Uncertainty and sensitivity analysis for bladed disks with random blade anisotropy orientations

Single crystal blades used in turbine bladed disks of modern gas turbine engines exhibit material anisotropy. The crystal orientations of blades in a bladed disk are usually different. The static and dynamic response of a mistuned bladed disk with a blade to blade variation in crystal orientations differs significantly from the tuned structure where all blades are identical. Based on detailed study of the available literature on mistuned bladed disk, a gap in knowledge on the effects of blade anisotropy orientation on static deformation and forced response of bladed disk was identified, since there are no studies for bladed disk mistuned by material anisotropy based on high-fidelity finite element models. In the first part of this study, the effects of blade material anisotropy orientation on non-linear static deformation of the mistuned bladed disk are thoroughly investigated. Moreover, sensitivity and uncertainty analyses for non-linear static deformation are performed to quantify the effects of scattering in blade crystal orientation. A method based on Sobol indices, hitherto unused in the analysis of mistuned bladed disk, is introduced for global sensitivity analysis with respect to blade anisotropy angles. The usefulness of polynomial chaos expansion as an efficient method for uncertainty analysis of mistuned blade disk is demonstrated. For mistuned bladed disk, with numerous design parameters in the form of blade anisotropy angles, the following two strategies are proposed to address the “curse of dimensionality” problem associated with uncertainty analysis: (i) reduce the dimension of the random space by screening the anisotropy angles based on their rank order of importance obtained from sensitivity analysis, (ii) by using gradient values, in addition to function evaluations, to calculate the coefficients in the polynomial chaos expansion. Due to manufacturing errors, the contact geometry of blades at fir-tree root and shrouds will be different from the design geometry. The effects of variation in crystal orientation on non-linear static deformation of a tuned bladed disk is investigated for different variants of fir-tree root and shroud geometry. In the second part of this study, the effects of blade material anisotropy orientation on the linear forced response of mistuned bladed disks are investigated. Considering blade anisotropy angles as random design parameters, uncertainty in forced response of mistuned bladed disk is quantified using gradient-based polynomial chaos expansion. Further, the crystal orientations of blades are optimised in order to achieve a reduction in the maximum forced response amplitude of a mistuned bladed disk.