Mathematical Modeling of Kinetics and Optimization of Grain Material Separation Processes on Sieve Classifiers
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Mathematical Modeling of Kinetics and Optimization of Grain Material Separation Processes on Sieve Classifiers F. G. Akhmadiev1* , R. F. Gizzyatov1** , and I. T. Nazipov1*** (Submitted by A. M. Elizarov) 1
Kazan State University of Architecture and Engineering, Kazan, Tatarstan, 420043 Russia Received January 16, 2020; revised March 19, 2020; accepted March 21, 2020
Abstract—A mathematical model of the kinetics of thin-layer separation of granular materials on multiple-deck sieve classifiers was constructed based on the theory of Markovian processes. We identified the kinetic models using the oversize residues from sieves. The problem of optimization is formulated and solved in a multi-criteria formulation, where the criteria are selected device performance and the separation efficiency on its sieves. DOI: 10.1134/S1995080220070070 Keywords and phrases: kinetic model, optimization, separation, granular material, sieve probability.
1. INTRODUCTION The most common type of technological equipment for the separation of granular materials into specific fractions by size is sieve classifiers. Despite the obvious achievements in the quantitative description of the processes of separation of granular materials [1–6], which was facilitated by the development of mathematical modelling and the widespread use of computer technology, a description of these processes taking into account discreteness, stochastic and their optimal design are an urgent task of chemical technology and other industries. Mathematical models of the processes that occur during the separation of granular materials are the basis for the optimal design and technological calculation of the sieve classifier. The optimal values of the operating and design parameters of the classifier are determined from the solution of some optimization problems in a single-criterion or multi-criteria problem statement [7]. As optimization criteria, productivity, efficiency, and other economic indicators can be considered. The aim of the work is to study and build a mathematical model of the kinetics of the processes of separation of granular materials on sieve classifiers and their optimization based on the constructed models. 2. MATHEMATICAL MODEL Multilevel sieve classifiers are often used for the separation of granular materials by size. The particle diameter of the granular material is considered as a one-dimensional random variable and its dispersion is determined by the particle size distribution density W (d). It is required to divide the source material into fractions by size (dj , dj+1 ). Then the number of particles of the j-th fraction is determined by the expression dj+1
ndj =
W (d)dd. dj
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E-mail: [email protected] E-mail: [email protected] *** E-mail: [email protected] **
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The working process in sieve classifiers consists of three components of the vibrational motion: the movement of the material layer along the vibrating surface of the sieve, the movement of smaller particles to the surface of the sieve in the transverse direction and the
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