The article describes how different friction coefficients under certain cutting conditions and parameters affect the formation of the stress-strain and thermal states of the product when titanium alloy machining. A new research methodology is used for the study. Firstly, in the initial data for simulation, each time a different declared coefficient of friction is proposed, and every such task of the cutting process modelling is solved for various cutting parameters. The second stage analyzes how these coefficients influence the stress-strain and thermodynamic state of the workpiece and tool during cutting, as well as the tool wear dynamics. In the third stage of the study, ways for ensuring these analytically-grounded tribological cutting conditions are proposed. The analysis of different wear criteria in the simulation models of titanium alloys cutting is carried out. Experimental studies confirm simulation results.