Mathematical representation of crushing and grinding systems has, for many years, been concerned with energy and efficiency considerations. Whilst accurate forecasting of energy requirements is of economic importance it is a machine property and of no use when prediction of product size distributions is desired. The use of breakage functions to represent product size distributions has proved effective over small size ranges but is not applicable to the larger particle sizes or to a wide range of feed sizes. Solution of the integro-differential equations which describe crushing operations has in the past led to extremely complex problems that have so far proved unsolvable without drastic and unreasonable assumptions being made. The representation of comminution in this work is made by means of an experimentally determined plant operator matrix. It is shown that such a matrix, whose elements are determined by crushing the feed size fractions separately, gives excellent predictions of product size distributions for a mixed feed. The technique is extended to consider different milling actions and feed materials. It is demonstrated that the simulation of multistage, series grinding is possible by this method enabling optimum utilisation of crushing equipment. By a minimum of experimental observations a multiparameter mill model is produced using linear interpolation between data points. This model is used in digital computer simulation of mill operating conditions in open and closed circuit grinding to select mill parameters for constraints on feed and product size distributions.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.