Mathematical modeling of titanium alloy turning process

Objective. To solve a scientific and technical problem related to the technological support of high-performance mechanical processing of titanium parts by optimizing and controlling their machinability with hard alloy tools on CNC machines, under the conditions of solving optimization problems. Methodology. The methodological basis of the work is a systematic approach and analysis of the research object to solve the set task of nonlinear programming. Effective numerical optimization methods are used – these are methods of approximate or exact solutions to mathematical optimization problems, which boil down to performing a finite number of elementary operations on numbers. Results. The numerical results of the research obtained for a scientifically based approach to solving the technical problem of high-performance turning of titanium parts on CNC machines, which contains a set of adjusted methods and algorithms for predicting their machinability while ensuring the reliability of cutting tools made of hard alloys. The results obtained make it possible to construct graphs and increase tool stability, determine the optimal cutting depth, machine power, and the value of the main angle in the cutter plane. Scientific novelty. The solution to the nonlinear programming problem consists in selecting such non-negative values of variables subject to a system of constraints in the form of inequalities at which the maximum (or minimum) of a given function is achieved. Establishing a complete and systematic relationship between the processing parameters and the properties of the material being processed, the geometry of the tool for the rational use of optimized control technology on CNC machines. The processing of experimental data made it possible for the first time to obtain complex dependencies that give a clear idea of the influence of each parameter of the turning process on the stability period of the tool when compiling the optimal technology for mechanical processing. Practical significance. It consists in substantiating the optimal cutting parameters, establishing the nature of the influence of the conditions of turning titanium alloy on the main indicators of the process, tool stability, cutting power, and main angle in the plane.