System and criterial method of the identification and quantitative estimation of the geometrical shape of the abrasive powder grain projection

A new method of identification and quantitative estimation of geometrical shape of the projection of abrasive powder grains has been proposed. The method is based on the system and criterial approach. As analogs of 2D geometric figures (circles, ellipses, triangles, canonized shapes of tetragons, regular pentagons, hexagons, and octagon) that admit nonadditive analytical representation of the area via generating parameters, whose number does not exceed three, have been taken. Differential and integral characteristics of the shape similarity are introduced and the analytical apparatus of determining the characteristic values is proposed. The results of the appraisal of the method using mesh-size powders of synthetic diamond, tungsten carbide, garnet, and electrocorrundum are discussed.