SUMMARY
The object of research is the milling process with the crossed axes of the cylindrical surface and the tool. During the research, general modular three-dimensional models of the tool surface, the processes of removing the allowance and the shaping of the cylindrical surface are used on the basis of three unified modules: tool, shaping and orientation. Computer simulation is also used to build a three-dimensional model of the milling process of a cylindrical surface with an oriented tool. A graphic scheme of milling a cylindrical surface with an oriented tool has been created. The developed cylindrical module for shaping the tool surface, which is described by the product of the displacement matrices along the corresponding axes and the surface of the machined part, is represented by the product of the radius of the tool vector and its orientation module in the shaft coordinate system. The resulting graph of the distribution of the specific productivity of the milling process along the tooth profile of the tool during processing with crossed axes of the cutter and part. An analysis of this graph shows that the milling method with an oriented tool makes it possible to increase the accuracy of the shaping process due to uniform wear of the tool. The intersection angle of the cylindrical surface and the tool is also determined, the value of which is taken from the condition of ensuring the maximum removal of the material layer with uniform loading of the end part of the cutter. For this, a three-dimensional model of the process of milling a cylindrical surface with crossed axes of the tool and the part is developed, in which rough milling is carried out by the end part of the tool, and the finish – by the peripheral. In the course of the research, it is found that when finishing milling, the value of the rotation angle of the cutter is taken from the condition that the peripheral part of the cutter is fully loaded. Improving the processing efficiency is achieved by crossing the axes of the tool and the part, which allows to program the intersection point, and uniform wear of the cutter, which improves the quality of the machined surface. It is also possible to use high-speed milling to provide increased processing productivity.