Simplified Mathematical Model of Lateral Behavior of Moving Elastic Webs

Abstract

The lateral position of a moving web in production lines for the paper, plastics and textile industries has to be corrected by means of web guiding systems. In Part 1 the continuous two- dimensional web has been approximated through a harp of non-interlinking threads in a system of two driven rollers. Two important cases have been investigated: A thread with predominant tensile stress and a thread with predominant bending stress. The thread with predominant tensile stress revealed to be a first-order lag with the same time constant as is characteristic for the longitudinal web dynamics. The thread with bending stress exhibits a smaller time constant and a smaller reachable displacement relative to a guiding roller. In the following Part 2 a three and a four roller system is investigated, the latter one being investigated only in the case of predominant tensile stress of the thread. In these industrial systems non-driven guiding rollers are assumed which are located between driven rollers.