Modeling and Analysis of Web Span Tension Dynamics Considering Thermal and Viscoelastic Effects in Roll-to-Roll Manufacturing

Abstract

A governing equation for web tension in a span considering thermal and viscoelastic effects is developed in this paper. The governing equation includes thermal strain induced by web temperature change and assumes viscoelastic material behavior. A closed-form expression for temperature distribution in the moving web is derived, which is utilized to obtain thermal strain. A model for web tension in a multispan roll-to-roll system can be developed using this governing equation. To evaluate the governing equation, measured data from an industrial web process line are compared with data from model simulations. Since the viscoelastic behavior of web materials is affected by the web temperature change, elevated temperature creep, and stress-relaxation experiments are conducted to determine the temperature-dependent viscoelastic parameters of the utilized viscoelastic model. Comparisons of the measured data with model simulation data are presented and discussed. An analysis of the web tension disturbance propagation behavior is also provided to compare transport behavior of elastic and viscoelastic materials.