The present study investigates the optimization of cutting parameters in CNC milling operations through the development of a mathematical model based on machining constraints and technological requirements. The research focuses on determining optimal cutting speed and feed rate values for finishing operations while ensuring the required surface roughness, tool performance, and machine power limitations. A system of nonlinear constraints describing the milling process was transformed into a linear form using logarithmic transformations, allowing the optimization problem to be solved graphically through linear programming methods. The feasible solution region was constructed based on technological and kinematic constraints, and the optimal cutting parameters were determined from the extremum point of the objective function. The obtained results demonstrate that the proposed optimization approach improves machining efficiency while maintaining the required surface quality and machining stability. The developed algorithm can be applied to similar three-axis CNC milling machines with appropriate adaptation of experimentally determined coefficients for different cutting tools and workpiece materials.

CNC milling, cutting parameter optimization, mathematical modeling, linear programming, surface roughness, cutting speed, feed rate, machining efficiency.

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