Vibrations and fluid structure interactions in web handling systems.

摘要

The works contained within this dissertation are related the manufacturing process known as roll-to-roll processing and a guide known as an air reverser. The process starts with a roll of thin, flexible sheet like continuous material. The material is unwound, from the roll and proceeds to undergo various manufacturing processes depending on the application (e.g newsprint, magnetic recording). As the web travels, a change of direction is achieved though a series of guides and rollers. A specific type of guide is known as an air reverser or a turn-bar. An air reverser is a porous, cylindrical drum used to create a cushion of air on which the web floats in order to reduce contact. In this dissertation three separete design issues, related to roll-to-roll manufacturing of webs are investigated.The aspect ratio of the web's longitudinal length versus web thickness during manufacturing makes the process highly susceptible to transverse vibration. A free vibration analysis of a thin tensioned web wrapped around a reverser was preformed. The governing equation of a tensioned plate wrapped around a cylindrical drum in a helical fashion was derived by energy method. An eigenvalue problem was formed using a two-dimensional beam model and a full three-dimensional finite element model. Design parameters such as tension, radius of cylinder, wrap angle, width of the web, lengths of non-wrapped web and helical wrap angle were investigated. It was seen that the free edges cause a frequency clustering of the lateral-modes about the dominant longitudinal-mode. It was also seen that the effectiveness of the plate-to-shell junction to act as a stiff support depends on problem parameters. Eigenmodes with same mode-shape numbers are observed in symmetric and anti-symmetric fashion about the center of the plate, for configurations with equally long unwrapped sections. The results also showed that the first natural frequency is reduced at large helical angles for the parameters studied.The fluid structure interaction between a web and air reverser has been previously modeled under the assumption that tension was constant and chord length does not change, but for large deflections this may not be the case. The questions to be answered here are: How does the chord length change under large deformation? How must the fluid mechanics be modeled under large deformation? For this study, to simplify the mechanics, the web and air reverser are modeled two-dimensionally or in an infinitely wide manner. Two numerical models were developed to answer these questions. The first fluid structure interaction model consists of an elastica beam coupled with a one-dimensional averaged flow model. The second fluid structure interaction model consists of an elastica beam coupled with a fluid model utilizing a two-dimensional Navier-Stokes model. The two models were verified experimentally using a scaled down version of an air reverser. A parameter study showed the flow near the edges of the fluid domain becomes more complex as clearance increases and/or wrap angle decreases. The length of the web was shown to vary as much as 1-2%, depending on floatation height and design parameters. Based on these results, in order to truly capture the FSI of a web and an air reverser, the fluid mechanics must be modeled two-dimensionally and chord length must be non-constant.The flow due to the air jets, pressurizing the web-reverser interface is subjected to fluid mechanical losses. These losses are typically lumped into a discharge coefficient whose magnitude varies between zero and one. In this work the fluid mechanics of a series of slot jets are modeled in three dimensions using computational fluid dynamics, and the results are compared to a series of experiments that mimic the modeled geometry. While, the hardware limitations did not allow for an accurate representation of a setup up with open lateral edges, the combined the experimental and CFD analysis were helpful in establishing the relationships for discharge coefficient. Global discharge coefficient was seen to decrease as the number of slot jets decreased and/or clearance increased.