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The article probes into a relationship of the shear strain intensity and the shear strain rate in the surface layer and the sliding velocity of a spherical indentor and its loading repetition factor. It brings forward an experimental procedure to evaluate the shear strain intensity and rate by analyzing the geometrical parameters of the bulge of plastically edged metal and the thickness of the shifted layer relative to different sliding velocities and feed rates.

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The article considers the problems of the mathematical modeling of thermal physics of the tool for nanostructuring burnishing. Physical and equivalent heat diagram of the system are developed. On the basis of the equivalent heat transfer diagram, the equivalent circuit and the system of equations of the mathematical model are created. The dependence of the tool indenter tip temperature on cooling system thermal parameters is obtained. The comparison of efficiency of heat removal from the tool indenter when using the developed two-circuit cooling system and the system supplying lubricant cooling liquid through the lathe centre spindle, as well as when applying nanostructuring burnishing without cooling is carried out.