Ball-impact energy analysis of wet tumbling mill using a modified discrete element method considering the velocity dependence of friction coefficient

Abstract

A modified three-dimensional quasi-wet discrete element method (DEM), which is constructed by adding the drag force and buoyancy and the velocity dependence of the friction coefficient of a ball to a conventional dry DEM model, is proposed for analyzing the impact energy of balls in wet ball-milling processes. A comparison of the calculated ball motion in water as the liquid medium with the experimental results demonstrated the validity of the proposed model. The friction coefficient decreased with the increase in the vessel rotational speed and was expressed as a function of the rotational speed and loading amount of the balls. The velocity dependence of the friction coefficient was similar to the variation in the friction coefficient with the sliding velocity, as derived from the lubrication theory. A numerical analysis of the impact energy distribution in the vessel showed that relatively high-impact energies of the balls were intensively generated near the vessel wall, indicating that the wet ball-milling processes were controlled by the impact energy between the ball and the wall. Our model can contribute to reducing the calculation load for simulating the ball motion in wet ball-milling processes compared with the coupling models such as DEM-CFD.