Authors: V.I. Udovitsky, V.A. Kandinsky, E.G. Shubina, Kostenyuk

Title of the article: Numerical method for predicting the results of dilute coal density separation into coal mixture and waste rock in a gravity apparatus with water environment

Year: 2022, Issue: 6, Pages: 107-117

Branch of knowledge: 2.8.9. Mineral processing

Index UDK: 622.7; 622.73/.75; 622.75/.77

DOI: 10.26730/1999-4125-2022-6-107-117

Abstract: To predict the results of separation of denuded coals by density in gravity machines use mathematical models, in which the values of the probability integral F(x) are selected from tables. Calculations, as a rule, are made in Excel and very rarely use the function NORMSTRASP(z), which returns a standard normal integral distribution. Topicality of the topic: application of numerical integration and programs for computers allows to determine optimal parameters of technological processes of production and processing of coal with higher accuracy and lower costs. Purpose of work: creation of methods of simulation on computer technologies of gravitational separation of coal denuded in gravitational apparatuses for increasing efficiency of coal mining and processing. In this work eleven methods of numerical integration are considered and analytically justified. For each method, subroutines for the calculation of F(x) were developed. The subroutine "IntGauss" of calculating integral of power series was the best in time of calculations with the accuracy <0,0000001 (in absolute value) in the range of argument changes from 0,00 to 3,83 with step 0,01. The computational experiment showed that the standard deviation for function F(x), calculated with Excel in this range, is 0.00005001, in Turbo Pascal - 0.00005030. The IntGauss subroutine was included in the developed numerical method for predicting the results of stripped coal separation in gravity apparatuses with aqueous medium

Key words: numerical methods integration methods Gauss integral probable mean deviation standard deviation separation error diluted coal mechanized separation rough coal concentrate

Receiving date: 22.11.2022

Approval date: 16.12.2022

Publication date: 27.12.2022

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