Nowadays, the machine-building complex is actively saturated with high-tech equipment, without which an enterprise cannot enter the global market or keep up with its competitors. And it's not just about using systems with artificial intelligence elements as scientific and technical solutions to improve quality and reduce production costs. It is also about reducing the time required to prepare products for production and bringing them to the consumer ahead of schedule. Today, the most preferred method in the competitive struggle is to equip CAD/CAM production with computer-aided design systems. With their help, engineering and technology services cannot only design models of new products but also generate CNC control software for manufacturing parts on CNC machines. At the same time, program frames composed in G-codes have several drawbacks, the main one being a "rigid" algorithm of action, i.e., the lack of variability for final solutions when the required accuracy is achieved by correcting the numerical values of the coordinates of the points of formation of individual surfaces in the PC. In this case, the operator largely intuitively corrects individual program frames based on his or her own experience, which is almost impossible without appropriate calculations for controllers with linear-circular and angular motions. In addition, after some such changes, the program loses its geometric adequacy to the part drawing, and by correcting one element of the shaped profile, we invariably violate the laws of contact with neighboring elements specified in the drawing. The paper considers the analytical geometry apparatus that allows a line on a double curvature surface, the theoretical trajectory of tool movement, to be represented not as a set of scalar points but in a vector representation, considering its possible torsion. This approach is ensured by parametric programming with computational frames of point coordinates and logical transitions, determining the angles of inclination of the cutter axis relative to the normal to the surface in the case of multi-axis machining. However, the main advantage of this method is the ability to correct processing errors not by local changes in the numerical values of the coordinates, but by introducing correction coefficients into the equation of the shape formation trajectory - reactors for the appearance of errors in the shape or location of surfaces, arising, for example, from elastic movements. The value of the coefficients per group of personnel can be set in the process of research and industrial production and change depending on the properties of the blanks. For example, according to the current standards, variations in hardness of up to 10-12% were allowed for the blanks of rolling mill rolls. The article presents the experimental data of the research of the correction task in a parametric form and the results of their application for machining parts with radius cutters in real production..

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