SIKIŞTIRILMIŞ YATAK TESTİNDE TANE BOYUNA BAĞIMLI KIRILMA MODELİNİN UYGULANABİLİRLİĞİ

Öz

Manyetit, platin ve fosforit cevherlerinin basınç altında kırılma karakteristiği sıkıştırılmış yatak testi ile incelenmiştir. Bu amaçla, piston pres test aleti kullanılmıştır. Testler sonucunda elde edilen veriler kullanılarak enerji ve tane boyunun kırılma üzerine etkisi incelenmiştir. Literatürde yaygın olarak kullanılan ürün inceliğini ifade eden t₁₀ değeri ile E_CS (Özgül Ufalama Enerjisi) arasında ilişki kurulmuştur. Sonrasında ürün inceliği ile tane boyutu ilişkisi incelenmiş ve test sonucunda elde edilen verilerin tane boyuna bağımlı kırılma modeline uyumu değerlendirilmiştir. Çalışma sonunda, tane boyuna bağımlı kırılma modelinin tane boyundan bağımsız kırılma modeline göre verilere daha iyi uyum sağladığı ve malzemelerin basınç altında kırılma davranımının belirlenmesinde de kullanılabileceği sonucuna varılmıştır.

Anahtar Kelimeler

• yatak kırma,kırılma modeli

THE APPLICABILITY OF SIZE-DEPENDENT BREAKAGE MODEL IN COMPRESSED BED BREAKAGE

Öz

   Breakage characteristics of magnetite, platinum and phosphorite ores were investigated via compressed bed breakage tests. With this aim, piston-die test equipment was used. Effects of specific comminution energy (E_CS) and particle size on breakage was investigated by using obtained data from the breakage tests. The relationship between E_CS (Specific Comminution Energy) and t₁₀ value, which is commonly used in literature, was established. Then, the product fineness and particle size relationship were analysed, and the compatibility of the data obtained from the tests, with size dependent breakage model was evaluated. It was concluded that the size-dependent breakage model better fitted to the data than the size-independent model and this model could be used to determine the breakage behaviour under compression force.

Anahtar Kelimeler

• bed breakage,breakage model

Kaynakça

1. [1] EPSTEIN, B., “Logarithmico-Normal Distribution in Breakage of Solids", Industrial and Engineering Chemistry, 40, 2289-2291, 1948. [2] BROADBENT, S.R., CALLCOTT T.G., “A Matrix of Processes Involving Particle Assemblies”, Phil. Trans. R. Soc. Lond., Ser., A, 249: 99-123, 1956.[3] GARDNER, R.P., AUSTIN L.G., 1962, “A Chemical Engineering Treatment of Batch Grinding”, In: H.Rumpf and D. Behrens (Editors), Proceedings, 1st European Symp. Zerkeinern. Verlag Chemie, Weinheim, 217-247,1962.[4] KELSALL, D.F., REID K.J., “The Derivation of a Mathematical Model for Breakage in a Small Continuous Wet Ball mill”, Proc. A.I. Ch. E./I.Chem.E. Joint Meeting, London, June, Section 4: 14-20, 1965.[5] AUSTIN, L.G., KLIMPEL, R.R., BEATTIE, A.N., “Solution of Equations of Grinding”, Second European Symposium on Comminution, Amsterdam, 281-312, 1966.[6] HERBST, J.A, FUERSTENAU D.W., “Scale-Up Procedure for Continuous Grinding Mill Design Using Population Balance Models”, International Journal of Mineral Processing, 7, 1-31, 1980.[7] STEWART, P.S.B., RESTARICK, C.J., “A Comparison of Mechanism of Breakage in Full Scale and Laboratory Scale Grinding Mills”, Proc. Australas. Inst. Min. Metall., 239, 81-92, 1971.[8] SCHOENERT, K., 1972, “Role of Fracture Physics in Understanding Comminution Phenomena”, Transactions of Society of Mining Engineers AIME, 252, 21-26, 1972.[9] FRUHWEIN, P., 1976, “Algorithm for Estimating The Process Parameters of Continuous Grinding”, Zerkleinern Dechema Monographien, 79, 505-518, 1976.[10] WHITEN, W.J., “A model for simulating crushing plants”, Journal of the South African Institute of Mining and Metallurgy 72, 257–264, 1972.[11] LYNCH, A.J., “Mineral Crushing and Grinding Circuits, Their Simulation, Optimization, Design and Control”, Elsevier Scientific Publishing Co., Amsterdam, 1-65, 1977.[12] KROGH, S.R., “Determination of Crushing and Grinding Characteristics Based on Testing of Single Particles”, Transactions AIME/SME, 266, 1957-1962, 1978.[13] Kavetsky, A., Whiten, W.J., Narayanan, S.S., “Studies on the Scale-up of Ball Mills”, Mill Operations Conference, Sept. Australas. Inst.Min.Metall., 113-121, 1982.[14] SCHOENERT, K., “Advances in Comminution Fundamentals and Impacts on Technology”, Aufbereit.-tech. 32, 487-494, 1991..[15] KRAJCINOVIC, D., Damage Mechanics, Elsevier, Oxford, UK, 159-166, 1996.[16] TAVARES, L.M., KING R.P., “Single-particle Fracture Under Impact Loading”, International Journal of Mineral Processing, 54, 1-28, 1998.[17] FANDRICH, R. G., CLOUT, J. M. F., BOURGEOIS, F. S., “The CSIRO Hopkinson Bar Facility for Large Diameter Particle Breakage”, Minerals Engineering, 11, 803-890, 1998.[18] YASHIMA, S., KANDA Y., SANO S., “Relationships between Particle Size and Fracture Energy or Impact Velocity Required to Fracture as Estimated from Single Particle Crushing”, Powder Technology, 51, 277-282, 1987. [19] UNLAND, G., SCZELINA, P., “Coarse Crushing of Brittle Rocks By Compression”, International Journal of Mineral Processing, 7, 209-217, 2004.[20] PAUW, O.G., MARÉ M.S., “The Determination of Optimum Impact-Breakage Routes for an Ore”, Powder Technology, 54, 3-13, 1988.[21] GAO, M.E., FORSSBERG, K.S.E., “Simulation of Batch Grinding of Iron Ore”, Trans. Inst. Min. Metall., 99, C142-C146, 1990.[22] BANINI, G.A., An Integrated Description of Rock Breakage in Comminution Machines., PhD Thesis, University of Queensland (JKMRC), Australia, 2000.[23] VOGEL, L., PEUKERT, W., “Breakage Behaviour of Different Materials-Construction of a Mastercurve for the Breakage Probability”, Powder Technology, 129, 101-110, 2003.[24] VOGEL, L., PEUKERT, W., “Determination of Material Properties Relevant to Grinding by Practicable Labscale Milling Tests”, International Journal of Mineral Processing, 74S, 329-338, 2004. [25] SHI, F., KOJOVIC, T., “Validation of A Model for Impact Breakage Incorporating Particle Size Effect”, International Journal of Mineral Processing, 82, 156-163, 2007.[26] EKSI, D., BENZER, H., SARGIN, A., GENC, O., “A new method for determination of fine particle breakage”, Minerals Engineering, 24, 216-220, 2011. [27] 27- LIU, J., SCHÖNERT, K., “Modelling of interparticle breakage”. Int. J. Miner. Process.44-45, 101-105, 1996.[28] HAWKINS, R., A Piston and Die Test to Predict Laboratory-Scale HPGR Performance, Master Thesis. JKMRC, University of Queensland, 2007.[29] DUNDAR, H., BENZER, H., AYDOGAN, A.N., “Application of population balance model to HPGR crushing”, Minerals Engineering, 50-51, 114-120, 2013.[30] ASBJORNSSON, G., HULTHEN, E., EVERTSSON, M., “Modelling and simulation of dynamic crushing plant behavior with MATLAB/Simulink”, Minerals Engineering, 43-44, 112-120, 2013.[31] ALTUN, D., Mathematical modelling of vertical roller mills, PhD Thesis, Hacettepe University, Turkey, 2017.[32] NARAYANAN, S.S., “Single particle breakage tests: A review of principles and applications to comminution modelling”, Bull Proc. Australas. Inst. Min. Metal, 291, pp.49-58, 1986.