Scaling Energy Transfer in Ball Mills: A Scale-Agnostic Approach through a Universal Scaling Constant

Abstract

Ball mills are widely used for size reduction in mineral processing, but effective scaling from laboratory to industrial scale remains challenging. This study introduces a novel scaling constant approach to replicate energy transfer to ore during milling across different scales by adjusting rotational speed and grinding medium size distribution. The scaling constant encapsulates parameters like the number of balls per working area, rotational speed, and an average ball’s maximum potential and kinetic energies. Experiments were conducted using a laboratory ball mill with interchangeable drum sizes (300, 400, and 500 mm) and a Design of Experiments methodology. Statistical analysis revealed that the scaling constant was more effective at maintaining consistent specific energy and energy per rotation across scales than size reduction, especially in dry milling. Wet milling results showed no significant differences in all metrics across scales. The dominant charge motion shifted from centrifuging to cascading as the mill diameter increased, highlighting the complex scaling dynamics. While the scaling constant shows promise for maintaining energy utilization, additional factors like charge motion and particle breakage mechanisms should be considered. The findings provide insights for improving ball mill design and optimization in mineral processing.