Statistical analysis of sizing features of dust generated under the mechanical metal-working

Introduction. The paper considers the mathematical analysis of the fractional composition of dust generated during the operation of the rail-cutting machine. It is established that the studied polydisperse material is well described by the one-parameter exponential distribution. At the same time, the lognormal particle size distribution, whose parameters are determined by mathematical programming methods, seems adequate for the purposes of calculating cyclones. The work objective was to develop mathematical methods for correct averaging of the size and mass parameters of dust under the solid metal machining.

Materials and Methods. We studied the possibility of approximating experimental data by Rosin – Rammler distributions (classical, generalized three-parameter P(x, D, n, m), and simplified exponential P(x), in which n = 1). The corresponding results were compared to each other and to the data of approximation of the lognormal and double lognormal functions. These results indicate close approximation quality using the following model distributions P(x):

• five-parameter double lognormal;

• three-parameter type of Rosin-Rammler;

• two-parameter classical Rosin - Rammler;

• one-parameter exponential.

Results. The primary physical analysis of cutting waste was carried out by the laboratory measuring complex Fritsch Analysette 22 Compact which uses the LALLS – low angle laser scattering method. The built-in software provides output of measurement results in primary graphic and digital forms. It was found that the simplest exponential distribution is best suited for a detailed analysis of the dust particle-size distribution based on the experimental data.

This distribution enables reproduction of all the integral indicators provided by the instrumental measuring complex along with the graphical data.

Discussion and Conclusions. The results obtained can be used to rationalize the local suction machine, and the mathematical models and algorithms can be used for the parametric analysis of any dust captured by cyclones.

1. Страус, В. Промышленная очистка газов : пер. с англ. / В. Страус. ― Москва : Химия, 1981. ― 616 с.

2. Зиганшин, М. Г. Проектирование аппаратов пылегазоочистки / М. Г. Зиганшин, А. А. Колесник, В. Н. Посохин. ― Москва : Экопресс ― 3М, 1998. ― 505 с.

3. J. Sauter. Grössenbestimmung von Brennstoffteilchen // Forschungsarbeiten auf dem Gebiete des Ingenieurwesens. ― 1926. ― Heft 279.

4. J. Sauter. Untersuchung der von Spritzvergasern gelieferten Zerstäubung // Forschungsarbeiten auf dem Gebiete des Ingenieurwesens. ― 1928. ― Heft 312.

5. H. Wadell. Volume, Shape and Roundness of Quartz Particles // J. Geology. ― 1935. ― Vol. 43, no. 3. ― P. 250-280.

6. Адушкин, В. B. Анализ мелкодисперсной фракции при разрушении горных пород взрывом и образовании скальных оползней / В. B. Адушкин, С. И. Попель, С. И. Шишаева // Записки Горного института. ― 2007. ― Т. 171. ― С. 32–38.

7. T. Hatch, S.P. Choate Statistical description of the size properties of non-uniform particulate substances // J. Franklin Inst. ― 1929. ― Vol. 207. ― P. 369–387.

8. W. Kaye, J.B. McDaniel Low-Angle Laser Light Scattering – Rayleigh Factors and Depolarization Ratios // Applied Optics. ― 1974. ― Vol. 13, iss. 8. ― P. 1934–1937.

9. Бочкарева, Е. А. Сравнительный анализ программ оцифровки графиков / Е. А. Бочкарева // Современные научные исследования и инновации. ― 2015. ― № 11. ― URL : http://web.snauka.ru/issues/2015/11/60095 (дата обращения : 02.02.2020).

10. Шарапова, Э. Н. Система оцифровки графических данных / Э. Н. Шарапова, В. Л. Дмитриев // Математическое и программное обеспечение систем в промышленной и социальной сферах. ― 2011. ― № 1–2. ― С. 166–171.

11. Grafula ― оцифровка координат точек отсканированных графиков для переноса их в Excel : Математическое моделирование. ― URL : https://mmodelling.blogspot.com/2012/07/excel.html (дата обращения : 02.02.2020).

12. M. Minoux Mathematical Programming: Theory and Algorithms. New York: John Wiley, 1986. ― 489 p.