A perfect mixing matrix model for ball mills

Abstract

A comminution model is developed for ball mills using the principles of perfect mixing. T-lines are developed from data arising from single particle breakage tests using a laser monitored, twin pendulum breakage device. A t1.4 parameter is developed that produces a family t-lines which can be modeled using linear equations. This eliminates the current problem of using splines to model t-curves as is the case with the t10 parameter. A linear relationship is also found between the natural logs of the t-number and the slopes of the t-lines making calculation of breakage progeny fractions much easier. A simpler exponential relationship between the comminution energy Ecs and the t1.4 parameter is developed which eliminates the need for constants. A lower triangular appearance matrix H is derived from these t-lines using data from an existing survey carried out on he Cu Concentrator circuit at Mt Isa Mines, Mt Isa, Australia. The model uses a top-down method of calculating the elements in the matrix and each hij element in the matrix is the t1.4 parameter relating to a particular feed size fraction. The comminution energy Ecs can then be scaled to account for various changes in mill operating conditions particularly feed tonnage.