Lateral Dynamics of a Moving Web With Geometrical Imperfection

Abstract

In this paper, an analysis is provided for the steering of a long, warped web that is transported between two rollers. The web is modeled using the Timoshenko beam theory, which admits small amounts of elastic bending and transverse shearing. Closed-form solutions are obtained for three commonly encountered forms of in-plane imperfection: (1) a splice, (2) a sinusoidal warpage, and (3) a cambered web with a constant radius-of-curvature. The fact that partial wrinkling in the web can affect the lateral dynamics is demonstrated in a simple example. This analysis reveals information on the phenomenon of weave regeneration and will be useful to designers of transport systems who wish to control the lateral tracking of webs with geometrical flaws.