Multimodal Rotor-Dynamic Optimization Based on Transfer Matrix Method for Different Rotor Structures

Abstract Considering the thrust/weight ratio in the aviation industry, the most efficient engines are turbomachines. In the design of high-speed turbomachines, certain design requirements must be met, such as avoiding natural frequencies within the operating speed range, ensuring that bearing loads do not exceed a specific limit, maintaining clearances between the rotor and stator within a certain range, and achieving a lightweight rotor design. Evaluating all these requirements together requires a comprehensive optimization study rather than a simple trial/error approach. An important factor in optimization studies is selecting the appropriate optimization algorithm based on the problem type. Due to the No Free Lunch Theorem, the performance of optimization algorithms varies significantly depending on the nature of the problem. Therefore, optimizing a mini turbojet rotor and optimizing a conventional turboshaft or turbojet rotor are fundamentally different optimization problems in terms of design space and the behavior of objective functions. In this study, metaheuristic optimization methods such as Genetic Algorithm, Differential Evolution, Simulated Annealing, Gravitational Search Algorithm, Black Hole, Particle Swarm Optimization, and Artificial Bee Colony, as well as the non-metaheuristic Pattern Search method, were used for various rotordynamics optimization problems. A variety of rotordynamics optimization problems were examined, covering multi-objective functions with different design spaces involving both fewer and more design variables, as well as multimodal and unimodal fitness functions, and the performances of the algorithms were compared. Additionally, unlike the Finite Element Method (FEM) used in the literature, a rotordynamic solver based on the Complex Transfer Matrix Method (CTMM), which we developed, was used to obtain the objective functions in optimization problems. Thus, CTMM has proven its applicability for complex rotordynamics optimization problems.