Probabilistic manufacturing variability quantification from measurement data for robust design of turbine blades.
University of Southampton, School of Engineering Sciences,
Turbine blades are critical to the performance of an aircraft engine and their life is central to the integrity of the engine. These blades, when manufactured, inevitably exhibit some deviations in shape from the desired design specifications as a result of manufacturing variability. An approach to characterizing these deviations may be made by analysing the blade measurements for any changes from the datum design values. The measurement data, is however, always affected by measurement errors that cloud these effects.
In the present study, a methodology is proposed that employs the probabilistic data analysis techniques of Principal Component Analysis (PCA) and Fast Fourier Transform (FFT) analysis for de-noising the measurement data to capture the underlying effects of manufacturing variability as manufacturing drift with time and blade to blade manufacturing error. An approach using dimensionality reduction in the case of PCA and sub-selecting Fourier coeffcients in the case of FFT is proposed that uses prior knowledge on the measurement error. A Free-Form Deformation (FFD) based methodology is then presented for characterizing the 3-dimensional (3-d) geometric variability in blade shapes from the limited number of available measurements. This is followed by the application of a linear elasticity based approach for generating and morphing 3-d volume meshes in FEA ready form. A finite element analysis (FEA) of the resulting probable blade shapes indicates that the presence of manufacturing variability reduces their mean life by about 1.7% relative to the nominal design with a maximum relative reduction in life of around 3.7%. The probabilistic estimates of manufacturing perturbations are employed for robust design studies with the objectives of maximizing the mean and nominal lives and minimizing the blade life variability. A comparison of the robustoptimal solution with an optimal deterministic design is also performed. The designs explored by the multiobjective optimization process are analysed to understand the effects of geometric changes in turbine blades on the nominal values of life and the variations in blade life.
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