The development of the probability theory of autogenous grinding ore

V.P. Malyshev; A.M. Makasheva; D.A. Kajkenov; Yu.S. Krasikova

doi:10.31643/2018/6445.34

Authors

V.P. Malyshev Chemical and Metallurgical Institute named after Zh.Abishev
A.M. Makasheva Chemical and Metallurgical Institute named after Zh.Abishev
D.A. Kajkenov Karaganda State University named after academician E. A. Buketov
Yu.S. Krasikova Chemical and Metallurgical Institute named after Zh. Abishev

DOI:

https://doi.org/10.31643/2018/6445.34

Keywords:

probability theory, ore, autogenous grinding, ball mill, autodestruction, math modeling, grinding bodies.

Abstract

The aim is to develop a general theory of autogenous grinding, which takes into account the impact of large pieces as the bodies destroying themselves, as well as grinding and grinded bodies. The most difficult process of mechanical destruction of substance – the process of autogenous grinding ore materials – is considered in the framework of probability theory, developed by authors. This theory includes probabilistic exposure of concentration, steric, activation and frequency factors and the likeness of the kinetics of consecutive irreversible reactions of unlimited order exact solution of the system of differential equations for the rate of destruction and accumulation of each fraction. Created a general mathematical model, which takes into account the impact of large pieces as autodisable, grinded and grinding bodies. Calculations based on the developed mathematical model theoretically substantiate, known from practice, formation of “pieces of critical size” which is not able to serve either as grinding or as grinded bodies and to be withdrawn from the process. Thanks to the “relay” transfer of functions of the grinding bodies from the larger fractions to the forming as a result of their self-destruction and the destruction is formed a more uniform distribution of fractions, characteristic for these mills. Therefore, probabilistic model of autogenous grinding can use to analyze, forecast and manage of the process.

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Author Biographies

V.P. Malyshev, Chemical and Metallurgical Institute named after Zh.Abishev

Doctor of Technical Sciences, Professor, Academician of the International Academy of Informatization and of the Kazakhstan National Academy of Natural Sciences, Head of Laboratory of entropy-information analysis of Chemical and Metallurgical Institute named after Zh. Abishev.

A.M. Makasheva, Chemical and Metallurgical Institute named after Zh.Abishev

Doctor of Technical Sciences, Professor, Chief Researcher of Laboratory of entropy-information analysis of Chemical and Metallurgical Institute named after Zh. Abishev, Academician of the International Academy of Informatization.

D.A. Kajkenov, Karaganda State University named after academician E. A. Buketov

Specialist of testing laboratory of engineering profile “Physico-chemical methods of investigation”, Master of Karaganda State University named after academician E. A.Buketov.

Yu.S. Krasikova, Chemical and Metallurgical Institute named after Zh. Abishev

Master, Junior Researcher of Laboratory of entropy-information analysis of Chemical and Metallurgical Institute named after Zh.Abishev.

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