STOCHASTIC MODELING OF SEPARATION PROCESS ON COMBINE CLEANING SHOE

This paper describes a comprehensive mathematical model of grain separation process over the sieve length of combine cleaning unit. The model is based on: • Deriving the characteristic function associated to a stochastic process regarded as a continuous space bi-dimensional random walk in the limit of small jumps; • Deriving an expansion for the Fokker-Planck equation, that describes the physical laws of grain segregation and diffusion within longitudinal cross-section of material layer on the sieve; • Using two parameters obtained by fitting the theoretical curve to experimental data of cumulative separated grain. The model emphasizes the functions of un-segregated grain, separable segregated grain and separated grain fractions over the length of the sieve. A bi-dimensional function of vertical grain distribution within any longitudinal cross-section of material layer has been derived. The developed model has been validated with reliable experimental data. The nonlinear regressions analysis are characterized by a coefficient of determination R2 = 0.99 ÷ 1.00. Separation loss is also predicted. Graphs of above-mentioned functions are displayed. The comparison of predicted and experimental data qualifies and quantifies the theory certainty. This model represents an incremental progress toward the more complete understanding of harvesting combine processes and a friendly tool for designers and researchers, which want to simulate and optimize these processes.