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Purpose. Construction of a general modular mathematical spatial model of the removal allowance process and shaping when milling round surfaces of rotation, such as camshaft necks, cylindrical surfaces of gearbox shafts and others. Determination of the components of the cutting forces when machining with crossed axes of the milling cutter and part in order to use the results when assigning machining modes.   Methodology. Theoretical development of a modular mathematical model of the removal allowance process and shaping during milling of cylindrical surfaces was carried out using a matrix apparatus for converting coordinate systems. Unified modules were developed: instrumental, orientation and shaping, which allowed us to describe the processing of the part more clearly. All calculations were performed in the mathematical package Mathcad. Using the functions available in the package, a graphical representation of the mathematical model of the tool and machined surfaces was obtained. Using the logical blocks developed in the program, the characteristics of the treated surface were investigated, such as roughness in the axial and radial planes. The influence of the tool orientation angle and the number of cutter teeth on the roughness of the machined surface was investigated. The known formulas for calculating the cutting forces during milling are specified.   Findings. A general modular mathematical spatial model is constructed of the removal process of an allowance and formation at milling by the oriented tool of round surfaces of rotation, such as necks of camshafts, cylindrical surfaces of shafts of transmissions and others. The roughness parameters of the treated surface are determined. The outflow of the tool characteristics and the angle of its orientation on the geometric roughness in the axial and radial sections is investigated. The area of the layer cut off by one tooth of a mill is defined. The calculation formulas are specified for finding the components of cutting forces during milling.   Originality. A modular spatial model of the process of milling cylindrical surfaces with an oriented tool is proposed, on the basis of which the components of cutting forces are calculated, which can be used in designing new tools and improving machining conditions by the existing ones.   Practical value. Based on the use of modern computer facilities and software, the developed calculation program allows controlling the process of forming cylindrical surfaces during their milling with an oriented tool. It also allows predicting the initial machining accuracy by determining the parameters of geometric roughness in axial and radial sections. This makes it possible to choose the optimal tool orientation angle, milling cutter parameters and cutting modes to achieve high productivity and processing quality.

Determination of the cutting force components while milling cylindrical surfaces with an oriented tool