An approach for the modeling of batch grinding with single particle fracture studies and impact energy spectra

A number of studies have described methods to conduct laboratory scale milling tests and mathematical models to estimate the breakage rate. However, it is not possible to conduct laboratory milling studies for semiautogenous and autogenous mills. Hence, there is a need for determining breakage rates or modeling such mills via an alternate route. As far as semi-autogenous and autogenous mills are concerned, the two primary modes of breakage are impact and attrition, which can be readily studied in the laboratory. Such an approach is detailed in the current work.;The proof of the modeling concepts was shown for a 90 cm laboratory scale ball mill. The material used in the study was limestone. In the batch mill, approximately a 10 kg mass of limestone in the 32x25 mm size was ground with 100 kg of 50 mm steel ball charge.;The fundamental material breakage information was converted into energy based breakage distribution function and breakage rate function. These functions or sets of values constitute the parameters of the batch population balance model. It is shown that accurate particle size distribution predictions are possible with the modeling approach detailed in the current work.;The impact breakage mode was experimentally studied in a drop-weight apparatus and in a specialized device known as the ultra fast load cell. The abrasion mode of breakage was studied in a laboratory scale ball mill. In each of these studies the energy input for breakage was noted. Next, to convert the particle breakage versus energy data into breakage rates a mill-charge motion software was used. This software, which implements the discrete element method at its core, gives the impact energy spectra of the grinding mill. Thus, the fundamental breakage data gathered are converted into rates of breakage in the grinding mill.