Tumbling Mill Power at Cataracting Speeds

The correlation of power consumed by a tumbling mill with the dimensions, speed, and load has been attempted by three principal methods. One of these, the torque formula, has been reviewed critically elsewhere. This approach, while analytical, disregards the individual motion and speed of the tumbling bodies and assumes that the gross geometry of the entire load is sufficient to establish the power requirement. A more general approach, using dimensional analysis, has been applied in this laboratory by the present authors, and more recently by Rose. This disregards the internal conditions within the mill entirely and in effect is an empirical procedure for correlating data. Finally, the complete analysis of tumbling mill dynamics as first made by Davis attempts to develop the power requirement from individual ball and rod paths and velocities. Although Davis' result is applicable only at a single speed for a given size and load it could be useful, since his optimum speed is at the upper limits of conventional tumbling mill practice. Where power values predicted by the Davis equation were compared with actual mill requirements, they were found too low for small mills and much too high for the largest mills. This suggested that the agreement with actual intermediate range requirements might be fortuitous, and the development of the equation was examined critically.