Model-Based Analysis of Stretch Film Consumption for Wrapping Cylindrical Baled Silage Using Combined 3D Method

Abstract

Abstract. A combined method for wrapping round (i.e., cylindrical) bales of agricultural materials based on biaxial rotation of the film applicators is considered in this study. A complete mathematical model is derived describing the consumption of the film used to wrap the bales that can be applied for film consumption estimation and design purposes. The bale and film dimensions, mechanical properties of the stretch film described by Poisson ratio and unit deformation, dimensionless relative overlap ratios determining the width of the contact area between adjacent film strips, and the assumed number of nominal film layers are taken into account. There is a need for good understanding of the influence of the wrapping process parameters on film consumption so that this method can be applied with lower cost and less damage to the environment. Based on the derived model, insight is obtained into the influence of the film width and wrapping parameters on film consumption when the combined method is used. Robustness on disturbances of the wrapping process, which lead to parameter uncertainty, is examined, and a simple algorithm for robust design of the overlaps of the bottom film layers is developed. The alternative method for wrapping round bales is the conventional method used by bale wrappers with a rotating table or with rotating arms. In this study, film consumption is compared between the combined and conventional wrapping methods. The combined wrapping method may offer substantial advantages in reduced film use compared with the conventional method. The potential reduction in film usage depends on the bale, film, and wrapping parameters. Without the proper choice of parameters, film consumption may be unjustifiably high. The model-based necessary and sufficient conditions for film usage reduction are obtained under typical assumptions concerning the bale and film parameters as well as the wrapping process parameters. No specific assumptions are made concerning the assumed number of film layers. The results concerning film usage reduction are written in the form of mathematical inequalities in terms of film, bale, and wrapping parameters. The stated conditions are useful for film consumption analysis and provide easy-to-use tools for analytical and numerical design of bale wrapping processes. A fast scheme is proposed for determining if the considered film parameters, together with the assumed number of film layers, could result in reduced film usage. For the algorithms, the executable and readable source codes are written in Matlab. Model-based simulations provide valuable insight into the underlying processes of film consumption and are shown to be useful for wrapping process design. To ensure a fair comparison, four to ten film layers are considered. Keywords: Baled silage, Film usage reduction, Mathematical models, Robustness, Stretch-wrap film consumption.