Determination of Breakage Parameters in Mathematical Grinding Model by Weight-adjustment Modification

doi:10.12972/ksmer.2013.50.1.080

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2013 Vol.50, Issue 1 Preview Page Next Page

Research Paper

Determination of Breakage Parameters in Mathematical Grinding Model by Weight-adjustment Modification 가중치 보정법에 의한 수학적 분쇄 모델의 인자 결정: 이 훈·김관호·김완태·김상배
Hoon Lee, Kwanho Kim, Wantae Kim and Sangbae Kim

28 February 2013. pp. 80-87

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Abstract

Comminution is a representative energy consuming process, and modeling techniques are indispensable for the improvement of the process efficiency. Among various modeling techniques, the Population Balance Model (PBM) is widely used since it enables grinding circuits with classifiers and the reproduction of the size distribution of the ground products. The parameters of the relevant model are determined from comminution experiments using PC-based back-calculations. Back-calculations, from actual data that include the characteristics of substances and measurement errors, etc., often draw model parameters that are different from the actual parameters. Therefore, in the present study, the characteristics of the errors that occurred were grasped and the back-calculation algorithms were improved through heuristic analysis of the characteristics to present a method to arrive at the most appropriate model parameters. Back-calculations were conducted using corrected functions and, according to the results, the experimental values agree with the calculated values and the proposed functions were identified to be effective in the back-calculation method.

Keywords

Comminution

Ball mill

Back-calculation

Weight-adjustment

Mathematical grinding model

Mass balance

분쇄는 대표적인 에너지 소모형 공정이며 공정의 효율 개선을 위하여 모델링 기법은 필수적이다. 여러 모델링 기법 중 PBM(Population Balance Model)은 분급기가 결합된 분쇄회로 및 분쇄산물의 입도분포 재현이 가능하여 널리 사용되고 있다. 해당 모델 인자는 분쇄 실험으로부터 PC기반의 역산법을 이용하여 결정되는데, 물질의 특성 및 측정오류 등이 포함된 실제 데이터로부터의 역산은 종종 실제와는 다른 모델인자를 도출하기도 한다. 따라서 본 연구에서는 발생하는 오류의 특징을 파악하고 이를 휴리스틱 분석을 통해 역산알고리즘을 개선하여 가장 적합한 모델인자에 도달할 수 있는 방법을 제시하였다. 수정된 함수로 역산결과, 실험값은 계산값와 일치 하였으며 제안된 함수가 역산방법에 있어 효과적임을 확인하였다.

키워드

분쇄공정

볼밀

역산법

가중치보정법

수학적 분쇄 모델

물질수지 모델

References

Austin, L.G., 1971, “Introduction to the mathematical description of grinding as a rate process,” Powder Technology, Vol. 5, No. 1, pp. 1-17.
Austin, L.G. and Luckie, P.T., 1972, “Methods for Determination of Breakage Distribution Parameters,” Powder Technology, Vol. 5, No. 4, pp. 215-222.
Austin, L.G., Klimpel, R.R. and Luckie, P.T., 1984, Process Engineering of size Reduction: ball milling, American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc., New York, NY, pp. 61-77, 124, 208.
Avriel, M., 1976, Nonlinear programing, Prentice-hall,INC, Englewood cliffs, New Jersey.
Lee, H. and Cho, H.C., 2002, “Determination of the Breakage Parameters on the Nonmetallic minerals,” Journal of the Korean society for Geosystem Engineering, Vol. 39, No. 4, pp. 248-256.
Lee, H. and Cho, H.C., 2006, “Breakage characteristics of some industrial minerals in a ball mill,” Journal of the Korean society for Geosystem Engineering, Vol. 43, No. 6, pp. 533-542.
Luckie, P.T. and Austin, L.G., 1972, “A Review Introduction to the Solution of Grinding Equations by Digital Computation,” Mineral Science and Engineering, Vol. 4, No. 2, pp. 24-51.
Mishra, B.K., 2003, “A review of computer simulation of tumbling mills by discrete element method_Part I-contact mechanics,” International journal of mineral processing, Vol. 71, pp. 73-93.
Reid, K.J., 1965, “A Solution to the Batch Grinding Equation,” Chemical Engi neering Science, Vol. 20, No. 11, pp. 953-963.

Information

Publisher :The Korean Society of Mineral and Energy Resources Engineers
Publisher(Ko) :한국자원공학회
Journal Title :Journal of the Korean Society of Mineral and Energy Resources Engineers
Journal Title(Ko) :한국자원공학회지
Volume : 50
No :1
Pages :80-87
DOI :https://doi.org/10.12972/ksmer.2013.50.1.080

[1] Austin, L.G., 1971, “Introduction to the mathematical description of grinding as a rate process,” Powder Technology, Vol. 5, No. 1, pp. 1-17.

[2] Austin, L.G. and Luckie, P.T., 1972, “Methods for Determination of Breakage Distribution Parameters,” Powder Technology, Vol. 5, No. 4, pp. 215-222.

[3] Austin, L.G., Klimpel, R.R. and Luckie, P.T., 1984, Process Engineering of size Reduction: ball milling, American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc., New York, NY, pp. 61-77, 124, 208.

[4] Avriel, M., 1976, Nonlinear programing, Prentice-hall,INC, Englewood cliffs, New Jersey.

[5] Lee, H. and Cho, H.C., 2002, “Determination of the Breakage Parameters on the Nonmetallic minerals,” Journal of the Korean society for Geosystem Engineering, Vol. 39, No. 4, pp. 248-256.

[6] Lee, H. and Cho, H.C., 2006, “Breakage characteristics of some industrial minerals in a ball mill,” Journal of the Korean society for Geosystem Engineering, Vol. 43, No. 6, pp. 533-542.

[7] Luckie, P.T. and Austin, L.G., 1972, “A Review Introduction to the Solution of Grinding Equations by Digital Computation,” Mineral Science and Engineering, Vol. 4, No. 2, pp. 24-51.

[8] Mishra, B.K., 2003, “A review of computer simulation of tumbling mills by discrete element method_Part I-contact mechanics,” International journal of mineral processing, Vol. 71, pp. 73-93.

[9] Reid, K.J., 1965, “A Solution to the Batch Grinding Equation,” Chemical Engi neering Science, Vol. 20, No. 11, pp. 953-963.

Journal of the Korean Society of Mineral and Energy Resources Engineers ISSN:2288-0291(Print) 2288-2790(Online) 한국자원공학회지

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