Generalized mathematical model applied to a silica sand laboratory-controlled mill: Derivation of simplified ceramic ball entrance flux, ball wear consumption, and mass distribution functions

Abstract

A laboratory-controlled milling process of silica sand was carried out using aluminum oxide balls of three different sizes. The ball wear kinetic equations were experimentally obtained from the evolution curves of the ball diameter as a function of the operating time. From a generalized model, the ball entrance flux and ball wear consumption were calculated using exact two-parameter solution functions. One-parameter ball entrance flux and ball wear consumption functions were proposed to perform calculations that accurately describe the values provided by the two-parameter functions. In addition, a compact form of the ball mass distribution function is found. This set of simplified equations can be suitable for fast calculations in the milling industry.