A hybrid DEM-FRM-PBM model for parameter calibration and extended grinding in ball mills

• A hybrid DEM–FRM–PBM framework was developed for predicting ball mill grinding. • Accuracy of PBM prediction of PSD evolution in mills was improved by dynamically updating DEM energy distribution. • Grinding performance was affected by high-energy collisions and fines-induced buffering. • Variations in the mass fraction of product fines under different particle-ball mass ratios were successfully captured. • The model shows reasonable prediction of the evolution of PSD in a pilot-scale ball mill. Accurately predicting PSD evolution in ball mills is difficult because fully resolved breakage in DEM is computationally intensive, and conventionally calibrated PBMs often lack transferability. This work introduced a hybrid DEM–FRM–PBM approach that integrates short, targeted DEM runs using a fragment replacement method (FRM) with an energy-informed PBM to efficiently, mechanistically forecast grinding over long durations. In this framework, brief DEM–FRM intervals yielded internally consistent calibration of selection and breakage functions under realistic multi-impact energy conditions and continuously update the grinding energy spectra as the PSD evolves. Validation against short DEM–FRM simulations in a lab-scale mill showed the model closely reproduced early (