Chemical and Metallurgical Institute named after Zh. Abishev (Republic of Kazakhstan):

Malyshev V. P., Head of Laboratory, eia_hmi@mail.ru

Turdukozhaeva A. M., Chief Researcher, eia_hmi@mail.ru

Karaganda State University named after A. E. Buketov (Republic of Kazakhstan):

Kaykenov D. A., Researcher

Ore grinding in a ball mill in tumbling regime of random collisions between grinding bodies and ground particles (metal balls and material grains) is likened to kinetics of bimolecular successive irreversible reactions with unlimited number of stages. In both cases the process rate obeys the probabilities of random successive events in mutual presence of interacting bodies in any point of reaction space (concentration factor), collision of one body with another (steric or geometric factor), disintegration in collision (activation factor) and to frequency of collisions. The latter is set by mill's rotation velocity, concentration factor — by volume ratio of balls and ore material loads, steric by balls and grains size ratio with determination of «dead» spaces in collisions, activation — by resultant reaction from impact energy and heat energy, on the one hand, and grain crystal lattice disintegration energy — on the other hand. With that, ball mill grinding results, that were earlier not sufficiently clear, are explained: low energy-efficiency of process, «non-grindability» of fine size fractions, manifestation of double maximums in grain size distribution in initial process stage, this size distribution tending to logarithmic-normal distribution law in final grinding stage, preferred use of large and small balls mix, actual correspondence of optimal balls and grains loads to their equal volume fractions, negligible effect of temperature on process rate. In consequence of mathematical rigor of expression for grains successive disintegration rate, with consideration of each size fraction content accumulation and diminution, a model has been developed, permitting direct calculation of each size fraction yield at any moment of time with total yield of all size fractions being equal to unit. An example of such calculation for quartz ore uniformsize fraction grinding is presented.

1. Malyshev V. P. Kompleksnoye ispolzovaniye mineralnogo syrya, 1992, No. 12, pp. 43–49.

2. Malyshev V. P. Kompleksnoye ispolzovaniye mineralnogo syrya, 1993, No. 1, pp. 22–31.

3. Malyshev V. P. Obogashchenie Rud, 1995, No. 4–5, pp. 4–14.

4. Malyshev V. P., Ospanov K. N. Obshchaya teoriya posledovatelnykh prevrashcheniy (General theory of consecutive transformations). Tezisy dokladov V Mezhdunarodnoy konferentsii po khimii i tekhnologii khalkogenov i khalkogenidov (Theses of reports of V Intern. conf. on chalcogens and chalcogenides chemistry and technology). Karaganda, 1995. p. 35.

5. Malyshev V. P., Ospanov K. N. Formalno-kineticheskaya model posledovatelnykh reaktsiy dlya neogranichennogo chisla stadiy (Formal and kinetic model of consecutive reactions for unlimited number of stages). Ibidem, p. 50.

6. Malyshev V. P. K teorii protsessa izmelcheniya (To the theory of grinding process). Ibidem, p. 179.

7. Malyshev V. P., Nurmagambetova (Turdukozhayeva) A. M., Ospanov K. N. Raschet izmelcheniya materialov na osnove molekulyarnoy teorii soudareniy i formalnoy kinetiki posledovatelnykh i parallelnykh reaktsiy (Calculation of materials grinding on the basis of molecular theory of impacts and formal kinetics of consecutive and parallel reactions). Materialy Respublikanskoy nauchno-prakticheskoy konferentsii «Sostoyaniye i perspektivy razvitiya khimii i khimicheskoy tekhnologii v Tsentralno-Kazakhstanskom regione» (Proc. of Republican scientific and practical conf. «State and prospects for development of chemistry and chemical technology in the Central Kazakhstan region»). Karaganda, 2000, p. 8–11.

8. Malyshev V. P., Nurmagambetova A. M., Teleshev K. D. Veroyatnostnoye modelirovaniye prochnosti na istiraniye  (Probabilistic modeling of abrasive wear resistance). Fiziko-khimicheskiye i tekhnologicheskiye voprosy metallurgicheskogo proizvodstva Kazakhstana (Physicochemical and technological questions of metallurgical production of Kazakhstan). Book 1. Almaty, Iskander, 2002, pp. 317–322.

9. Malyshev V. P., Teleshev K. D., Nurmagambetova A. M. Razrushayemost’ i sokhrannost’ konglomeratov  (Collapsibility and safety of conglomerates). Almaty, Gylym, 2003, 336 p.

10. Turdukozhayeva A. M. Primeneniye raspredeleniya Boltsmana i informatsionnoy entropii Shennona k analizy tverdogo, zhidkogo i gazoobraznogo sostoyaniy veshchestva (na primere metallov). Avtoreferat dissertatsii... doktora tekhnicheskikh nauk (Application of Boltzmann’s distribution and Shannon's information entropy to the analysis of firm, liquid and gaseous conditions of substance (on an example of metals). Athor’s abstract of Doctor’s dissertation). Karaganda, Chemical and Metallurgical Institute, 2008, 32 p.

11. Malyshev V. P., Abdrakhmanov B. T., Nurmagambetova A. M. Plavkost’ i plastichnost’ metallov (Fusibility and plasticity of metals). Moscow, Nauchnyy mir, 2004, 148 p.

12. Rodigin N. M., Rodigina E. N. Posledovatelnyye khimicheskiye reaktsii. Matematicheskiy analiz i raschet (Consecutive chemical reactions. Mathematical analysis and calculation). Moscow, Academy of Sciences of the USSR, 1960, 140 p.

13. Rozovskiy A. Ya. Geterogennyye khimicheskiye reaktsii (Kinetika i makrokinetika) (Heterogeneous chemical reactions (Kinetics and macrokinetics)). Moscow, Nauka, 1988, 324 p.

14. Nurmagambetova A. M. Programmirovaniye kineticheskoy zadachi po izmelcheniyu polifraktsionnogo materiala (Programming of kinetic task of polyfractional material grinding). Mаterialy Mezhdunarodnoy nauchno-prakticheskoy konferentsii «Teoreticheskaya i eksperimentalnaya khimiya» (Proc. of Intern. scientific and practical conf. «Theoretical and experimental chemistry»). Karaganda, 2002, pp. 49–52.

15. Khodakov G. S. Fizika izmelcheniya (Physics of grinding). Moscow, Nauka, 1972, 308 p.

16. Kolmogorov A. N. Doklady Akademii nauk SSSR — Proc. of the USSR Academy of Sciences , 1941, Vol. 31, No. 2, p. 99.