Optimization and Validation of Multi-Size Ball Load Scheme for an Industrial Ball Mill Based on Semi-Theoretical Calculations and DEM Simulations: A Case Study of a Copper Mine

A comprehensive and systematic study was conducted to address a series of key technical challenges encountered in the grinding process at a copper mine. These issues included the complex mechanical properties of the feed ore, which led to low grinding efficiency, difficulty in achieving the required grinding fineness for flotation, uneven particle size distribution in the grinding products, and severe occurrences of overgrinding and undergrinding. Based on the semi-theoretical ball diameter formula, the optimal initial ball size distribution for the ball mill was precisely calculated as Φ70:Φ50:Φ40:Φ30 = 15:25:35:25. Through laboratory-scale grinding tests and Discrete Element Method (DEM) simulations, a systematic analysis of multiple indicators under three different ball loading schemes was performed, including the motion state of particles inside the mill, the collision behavior of the grinding media, and the energy distribution. This analysis confirmed the rationality and effectiveness of the literature scheme. Industrial trial results showed the following: the yield of the +0.20 mm fraction decreased by 4.15 percentage points, and the yield of the −0.010 mm fraction and its proportion relative to the −0.074 mm fraction decreased by 10.17 and 19.10 percentage points, respectively. Conversely, the yields of the intermediate separated fraction (−0.20 + 0.010 mm), the easily separated fraction (−0.074 + 0.018 mm) and the −0.074 mm qualified fraction increased by 14.32, 14.13, and 7.29 percentage points, respectively. The grinding technical efficiency improved by 19.55 percentage points. Furthermore, the specific steel ball consumption decreased by 46 g/t, a reduction of 5.07%. The copper concentrate recovery increased by 0.65 percentage points, resulting in an annual increase of 40.51 tons of copper metal, additional revenue of CNY 3.2483 million, and steel ball cost savings of CNY 603,500. Collectively, this optimization generated a total economic benefit of CNY 3.8518 million. By optimizing the ball size distribution, the particle size composition of the grinding products was significantly improved, the flotation indicators were enhanced, and the grinding media consumption cost was reduced, achieving quality improvement and efficiency increase in the mineral processing. This study provides a valuable reference for solving similar grinding problems.