Optimal Versus Equal Dimensions of Round Bales of Agricultural Materials Wrapped with Plastic Film—Conflict or Compliance?

Anna Stankiewicz

doi:10.3390/app112110246

Abstract

For the assumed bale volume, its dimensions (diameter, height), minimizing the consumption of the plastic film used for bale wrapping with the combined 3D method, depend on film and wrapping parameters. Incorrect selection of these parameters may result in an optimal bale diameter, which differs significantly from its height, while in agricultural practice bales with diameters equal or almost equal to the height dominate. The aim of the study is to formulate and solve the problem of selecting such dimensions of the bale with a given volume that the film consumption is minimal and, simultaneously, the bale diameter is equal or almost equal to its height. Necessary and sufficient conditions for such equilibria of the optimal bale dimensions are derived in the form of algebraic equations and inequalities. Four problems of the optimal bale dimension design guaranteeing assumed equilibrium of diameter and height are formulated and solved; both free and fixed bale volume are considered. Solutions of these problems are reduced to solving the sets of simple algebraic equations and inequalities with respect to two variables: integer number of film layers and continuous overlap ratio in bottom layers. Algorithms were formulated and examples regarding large bales demonstrate that they can handle the optimal dimensions’ equilibria problems.

Highlights

The demand to limit consumption of the film used to wrap bales of agriculture materials has been receiving increasing attention to reduce both costs and damage to the environment caused by plastic waste [1,2,3,4]
These studies were based on a rough model which describes film usage as a continuous function of bale dimensions, film width and a number of wrapped film strips; the model did not take into account mechanical properties of the stretch film and the direct relation between the number of wrapped film strips and bale and film parameters
For given: bale volume Vb0, width b f of the film and its mechanical parameters v f, εl f, numbers of film layers pb, pu and the overlaps δ, k f b, k f, such that the applicability condition expressed by Equation (A4) holds, the optimal Hb∗ with order ε0 in the sense of Definition 2 bale diameter if and only if

Summary

Introduction

The demand to limit consumption of the film used to wrap bales of agriculture materials has been receiving increasing attention to reduce both costs and damage to the environment caused by plastic waste [1,2,3,4]. In [11], where the dependence of the film consumption on the bale diameter for the conventional wrapping technique was investigated, the analytical analysis showed that the larger the bale diameter is, the lower is the film consumption per unit of bale volume, which led to the conclusion that the use of the bale with the largest permissible diameter ensures the smallest film consumption These studies were based on a rough model which describes film usage as a continuous function of bale dimensions, film width and a number of wrapped film strips; the model did not take into account mechanical properties of the stretch film and the direct relation between the number of wrapped film strips and bale and film parameters

Objectives

Methods

Results

Conclusion