Advances on the Fragmentation-Energy Fan Concept and the Swebrec Function in Modeling Drop Weight Testing

The breakage index equation (BIE), or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>t</mi><mrow><mn>10</mn></mrow></msub></mrow></semant...

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Autores principales:	Finn Ouchterlony, José A. Sanchidrián, Ömürden Genç
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	rock fragmentation drop weight testing (DWT) fragment size distribution Swebrec function fragmentation-energy fan breakage index equation Mineralogy QE351-399.2
Acceso en línea:	https://doaj.org/article/c364cf3a3a2140e1819e5a282f55c5c9
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spelling	oai:doaj.org-article:c364cf3a3a2140e1819e5a282f55c5c92021-11-25T18:26:41ZAdvances on the Fragmentation-Energy Fan Concept and the Swebrec Function in Modeling Drop Weight Testing10.3390/min111112622075-163Xhttps://doaj.org/article/c364cf3a3a2140e1819e5a282f55c5c92021-11-01T00:00:00Zhttps://www.mdpi.com/2075-163X/11/11/1262https://doaj.org/toc/2075-163XThe breakage index equation (BIE), or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>t</mi><mrow><mn>10</mn></mrow></msub></mrow></semantics></math></inline-formula> model from drop weight testing (DWT) data for rocks and ores is used in the design of crushers and mills. Such models are becoming increasingly difficult to visualize as the number of variables increases. The so-called double fan BIE, combined with the Swebrec distribution’s accurate description of the sieving curves, is applied to the modelling of drop-weight test fragmentation. The key parameters are geometric properties visible in the fan plot; slopes of straight lines and their point of convergence. The ability of the double fan BIE to reproduce DWT data had been previously established for 8 rocks with 480 DWT data sets. Here the fidelity of the double fan BIE is further evaluated for 18 new materials, based on 281 data sets. The fidelity of the double fan BIE with three fan lines is on par with the fidelity of the current state-of-the-art models for the new materials. Besides the breakage index equation, the new double fan BIE’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>t</mi><mrow><mn>10</mn></mrow></msub></mrow></semantics></math></inline-formula> equation produces, without additional parameters or fitted constants, the general breakage surface equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>t</mi><mi>n</mi></msub></mrow></semantics></math></inline-formula> for an arbitrary <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>n</mi></semantics></math></inline-formula> value as a bonus. The specific sieving curve for any combination of particle size and impact energy is also contained in the same formula. The result is an accurate, compact and transparent model.Finn OuchterlonyJosé A. SanchidriánÖmürden GençMDPI AGarticlerock fragmentationdrop weight testing (DWT)fragment size distributionSwebrec functionfragmentation-energy fanbreakage index equationMineralogyQE351-399.2ENMinerals, Vol 11, Iss 1262, p 1262 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	rock fragmentation drop weight testing (DWT) fragment size distribution Swebrec function fragmentation-energy fan breakage index equation Mineralogy QE351-399.2
spellingShingle	rock fragmentation drop weight testing (DWT) fragment size distribution Swebrec function fragmentation-energy fan breakage index equation Mineralogy QE351-399.2 Finn Ouchterlony José A. Sanchidrián Ömürden Genç Advances on the Fragmentation-Energy Fan Concept and the Swebrec Function in Modeling Drop Weight Testing
description	The breakage index equation (BIE), or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>t</mi><mrow><mn>10</mn></mrow></msub></mrow></semantics></math></inline-formula> model from drop weight testing (DWT) data for rocks and ores is used in the design of crushers and mills. Such models are becoming increasingly difficult to visualize as the number of variables increases. The so-called double fan BIE, combined with the Swebrec distribution’s accurate description of the sieving curves, is applied to the modelling of drop-weight test fragmentation. The key parameters are geometric properties visible in the fan plot; slopes of straight lines and their point of convergence. The ability of the double fan BIE to reproduce DWT data had been previously established for 8 rocks with 480 DWT data sets. Here the fidelity of the double fan BIE is further evaluated for 18 new materials, based on 281 data sets. The fidelity of the double fan BIE with three fan lines is on par with the fidelity of the current state-of-the-art models for the new materials. Besides the breakage index equation, the new double fan BIE’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>t</mi><mrow><mn>10</mn></mrow></msub></mrow></semantics></math></inline-formula> equation produces, without additional parameters or fitted constants, the general breakage surface equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>t</mi><mi>n</mi></msub></mrow></semantics></math></inline-formula> for an arbitrary <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>n</mi></semantics></math></inline-formula> value as a bonus. The specific sieving curve for any combination of particle size and impact energy is also contained in the same formula. The result is an accurate, compact and transparent model.
format	article
author	Finn Ouchterlony José A. Sanchidrián Ömürden Genç
author_facet	Finn Ouchterlony José A. Sanchidrián Ömürden Genç
author_sort	Finn Ouchterlony
title	Advances on the Fragmentation-Energy Fan Concept and the Swebrec Function in Modeling Drop Weight Testing
title_short	Advances on the Fragmentation-Energy Fan Concept and the Swebrec Function in Modeling Drop Weight Testing
title_full	Advances on the Fragmentation-Energy Fan Concept and the Swebrec Function in Modeling Drop Weight Testing
title_fullStr	Advances on the Fragmentation-Energy Fan Concept and the Swebrec Function in Modeling Drop Weight Testing
title_full_unstemmed	Advances on the Fragmentation-Energy Fan Concept and the Swebrec Function in Modeling Drop Weight Testing
title_sort	advances on the fragmentation-energy fan concept and the swebrec function in modeling drop weight testing
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/c364cf3a3a2140e1819e5a282f55c5c9
work_keys_str_mv	AT finnouchterlony advancesonthefragmentationenergyfanconceptandtheswebrecfunctioninmodelingdropweighttesting AT joseasanchidrian advancesonthefragmentationenergyfanconceptandtheswebrecfunctioninmodelingdropweighttesting AT omurdengenc advancesonthefragmentationenergyfanconceptandtheswebrecfunctioninmodelingdropweighttesting
_version_	1718411156588068864

Advances on the Fragmentation-Energy Fan Concept and the Swebrec Function in Modeling Drop Weight Testing

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