Open AccessFRACTURE KINETICS OF THE MATERIAL PARTICLES IN DISINTEGRATOR USING STATISTICAL APPROACH
Author(s) -
И А Семикопенко,
И А Семикопенко,
S. S. Latyshev,
S. S. Latyshev,
V. P. Voronov,
V. P. Voronov,
Денис Беляев,
Denis Belyaev
Publication year - 2019
Publication title -
vestnik bgtu im. v.g. šuhova
Language(s) - English
Resource type - Journals
ISSN - 2071-7318
DOI - 10.34031/article_5da463e3b2fce8.88813745
Subject(s) - grinding , markov chain , constant (computer programming) , mechanics , particle (ecology) , materials science , range (aeronautics) , shock (circulatory) , mathematics , statistical physics , physics , computer science , composite material , statistics , medicine , oceanography , programming language , geology
Disintegrators are one of the types of equipment that has the ability to combine grinding, mixing and activation of materials of medium strength and hardness. The advantages of disintegrators are the ability to integrate into existing technological schemes and obtain a grinding product with a given particle size distribution, as well as the simplicity of the design. This article analyzes the kinetics of particle destruction in the inter-row spaces of the disintegrator grinding chamber. A diagram of the disintegrator grinding chamber is presented. The mathematical description of impact destruction of particles in the grinding chamber is considered in the framework of the inhomogeneous Markov process. An equation is presented that describes the change in the statistical quantity m (t) - the mathematical expectation. It has been suggested that the intensity of the Markov process ( ) is proportional to the frequency (ω) of rotor rotation multiplied by the time function f (t). This functional dependence is determined from the condition of the same interaction time 0 of the material particle in the inter-row spaces of the grinding chamber. If we assume that the probability of destruction of the particles of the material in the interaction with each shock element is constant, then the mathematical expectation value m (t) will be proportional to the number of particles n (t). The resulting relation (11) determines the law of change in the number of particles during the passage of each row of shock elements. The article derived formulas for determining the change in the number of particles in each inter-row space of the grinding chamber. The obtained relations (24) and (25) describe the kinetics of grinding material particles in the grinding chamber of the disintegrator in the framework of the statistical approach and make it possible to determine the relationship between the size of the initial particles and the size of the grinding product.