This paper investigates grinding media's dynamic voidage to improve the Morrell-C model's accuracy in predicting the ball mills’ power draw. Using a three-level factorial design, we provided an empirical model to determine the voidage of each ball size distribution proposed by Bond for ball mills’ first filling in various ranges of fractional mill filling and mill rotating speed. Moreover, by employing the multiple regression method, a general model was developed to predict the balls’ dynamic voidage by calculating the mean absolute deviation (MAD) of the balls’ diameter. Results revealed that the balls’ dynamic voidage increases with increasing the rotating speed and decreasing the fractional filling and MAD of the balls’ diameter. The evaluation of the grinding media's voidage prediction models’ performance in improving the Morrell-C model's accuracy indicated an increase in the model's predictive power by calculating the ball mills’ load bulk density based on the dynamic voidage of grinding media.
Al SadiJ.2018. Designing experiments: 3 level full factorial design and variation of processing parameters methods for polymer colors. ASTESJ. 3:109–115.
2.
AmanNejadM, BaraniK.2020. Effects of ball size distribution and mill speed and their interactions on ball milling using DEM. Miner Process Extr Metall Rev. 42:374–379. doi:10.1080/08827508.2020.1781630.
3.
BenyahiaF, O'NeillKE.2005. Enhanced voidage correlations for packed beds of various particle shapes and sizes. Part Sci Technol. 23:169–177.
4.
BierwagenGP, SandersTE.1974. Studies of the effects of particle size distribution on the packing efficiency of particles. Powder Technol. 10:111–119.
5.
BondFC.1958. Grinding ball size selection. Trans AIME. 211:592–595.
6.
ChristineF, KaderG, MewbornD, MorenoJ, PeckR, PerryM, ScheafferR.2007. Guidelines for assessment and instruction in statistics education. Boston: American Statistical Association.
7.
CorneilleEK.1987. Design, capital and operating costs of mineral processing plants. Miner Process Extr Metall Rev. 4:255–288.
8.
DavisEW.1919. Fine crushing in ball mills. AIME Trans. 61:250–296.
9.
DesmondKW, WeeksER.2014. Influence of particle size distribution on random close packing of spheres. Phys Rev J. 90:022041–6.
10.
DjordjevicN.2003. Discrete element modelling of power draw of tumbling mills. Min Proc Extractive Metall. 112:109–114.
11.
GhasemiAR, RaziE, BanisiS.2020. Determining a lower boundary of elasticity modulus used in the discrete element method (DEM) in simulation of tumbling mills. Adv Powder Technol. 31:1365–1371.
12.
GolpayeganiMH, AbdollahzadehAA.2017. Optimization of operating parameters and kinetics for chloride leaching of lead from melting furnace slag. Trans Nonferrous Met Soc China. 27:2704–2714.
13.
GolpayeganiMH, RezaiB.2022. Modeling the power draw of tumbling mills: a comprehensive review. Physicochem Probl Miner Process. 58:151600.
14.
GovenderN, RajamaniRK, KokS, WilkeDN.2015. Discrete element simulation of mill charge in 3D using the BLAZE-DEM GPU framework. Miner Eng. 79:152–168.
15.
GuptaA, YanD.2016. Mineral processing design and operations. 2nd ed.Amsterdam: Elsevier Science.
16.
GutiérrezA, AhuesD, GonzálezF, MerinoP.2019. Simulation of material transport in a SAG mill with different geometric lifter and pulp lifter attributes using DEM. Min Metall Explor. 36:431–440.
17.
HarrisJW, StockerH.1998. Segment of a circle. In: Handbook of mathematics and computational science. New York: Springer-Verlag; p. 102–104.
18.
HerdanG.1960. Small particle statistics. 2nd ed.New York: Butterworth.
19.
HesamiR.2016. A laboratory investigation of the effect of charge density on power draw in tumbling mills [master thesis]. Bahonar University. (In Persian).
20.
HildenMM, PowellMS, YahyaeiM.2021. An improved method for grinding mill filling measurement and the estimation of load volume and mass. Miner Eng. 160:106638.
21.
HlostaJ, JezerskáL, RozbrojJ, ŽurovecD, NěcasJ, ZegzulkaJ.2020. DEM investigation of the influence of particulate properties and operating conditions on the mixing process in rotary drums: part 1—determination of the DEM parameters and calibration. Processes. 8:1–26.
22.
HoggR, FuerstenauDW.1972. Power relationships for tumbling mills. Trans SME/AIME. 252:418–423.
23.
JacoxGG, FargeJC.1980. Recent developments in the production and testing of grinding media. ClM Bull. 1980:205–210.
24.
JeswietJ, SzekeresA.2016. Energy consumption in mining comminution. Procedia CIRP. 48:140–145.
25.
KiangiK, PotapovA, MoysMH.2013. DEM validation of media shape effects on the load behaviour and power in a dry pilot mill. Miner Eng. 46-47:52–59.
LatchireddiSR.2002. modeling the performance of grates and pulp lifters in autogenous and semiautogenous mills [PhD thesis]. University of Queensland.
28.
LiddellKS, MoysMH.1988. The effects of mill speed and filling on the behaviour of the load in a rotary grinding mill. J South Afr Ins Min Metall. 88:49–57.
29.
MishraBK, RajamaniRK.1992. The discrete element method for the simulation of ball mills. Appl Math Model. 16:598–604.
30.
MontgomeryDC.2005. Design and analysis of experiments. 6th ed. New York: John Wiley and Sons.
31.
MorrellS.1993. The prediction of power draw in wet tumbling mills [PhD thesis]. University of Queensland.
32.
MorrellS.2016. Modelling the influence on power draw of the slurry phase in autogenous (AG), semi-autogenous (SAG) and ball mills. Miner Eng. 89:148–156.
33.
MorrellS.2019. Testing and calculations for comminution machines. In: Kumar KavatraS, YoungCA, editors. SME mineral processing & extractive metallurgy handbook. Englewood: Society for Mining, Metallurgy, and Exploration (SME); p. 550–562.
34.
MoysMH.1993. A model of mill power as affected by mill speed, load volume, and liner design. Southern Afr Ins Min Metall. 93:135–141.
35.
PanjipourR, BaraniK.2014. The effect of ball size distribution on power draw, charge motion and breakage mechanism of tumbling ball mill by discrete element method (DEM) simulation. Physicochem Probl Miner Process. 54:258–269.
36.
RajamaniRK, KumarP, GovenderN.2019. The evaluation of grinding mill power models. Min Metall Explor. 36:151–157.
37.
SohnHY, MorelandC.1968. The effect of particle size distribution on packing density. CJChE. 46:162–167.
38.
Soleymani YazdiMR, KhorramA.2010. Modeling and optimization of milling process by using RSM and ANN methods. IJET. 2:474–480.
39.
TavaresL.2017. A review of advanced ball mill modelling. KONA. 34:106–124.
40.
U.S. DOE. 2007. Mining industry energy bandwidth study. Washington (DC): U.S. Department of Energy.
41.
ValeryW, JankovicA.2002. The future of comminution. In: 34th International October Conference on Mining and Metallurgy, p. 287–298.
42.
WhiteHA.1905. Theory of tube-mill action. J Chem Met Min Soc South Africa. 5:290–305.
43.
WillsBA, FinchJA.2016. Mineral processing technology: an introduction to the practical aspects of ore treatment and mineral recovery. Amsterdam: Elsevier.
44.
YangWC.2003. Liquid-solids fluidization. In: YangWC, editor. Handbook of fluidization and fluid–particle system. New York: Marcel Dekker; p. 28–30.
45.
YoshidaT, KurataniF, ItoT, TaniguchiK.2019. Vibration characteristics of an operating ball mill. J Phys. 1264:1–9.
46.
ZhangJ, BaiY, DongH, WuQ, YeX.2014. Influence of ball size distribution on grinding effect in horizontal planetary ball mill. Adv Powder Technol. 25:983–990.
