КИНЕТИКА РАЗРУШЕНИЯ ЧАСТИЦ МАТЕРИАЛА В ДЕЗИНТЕГРАТОРЕ В РАМКАХ СТАТИСТИЧЕСКОГО ПОДХОДА

D Belyaev,I Semikopenko,S Latyshev,V Voronov,В Воронов,Д Беляев,И Семикопенко,С Латышев

doi:10.34031/article_5da463e3b2fce8.88813745

Abstract

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.

Highlights

В данной статье дан анализ кинетики разрушения частиц в междурядных пространствах камеры помола дезинтегратора
This article analyzes the kinetics of particle destruction in the inter-row spaces of the disintegrator grinding chamber
The mathematical description of impact destruction of particles in the grinding chamber is considered in the framework of the inhomogeneous Markov process

Summary

Introduction

В данной статье дан анализ кинетики разрушения частиц в междурядных пространствах камеры помола дезинтегратора. Математическое описание ударного разрушения частиц в камере помола рассмотрено в рамках неоднородного Марковского процесса. Что вероятность разрушения частиц материала при взаимодействии с каждым ударным элементом является постоянной величиной, тогда величина математического ожидания m(t) будет пропорциональна числу частиц n(t). В статье выведены формулы для определения изменения числа частиц в каждом междурядном пространстве камеры помола.

Results

Conclusion