Evaluation of the relationship between energy input and particle size distribution in comminution with the use of piecewise regression analysis

It is known that the single linear Gates–Gaudin–Schuhmann (GGS) model is in some cases unable to fully describe the particle size distribution of comminution products. In order to overcome this shortcoming, piecewise regression analysis was used to predict the size distributions derived, after grinding for various periods four mono-sized fractions of quartz and marble in a laboratory ball mill. The single line was divided into two straight lines, which indicate the presence of two domains of particle sizes and therefore the involvement of two distinct breakage mechanisms. The obtained GGS model parameters were used to determine the evolution of particle size distribution as a function of the energy input.In addition, the existing relationships between energy input and particle size distribution were improved, by taking into account the effects of the feed size and material type. The new relationships obtained can be used for a more accurate estimation of the required energy for breakage.