Modeling And Simulation Of Ultra-Fine Grinding Of Alumina In A Planetary Ball Mill

Liberation of valuable minerals from low-grade ores is an important challenge faced by the minerals industry. It is necessary to grind the ore to extremely fine size in order to liberate the mineral from such ores. As it is generally difficult to produce ultra-fine particles of diameter less than 1-10 mm using traditional grinding equipment such as the ball mill and the rod mill, several new types of grinding equipment are being explored to produce ultra-fine particles. The planetary ball mill is promising in that it makes grinding to submicron sizes possible by imparting high energy to the ground powder. It consists of four pots mounted on a disc. The pots and the disc rotate in opposite directions. The high-speed rotation of the pots and the disc makes the grinding media move at high centrifugal velocities leading to high impact energy and thus improving the grinding performance. The planetary mill is currently being explored for its capability to produce ultra-fine particles on a large scale. In this context, there is a need to understand the dynamics of the ultra-fine grinding process within the planetary ball mill. Here, we address this need by studying the movement of media inside the pots and the grinding kinetics, employing both experimental and modeling techniques. The experiments were conducted on a laboratory scale planetary ball mill. The particle size distribution of the powder was monitored to allow an estimate of the grinding kinetics to be made while video images of the media profiles inside the pots were taken to allow quantification of the media movement as a function of process variables such as the media size, percent loading, etc. The population balance modeling (PBM) framework was used to simulate the kinetics of grinding while the discrete element modeling (DEM) approach was utilized to simulate the media motion. The parameters in the population balance model, namely, the specific breakage rate and the breakage distribution function were determined by fitting the batch grinding equation to the experimental data. The predicted powder size distributions were found to be in good agreement with the experimental data. The experimental results have shown that the mean size of product powder decreases as the size of the grinding media decreases. Keywords: population balance modeling, grinding, planetary mill, grinding media, grinding equation