On the influence of roller misalignments on the web behavior during roll-to-roll processing

Roll-to-Roll (R2R) web transportation has been widely applied in numerous industrial material processes, such as nano-imprinting, continuous plasma deposition, paper rolling, and steel sheet forming. During a typical web transportation process, a pre-applied tensile stress is required for overcoming possible compressive buckling failure due to geometrical misalignments. However, the applied tensile stress must be limited to within the material yield strength. As a result, the relationship between the minimum required pre-tensile, geometrical misalignments, and material properties, must be clarified. The traditional approach to handle the relationship is based on a beam theory, which is not practical in typical wide web structures. Therefore, a modified formula for finding the required minimum tensile load is presented, using the finite element method and plate theory in this article. In addition, the effects of in-plane and out-of-plane misalignments of rollers on the web buckling are also investigated and quantified. It was found that web stress distribution is more sensitive to in-plane misalignment. On the other hand, although out-of-plane misalignment is not critical, it could trigger web buckling with the presence of an in-plane misalignment. Finally, material characterization to investigate the relationship among the allowable pre-tension, the misalignment angle, and the web width was performed. It was found that a misaligned web could carry less pre-tension than a perfectly aligned web. In addition, the situation deteriorates once the web width is further increased. These mechanical analyses, combined with specific material characterizations presented in this study, provide crucial information for improving the next generation of R2R applications.