Elastic buckling analysis of webs transported through rollers with misalignment

Emerging flexible electronics industries, such as solar cells and RFID tags manufactures, adopt the roll-to-roll (R2R) technology to improve their production efficiency. However, the flexible webs used in these fields wrinkle easily due to their tiny thickness and complex structure. Moreover, the webs are easily buckled if the rollers are misaligned. Therefore, it is desired to introduce an efficient method which can help to determine the critical buckling conditions of the webs when there is misalignment of rolls during their production. The current research presents a model based on the Kirchhoff plates buckling theory to determine the critical buckling misalignment and tension for webs transported through misaligned rollers. Webs are modeled as tensioned Timoshenko beams to obtain their stress distributions. The critical buckling conditions are calculated using the Galerkin method in the current research. Results indicate that the calculated critical conditions are close to the practical ones considering the parabolic variation of shear stress and the linear variation of bending stress. The results also indicate that the critical misalignment increases with the increase of the span ratio and tension, and critical misalignment decreases with the increase of the elastic modulus and web width. Moreover, the critical tension increases as the thickness and elastic modulus increases. The presented model provides a useful method to design and maintain R2R equipment.