New governing equation for web tension by employing a Neo-Hookean material model

Abstract

In this work, we derive a governing equation for web tension in a span by employing a Neo-Hookean material model that is applicable for transport of web materials under both small and large strains. This governing equation may be employed to study the evolution of tension within a span as well as propagation of tension variations from span to span as the web is transported in the machine. First, we find the stretch in a web span and relate it to web tension via a Neo-Hookean material model; the Neo-Hookean model is linear for small strain and nonlinear otherwise. Second, we conduct a dimensional analysis by defining several key coefficients that aid in grouping the machine and web material parameters separately in order to obtain a compact system of governing equations; this representation may be utilized to efficiently study the impact of web and roller properties on transport behavior.