2D Model for Ball Mills

Abstract

This work develops a mathematical model that explains the ball mills operational speed. The scope of the model is defined by the powder as the number of particles per cm3 and the Relevance defined as the ratio between different forces. In this study, the Relevance is defined as the ratio between superficial tension and inertial forces. The conditions for a free flowing powder and a single particle are differenced and non-dimensional numbers are found. The model proposed use the friction force between mill walls and the powder mass is related by a friction coefficient that can be calculated from angle repose. An experimental approach proves that the suppositions made in order to develop the model were adequate in this way the existence of the non-dimensional numbers is confirmed. It is also discussed the use of non-dimensional numbers to increase processing speeds with by increasing gravity clarifying that a given Relevancy, it is not dependent of the non-dimensional numbers. Thus, the model can help in the design process of ball mills with a deeper understanding of the phenomena.