Improvement of the accuracy of Hogg and Fuerstenau's model in predicting the power draw of ball mills based on determining the grinding media’s dynamic voidage

Abstract

In the development of tumbling mills' power models, the voidage of grinding media is assumed to be static and equal to 40%. While the grinding media's voidage is dynamic; and hence is varied by changing the operating parameters. In this paper, to improve the Hogg and Fuerstenau model's accuracy in predicting the ball mills' power draw, the grinding media's static and dynamic voidage was studied for Bond's proposed ball size distributions (BSD) for the ball mills' first filling. To this end, by scaling down balls to one-tenth of actual size, developing a novel method to measure the dynamic voidage, and employing the three-level factorial method, a separate empirical model was developed for determining the dynamic voidage of each Bond's BSD with respect to mill's fractional filling and rotating speed. Moreover, using the multiple regression method, a general empirical model was derived to determine the dynamic voidage of each supposed BSD based on calculating the mean absolute deviation of balls diameter (MAD). Results indicated that grinding media's dynamic voidage increases with an increase in rotating speed and a decrease in fractional filling and balls diameter's MAD. The maximum and minimum static and dynamic voidage occurred for the seventh and first Bond's BSDs. By employing an industrial database and analyzing the mean absolute percentage error (MAPE) of predicted ball mills' power draw, it was found that the Hogg and Fuerstenau model's accuracy enhances by calculating the load's bulk density based on the grinding media's dynamic voidage.