# Identification of energy efficiency of ore grinding and the liner wear by a three­phase motion of balls in a mill

## Authors

• Vasyl Kondratets Central Ukrainian National Technical University Universytetskyi ave., 8, Kropyvnytskyi, Ukraine, 25006, Ukraine
• Anatolii Matsui Central Ukrainian National Technical University Universytetskyi ave., 8, Kropyvnytskyi, Ukraine, 25006, Ukraine
• Volodymyr Yatsun Central Ukrainian National Technical University Universytetskyi ave., 8, Kropyvnytskyi, Ukraine, 25006, Ukraine
• Mihail Lichuk Central Ukrainian National Technical University Universytetskyi ave., 8, Kropyvnytskyi, Ukraine, 25006, Ukraine

## Keywords:

energy efficiency, automated control, ore grinding, ball mill, elastic converters.

## Abstract

We have analytically derived an equation that relates the technological parameters of a ball mill, grinding material, to the parameters of a rod primary converter of energy efficiency of ore grinding. By using a method of applying a basic rod primary converter with a large cross-sectional area, at the side end of which large pieces of ore are destroyed at balls impacts, and an additional rod converter with identical parameters and a smaller cross-sectional area, which interacts only with balls, we have achieved invariance in determining the energy efficiency of ore grinding by a ball mill to a change in the motion speed of grinding bodies. We have analytically derived a mathematical model of energy-saving ore grinding by a ball mill with a three-phase motion of grinding bodies, invariant to a change in the length of rods during wear. The model can estimate the energy efficiency of grinding larger pieces of ore based on the resulting volume of crushed large-lump material. The mathematical model includes such constants as the cross-sectional areas of rod primary converters, the initial length of rod primary converters, the length of a basic section of strain gauges arrangement, the value for Young's modulus of the primary converters' material, as well as the changing constants that are defined by the ground material. In addition, the dependence has been derived analytically for determining the length of a main rod primary converter, based on which one can estimate the height of a liner, which wears out in the course of operation.

We have devised a functional circuit for the automated control system of energy efficiency of ore grinding by a ball mill that makes it possible to obtain estimation parameters using modern microprocessor tools. According to the devised circuit, one can build algorithms for determining the volume of ore to be crushed, as well as the thickness of a liner in a ball mill, which open up an avenue for developing software products.

Computer simulation has proven the possibility of applying the proposed method in order to estimate energy efficiency of ore grinding by a ball mill with a three-phase ball motion. We have established high sensitivity of the proposed approach to a deviation in energy efficiency of ore grinding from the best value. A possibility to estimate the parameter with a relative error of ±2.5 % has been confirmed.

## Author Biographies

### Vasyl Kondratets, Central Ukrainian National Technical University Universytetskyi ave., 8, Kropyvnytskyi, Ukraine, 25006

Doctor of Technical Sciences, Professor

Department of Automation of Production Processes

### Anatolii Matsui, Central Ukrainian National Technical University Universytetskyi ave., 8, Kropyvnytskyi, Ukraine, 25006

PhD, Associate Professor

Department of Automation of Production Processes

### Volodymyr Yatsun, Central Ukrainian National Technical University Universytetskyi ave., 8, Kropyvnytskyi, Ukraine, 25006

PhD, Associate Professor

Department of Road Cars and Building

### Mihail Lichuk, Central Ukrainian National Technical University Universytetskyi ave., 8, Kropyvnytskyi, Ukraine, 25006

PhD, Associate Professor

Department of Mathematics and Physics

## References

1. Shinkorenko, S. F. (2002). Gidromekhanika rabochey sredy sharovyh mel'nic mokrogo izmel'cheniya. Gorniy zhurnal, 7, 19–24.
2. Naumenko, Yu. V. (2014). Osnovy teoriyi rezhymiv roboty barabannykh mlyniv. Rivne: NUVHP, 336.
3. Sanfratello, L., Caprihan, A., Fukushima, E. (2006). Velocity depth profile of granular matter in a horizontal rotating drum. Granular Matter, 9 (1-2), 1–6. doi: https://doi.org/10.1007/s10035-006-0023-1
4. Yang, R. Y., Yu, A. B., McElroy, L., Bao, J. (2008). Numerical simulation of particle dynamics in different flow regimes in a rotating drum. Powder Technology, 188 (2), 170–177. doi: https://doi.org/10.1016/j.powtec.2008.04.081
5. McElroy, L., Bao, J., Yang, R. Y., Yu, A. B. (2009). A soft-sensor approach to flow regime detection for milling processes. Powder Technology, 188 (3), 234–241. doi: https://doi.org/10.1016/j.powtec.2008.05.002
6. Kondratets, V. (2014). Adaptive control of ore pulp thinning in ball mills with the increase of their productivity. Metallurgical and Mining Industry, 6, 12–15.
7. Morozov, V. V., Topchaev, V. P., Ulitenko, K. Ya., Ganbaatar, Z., Delgerbat, L. (2013). Razrabotka i primenenie avtomatizirovannyh sistem upravleniya processami obogascheniya poleznyh iskopaemyh. Moscow: Izd. dom «Ruda i Metally», 512.
8. Tang, J., Yu, W., Chai, T., Liu, Z., Zhou, X. (2016). Selective ensemble modeling load parameters of ball mill based on multi-scale frequency spectral features and sphere criterion. Mechanical Systems and Signal Processing, 66-67, 485–504. doi: https://doi.org/10.1016/j.ymssp.2015.04.028
9. Pedrayes, F., Norniella, J. G., Melero, M. G., Menéndez-Aguado, J. M., del Coz-Díaz, J. J. (2018). Frequency domain characterization of torque in tumbling ball mills using DEM modelling: Application to filling level monitoring. Powder Technology, 323, 433–444. doi: https://doi.org/10.1016/j.powtec.2017.10.026
10. Roux, J. D. le, Craig, I. K. (2017). Requirements for estimating the volume of rocks and balls in a grinding mill. IFAC-PapersOnLine, 50 (1), 1169–1174. doi: https://doi.org/10.1016/j.ifacol.2017.08.403
11. Rezaeizadeh, M., Fooladi, M., Powell, M. S., Mansouri, S. H., Weerasekara N. S. (2010). A new predictive model of lifter bar wear in mills. Minerals Engineering, 23 (15), 1174–1181. doi: https://doi.org/10.1016/j.mineng.2010.07.016
12. Pivnyak, G. G., Vaysberg, L. A., Kirichenko, V. I., Pilov, P. I., Kirichenko, V. V. (2007). Izmel'chenie. Energetika i tekhnologiya. Moscow: Izd. dom «Ruda i metally», 296.
13. Nikitin, S. V., Karelina, M. Yu. (2014). Prikladnaya mekhanika. Ch. 1. Soprotivlenie materialov. Moscow: MADI, 244.
14. Andreev, S. Е., Perov, V. A., Zverevich, V. V. (1980). Droblenie, izmel'chenie i grohochenie poleznyh iskopaemyh. Moscow: Nedra, 415.
15. Deshko, Yu. I., Kreymer, M. B., Kryhtin, G. S. (1966). Izmel'chenie materialov v cementnoy promyshlennosti. Moscow: Stroyizdat, 270.
16. Bogdanov, V. S., Hahalev, P. A. (2014). Vliyanie profilya konusno-volnistoy futerovki barabannyh mel'nic na energeticheskie pokazateli sharovoy zagruzki. Cement i ego primenenie, 2, 93–97.
17. Motra, H. B., Hildebrand, J., Dimmig-Osburg, A. (2014). Assessment of strain measurement techniques to characterise mechanical properties of structural steel. Engineering Science and Technology, an International Journal, 17 (4), 260–269. doi: https://doi.org/10.1016/j.jestch.2014.07.006
18. Yurdem, H., Degirmencioglu, A., Cakir, E., Gulsoylu, E. (2019). Measurement of strains induced on a three-bottom moldboard plough under load and comparisons with finite element simulations. Measurement, 136, 594–602. doi: https://doi.org/10.1016/j.measurement.2019.01.011
19. Zhou, K., Wu, Z. Y. (2017). Strain gauge placement optimization for structural performance assessment. Engineering Structures, 141, 184–197. doi: https://doi.org/10.1016/j.engstruct.2017.03.031

2019-06-28

## How to Cite

Kondratets, V., Matsui, A., Yatsun, V., & Lichuk, M. (2019). Identification of energy efficiency of ore grinding and the liner wear by a three­phase motion of balls in a mill. Eastern-European Journal of Enterprise Technologies, 3(5 (99), 21–28. https://doi.org/10.15587/1729-4061.2019.167046

Applied physics