# Optimizing Roller Design to Improve Web Strain Uniformity in Roll-to-Roll Process
## 1 Introduction  
Flexible devices are part of the next generation of mobile technology and include foldable displays, wearable devices, and implant sensors. Their core component is a flexible printed circuit board (FPCB). To popularize flexible devices, FPCBs must be inexpensively and efficiently produced. However, conventional circuit board production methods (e.g., lithography and etching processes) cannot meet these requirements. Since the roll-to-roll process is suitable for the low-cost mass production of flexible substrates, researchers have attempted to develop the process for manufacturing flexible devices. In the roll-to-roll process, electronic circuit patterns are printed onto flexible substrates which are transferred between unwinding and rewinding rollers. These flexible substrates are composed of a polymer film, which is called a \"web\". In the actual process, the two unwinding and rewinding rollers, along with many additional rollers, generate the electronic circuit patterns. The electronic circuit patterns are printed on the web, inspected, and packaged. The space between any two rollers in the process is called the \"span\". The direction along the transfer is \"machine direction (MD)\". The direction perpendicular to MD is \"cross direction (CD)\". If the web has an uneven strain distribution in the span between these rollers, defects may form. In a given span, the two rollers at both ends exert tension on the web, generating a strain distribution in the web. To construct the electronic circuit pattern, multilayer printing is performed with severalspans. A register error is a relative positional error between the patterns of the previous and next spans. A register error occurs if the strain generated on the web in each span is uneven. Further, an uneven strain can cause pattern errors because there is a contraction difference between the two patterns in the center. Therefore, this non-uniform strain distribution causes a register error in the machine direction (MD) and cross direction (CD) of the web [1]. If the strain deviation in the MD is reduced and the distribution becomes more uniform, this error is reduced. Existing processes using rollers include rolling processes for metalworking and the rotary press printing process. In the rolling process, metal materials are reshaped to obtain a product. Thus, researchers have focused on plastic rather than elastic deformation [2; 3]. In the rotary printing process, characters or images are printed on a paper substrate. Researchers have attempted to minimize the register error to improve print quality; however, micro-scale printing precision is not required [4; 5; 6]. The electronic circuit pattern created in the roll-to-roll process is finely detailed; therefore, micro-scale printing precision is important for multilayer printing. A register error due to a shape error or misalignment of the pattern creates defects in the electronic circuit. Thus, a great deal of research has focused on reducing register errors in order to manufacture high-performance electronic components. [PERSON], [PERSON] et al. measured the register error using a high-resolution microscope camera and studied motion-base calibration using the micro-movement of the print head [7]. [PERSON], [PERSON] et al. conducted and compensated for the register error by controlling the span length and tension using an active motion-based roller between the upstream and downstream printing rollers [8]. [PERSON], [PERSON] et al. compensated for the register error using the phase shift of the upstream roller and continuously compensating the register error of the downstream roller through PID control [9]. [PERSON], [PERSON] et al. reduced the register error by locally releasing tension on the web locally through a successive chucking system, clamping unit, and guide roller descending [10]. [PERSON], [PERSON] et al. reduced the strain on the web by controlling the tension using a dancer roller to reduce the web shrinkage that occurs during the drying process [11]. [PERSON], [PERSON] et al.