#### 519.6, 621.4 Mathematical model of conditional pressure optimization in the crack detection system of gas turbine blades

##### Andrianov I. K. (Комсомольский-на-Амуре государственный технический университет), Chepurnova E. K. (Комсомольский-на-Амуре государственный технический университет)

doi: 10.18698/2309-3684-2024-2-316

The study considers the problem of optimizing the crack detection system of gas turbine blades. The shell of the capsule of the damage detection system, which is under the influence of internal pressure, is considered as an object of research. The task of the study was devoted to the mathematical modeling of optimal pressure in capsules of the damage detection system. As part of solving the research problem, a mathematical formulation of the problem of optimizing the nonlinear pressure function was carried out in the presence of restrictions on variable parameters: wall thickness and outer diameter of the cylindrical capsule shell. The construction of the optimization objective function was carried out on the basis of the equilibrium condition of the shell element in the area of crack opening of the turbine blade, the limit state criterion using the Tresk-Saint-Venant strength theory. The research methodology was based on the approximate decomposition of the function into a Taylor series, the Lagrange multiplier method, and the Kuhn-Tucker theorem. When solving the problem of conditional optimization, the cases of violation of the regularity conditions of the limiting functions are analyzed. According to the calculation results, the minimum value of the required pressure for the destruction of the capsule shell in case of opening of the crack banks of the turbine blade is achieved at the maximum value of the outer diameter of the shell and the minimum thickness of its wall. According to the test calculation data, the area of acceptable solutions to the optimization problem is graphically presented, and the lines of the level of the target function of pressure optimization are shown. The constructed mathematical model and calculation algorithm will automate the process of calculating the required pressure in the capsules of the turbine blade crack detection system and obtain an estimate of the minimum pressure value in the presence of restrictions on the absolute and relative values of the capsule shell wall thickness, the outer diameter of the capsule.

Андрианов И.К., Чепурнова Е.К. Математическая модель условной оптимизации давления в системе обнаружения трещин лопаток газовых турбин. Математическое моделирование и численные методы, 2024, № 2, с. 3–16.