Minimizing the Consumption of Stretch Film for Wrapping Cylindrical Baled Silage Using the IntelliWrap Method

Abstract

HighlightsA complete mathematical model describes stretch film consumption for wrapping round bales using IntelliWrap.An algorithm is presented for optimal, in the sense of minimal, film usage based on film width selection.A solution is presented for selecting the optimal width of commercially available film.Optimal film width guarantees up to 10% savings in film usage, especially for not more than ten film layers.Abstract. The new IntelliWrap method is considered for wrapping round bales of agricultural materials using two different widths for the contact area between adjacent film strips for the bottom and upper film layers. A complete mathematical model describing the consumption of film for round bale wrapping is derived, which captures bale and film dimensions, the mechanical properties of the film as described by Poisson’s ratio and the unit deformation, the overlaps between adjacent film strips, and the numbers of bottom and upper film layers. The surface area of the film used to wrap the bale is used as a measure of film usage. To reduce film usage and protect the environment, the problem of achieving optimal, in the sense of minimal, film usage is mathematically formulated and solved. The original continuous optimization problem with a non-continuous goal function is reduced to solving two simpler integer programming tasks. An algorithm for selection of the optimal film width is proposed and numerically verified. If the common 50%, 66.7%, and 75% overlaps are used and the film width is optimal, then minimal film usage is achieved regardless of the composition of the bottom and upper film layers. In addition, the problem of choosing the best commercially available film width to guarantee minimal film usage is stated and solved. However, only near-optimal film usage is achieved for appropriately selected, commercially available film widths. Results of numerical experiments demonstrate that the relative errors for such approximations of minimal film usage do not exceed 0.1%, while inappropriate selection of the film width may result in increased film usage with almost 10% relative error, which indicates that up to 10% film cost savings can be achieved when the film width is optimally selected according to the proposed approach, especially when the number of layers is not more than ten. Keywords: Baled silage, Mathematical model, Mixed wrapping, Optimization, Stretch film consumption.