Simplified Modeling of Lateral Behavior of Elastic Webs

Abstract

The lateral position of moving webs in the paper, plastics, and textile industries has to be corrected by means of web guiding systems. In the paper, the continuous two-dimensional web is approximated by a harp of non-interlinking threads wrapping a system of driven and non-driven rollers. Two important cases are investigated: A thread with tensile stress which is compared to bending stress and, vice versa, a thread with bending stress which is compared to tensile stress. Combining kinematic relationships and the continuity equation of continuum mechanics, nonlinear differential equations are found that are only weakly coupled. Linearization results in a first-order lag for a two roller system. The method will be extended to three and four roller systems in part 2.