Anna Stankiewicz, Janusz Nowak, Andrzej A. Stępniewski
Abstract. 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.
Key words: baled silage, cylindrical bale, mathematical model, stretch foil consumption, optimization.