Mathematical model for ore particles movement along the vibrating table of a separator

Introduction. One of the vibration methods for processing loose finely dispersed mineral raw materials is the separation method on a vibrating surface. Separation occurs according to size, shape of particles, coefficient of friction, elasticity and other mechanical parameters of particles. The efficiency of the separation process depends on the correct choice of technological characteristics of the working equipment. To solve such problems, mechano-rheological models are widely used. The issues of rational construction of research models, based on the specific conditions of the considered dynamic processes, are important and relevant. Materials and methods of research. Identification of rational parameters and modes of operation of vibration equipment is carried out experimentally or by mathematical modeling of the vibration process of the interaction of particles of mineral raw materials with the vibrating body of the separator. Mathematical models are developed for the separated components of the original ore material, which allow studying the dynamics of the movement of particles of the material along the vibrating body of the separator, and as a result of the research, the most rational operating modes of the equipment are determined. Research results and discussion. The presented mechano-rheological system as a model of a material particle is designed to study the processes of interaction with the working body of the separator, a mathematical description of the model is given. The model makes it possible to study the influence of the mechanical properties of the material (elastic, dissipative, plastic) on the dynamics of the process of movement of a material particle along the working body of the separator. For different stages of particle motion, models of different levels of complexity are recommended, which greatly facilitates the solution of problems for the development of algorithms and software for the vibration process under study. This increases the efficiency of the practical application of mathematical models in determining the rational operating modes of the equipment and evaluating the effectiveness of the vibration separation process. Conclusion. To study the process of vibrational separation at various stages of the movement of particles of ore material, it is recommended to use mathematical models of different levels of complexity. A mathematical description of research models for various stages of the vibrational process is presented, the conditions for the transition between the stages of particle motion are given. Resume. Thus, the presented mathematical model makes it possible to study the dynamics of the movement of ore material along the working body of the separator, taking into account the main mechanical properties of the material. The use of the developed recommendations increases the efficiency of the practical application of mechanorheological models for research purposes.