1. Why is the steady state stick zone always at the roller entry regardless of the direction of micro slip? This is one of those innocent questions that stretches the mind. A latex web, operating at large strain, is used to demonstrate that, in the absence of acceleration, the micro slip predicted by the capstan equation is a process that propagates upstream from the exit.

2. The lateral entry slip criterion developed in the 2009 paper [1] takes no account of the wrap angle and yet there are clearly situations where wrap matters - even when there is no MD tension difference across the roller. How does this happen?

3. Is there a capstan equation for shear?

The 2D + w model, described in a companion paper [2], presented at this conference, will be used to put the cylindrical model on a more rigorous mathematical foundation, using curvilinear coordinates and the nonlinear elasticity equations.