Geometric Design of Tumbling Mill Lifter Bars Utilizing the Discrete Element Method

Abstract

The energy consumption of bulk materials handling consumes around 10% of the annual energy utilization on the planet, often driven by inefficient processes. A primary process in the reduction of particle size to fine grind are ball mills. Ball mills utilize ball charge to aid the grinding and are usually used as a primary grinding solution. Ball mills usually operate with charge around 30% with ball mill units utilizing up to 20 MW while standing up to a height of around 9 m. Industrial ball mills draw around 0.0011% of the world’s total power. We consider the geometric design optimization of the lifter bars for a ball mill. By utilizing the discrete element method (DEM) the collision frequency, relative velocity between colliding particles and contact force to estimate the specific impact energy for the ball mill is available. In this study we investigate the effect of the geometry of the lifter bar, that is height and bar angle with respect to the side wall, has on the specific impact energy for various charge distributions. In addition to the specific impact energy the energy spectra of the ball mill is computed to assess the energy distribution in normal and shear interactions. As the discrete element method is computationally demanding we investigate the extent to which the computational cost can be mitigated by following a multi-fidelity approach in which the number of particles and particle sizes are scaled to reduce the initial computational cost and only refined as the design optimization converges. Towards this aim we consider a virtual problem in which we aim to design the lifter of a tumbling mill for a specified power draw of the mill. The problem under consideration is denoted virtual as the solution of the problem is known a priori. This allows us to quantify and assess the quality of the obtained designs using the various strategies. The associated computational cost when considering the full computational model against the multi scaled computational models are then quantified.