Building a model of the abrasion grinding mechanism in a tumbling mill based on data visualization

Authors

DOI:

https://doi.org/10.15587/1729-4061.2024.301653

Keywords:

tumbling mill, intra-chamber loading, grinding by abrasion, granular temperature, grinding performance

Abstract

The object of this study is the grinding process in a tumbling mill when the mechanism of destruction by abrasion is implemented, which is caused by the mechanism of shear loading. The abrasive effect due to the impulse interaction during the mutual chaotic movement of granular particles in the shear layer of loading, characterized by the granular temperature, is taken into account.

The task solved was determining the parameters of the shear interaction, which is caused by the difficulties of modeling and complexity of the hardware analysis of behavior of the internal loading in the mill.

A mathematical model was built based on data visualization for the abrasion grinding mechanism.

The power of the shear interaction forces was taken as an analog of the grinding performance. The initial shear characteristic was considered to be the average value of the shear velocity gradient in the central averaged normal section of the shear layer. The impact on productivity of the granular temperature and mass fraction of the shear layer and loading turnover was taken into account.

The effect of rotation speed on performance was evaluated by experimental modeling at a chamber filling degree of 0.45 and a relative particle size of 0.0104. The maximum value of the energy and productivity of grinding by abrasion was established at the relative speed of rotation ψω=0.55–0.6.

The results have made it possible to establish a rational speed when grinding by abrasion, ψω=0.5–0.6. This value is smaller in comparison with grinding by crushing ψω=0.55–0.65 and breaking ψω=0.75–0.9. The established effect is explained by the detected activation of the chaotic quasi-thermodynamic movement of particles of the shear layer at slow rotation.

The model built makes it possible to predict rational technological parameters of the energy-saving process of fine grinding in a tumbling mill by abrasion

Author Biographies

Yuriy Naumenko, National University of Water and Environmental Engineering

Doctor of Technical Sciences, Associate Professor, Professor

Department of Construction, Road and Reclamation Machines

Kateryna Deineka, National University of Water and Environmental Engineering

PhD, Teacher of the Highest Category

Rivne Technical Vocational College

Serhii Zabchyk, National University of Water and Environmental Engineering

Institute of Mechanical Engineering

References

  1. Gupta, V. K. (2020). Energy absorption and specific breakage rate of particles under different operating conditions in dry ball milling. Powder Technology, 361, 827–835. https://doi.org/10.1016/j.powtec.2019.11.033
  2. Góralczyk, M., Krot, P., Zimroz, R., Ogonowski, S. (2020). Increasing Energy Efficiency and Productivity of the Comminution Process in Tumbling Mills by Indirect Measurements of Internal Dynamics – An Overview. Energies, 13 (24), 6735. https://doi.org/10.3390/en13246735
  3. Tavares, L. M. (2017). A Review of Advanced Ball Mill Modelling. KONA Powder and Particle Journal, 34, 106–124. https://doi.org/10.14356/kona.2017015
  4. Semsari Parapari, P., Parian, M., Rosenkranz, J. (2020). Breakage process of mineral processing comminution machines – An approach to liberation. Advanced Powder Technology, 31 (9), 3669–3685. https://doi.org/10.1016/j.apt.2020.08.005
  5. Napier-Munn, T. J., Morrell, S., Morrison, R. D., Kojovic, T. (1996). Mineral comminution circuits: their operation and optimisation. JKMRC Monograph series in mining and mineral processing, 2.
  6. Ye, X., Gredelj, S., Skinner, W., Grano, S. R. (2010). Regrinding sulphide minerals — Breakage mechanisms in milling and their influence on surface properties and flotation behaviour. Powder Technology, 203 (2), 133–147. https://doi.org/10.1016/j.powtec.2010.05.002
  7. Hasan, M., Palaniandy, S., Hilden, M., Powell, M. (2017). Calculating breakage parameters of a batch vertical stirred mill. Minerals Engineering, 111, 229–237. https://doi.org/10.1016/j.mineng.2017.06.024
  8. Chen, X., Peng, Y., Bradshaw, D. (2014). The effect of particle breakage mechanisms during regrinding on the subsequent cleaner flotation. Minerals Engineering, 66-68, 157–164. https://doi.org/10.1016/j.mineng.2014.04.020
  9. Wills, B. A., Finch, J. (2015). Wills’ Mineral Processing Technology. Butterworth-Heinemann. https://doi.org/10.1016/c2010-0-65478-2
  10. Naumenko, Y., Deineka, K. (2023). Building a model of the compression grinding mechanism in a tumbling mill based on data visualization. Eastern-European Journal of Enterprise Technologies, 5 (1 (125)), 64–72. https://doi.org/10.15587/1729-4061.2023.287565
  11. Naumenko, Y., Deineka, K. (2023). Building a model of the impact grinding mechanism in a tumbling mill based on data visualization. Eastern-European Journal of Enterprise Technologies, 3 (7 (123)), 65–73. https://doi.org/10.15587/1729-4061.2023.283073
  12. Morrison, A. J., Govender, I., Mainza, A. N., Parker, D. J. (2016). The shape and behaviour of a granular bed in a rotating drum using Eulerian flow fields obtained from PEPT. Chemical Engineering Science, 152, 186–198. https://doi.org/10.1016/j.ces.2016.06.022
  13. de Klerk, D. N., Govender, I., Mainza, A. N. (2019). Geometric features of tumbling mill flows: A positron emission particle tracking investigation. Chemical Engineering Science, 206, 41–49. https://doi.org/10.1016/j.ces.2019.05.020
  14. Jaeger, H. M., Nagel, S. R., Behringer, R. P. (1996). Granular solids, liquids, and gases. Reviews of Modern Physics, 68 (4), 1259–1273. https://doi.org/10.1103/revmodphys.68.1259
  15. Forterre, Y., Pouliquen, O. (2008). Flows of Dense Granular Media. Annual Review of Fluid Mechanics, 40 (1), 1–24. https://doi.org/10.1146/annurev.fluid.40.111406.102142
  16. Forterre, Y., Pouliquen, O. (2011). Granular Flows. Glasses and Grains, 77–109. https://doi.org/10.1007/978-3-0348-0084-6_4
  17. Brown, R. L., Richards, J. C. (2016). Principles of powder mechanics: essays on the packing and flow of powders and bulk solids. Elsevier. https://doi.org/10.1016/c2013-0-01576-9
  18. Savage, S. B. (1984). The Mechanics of Rapid Granular Flows. Advances in Applied Mechanics, 289–366. https://doi.org/10.1016/s0065-2156(08)70047-4
  19. Campbell, C. (1990). Rapid Granular Flows. Annual Review of Fluid Mechanics, 22 (1), 57–92. https://doi.org/10.1146/annurev.fluid.22.1.57
  20. Campbell, C. S. (2006). Granular material flows – An overview. Powder Technology, 162 (3), 208–229. https://doi.org/10.1016/j.powtec.2005.12.008
  21. Jiang, Y., Liu, M. (2009). Granular solid hydrodynamics. Granular Matter, 11 (3), 139–156. https://doi.org/10.1007/s10035-009-0137-3
  22. Ogawa, S. (1978). Multitemperature theory of granular materials. Proc. of the US-Japan Seminar on Continuum Mechanical and Statistical Approaches in the Mechanics of Granular Materials, 208–217.
  23. Ogawa, S., Umemura, A., Oshima, N. (1980). On the equations of fully fluidized granular materials. Zeitschrift Für Angewandte Mathematik Und Physik ZAMP, 31 (4), 483–493. https://doi.org/10.1007/bf01590859
  24. Sun, Q., Song, S., Jin, F., Jiang, Y. (2012). Entropy productions in granular materials. Theoretical and Applied Mechanics Letters, 2 (2), 021002. https://doi.org/10.1063/2.1202102
  25. Sun, Q., Song, S., Liu, J., Fei, M., Jin, F. (2013). Granular materials: Bridging damaged solids and turbulent fluids. Theoretical and Applied Mechanics Letters, 3 (2), 021008. https://doi.org/10.1063/2.1302108
  26. Sun, Q., Jin, F., Wang, G., Song, S., Zhang, G. (2015). On granular elasticity. Scientific Reports, 5 (1). https://doi.org/10.1038/srep09652
  27. Yang, H., Li, R., Kong, P., Sun, Q. C., Biggs, M. J., Zivkovic, V. (2015). Avalanche dynamics of granular materials under the slumping regime in a rotating drum as revealed by speckle visibility spectroscopy. Physical Review E, 91 (4). https://doi.org/10.1103/physreve.91.042206
  28. Li, R., Yang, H., Zheng, G., Zhang, B. F., Fei, M. L., Sun, Q. C. (2016). Double speckle-visibility spectroscopy for the dynamics of a passive layer in a rotating drum. Powder Technology, 295, 167–174. https://doi.org/10.1016/j.powtec.2016.03.031
  29. Yang, H., Zhang, B. F., Li, R., Zheng, G., Zivkovic, V. (2017). Particle dynamics in avalanche flow of irregular sand particles in the slumping regime of a rotating drum. Powder Technology, 311, 439–448. https://doi.org/10.1016/j.powtec.2017.01.064
  30. Li, R., Yang, H., Zheng, G., Sun, Q. C. (2018). Granular avalanches in slumping regime in a 2D rotating drum. Powder Technology, 326, 322–326. https://doi.org/10.1016/j.powtec.2017.12.032
  31. Yang, H., Zhu, Y., Li, R., Sun, Q. (2020). Kinetic granular temperature and its measurement using speckle visibility spectroscopy. Particuology, 48, 160–169. https://doi.org/10.1016/j.partic.2018.07.011
  32. Jing, Z., Yang, H., Wang, S., Chen, Q., Li, R. (2021). Comparison of granular temperature measured by SVS and DEM in the rotating cylinder. Powder Technology, 380, 282–287. https://doi.org/10.1016/j.powtec.2020.11.073
  33. Dolgunin, V. N., Ivanov, O. O., Akopyan, S. A. (2020). Quasithermal Effects During Rapid Gravity Flow of a Granular Medium. Advanced Materials & Technologies, 3 (19), 047–055. https://doi.org/10.17277/amt.2020.03.pp.047-055
  34. Li, S., Yao, Q., Chen, B., Zhang, X., Ding, Y. L. (2007). Molecular dynamics simulation and continuum modelling of granular surface flow in rotating drums. Chinese Science Bulletin, 52 (5), 692–700. https://doi.org/10.1007/s11434-007-0069-4
  35. Yin, H., Zhang, M., Liu, H. (2014). Numerical simulation of three-dimensional unsteady granular flows in rotary kiln. Powder Technology, 253, 138–145. https://doi.org/10.1016/j.powtec.2013.10.044
  36. Yang, S., Sun, Y., Zhang, L., Chew, J. W. (2017). Segregation dynamics of a binary-size mixture in a three-dimensional rotating drum. Chemical Engineering Science, 172, 652–666. https://doi.org/10.1016/j.ces.2017.07.019
  37. Yang, S., Wang, H., Wei, Y., Hu, J., Chew, J. W. (2020). Flow dynamics of binary mixtures of non-spherical particles in the rolling-regime rotating drum. Powder Technology, 361, 930–942. https://doi.org/10.1016/j.powtec.2019.10.110
  38. Longo, S., Lamberti, A. (2002). Grain shear flow in a rotating drum. Experiments in Fluids, 32 (3), 313–325. https://doi.org/10.1007/s003480100359
  39. Chou, H.-T., Lee, C.-F. (2008). Cross-sectional and axial flow characteristics of dry granular material in rotating drums. Granular Matter, 11 (1), 13–32. https://doi.org/10.1007/s10035-008-0118-y
  40. Chou, S. H., Hsiau, S. S. (2011). Experimental analysis of the dynamic properties of wet granular matter in a rotating drum. Powder Technology, 214 (3), 491–499. https://doi.org/10.1016/j.powtec.2011.09.010
  41. Chou, S. H., Hu, H. J., Hsiau, S. S. (2016). Investigation of friction effect on granular dynamic behavior in a rotating drum. Advanced Powder Technology, 27 (5), 1912–1921. https://doi.org/10.1016/j.apt.2016.06.022
  42. Liao, C.-C., Lan, H.-W., Hsiau, S.-S. (2016). Density-induced granular segregation in a slurry rotating drum. International Journal of Multiphase Flow, 84, 1–8. https://doi.org/10.1016/j.ijmultiphaseflow.2016.04.015
  43. Liao, C.-C. (2019). Effect of dynamic properties on density-driven granular segregation in a rotating drum. Powder Technology, 345, 151–158. https://doi.org/10.1016/j.powtec.2018.12.093
  44. Liao, C.-C., Ou, S.-F., Chen, S.-L., Chen, Y.-R. (2020). Influences of fine powder on dynamic properties and density segregation in a rotating drum. Advanced Powder Technology, 31 (4), 1702–1707. https://doi.org/10.1016/j.apt.2020.02.006
  45. Chung, Y.-C., Liao, C.-C., Zhuang, Z.-H. (2021). Experimental investigations for the effect of fine powders on size-induced segregation in binary granular mixtures. Powder Technology, 387, 270–276. https://doi.org/10.1016/j.powtec.2021.04.034
  46. Govender, I., Richter, M. C., Mainza, A. N., De Klerk, D. N. (2016). A positron emission particle tracking investigation of the scaling law governing free surface flows in tumbling mills. AIChE Journal, 63 (3), 903–913. https://doi.org/10.1002/aic.15453
  47. Xiu, W., Li, R., Chen, Q., Sun, Q., Zivkovic, V., Yang, H. (2023). Prediction of segregation characterization based on granular velocity and concentration in rotating drum. Particuology, 73, 17–25. https://doi.org/10.1016/j.partic.2022.03.008
  48. Naumenko, Y. (2017). Modeling a flow pattern of the granular fill in the cross section of a rotating chamber. Eastern-European Journal of Enterprise Technologies, 5 (1 (89)), 59–69. https://doi.org/10.15587/1729-4061.2017.110444
  49. Naumenko, Y. (2017). Modeling of fracture surface of the quasi solid-body zone of motion of the granular fill in a rotating chamber. Eastern-European Journal of Enterprise Technologies, 2 (1 (86)), 50–57. https://doi.org/10.15587/1729-4061.2017.96447
  50. Naumenko, Y., Sivko, V. (2017). The rotating chamber granular fill shear layer flow simulation. Eastern-European Journal of Enterprise Technologies, 4 (7 (88)), 57–64. https://doi.org/10.15587/1729-4061.2017.107242
  51. Deineka, K., Naumenko, Y. (2019). Revealing the effect of decreased energy intensity of grinding in a tumbling mill during self-excitation of auto-oscillations of the intrachamber fill. Eastern-European Journal of Enterprise Technologies, 1 (1 (97)), 6–15. https://doi.org/10.15587/1729-4061.2019.155461
  52. Deineka, K., Naumenko, Y. (2019). Establishing the effect of a decrease in power intensity of self-oscillating grinding in a tumbling mill with a reduction in an intrachamber fill. Eastern-European Journal of Enterprise Technologies, 6 (7 (102)), 43–52. https://doi.org/10.15587/1729-4061.2019.183291
  53. Deineka, K., Naumenko, Y. (2020). Establishing the effect of decreased power intensity of self-oscillatory grinding in a tumbling mill when the crushed material content in the intra-chamber fill is reduced. Eastern-European Journal of Enterprise Technologies, 4 (1 (106)), 39–48. https://doi.org/10.15587/1729-4061.2020.209050
  54. Deineka, K., Naumenko, Y. (2021). Establishing the effect of a simultaneous reduction in the filling load inside a chamber and in the content of the crushed material on the energy intensity of self-oscillatory grinding in a tumbling mill. Eastern-European Journal of Enterprise Technologies, 1 (1 (109)), 77–87. https://doi.org/10.15587/1729-4061.2021.224948
  55. Deineka, K., Naumenko, Y. (2022). Revealing the mechanism of stability loss of a two-fraction granular flow in a rotating drum. Eastern-European Journal of Enterprise Technologies, 4 (1 (118)), 34–46. https://doi.org/10.15587/1729-4061.2022.263097
  56. Deineka, K. Yu., Naumenko, Yu. V. (2018). The tumbling mill rotation stability. Scientific Bulletin of National Mining University, 1, 60–68. https://doi.org/10.29202/nvngu/2018-1/10
  57. Gupta, V. K., Sharma, S. (2014). Analysis of ball mill grinding operation using mill power specific kinetic parameters. Advanced Powder Technology, 25 (2), 625–634. https://doi.org/10.1016/j.apt.2013.10.003
  58. Hanumanthappa, H., Vardhan, H., Mandela, G. R., Kaza, M., Sah, R., Shanmugam, B. K. (2020). A comparative study on a newly designed ball mill and the conventional ball mill performance with respect to the particle size distribution and recirculating load at the discharge end. Minerals Engineering, 145, 106091. https://doi.org/10.1016/j.mineng.2019.106091
  59. ISO 924:1989. Coal preparation plant. Principles and conventions for flowsheets. Available at: https://www.iso.org/standard/5340.html
  60. DIN EN 1009-3. Maschinen für die mechanische Aufbereitung von Mineralien und ähnlichen festen Stoffen - Sicherheit - Teil 3: Spezifische Anforderungen für Brecher und Mühlen; Deutsche Fassung EN 1009-3:2020. Available at: https://www.din.de/de/mitwirken/normenausschuesse/nam/veroeffentlichungen/wdc-beuth:din21:316006092
Building a model of the abrasion grinding mechanism in a tumbling mill based on data visualization

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Published

2024-04-30

How to Cite

Naumenko, Y., Deineka, K., & Zabchyk, S. (2024). Building a model of the abrasion grinding mechanism in a tumbling mill based on data visualization. Eastern-European Journal of Enterprise Technologies, 2(1 (128), 21–33. https://doi.org/10.15587/1729-4061.2024.301653

Issue

Vol. 2 No. 1 (128) (2024): Engineering technological systems

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Engineering technological systems

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Copyright (c) 2024 Yuriy Naumenko, Kateryna Deineka, Serhii Zabchyk

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