Introduction. When milling complex-profile surfaces of parts, the selection of tool trajectories and orientations affect the roughness parameters. However, in the studies devoted to the formation of trajectories, recommendations to provide the quality of microgeometry of surfaces were not taken into account. Moreover, when writing programs for CNC equipment in CAM systems, the limitations of cutting modes were determined exclusively using a geometric approach. It did not take into account the influence of the orientation angles of the sphero-cylindrical tool relative to the normal plane on the quality of surface treatment, namely on roughness. The work was aimed at the creation of the methodology for selecting the limiting values of the orientation angles of a sphero-cylindrical tool to optimize the process of machining spatially complex surfaces. The tasks included achieving the minimum values of the amplitude roughness parameter Rz and determining the effectiveness of various machining paths.Materials and Methods. Methods of correlation and regression analysis were used, the results were compared and generalized. The least-squares method was applied to estimate the parameters of the regression equation. The DMU 50 ecoline processing center was used for the experimental studies. Roughness was measured on a Surfcam 1800 D profilometer. The material of the samples was steel 12X18N10T. The material of the tool was hard alloy 1620 Sandvik with PVD coating (physical vapor deposition, the closest domestic analogue is T15K6).Results. It has been shown in detail how roughness parameters Rz depend on the angle of inclination and the diameter of the tool. Twenty examples were summarized in a table. Natural regression coefficients were calculated using linear and hyperbolic models. It was found that the diameter of the tool had a greater effect on the formation of roughness parameter Rz than the angle of inclination. For a detailed description of the influence features, the coefficients of multiple, partial, paired correlation and multiple determination were compared. The limitations associated with the angles of inclination of the tool when processing complex surfaces were determined. A scheme for calculating the angle of the normal was visualized, which included the selected step along the axis to determine the lengths of the segments of the broken curve. The profilograms of surfaces obtained with different shaping trajectories were given in the form of drawings. This allowed us to conclude that milling from top to bottom is unsuitable when the tool is tilted 5°– 35°. A map has been compiled by which it is possible to judge the roughness, knowing the type of milling and the inclination angle (from 5° to 80 °). The dependence of the roughness parameter on the processing speed and the use of coolant was represented graphically. The calculated parameters for determining the optimal angle of inclination of the tool were tabulated. Their analysis proved the adequacy of the proposed method of preparing control information.Discussion and Conclusion. The presented technique made it possible to determine the optimal values of the orientation angles of the sphero-cylindrical tool, taking into account the cutting speed and the minimum possible amplitude roughness parameter Rz. The pattern of feeding fz = 0.4 mm/tooth for surface areas with a total angle of 5°– 50°was considered. In this case, processing along trajectories in the passing, opposite and bottom-top directions, provided roughness in the range of 3–6 µm according to parameter Rz. The top-down toolpath is not recommended for use in final operations due to the significant height of parameter Rz.
