A Study on the Symmetry-Breaking Bifurcation Phenomenon in Transportation of Low-Strength Composites Sheets by Rolls

Abstract

In the manufacturing of low-strength composites sheets, the symmetry-breaking bifurcation phenomenon may happen when the sheets are transported by rolls, which can lead to vibration and crack in the sheets. However, the mechanism and the conditions for this phenomenon has not been studied so far. In this paper, we propose a theoretical model to study the formation mechanism of the bifurcation phenomenon in a driven-idle-driven rolls system, and the critical length of the thin-sheets between rolls is obtained, above which the bifurcation will happen. Results show that the bifurcation occurs because the relationship between the lengths of the sheet between rolls and the tension caused by gravity in sheets is not monotonic, and the critical length is about 2.5 times the distance between the rolls. We also carry out experiments to verify the validity of the proposed model. This study is of great importance for the design of the multi-roll system to transport the low strength sheet materials, such as paper and composite sheets.