Technical Notes - A Three Dimensional Derivation of the Gaudin Size Distribution Equation

Recently, Gilvarry1 has criticized the Gaudin-Meloy2 derivation of the size distribution equation for impact grinding. The criticism states that as the derivation stands it is good for only a long, thin wire being fractured. This paper contains a second derivation in reply to the criticism. Consider a homogeneous solid particle. This particle is broken into fragments by impact. It is assumed that the material resembles galena and that the particles were broken into chunky parallelepipedes which may be treated as cubes. The fragments are now reassembled — as seen in Fig. 1 — and a line is passed through the fractured solid perpendicular to one of its faces. For simplicity, the length of the line segment in the cube is considered to be 1. Fig. 2 represents the line segment in the cube showing the locations of the crack surfaces cutting the line and one point, P, chosen at random on it. The question arises as to what is the probability of the point, P,