In the article the results of studies of the current state of the working surface of the abrasive tool, which is de-termined by the shape of the cutting edges, their number, distribution, shape of the tool, the presence of cutting edges and in the pores of the circle of particles of the processed material are presented. Form the cutting edges, their "sharpness" significantly affect the performance of the treatment process, the magnitude of the cutting force and the grinding temperature. Experimental studies were conducted to assess the adequacy of the obtained dependencies. As an indenter, we used cones made of alloy steel, high-speed steel and hard alloy with a vertex shape in the form of a paraboloid of rotation. In the process, in the plane of the vector cutting speed appears pad wear, which continually increases in a plane perpendicular to the velocity vector, form the top of the grain remains close to the form of a paraboloid, but the radius increases continuously. Comparison of calculated and experimental data shows that their deviations from each other do not exceed 9%, which allows us to recommend the obtained dependencies for practical application. (C) 2020 Elsevier Ltd. All rights reserved.