EXPERIMENTAL INVESTIGATION OF THE ENERGY-SIZE REDUCTION RELATIONSHIP IN COMMINUTION USING FRACTAL THEORY

On the basis of Kick's, Rittinger's, and Bond's theories, this paper shows that the three traditional expressions based on these theories are generally stated as follows: dE=-C dx/x(4-D)s , where E is energy input, C is a constant, x is the particle size, and D(S) is the fractal dimension of a rock-fractured particle surface: and that three expressions may be derived as special cases of this general equation and Rittinger's theory is obeyed for common comminution systems. Semi-automatic image analysis was used for fractal dimension measurement of 450 rock-fractured particle profiles chosen from 45 samples obtained by different fracture methods, such as high static compression, impact, jaw crushing and ball mill grinds. The experimental data show good agreement between the authors' equation and the empirical equations derived from the experiments of Charles, Hukki, Kwong et al and Brown et al; and also indicate thal the smaller the particle size, the slightly bigger is the fractal dimension D(S);in other words, the more irregular is the particle surface. This investigation shows that values of D(S) are different for different size reduction methods, and ball mill grinds can produce the smoothest particle surfaces. A conclusion of this paper is that the actual particle surface area may be more than 1.26 times that of traditional estimates.