Insights into advanced ball mill modelling through discrete element simulations

Important advances have been made in understanding ball milling during the last 25 years or so, a great part of it owing to the widespread application of the discrete element method (DEM), which is now an integral part of several advanced ball mill models. These models, however, must rely on assumptions regarding the mill mechanical environment that can help make the problem more manageable. The paper analyzes the validity of some assumptions that have been the basis of several advanced ball mill models by conducting DEM simulations of dry batch mills including both grinding media and particles. The validity of the assumption of perfect mixing of grinding media and particles, as well as of simulating exclusively the grinding media in order to collect the collision energy information for prediction of breakage and, thus, saving computational effort, are analyzed in great detail. It is concluded that the assumption of perfect mixing in the radial direction is generally valid, except for mill frequencies that are unusually high and exceedingly large ratios of mean ball and particle sizes being ground. It is also observed that a fraction of the number of collisions inside the mill do not involve particles, so that an empirical expression that is based on the ratio of surface areas of the ball and particle charge is proposed to estimate such proportion of unsuccessful collisions. Finally, a model from the authors laboratory, that assumes that each collision in the mill will involve a monolayer bed of particles, is tested, demonstrating reasonable agreement when compared to simulations.