Modeling web traction on rollers

Abstract

When web tension changes between entry and exit on a roller, the tension change occurs in a slip zone in the last part of the wrap, whose size is given by the well-known Capstan or Belt equation. A method for modelling moving film over rollers has been developed using the Finite Element analysis program ABAQUS. This has been used to reproduce the analytical results for the angular extent of the slip zone, and the relative movement on the roller surface of the web as it extends or contracts.

Normally, the web has a non-zero Poisson's Ratio, and therefore a tension change is accompanied by changes in stress and strain in the transverse (width) direction. As a consequence, the relative motion of the web has a transverse component in the slip zone. ABAQUS has been used to model this, as an analytic solution is no longer possible. The slip zone is larger at the edges of the web, and transverse movement changes continuously from zero in the centre of the web to a value similar to that in the machine direction at the edge. The effect of varying web modulus, entry and exit tensions, and friction coefficient has been studied.

More commonly, machines use sequences of rollers and it is desirable to know how web tension varies from one span to the next. If the roller surface speeds differ by only a fraction of a percent, large tension differences can be set up resulting in slip on some of the rollers. A scheme for obtaining a self-consistent solution for the tensions has been developed. An elementary system of rollers driven at set speeds with controlled unwind and rewind tensions has been modelled analytically at steady state. Common drive strategies increase roller speed through the machine, but the simulation shows this can lead to slippage on many rollers and tensions greatly exceeding the unwind and rewind values midway through the roller sequence.