SAG mill ball diameter semi-theory based on pebble fracture strength and DEM validation

The semi-autogenous grinding (SAG) mill, widely used in large mineral processing plants, is known for its high throughput and production efficiency. However, an accumulation of pebbles can lead to a reduction in throughput and an increase in power consumption during the grinding process. This study investigates the strength of pebbles in conjunction with Davis’ theory of ball movement, considering parameters such as pebble size, mill diameter, rotational speed, filling rate, and grinding concentration. Based on these factors, a semi-theoretical formula is developed to determine the optimal diameter of SAG mill balls. The validity of this formula was verified using discrete element numerical simulations and the Tavares breakage model. The results show that for a SAG mill with dimensions of Φ6.7 × 3.4 m at a tin mine, the steel ball gradation calculated by the semi-theoretical formula is n (Φ140mm): n (Φ110mm) = 1:2. According to the Tavares breakage model simulation, the total crushed mass for the 140–110 scheme was 75.87 kg, which represents a 6.59 % increase compared to the 71.18 kg from the on-site 120–100 scheme. In addition, the cumulative impact power of the steel balls on the rock in the 140–110 scheme was 0.23 % higher than in the on-site 120–100 scheme, while the cumulative impact power of the rock on itself increased by 3.36 %. These findings suggest that the proposed formula has the potential to reduce pebble accumulation and improve grinding efficiency.