# Optimizing Roller Design to Improve Web Strain Uniformity in Roll-to-Roll Process
## 1 Introduction
used a register control algorithm to reduce the tension error [12]. [PERSON], [PERSON] et al. analyzed the deformation of the substrate in the ink transfer process using computational fluid dynamics (CFD) [13]. However, there are few studies that proactively correct the uneven strain distribution during the roller design stage prior to using a separate actuator or controlling the system. In the roll-to-roll process, the electronic circuit is printed on an arbitrary printing line in the CD. Therefore, the non-uniformity of the strain in the printing line is more important than the absolute value of the strain in the web. The strain is concentrated in the center of the CD and decreases toward both sides [14]. In addition, the strain deviation in the web is proportional to the web width and inversely proportional to the distance in the MD from the line where the roller and web touch. To reduce the register error, the strain deviation must not exceed a certain level within a single span; if the strain variation is great, the effective printing area is reduced, which limits productivity. In addition, the strain generated by tension during the process is recovered when the tension is disengaged after the process. This elastic change can also result in pattern error. If the strain distribution is uneven, the pattern is misaligned, resulting in an MD register error and poor print quality. In this study, we investigated the strain distribution in the flexible web in the roll-to-roll process. We sought to equalize the strain distribution in the MD on the printing line in the CD. To maintain high print quality and productivity, we proposed a new roller design that compensates the non-uniformity of the strain. Moreover, we developed a finite element (FE) model of a single-span roller and web and evaluated the compensation performance of the roller. To maximize the compensation, we optimized the design parameters of the roller using the design of experiments (DOE) methodology and analysis of variance (ANOVA). To minimize the strain deviation in the MD, we constructed the compensation roller with a convex roller core. The convex core was wrapped in a flexible material (rubber skin) such that the roller and web were always in contact. The outer diameter of the roller with the core and rubber is uniform. This roller configuration changes the contact stiffness along the CD on the web when the rollers and the web touch to compensate for the strain deviation. To optimize the compensation performance, we varied the thickness gradient of the rubber skin surrounding the roller, the total diameter of the roller, and the material properties of the rubber skin. The thickness gradient is the thinnest minus the thickest diameters of the core. Additionally, we considered interactions between the design parameters. From this analysis, we found that the strain of the web was most uniform in the roller with a barrel-type core with a thickness gradient of approximately 8 mm. This roller compensated the uneven strain distribution by approximately 48% with respect to the conventional roller.