Vibrations of Air-Coupled Web Systems

The prediction and measurement of vibrations of the low-frequency transverse modes of tensioned webs are of increasing interest for process monitoring, quality control, and process stability in roll-to-roll flexible hybrid and stretchable electronics manufacturing, nanomanufacturing, coated layer patterning, and other continuous manufacturing technologies. Acting as distributed added mass, the surrounding air significantly affects the frequency responses of taut thin webs in ambient roll-to-roll processes in comparison with those in vacuo. In this paper, we present closed-form, semi-analytical, universal hydrodynamic functions used to accurately predict the lowest symmetric and anti-symmetric transverse frequency response for any uniaxially tensioned web of arbitrary material and aspect ratio used in roll-to-roll processes. Experimental validation is carried out by using pointwise laser measurements of acoustically excited webs with different pre-tensions, web materials, and aspect ratios. These closed-form hydrodynamic functions provide roll-to-roll process designers a convenient way to predict the lowest frequencies of such web systems without the need to resort to computationally intensive methods; alternately, these functions allow for the quick identification of conditions when air-coupling is important to determine the web’s vibration response. The results presented herein are expected to help ongoing efforts to improve process monitoring and control in a variety of roll-to-roll continuous manufacturing technologies.