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Fractal dimension of crushing products: effects of feed size distribution and feed rate

Abstract In mineral crushing operations, the feed rate and feed size distribution affect the crushing rate and particle size distribution of the crushed products. In the present study, copper ore feed charges of different size distributions were prepared. These feed charges were fed to the jaw, cone, and roll crushers at different feed rates in the laboratory scales. The effects of these parameters on the crushed particle size distributions and crushing rates were investigated and described using the fractal geometry by the calculation of the product fractal dimensions. The fractal dimension was calculated based on a proportional relation between the size and weight of the particles. The obtained fractal dimensions of the particle size distributions for the particles crushed by the jaw, cone, and roll crushers were in the range of (2.16–2.38), (2.13–2.31), and (2.23–2.46) respectively. In all of three types of crushers, the fractal dimensions and crushing rate of the ore were increased with an increase in feeding feed size distribution and by increasing the amount of particles with sizes bigger than the setting size. Increasing the feed rate at the permitted capacity had an inverse relation with the fractal dimension and led to a reduction in both the fractal dimension and the crushing rate. However, an increase in the feed rate at the unpermitted capacity, having a direct relationship to the fractal dimension, was resulted an increase in crushing rate and fractal dimension of the ore due to the choke feeding.