Modeling Periodic Defects Under Zigzag Scanning in Roll-to-Roll Manufacturing

Roll-to-roll (R2R) processing is a critical technique widely used in flexible electronics, sensors, solar cells, and display devices, where sheets or films are transported between rollers. A major challenge in R2R processing is maintaining the uniform thickness of the material. Roll eccentricity and back roll irregularities are factors that can lead to periodic defects in thickness, significantly degrading product performance, lifespan, and quality. Despite their importance in R2R processing, it has received limited attention in the existing literature. This paper proposes a Spatial Fourier Series Model (SFSM) designed to model periodic defects resulting from roll eccentricity and back roll irregularities under zigzag scanning, thereby addressing their impact on thickness uniformity. The model, leveraging a two-dimensional framework that integrates spatial and periodic signal components, enables the quantification of defects introduced by the back roll and characterizes their spatial distribution. The SFSM’s effectiveness is validated through a case study in an industrial setting. The proposed model approximated periodic defects across CD profiles with an accuracy of 81%, achieving a better performance among relevant studies. The simplicity and flexibility of the SFSM provide a universal solution for estimating periodic defects, reducing sensor costs, facilitating the design of subsequent controllers, and enhancing R2R manufacturing processes by improving thickness uniformity and product quality.