Evaluation of Ball Mill Performance and Energy Consumption through the Discrete Element Method

Abstract

Ball mills are a frequently used technology for comminution in the chemical and mineral processing industries, yet their characteristically low energy efficiency presents a persistent operational challenge; even marginal improvements can yield substantial economic and environmental benefits. This research investigates the relationship between mill geometry, operational parameters, and grinding efficiency by employing an integrated computational and experimental framework. The study compares the performance of two distinct mill designs - polygonal and cylindrical geometries—under varied configurations (with and without lifters). The Discrete Element Method (DEM) was used to simulate particle dynamics, charge motion, and wear, while a Population Balance Model (PBM) was applied to determine ore-specific breakage parameters and predict product size distributions. Simulations were validated against experimental data obtained from a custom-designed milling setup capable of precise speed control and in-line torque monitoring. Key findings from the DEM analysis demonstrate that geometry fundamentally alters charge behavior. At 75% of critical speed, a polygonal mill without lifters increased effective interparticle interactions by 10% and minimized particle centrifuging compared to a lifter-less cylindrical mill. The introduction of lifters further optimized performance: in the polygonal design, lifter addition enhanced collision frequency, resulting in a significant 26% reduction in power draw and a reduced Archard wear rate of 1.18×〖10〗^(-3) m. The cylindrical mill equipped with lifters achieved high collision intensity similar to the polygonal design but exhibited superior operational stability and about 30% lower wear rate. The developed DEM model demonstrated strong predictive capability, achieving a high Pearson correlation coefficient (>0.9) between simulated and experimental results. Predictions showed excellent quantitative agreement with experimental data, with root mean square errors (RMSE) of 2.3 W for power draw and 2.1° for shoulder angle. The grinding kinetics of two ore types, a gold ore and a malachite copper ore (averaging 4.7% Cu), were characterized using the PBM. The specific breakage rate (S_i) for the malachite ore increased with particle size, reaching a maximum of 2.892 min⁻¹ at 2 mm, a phenomenon attributed to the reduced agglomeration tendency and lower surface energy of larger particles. Breakage distribution functions and the optimum feed size for efficient milling were established. Furthermore, investigations into binary ore blends revealed that overall grindability is non-linear and disproportionately influenced by the harder ore component, potentially leading to a broader product size distribution when ores of differing hardness are combined. The DEM-calibrated parameters and PBM-derived kinetic models generated in this study provide a robust, scalable foundation for the design and optimization of industrial grinding circuits, directly linking particle-scale mechanics to full-circuit performance.

Keywords: Ball mill, Discrete Element Method, Population Balance Model, Milling kinetics.