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1. EFFECT OF THE PROCESSING AND TRANSPORT PARAMETERS ON MOLD FILLING IN ROLL-TO-ROLL NANOIMPRINT LITHOGRAPHY

   Gomez-Constante, J.P; Pagilla, P.R; Rajagopal, K.R (June 2019, Proceedings of the Fifteenth International Conference on Web Handling)

   Based on a model developed for the roll-to-roll imprinting process, this paper describes the relative importance of the processing, material properties, and transport parameters in Roll-to-Roll Nanoimprint Lithography (R2RNIL). In particular, the model is utilized to investigate the effect of web speed, fluid film thickness, viscosity, stress relaxation time, mold pattern geometry and size on mold filling. Based on a typical imprint roller configuration, kinematic analysis, and the conservation laws from classical mechanics, the behavior of the squeezing of a viscoelastic fluid film into a rigid mold cavity is described. Further, the effect of web speed, fluid film thickness and key rheological parameters, namely the Weissenberg and Deborah numbers, are discussed. These dimensionless numbers are typically employed to quantify viscoelastic effects in fluid flow problems. The effect of other scale-sensitive and geometric parameters, such as the capillary number and pattern width-to-height ratio, on the imprint process is also discussed. Numerical simulations are provided to corroborate the discussions and to quantify the relative importance of the parameters. 

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2. Mechanics of Cambered Web Belts on Aligned Rollers

   Shi, J.; Smith, J.; Markum, R.; Good, J.K. (June 2019, Proceedings of the Fifteenth International Conference on Web Handling)

   The lateral deformations of webs in roll-to-roll (R2R) process machines can affect the quality of the manufacturing process. Webs can enter a cylindrical roller normally if the forces required to sustain normal entry and do not exceed the available friction forces. Webs with simple non-uniform length variation across their width (camber) will steer toward the long side, affecting the steady state lateral deformation and hence registration. Most previous studies have focused on tests and modeling a cambered web span in a free span between two rollers. Often these studies assume some displacement and slope boundary conditions are known and seek the remaining condition(s) that would dictate the steady state lateral deformation of the cambered web in the free span. In many spans in a process machine there may be no known boundary conditions and no steady state deformation of the cambered web. The web may travel toward the long side continually from one web span until the next until a web guide attempts to return the web to an acceptable lateral location in the process machine. The simplest case of multiple span cambered web lateral behavior is that of a cambered web belt transiting two aligned rollers which is the focus of the current work. Dynamic simulation (Abaqus/Standard) has been used to better understand the response of cambered webs under tension that has been witnessed in tests. 

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3. A Review of Advanced Roll-to-Roll Manufacturing: System Modeling and Control

   https://doi.org/10.1115/1.4067053  

   Martin, Christopher; Zhao, Qishen; Patel, Anjali; Velasquez, Enrique; Chen, Dongmei; Li, Wei (April 2025, Journal of Manufacturing Science and Engineering)

   Abstract Roll-to-roll (R2R) manufacturing is a highly efficient industrial method for continuously processing flexible webs through a series of rollers. With advancements in technology, R2R manufacturing has emerged as one of the most economical production methods for advanced products, such as flexible electronics, renewable energy devices, and 2D materials. However, the development of cost-effective and efficient manufacturing processes for these products presents new challenges, including higher precision requirements, the need for improved in-line quality control, and the integration of material processing dynamics into the traditional web handling system. This paper reviews the state of the art in advanced R2R manufacturing, focusing on modeling and control, and highlights research areas that need further development. 

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4. Spatial-Terminal Iterative Learning Control for Registration Error Elimination in High-Precision Roll-to-Roll Printing Systems

   https://doi.org/10.1115/MSEC2023-106259  

   Wang, Zifeng; Jin, Xiaoning (June 2023, American Society of Mechanical Engineers)

   Abstract Roll-to-roll (R2R) printing techniques are promising for high-volume continuous production of substrate-based electronic products, as opposed to the sheet-to-sheet approach suited for low-volume work. However, one of the major challenges in R2R flexible electronics printing is achieving tight alignment tolerances, as specified by the device resolution (usually at micrometer level), for multi-layer printed electronics. The alignment of the printed patterns in different layers, known as registration, is critical to product quality. Registration errors are essentially accumulated positional or dimensional deviations caused by un-desired variations in web tensions and web speeds. Conventional registration control methods rely on model-based feedback controllers, such as PID control, to regulate the web tension and the web speed. However, those methods can not guarantee that the registration error always converges to zero due to lagging problems. In this paper, we propose a Spatial-Terminal Iterative Learning Control (STILC) method combined with PID control to enable the registration error to converge to zero iteratively, which achieves unprecedented control in the creation, integration and manipulation of multi-layer microstructures in R2R processes. We simulate the registration error generation and accumulation caused by axis mismatch between roller and motor that commonly exists in R2R systems. We show that the STILC-PID hybrid control method can eliminate the registration error completely after a reasonable number of iterations. We also compare the performances of STILC with a constant-value basis and a cosine-form basis. The results show that the control model with a cosine-form basis provides a faster convergence speed for R2R registration error elimination. 

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5. Spatial-Terminal Iterative Learning Control for Registration Error Elimination in High-Precision Roll-to-Roll Printing Systems

   Zifeng Wang, Xiaoning Jin (September 2023, Proceedings of the ASME 2023 18th International Manufacturing Science and Engineering Conference)

   Roll-to-roll (R2R) printing techniques are promising for high-volume continuous production of substrate-based electronic products, as opposed to the sheet-to-sheet approach suited for low-volume work. However, one of the major challenges in R2R flexible electronics printing is achieving tight alignment tolerances, as specified by the device resolution (usually at micrometer level), for multi-layer printed electronics. The alignment of the printed patterns in different layers, known as registration, is critical to product quality. Registration errors are essentially accumulated positional or dimensional deviations caused by un-desired variations in web tensions and web speeds. Conventional registration control methods rely on model-based feedback controllers, such as PID control, to regulate the web tension and the web speed. However, those methods can not guarantee that the registration error always converges to zero due to lagging problems. In this paper, we propose a Spatial-Terminal Iterative Learning Control (STILC) method combined with PID control to enable the registration error to converge to zero iteratively, which achieves unprecedented control in the creation, integration and manipulation of multi-layer microstructures in R2R processes. We simulate the registration error generation and accumulation caused by axis mismatch between roller and motor that commonly exists in R2R systems. We show that the STILC-PID hybrid control method can eliminate the registration error completely after a reasonable number of iterations. We also compare the performances of STILC with a constant-value basis and a cosine-form basis. The results show that the control model with a cosine-form basis provides a faster convergence speed for R2R registration error elimination. 

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