Analysis of Proportional Scopes on Probability Density Functions of Random Chords of Spherical Particles

• Autorzy: Gurgul D.

Identyfikatory

DOI

10.24425/afe.2021.138680

• Języki publikacji: EN

Abstrakty

EN

The paper presents an experimental confirmation of the fact that if a three-dimensional volume does not contain spherical particles with particular size, the Probability Density Function (PDF1) of half-chord lengths has proportional ranges. This fact has been deduced in work [1] during the derivation process of the Probability Density Function (PDF3) that maps the particle radii on the basis of data (PDF1) collected from flat cross-sections. The experiment has been executed virtually by using a simple computer program written in the C++11 language. The computer generation of particles allowed imposing various kinds of known PDF3 and the ranges in which the particles could not be created. Next, the virtual nodules have been used to produce sets of chords that served as input data to create histograms that approximated the continuous PDF1. Having such histograms, it was possible to reveal proportional scopes of the PDF1. The proportional dependencies occurred in the same ranges where the nodules had not been generated.

Słowa kluczowe

EN

metallographic analysis; particle size distribution; linear analysis; experiment executed virtually

• Wydawca: Komisja Odlewnictwa Polskiej Akademii Nauk Oddział w Katowicach
• Czasopismo: Archives of Foundry Engineering
• Rocznik: 2021
• Tom: Vol. 21, iss. 4
• Strony: 61--66
• Opis fizyczny: Bibliogr. 11 poz., rys., tab., wykr.

Twórcy

autor

Gurgul D.

• AGH University of Science and Technology, Kraków, Poland

Bibliografia

• [1] Gurgul, D., Burbelko, A. & Wiktor T. (2021). Derivation of equation for a size distribution of spherical particles in non-transparent materials. Journal of Casting & Materials Engineering. 5(4), 53-60.
• [2] Wicksell, S.D. (1925). The corpuscle problem: mathematical study of a biometric problem. Biometric. 17 (1/2), 84-89.
• [3] Sheil, E. (1935). Statistische gefügeuntersuchungen I. Zeitschrift für Metallkunde. 27 (9), 199-208.
• [4] Schwartz, H.A. (1934). The metallographic determination of the sze distribution of temper carbon nodules. Metals and Alloys. 5, 139-140.
• [5] Saltykov, S.A. (1967). The determination of the size distribution of particles in an opaque material from the measurement of the size distribution of their section. in the second international congress for stereology, Chicago, 8-13 April 1967. Berlin–Heidelberg–New York, Springer Verlag.
• [6] Cahn, J.W. & Fulmann, R.L. (1956) On the use of lineal analysis for obtaining particle size distributions in opaque samples. Transactions, American Institute of Mining, Metallurgical and Petroleum Engineers. 206, 177-187.
• [7] Lord, G.W. & Willis, T.F. (1951). Calculation of air bubble size distribution from results of a rosiwal traverse of aerated concrete. ASTM Bulletin. 177, 177-187.
• [8] Spektor, A.G. (1950). Analysis of distribution of spherical particles in non-transparent structures. Zavodsk. Lab. 16, 173-177.
• [9] https://www.cplusplus.com (date of access 06.06.2021).
• [10] Burbelko, A., Gurgul, D., Guzik, E. & Kapturkiewicz, W. (2018). Stereological analysis of the statistical distribution of the size of graphite nodules in DI. Materials Science Forum. 925, 98-103.
• [11] Fras, E., Burbelko, A.A. & Lopez, H.F. (1996). Secondary nucleation of eutectic graphite grains. Transactions of the American Foundrymen Society. 104, 1-4.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).