Probabilistic modeling and industrial validation of ore grinding in drum mills using a physically motivated activation factor

Abstract

This study presents a modified activation factor for probabilistic ore-grinding models in drum mills, based on thermodynamic considerations. The proposed formulation accounts for the combined contribution of the potential and kinetic energies of grinding bodies and refines the effective ball fall height in the cascading mode from 0.5D to 0.83D, resulting in a 17.6% increase in the estimated mechanical energy transfer. The activation energy is estimated from the material melting temperature, providing an alternative to conventional empirical fitting coefficients. The model was evaluated using quartz grinding calculations and industrial data from an MShR 3.2 × 3.1 mill at the Zhezkazgan concentrator. The comparison between the calculated and experimental particle size distributions showed a statistically significant correlation (R = 0.628), indicating that the proposed approach provides a physically meaningful description of the grinding process under the investigated industrial conditions.