Purpose. 3D-modeling of working process of abrasive grinding of structural steel by unit grain and the individual grains under different conditions of overlap and altitude. Methodology. Mathematical modeling of working processes of abrasive grinding of structural steel on steel 45 using the finite element method was performed. An electro-corundum wheel with ceramic binder was used as an abrasive tool. To simulate the surface of the tool the matrix method of coordinate transformation is applied. Findings. Contact problem of tool interaction of grain and the workpiece has been solved. The problem of modeling the cutting process in a chip formation and, consequently, the formation of new surfaces has been solved. Distribution of plastic strain, temperature, shear strain, strain rate, internal pressure, charts of cutting forces and kinetic energy were obtained. Originality. A general model of the tool surface whose calculation in MathCAD environment made it possible to obtain a graphical representation of various instrumental surfaces was obtained. As a result of mathematical modeling of working process abrasive grinding by individual grains with different variants of overlapping grains, characteristic curves of cutting forces and other parameters of the working process were obtained. Practical value. The results can form the basis of new structural steel processing technologies, developing management methodology for workflow of abrasive grinding.

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