Modeling of Vibration Separation of Bulk Materials Based on the Theory of Random Processes

The separation of granular materials into specific fractions by size on sieve classifiers is a large and complex system both in terms of the separation process and hardware design. The separation process depends on many design and operating parameters, the shape and size of the sieve cells, the number of sieves, as well as the fractional composition, shape and particle size of the material to be separated, i.e. is a cyber-physical system (CPS). The key to CPS is the mathematical model of the separation process, which is used in the control system. A mathematical model of the process of separation of granular materials on sieve classifiers based on the theory of random processes is developed. As a random process, the linear particle density of the considered fractions on the sieve surface is considered and a system of stochastic differential equations is constructed for its determination. The obtained solutions allow us to determine the recovery coefficient and evaluate the separation efficiency. Based on the constructed mathematical model, the design and operational parameters of the classifier were optimized. The performance criteria and separation efficiency are considered as optimization criteria. All this allows us to control the process of separation of granular materials by determining the optimal values of the operating parameters of the classifier depending on the fractional composition, shape and size of the particles of the original material to be separated and its other characteristics.