XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 3729
with higher mean absolute deviation (MAD) of balls’ diam-
eter. The seventh ball size distribution (BSD7) exhibited
the highest dynamic voidage (41.22% to 48.98%) with
the lowest MAD, while the first distribution (BSD1) had
the lowest dynamic voidage (35.61% to 40.92%) with the
highest MAD.
A general regression model was developed to predict
dynamic voidage based on fractional mill filling, rotating
speed, and MAD of balls’ diameter, achieving an adjusted
R-squared value of 99.21%. Evaluation using mean abso-
lute percentage error (MAPE) showed that employing the
proposed models led to a 3.9% to 3.2% reduction in MAPE
of the Hogg and Fuerstenau model, indicating improved
prediction accuracy. Similarly, the MAPE of the Morrell
C-model decreased by about 2.61% and 2.29% when using
the proposed models to calculate grinding media voidage,
respectively, enhancing model prediction accuracy.
REFERENCES
Benyahia, F., O’Neill, K. E., 2005. Enhanced Voidage
Correlations for Packed Beds of Various Particle Shapes
and Sizes. Particulate Science and Technology, 23,
169–177.
Bierwagen, G.P., Sanders, T.E, 1974. Studies of the Effects
of Particle Size Distribution on the Packing Efficiency
of Particles. Powder Technology, 10, 111–119.
Bond, F.C., 1958. grinding ball size selection. Trans AIME,
211, 592–595.
Christine, F., Kader, G., Mewborn, D., Moreno, J., Peck,
R., Perry, M., Scheaffer, R., 2007. Guidelines for
Assessment and Instruction in Statistics Education.
Boston: American Statistical Association.
Corneille, E. K., 1987. Design, capital and operating costs
of mineral processing plants. Mineral Processing and
Extractive Metallurgy Review, 4, 255–288.
Davis E.W, 1919. Fine crushing in ball mills. AIME
Transactions, 61, 250–296.
Desmond K.W., Weeks, E.R., 2014. Influence of particle
size distribution on random close packing of spheres.
Physical review Journal, 90, 022041–6.
Doll, A. G., 2016. An updated data set for sag mill power
model calibration. XXVIII International Mineral
Process Congress, Quebec, Canada, 1–22.
Golpayegani, M., Rezai, B., 2022. Modeling the power
draw of tumbling mills: A comprehensive review.
Physicochem. Probl. Miner. Process., 58, 151600.
Golpayegani, M.H., Abdollahzadeh, A.A., 2017.
Optimization of operating parameters and kinetics for
chloride leaching of lead from melting furnace slag.
Trans. Nonferrous Met. Soc. China, 27, 2704−2714.
Harris, J. W., Stocker, H., 1998. Segment of a Circle.
In: Handbook of Mathematics and Computational
Science. New York Springer-Verlag.
Herdan, G., 1960. Small Particle Statistics. 2rd ed, New
York: Butterworth.
Hesami, R., 2016. A laboratory investigation of the effect
of charge density on power draw in tumbling mills.
Master thesis. Bahonar University. (In Persian).
Figure 10. Comparison of Actual vs. Predicted Ball Mills’ Power Draw Using Original and Modified Power Draw Models. (a)
Hogg and Fuerstenau’s Model, (b) The Morrell C-Model
with higher mean absolute deviation (MAD) of balls’ diam-
eter. The seventh ball size distribution (BSD7) exhibited
the highest dynamic voidage (41.22% to 48.98%) with
the lowest MAD, while the first distribution (BSD1) had
the lowest dynamic voidage (35.61% to 40.92%) with the
highest MAD.
A general regression model was developed to predict
dynamic voidage based on fractional mill filling, rotating
speed, and MAD of balls’ diameter, achieving an adjusted
R-squared value of 99.21%. Evaluation using mean abso-
lute percentage error (MAPE) showed that employing the
proposed models led to a 3.9% to 3.2% reduction in MAPE
of the Hogg and Fuerstenau model, indicating improved
prediction accuracy. Similarly, the MAPE of the Morrell
C-model decreased by about 2.61% and 2.29% when using
the proposed models to calculate grinding media voidage,
respectively, enhancing model prediction accuracy.
REFERENCES
Benyahia, F., O’Neill, K. E., 2005. Enhanced Voidage
Correlations for Packed Beds of Various Particle Shapes
and Sizes. Particulate Science and Technology, 23,
169–177.
Bierwagen, G.P., Sanders, T.E, 1974. Studies of the Effects
of Particle Size Distribution on the Packing Efficiency
of Particles. Powder Technology, 10, 111–119.
Bond, F.C., 1958. grinding ball size selection. Trans AIME,
211, 592–595.
Christine, F., Kader, G., Mewborn, D., Moreno, J., Peck,
R., Perry, M., Scheaffer, R., 2007. Guidelines for
Assessment and Instruction in Statistics Education.
Boston: American Statistical Association.
Corneille, E. K., 1987. Design, capital and operating costs
of mineral processing plants. Mineral Processing and
Extractive Metallurgy Review, 4, 255–288.
Davis E.W, 1919. Fine crushing in ball mills. AIME
Transactions, 61, 250–296.
Desmond K.W., Weeks, E.R., 2014. Influence of particle
size distribution on random close packing of spheres.
Physical review Journal, 90, 022041–6.
Doll, A. G., 2016. An updated data set for sag mill power
model calibration. XXVIII International Mineral
Process Congress, Quebec, Canada, 1–22.
Golpayegani, M., Rezai, B., 2022. Modeling the power
draw of tumbling mills: A comprehensive review.
Physicochem. Probl. Miner. Process., 58, 151600.
Golpayegani, M.H., Abdollahzadeh, A.A., 2017.
Optimization of operating parameters and kinetics for
chloride leaching of lead from melting furnace slag.
Trans. Nonferrous Met. Soc. China, 27, 2704−2714.
Harris, J. W., Stocker, H., 1998. Segment of a Circle.
In: Handbook of Mathematics and Computational
Science. New York Springer-Verlag.
Herdan, G., 1960. Small Particle Statistics. 2rd ed, New
York: Butterworth.
Hesami, R., 2016. A laboratory investigation of the effect
of charge density on power draw in tumbling mills.
Master thesis. Bahonar University. (In Persian).
Figure 10. Comparison of Actual vs. Predicted Ball Mills’ Power Draw Using Original and Modified Power Draw Models. (a)
Hogg and Fuerstenau’s Model, (b) The Morrell C-Model