Fatigue Endurance Optimization of a Steam Turbine Blade Curved Fir-Tree Root

Abstract

In this paper, the guide curve of a fir-tree root is parametrically modeled forthe optimization of a newly designed free-standing low-pressure last-stageblade airfoil of a steam turbine. These geometrical parameters include thelocation of the center point of the curve root centerline and the radius ofthe root curvature, while the axial length and the pitch are kept fixed. Themechanical safety factor is computed at the upper section of a predefined rootprofile for each considered design parameter in a commercial finite elementsoftware. For high cycle fatigue failure analyses, the maximum alternatingstresses are calculated from harmonic responses under the dynamic fluidloading obtained from computational fluid dynamics (CFD) simulation atthe maximum continuous rating condition. Preliminary modal analysis isperformed to estimate the natural frequencies for the principal modes nearthe low engine order excitation. On this basis, dynamic stresses are calculatedat corresponding frequencies prone to low order engine modes of excitement.Moreover, harmonic response is obtained at nozzle passing frequency foreach set of design parameters. In addition, the total strain is computed atthe upper section of the root from elastic-plastic analysis under centrifugalloading resulting from 110% of nominal operating speed. Therefore, amulti-objective optimization genetic algorithm is used to optimize the rootdesign parameters with objectives of maximizing safety factors obtained fromboth strain-based low cycle fatigue and stress-based high cycle fatigue analyses.