Minerals Beneficiation - Correlation of Product Size, Capacity and Power in Tumbling Mills

Over the last one hundred years the problem of assessing the efficiency of energy consumption in producing rock breakage has been studied by many investigators from a variety of viewpoints. Their contributions fall into three main categories: (1) those characterized by a priori assumptions of a relation between the energy required for fracture and the degree of fragmentation produced (e.g. Rittinged(l), Kick(2) Bond(3)); (2) those studying simple systems with controlled energy applications (Gross(4)?(5) ); (3) those treating operating data to develop practical relative measures of efficiency (Coghill(6), Taggart(7)). Closely involved in the efficiency problem is the characterization of size distributions produced by comminution. Unless an experimental size distribution can be approximated by a distribution function and its constants, it becomes difficult if not impossible to develop quantitative energy-particle size relationships. While many such functions have been proposed, none are both completely adequate and convenient. The simpler fonns usually describe only a part of the sizing data, while those which apply to a greater extent are cumbersome(8). The thesis underlying the study here reported can be stated as follows: Size reduction in a tumbling mill subjects ore particles to a relatively constant fracture-producing environment. The intensity of the forces is determined by such factors as the mass of the breaking bodies (rods, balls, rock), and the speed and dimensions of the shell. For a particular ore the extent of size reduction will depend both on the intensity and on the duration of exposure. The latter is the residence time in a batch mill, or is determined by the effective volume and the flow rate in a continuous mill. Size reduction can thus be regarded as a rate process in which the weight of material in size intervals varies as a function of grinding time. Although both the rates of disappearance of coarser sizes and