General model of lateral web dynamics between two reels

Abstract

A flexible web unavoidably deviates from its prescribed (linear) path during processing. The lateral web dynamics can be caused by tilt of rollers, web defects, off axis motion of the reels and other factors. In this work we present a generalized model of web transport between two reels, supported by numerous rollers. The mechanics of the web between the two reels is represented by a single partial differential equation, hence coupling of web-spans or lack thereof can be predicted. Web-to-roller interaction is modeled by assuming that tape sticks to the roller surface. The results of this general model are compared to the well-known model by Shelton and Reid (SR), which is applicable in the free span between two rollers. Good agreement between the present model and SR-model is found when the upstream free-span is stiff (or the downstream free-span is compliant), when the wrap angle is large and lateral bending rigidity is high. The present model otherwise predicts coupling of the mechanics of the free spans. The model is flexible to consider a variety of imperfections related to the web geometry and the path components. The lateral motion of a weaved web which is transported on a path with tilted rollers is simulated. The amplitude and the direction of the scatter wind due to this effect are predicted. In general the model shows that the coupling between the upstream and downstream web spans around a roller should not be neglected

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