Purpose. Development of the finishing gear hobbing method based on the interaction of the change of the tool cutting edge and the machined surface. Methodology. The study includes the method of abstraction based on gear hobbing as the interaction of the tool cutting edge with the machined surface. In turn, the properties of the interaction of the tool cutting edge and the machined surface are studied with the help of models under computer simulated conditions. Findings. The specifications for the finishing gear hobbing method have been assigned. Possible variations of system of the tool cutting edge interaction with the machined surface were shown; the level of stability of the cutting process with specified variations of interaction was determined in terms of computer modeling. A dynamic model of the tool cutting edge interaction with the machined surface has been created. The model considers the nature (geometry) of the interaction, tension, damping and disturbance of technological system (self-adjustment - tool - component part). The directions to increase astatism of system were determined. Originality. For the first time the gear hobbing modeling method was created which shows the research opportunities of the tool cutting edge interaction with the cutting surface including the machined surface under conditions of both their coincidence, and non-coincidence. For the first time the finishing gear hobbing process of involute surfaces was created in which the cutting surface does not match the determined involute surface and is set at an angle to it. Practical value. The astatism level of the single-mass conservative oscillatory system has been increased by changing the nature (geometry) of the interaction between the tool cutting edge and the machined surface that is adequate to the insertion of integrating links into the system. The scheme of gear hobbing based on the contour interaction of the tool cutting edge and the machined surface has been implemented.

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