Extraction of Mathematical Correlations Applied in the Aerodynamic Separation of Solid Particles

Abstract

This article describes the methodology used to identify the mathematical equation that describes the correlations between the input and output parameters of an experiment. As a technological process, aerodynamic separation was chosen to represent the behavior of a solid particle within an ascending vertical airflow. The experimental data were used to identify two parameters, namely the average linear velocity and the angular velocity. The Table Curve 3D program was used to develop a mathematical equation describing the dependence between the input parameters (the shape and size of the solid particle, as well as the velocity of the airflow) and the monitored parameters. A pyramid-type analysis (following a filtering system, a general equation was determined from a large number of equations that characterize an experimental set mathematically) was designed in order to determine a single mathematical equation that describes the correlation between the input variables and those obtained as accurately as possible. The determination of the mathematical equation started with the number of equations generated by the Table Curve 3D program; then, the equations with a correlation coefficient greater than 0.85 were chosen; and finally, the common equations were identified. Respecting the working methodology, one equation was identified, which has for the average linear velocity, a correlation coefficient r2 of between 0.88-0.99 and 0.86–0.99 for the angular velocity.

Mathematical Perspectives in the Variable Texture Products Cutting Process

“…The mathematical equations that have been chosen to describe the cutting process have resulted from a methodology that can give the equations obtained a general character. An approach for processing the set of equations generated by Table Curve 3d software was created and designed for this purpose [35].…”