A system–analogue method of identification of geometric shape of the abrasive grain projection

An advanced method of identification and quantitative estimation of geometric shape of the projection of abrasive powder grains has been proposed. The method is based on a system–analogue approach. For analogues the two-dimensional geometric figures (circles, ellipses, triangles, canonical forms of tetragons, regular pentagons, hexagons, and octagons) that admit a nonadditive analytical representation of the area in terms of generating parameters (whose number does not exceed three) have been taken. A differential and integral characteristics of the shape similarity have been introduced and an analytical apparatus has been put forward to determine the values of these characteristics. The results of appraisal (testing) of the method on synthetic diamond and cBN grits are discussed.