# Research on the Transportation of Low-Strength Composites Sheets
## 1 Introduction  
The non-combustible sandwich panel is a new type of building material. Its core layer consists of less than 25 wt % polyacrylate and more than 75 wt % inorganic powders, which significantly enhances the safety of traditional sandwich panels. During the continuous manufacturing process of the core layer, fluidized state compound of polyacrylate and inorganic powder are transported through several machines to form solid-state panels [1]. As the majority of core panel precursors is inorganic powder, the material is extremely fragile and prone to crack, especially when being transported between rolls. The placement of the rolls and the sheet has an important influence on the tension in the sheet when the low-strength sheet is transported between rolls. To figure out the optimum placement, multiple experiments are needed at different transporting speeds and different polyacrylate portions in core panel. This trial and error method is inefficient since the non-contact measurement or processing equipment between the upstream and downstream rolls (as shown in Figure 1) is hard to move after installation. Previous studies on the roll-to-roll system mainly focused on the high-tension situation, most of which neglected the influence of the gravity, the shape and the relative position of rolls. Those approximations lead to the consequence that the track of the traveling materials is an approximately straight line. For example, the studies on the transverse vibrations of axially moving materials [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14] and studies on the transverse vibration control technique of axially moving materials [15; 16; 17; 18; 19; 20] all neglected the effect of gravity on the sheet and treated the traveling materials as tensioned. This means that the sag of the moving sheet is small compared to the distance between two rolls. The studies on the speed or tension control of axially moving materials [21; 22; 23; 24; 25; 26] assumed the moving materials as a 1D elastic beam and simplified the track of materials as a straight line. [PERSON] studied the low-tension, large-deflection shape of a transporting sheet hanging under gravity [27]. [PERSON] studied the gravity's influence on the stability of the travelling elastic beam using analytical and numerical methods [28]. However, they did not give the explicit expression of the relationship between positions of rolls and tension in the sheet. However, many novel composite materials (such as flame retardant composites) possess very low strength in processing [29; 30; 31] that even tension caused by gravity may cause the crack. Ignoring gravity is inappropriate for these novel materials. Moreover, engineering practice demonstrates that the size and position of rolls, as well as the sag of thin-sheet materials, influence the maximum tension in the moving thin-sheet material. Those parameters are also neglected in conventional studies. Since conventional models are not good at predicting thin-sheet material's behavior between rolls, a thorough study in tension distribution and motion state of thin-sheet materials between rolls is of great significance to the manufacturing of the non-combustible core panel and such low strength material sheets. In this study, we propose a model describing the steady-state behavior of low-tension moving thin-sheet materials. This model is developed from the previous studies on hanging materials [32; 33; 34; 35; 36; 37] and axially moving materials [19; 27]. We introduce a numerical method to calculate the shape of moving thin-sheet materials between rolls, taking into account the position and size of rolls. We further discuss how the sag of the thin-sheet material and placement of rolls influence the maximum tension in the thin-sheet material. Finally, we present approximate estimation methods to predict the optimum shape and the lower limit of the material's strength-density ratio (the Minimum Specific Strength) that two rolls can transport.