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Two problems of foil consumption optimization for cylindrical bales wrapping

Stankiewicz A., Nowak A., Stępniewski A.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

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2018

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Vol. 7, No 1

97--106

EN

The paper describes two optimization problems for minimization of the consumption of the stretch foil (film) used for wrapping bales to impart bale stability. The first problem consists in the optimal design of foil width. The foil consumption per unit of the bale volume index is used as a measure of foil expenditure. In the second problem a fixed volume of the bale silage must be optimally wrapped by stretch foil and the optimal bale dimensions (diameter, height) are sought out. Mechanical properties of the sealing foil characterized by its Poisson ratio are taken into account. The paper presents optimal and suboptimal solutions to both the problems. The formulas for computing optimal and near-optimal foil width and bale size dimensions are given and estimations of the solution errors are discussed. Simulation results are presented and analyzed for exemplary bale silage.

2

The effect of additional foil wraps on the tightness of the packaging of bales

Stępniewski A. A., Nowak J.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

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2018

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Vol. 7, No 1

145--150

EN

The work analyzed the effect of additional wraps on the number of layers and thus the tightness of the material under protection. It was assumed that all the overlaps of each two consecutive wraps are the same, and each additional wrap causes the same increase of all the tabs. The mechanical properties of the film and its dimensions were taken into account. We have written our own simulation program that allows us to calculate the percentage of a given number of film layers on the side of the bale and the visualization of the distribution of layers in its cross-section. Calculation examples have been provided. Conclusions and suggestions resulting from the obtained simulation results have been formulated.

3

On the mathematical modelling and optimization of foil consumption for cylindrical bale wrapping

Stankiewicz A., Stępniewski A. A., Nowak J.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

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2016

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Vol. 5, No 3

101--110

EN

Aspects of mathematical modelling of wrapping round (i.e. cylindrical) bale related to the optimization of foil consumption are considered for individual bales of agricultural materials wrapped in plastic foil. The article details the mathematical description of bale wrapping, while also identifying both some solved problems and a few open ones, which can be solved to optimize the foil consumption. Mechanical properties of the sealing foil characterized by its Poisson ratio, arbitrary foil and bale size dimensions and overlapping width of subsequent wrapped foil strips were taken into account. After providing a basic understanding of how the foil is consumed in the course of wrapping process, the mathematical model for determining the number of entire foil wrappings is determined. Next the results of mathematical analysis are used for optimization purposes. The foil consumption per unit of the bale volume index is used as a measure of foil expenditure. Two problems of foil consumption optimization are stated and solved. The formulas for computing the optimal foil width and optimal bale size dimensions are derived and estimations of the solution errors are given. Computational results are presented and analyzed for exemplary bale silage.

4

Analytical model of foil consumption for cylindrical bale wrapping

Stępniewski A., Nowak J., Stankiewicz A.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

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2016

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Vol. 5, No 2

99--104

EN

The work presents an algorithm for the calculation of the consumption of stretch foil used to wrap cylindrical bales of fodder in order to isolate the fodder from the air and other external factors. Mechanical properties of the foil, its arbitrary dimensions and any overlapping width of subsequent wrapped foil layers ware taken into account. A simulation program was written that allows to compute the number of foil layers in the bale lateral surface as a function of the width of the foil, the angle of the bale's rotation around its axis and the number of wrappings. The computer program contains graphical module which allows visualization of geometry of the distribution of subsequent foil strips and the arrangement of foil layer in a bale cross-section. The length and surface area of the foil taken from the roll are computed for different variants of the wrapping process. The computational example is presented for two geometrically different ways of wrapping and different initial widths of the foil. Conclusions and suggestions were formulated as a result of the simulation.