Purpose. Modelling the process of obtaining a modified profile of the teeth of cylindrical gears with disk cut- ters by the method of continuous radial-circular shaping and evaluating the characteristics of the modified profile of the teeth in a cylindrical gear transmission by the relative magnitude of the contact stresses between the teeth and the expected relative resistance to wear of the side surfaces of the teeth relative to the original involute cylindrical gear transmission. Methodology. The research was carried out using gear engagement theory principles, the theory of shaping by cutting tools related to gears, kinematic analysis, and analytical and differential geometry. Results. Mathematical models of forming a modified profile of the teeth of cylindrical gears have been developed by an improved method of radial-circular cutting of teeth with profileless disk cutters during continuous rotation of the gear. In comparison to the involute profile, the modified tooth profile exhibits enhanced operational characteristics. This improvement is expected to increase the efficiency of gear transmission by reducing contact stresses on the tooth surfaces and decreasing tooth slippage. Scientific novelty. The fundamentals of profiling the tooth surfaces of cylindrical gears using the radial-circular shaping method with a properly positioned disk cutter have been devel- oped. This approach ensures the production of gears with teeth that have the correct thickness and a convex-concave profile. The results obtained enhance the theoretical framework for synthesising gear meshes in cylindrical gears with a modified tooth profile. This synthesis involves a complex combination of tool parameters, the kinematic characteristics of the process, and the anticipated operational parameters of the gear transmission. Practical signifi- cance. The obtained modelling results are aimed at the application in cylindrical gear transmissions of vehicle transmissions as a special and traditional application, aviation gearboxes when implementing modernisation measures, repairing existing machines, vehicles, as well as designing cylindrical gear transmissions for new gear- boxes, units with simultaneous technological support for the practical manufacture of gears with improved opera- tional characteristics.
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