On the uniform distribution and optimal consumption of stretch film used for wrapping cylindrical baled silage

2019

Agriculture

Self Cite

A conventional method for wrapping round bales of agricultural materials by wrappers with a rotating table or with rotating arms is considered. In contemporary agriculture, the demand for minimal consumption of the film used to wrap bales is very high, in order to apply this method with lower cost and less damage to the environment. A combined model-based problem of such a design, focusing on the width of stretch film and the overlap between adjacent film strips that minimizes film consumption, was mathematically formulated and solved. It was proven that the complete set of optimal film widths is defined by a simple algebraic equation described in terms of film, bale, and wrapping parameters. The optimal overlap ratios were found to be irreducible fractions in which the dividend is the divisor minus one; however, only the first three factions, 1 2 , 2 3 , and 3 4 , are practically significant. Next, the robustness to disturbances in the functioning of an actual bale wrapper, which leads to overlap ratio uncertainty, is examined. It was shown that, unfortunately, the optimal film widths applied together with the optimal overlaps do not provide any robustness to overlap variations. To overcome this inconvenience, the problems of a choice of the best commercially available film width guaranteeing minimal film consumption or maximal tolerance on the overlap uncertainty were formulated and solved. A new algorithm for a robust design of wrapping parameters was developed, motivated, and numerically verified to achieve a trade-off between satisfactory robustness and low film usage. For the resulting wrapping parameters, near-optimal film usage was achieved; the relative errors of the minimal film consumption approximation did not exceed 4%. It was proven that for the overlap, slightly more than 50%, i.e., 51% or 52%, provides both optimality and robustness of the overlap over disturbances, which are ensured regardless of the number of film layers. Moreover, it was found that for these overlaps and for the commercially available film widths selected according to the algorithm, the film consumption was more than twice as small than the film usage for exactly 50% overlap, if the actual overlap was smaller than pre-assumed. Similarly, an overlap of slightly more than the commonly used 67% will result in about 30% to 40% reduction in film usage in the presence of unfavorable disturbances, depending on the number of film layers and wrapping parameters.

Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal and Robustly Optimal Consumption of Stretch Film Used for Wrapping Cylindrical Baled Silage

2019

Agriculture

Self Cite

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

Transactions of the ASABE

2020

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.

Optimization and Analysis of Plastic Film Consumption for Wrapping Round Baled Silage Using Combined 3D Method Considering Effects of Bale Dimensions

Transactions of the ASABE

2021

HighlightsSolved the problem of optimal design, in the sense of minimal film usage, of round bale diameter and height.Necessary and sufficient optimality conditions derived in the form of easy-to-solve cubic equations.Bales of a maximum volume achievable with an actual wrapper and of optimal dimensions ensure minimal film usage.Up to 10% savings in film usage if bale dimensions are optimally designed and wrapping parameters properly selected.Abstract. The combined 3D method is used for wrapping cylindrical bales of agricultural materials based on biaxial rotation of the film applicators. The demand for minimization of plastic film consumption keeps increasing, with the goal to save the environment, reduce plastic costs, and minimize wrapping time. Consequently, methods have been reported to solve the problem of optimal wrapping parameters for the conventional wrapping method. In this article, a model-based problem of such a design based on round bale dimensions (diameter and height) that minimizes film consumption for the combined 3D method is mathematically formulated and analyzed. The film consumption per unit of bale volume is used as a measure of film usage. Generally, it is difficult to find the optimal bale dimensions that minimize the original film usage index, due to the discontinuity of the index. Thus, near-optimal parameters, being as important as optimal parameters for engineering applications, are looked for. The problem of selecting near-optimal bale dimensions was constructed by minimizing the continuous lower bound of the original film usage index. The necessary and sufficient optimality conditions for near-optimal bale dimensions were established in the form of standard cubic equations, which can easily be solved using both analytical and numerical methods. Based on the optimality conditions, analytical and numerical analyses were performed of the influence of film width, pre-assumed bale volume, and numbers of bottom and upper film layers on the near-optimal bale dimensions and film usage. The results indicated that the near-optimal bale diameter and height, hereinafter called optimal, monotonically increase, while the optimal film consumption monotonically decreases, with increasing pre-assumed bale volume. Therefore, it is recommended to use bales of a maximum volume achievable with an actual wrapper and of optimal dimensions, i.e., diameter and height. The film width also influences the optimal bale dimensions and film usage: the wider the film, the smaller the minimal film usage. To confirm the effect of near-optimal bale design on film usage, the errors of the near-optimality were examined for four to sixteen film layers. The results of the numerical experiments demonstrated that for four to sixteen layers of film, there are compositions of the bottom and upper film layers for which the relative near-optimality errors do not exceed 0.01% whenever the optimal bale dimensions are used. Simultaneously, inappropriate selection of wrapping parameters may result in increased film usage, measured by mean relative errors of 1% to 9.5%, which means up to 10% film cost savings when the bale dimensions are optimally designed according to the proposed approach, and the wrapping parameters are appropriately selected. Keywords: 3D bale wrapping, Mathematical model, Minimal film consumption, Round bales, Stretch film usage.