3715
Enhancing the Predictive Accuracy of the Ball Mills’
Power Draw Models by Calculating the Dynamic Voidage of the
Grinding Media
M. H. Golpayegani, Bahram Rezai
Mining engineering faculty, Amirkabir University of Technology, Tehran, Iran
K. Kiaei
Enter Engineering Company, Tashkent, Uzbekistan
ABSTRACT: The objective of the study was to enhance the precision of power models for tumbling mills
by incorporating the dynamic voidage of grinding media. Conventionally, a fixed grinding media’s voidage of
40% was assumed in developing the power draw models, but it was discovered in this research that the voidage
fluctuates with changes in operating parameters. The research specifically focused on Bond’s proposed ball size
distributions (BSD) for the first filling of the ball mills. By scaling down the size of the balls, a novel methodology
was devised to measure the dynamic voidage, while a three-level factorial approach was employed to examine
the correlation between voidage, mill filling, and rotating speed. Through the multiple regression method, a
comprehensive empirical model was developed to determine the dynamic voidage based on the mean absolute
deviation of the ball’s diameter. The findings demonstrated that the dynamic voidage increased with higher
rotating speeds, lower fractional filling, and reduced deviations in the balls’ diameter. The seventh and first
Bond’s BSDs exhibited the highest and lowest voidage, respectively. By considering the dynamic voidage and
calculating the bulk density of the mill load, the accuracy of the Morell-C model and the Hogg and Fuerstenau
model in predicting power draw experienced improvement, as verified by an analysis of an industrial database.
Keywords: Ball mill dynamic voidage grinding media, power draw
INTRODUCTION
The mineral processing sector heavily relies on commi-
nution processes to attain the desired liberation degree of
minerals. Tumbling mills stand as the linchpin of metal
production operations, as all minerals utilized in min-
eral and metallurgical processes must undergo grinding
(Gupta and Yan, 2016 Wills and Finch, 2016). Grinding
operations contribute significantly to the total energy con-
sumption in the mining industry and operational costs in
mineral processing plants (Corneille, 1987 U.S. DOE,
2007 Jeswiet and Szekeres, 2016). Thus, optimizing power
consumption is crucial, leading to efforts in developing
models predicting tumbling mills’ power draw accurately.
Models for tumbling mills’ power draw description are
categorized into empirical and fundamental, with various
subsets like energy balance, friction method, torque-arm
approach, and discrete element method (Tavares, 2017
Morrell, 2019 Golpayegani and Rezai, 2022). Empirical
Enhancing the Predictive Accuracy of the Ball Mills’
Power Draw Models by Calculating the Dynamic Voidage of the
Grinding Media
M. H. Golpayegani, Bahram Rezai
Mining engineering faculty, Amirkabir University of Technology, Tehran, Iran
K. Kiaei
Enter Engineering Company, Tashkent, Uzbekistan
ABSTRACT: The objective of the study was to enhance the precision of power models for tumbling mills
by incorporating the dynamic voidage of grinding media. Conventionally, a fixed grinding media’s voidage of
40% was assumed in developing the power draw models, but it was discovered in this research that the voidage
fluctuates with changes in operating parameters. The research specifically focused on Bond’s proposed ball size
distributions (BSD) for the first filling of the ball mills. By scaling down the size of the balls, a novel methodology
was devised to measure the dynamic voidage, while a three-level factorial approach was employed to examine
the correlation between voidage, mill filling, and rotating speed. Through the multiple regression method, a
comprehensive empirical model was developed to determine the dynamic voidage based on the mean absolute
deviation of the ball’s diameter. The findings demonstrated that the dynamic voidage increased with higher
rotating speeds, lower fractional filling, and reduced deviations in the balls’ diameter. The seventh and first
Bond’s BSDs exhibited the highest and lowest voidage, respectively. By considering the dynamic voidage and
calculating the bulk density of the mill load, the accuracy of the Morell-C model and the Hogg and Fuerstenau
model in predicting power draw experienced improvement, as verified by an analysis of an industrial database.
Keywords: Ball mill dynamic voidage grinding media, power draw
INTRODUCTION
The mineral processing sector heavily relies on commi-
nution processes to attain the desired liberation degree of
minerals. Tumbling mills stand as the linchpin of metal
production operations, as all minerals utilized in min-
eral and metallurgical processes must undergo grinding
(Gupta and Yan, 2016 Wills and Finch, 2016). Grinding
operations contribute significantly to the total energy con-
sumption in the mining industry and operational costs in
mineral processing plants (Corneille, 1987 U.S. DOE,
2007 Jeswiet and Szekeres, 2016). Thus, optimizing power
consumption is crucial, leading to efforts in developing
models predicting tumbling mills’ power draw accurately.
Models for tumbling mills’ power draw description are
categorized into empirical and fundamental, with various
subsets like energy balance, friction method, torque-arm
approach, and discrete element method (Tavares, 2017
Morrell, 2019 Golpayegani and Rezai, 2022). Empirical