Application of dimensional analysis to roll-to-roll manufacturing systems

Abstract

In this paper, we investigate the application of dimensional analysis for R2R systems. First, dimensional form of governing equations for web tension and speed are transformed to non-dimensional form using dimensional analysis, and discussions are provided to highlight their usefulness in further analysis and design of R2R systems. Second, two specific cases are considered to show application of dimensional analysis to R2R systems: analysis of an accumulator and redesign for capacity scaling and scaling of process and controller parameters of an example R2R system for a change in the web material. In the first case, we provide results from model computer simulations to evaluate the method, and in the second case, results from experiments conducted on a large R2R platform are presented and discussed. Further, frequency response experiments are conducted for a subsystem of web spans and rollers for different materials to also evaluate the results of applying dimensional analysis to R2R systems.