Русская версия English version

Justifying the choice of a dependence for the Tromp separation curve approximation

S.I. Shuvalov, S.S. Novoseltseva, V.P. Zhukov

Vestnik IGEU, 2018 issue 6, pp. 15—23

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Abstract in English: 

Background. Calculations for classifying powder materials by size are made based on the Tromp separation curve, a dependence of the probability of particle separation into small or large separation products on the particle size. The values of these probabilities are determined experimentally from the results of dispersive analysis of the separation products. Prognostic calculations are made based on various analytical dependences, approximating dependences, in which the agreement between the calculated and experimental data is achieved by an appropriate selection of the numerical coefficient values included in these dependences. The diversity of analytical dependences used to approximate experimental data makes it difficult to compare the results obtained by applying various types of classifiers. All this makes it necessary to analyse the dependences used and to select the optimal variants.

Materials and methods. The analysis has been done based on the available experimental data about the efficiency of dust separation in classifiers of different types by applying methods of statistical analysis.

Results. The paper considers nine variants of analytical dependences, most often used to describe separation curves. According to the results of separating several materials in different types of classifiers by statistical methods according to the Fisher criterion, we have evaluated the adequacy of approximation of the separation curve of each of these dependences and ranked them according to the calculated values of the experimental results. It is shown that in most cases, at the corresponding efficiency of classifiers separation, all the formulas adequately describe the experimental results. This explains the variety of dependences used. However, when the classification efficiency changes, the most theoretically justified formulas proposed by O. Molerus lead to a fundamental discrepancy between the experimental and calculated data, which narrows the scope of their use.

Conclusions. For practical application, we recommend the Plitt formula and the integral function of the log-normal Gaussian distribution, providing the best agreement between the experimental and calculated values in the whole separation efficiency range that is of practical interest.

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Key words in Russian: 
кривая разделения Тромпа, аппроксимация кривых разделения, дисперсный анализ пыли, параметры идентификации
Key words in English: 
Tromp separation curve, approximation of separation curves, dispersion analysis, identification parameters
The DOI index: 
10.17588/2072-2672.2018.6.015-023
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19