Multi-objective optimization design of turbine final stage long blades

The final-stage long blade of the steam turbine is selected as the research subject, and its strength performance and vibration characteristics are analyzed. A multi-objective parameter optimization is conducted, with blade tension height (P1), tension angle (P2), and perimeter band thickness (P3) as the design variables. The equivalent force and maximum deformation are set as constraints, while the resonance frequency at each of the “three key points” is defined as the objective function. The structural parameters are optimized using response surface methodology and the multi-objective genetic algorithm (MOGA). Numerical results show that the optimal parameter set is P1 = 804.1 mm, P2 = 8.91°, and P3 = 20.9 mm. After optimization, the avoidance rate for the intersection of the second-order three pitch diameter curve with the frequency multiplier curve ( K = 3) increases to 10%, a 3.4% improvement compared to pre-optimization. Similarly, the avoidance rate for the intersection of the third-order seven pitch diameter curve with the frequency multiplier curve ( K = 7) improves to −6.1%, reflecting a 3.43% increase over pre-optimization. This effectively mitigates the resonance risk associated with turbine blades, thereby enhancing turbine efficiency and stability, and offering a significant reference for turbine blade design optimization.