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: | , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/c364cf3a3a2140e1819e5a282f55c5c9 |
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| Sumario: | 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. |
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