Mathematical Modeling and Parameter Identification of Seed Motion During Density Separation in a Vibro-Pneumo-Fluidized Bed

Vibro-pneumatic separation is widely used to sort grain mixtures by density. However, optimizing operational regimes requires an accurate description of the dynamics of internal bed resistance. This study aims to develop a mathematical model of grain movement in a vibro-pneumo-fluidized bed based on simplified physical and mechanical concepts, and to identify its parameters using direct experimental data. Experimental studies on particle immersion kinetics were conducted to identify empirical medium resistance coefficients. Numerical simulations of spatial trajectories for coarse and fine seed fractions were executed using the 4th-order Runge-Kutta numerical integration using the computer algebra system. Model calibration confirmed that resistance anisotropy and inter-layer shear friction significantly affect longitudinal particle translation. The coupled influence of seed layer height and superficial airflow velocity on the target particle immersion time was evaluated using a two-factor central composite rotatable design (CCRD). The regression model proved that layer height exerts the dominant positive effect on the target particle immersion time. Simultaneously, increasing airflow velocity accelerates descent by enhancing the bed’s porosity. Validation demonstrated high convergence between numerical simulation trajectories and empirical CCRD data, with relative errors below 9.4 %. The derived response surface equations provide a reliable foundation for optimizing the operating regimes of vibro-pneumatic seed separators.