ArticleName |
Probabilistic model of material grinding as a self-organization operator and process attractor |
ArticleAuthorData |
Zh. Abishev Chemical-Metallurgical Institute, Karaganda, Republic of Kazakhstan:
V. P. Malyshev, Head of Entropic-Information Analysis Laboratory, e-mail: eia_hmi@mail.ru A. M. Makasheva, Chief Researcher of Entropic-Information Analysis Laboratory Yu. S. Zubrina, Master's Degree Student of Karaganda State Technical University, Laboratory Assistant of Entropic-Information Analysis Laboratory
JSC “National Scientific-Technological Holding “Parasat”, Astana, Republic of Kazakhstan:
N. S. Bekturganov, Chairman of Board |
Abstract |
In the recent years, grinding process has been theoretically represented by the development of cell models and the models, based on the use of the “maximum entropy method”. However, the recent material grinding investigations show the regularities, requiring the experimental identification of functional parameters, with any private parts of process implementation. The authors made a complete probabilistic model of the grinding process, which takes into account the consecutive probabilistic events of rapprochement, contact and interaction between the grinded and grinding bodies, as well as the consistent transformation of the major fractions into the small ones. Other researchers have also started to use this model. The randomized state of the system of grinded and grinding bodies during the ball mill operation in the tumbling regime allows to assimilate the grinding process to the kinetics of molecular collisions based on the generalized probabilistic expression of the process rate (V): V = Z P_{conc} P_{st} P_{а}, using the frequency (Z), concentration (P_{conc}), steric (P_{st}) and activation (P_{а}) factors. Each factor is determined by the probability of the corresponding elementary event. Accounting of the rates of decrease and accumulation of each fraction, according to the kinetics of consecutive irreversible reactions (in relation to the grinding process), leads to the integral model of the process. This shows the possibility of calculation of a share of each fraction in the process with the corresponding decrease of fraction mixture entropy, pointing on selforganization of crushing in randomized system. Application of probabilistic model to the description of industrial mill operation testifies to its sufficient adequacy in the conditions of accounting of the whole set of influencing factors. |
References |
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