Uncertainty and global sensitivity analysis of bladed disk statics with material anisotropy and root geometry variations

Abstract

Monocrystalline blades used in gas turbines exhibit material anisotropy, and the orientation of the anisotropy axis affects the deformation of the bladed disk. Considering the orientation of the anisotropy axis as a random design parameter, the uncertainty and sensitivity analysis for static blade deformations are presented for the first time. The following two cases are analyzed using a realistic bladed disk model with friction contacts: (i) deformation of the tuned bladed disks considering the uncertainty in anisotropy orientation and variations in fir tree root geometry and (ii) deformation of mistuned bladed disks with uncertain blade crystal orientations. For efficient uncertainty and sensitivity analysis, the applicability of the following surrogate models are explored: (i) an ensemble of regression trees (random forest) and (ii) gradient‐based polynomial chaos expansion. Faster convergence in statistical characteristics has been obtained using a surrogate model compared to that obtained from finite element model based Monte Carlo simulation. From sensitivity analysis, it has been inferred that the uncertainty in static displacements of a blade in a bladed disk is primarily due to the uncertainty in anisotropy angles of that blade itself and secondarily due to the interaction of different blade anisotropy angles.

Stochastic reduced order modelling and analysis of rotating bladed discs

“…The numerical examples considered only Young’s modulus to have spatial randomness [18] and did not consider geometric imperfections. Thus the randomness was only in the stiffness matrix.…”

“…While bladed disc systems are designed to be perfectly periodic structures, with each blade and sector being identical, manufacturing tolerances inevitably result in geometric imperfections that can be captured through coordinate capturing machine (CMM) [17] or in material imperfections arising due to differences in grain orientation [18] or other material microstructure imperfections. As these variations are random in nature, no blade is perfectly identical and there are variations in their natural frequencies [17,18]. As a result, the bladed disc can be said to have random mistuning, resulting in deviations from designed behaviour.…”

Multi-source uncertainty propagation and sensitivity analysis of turbine blades with underplatform dampers

“…In addition, the adaptive algorithm overcomes the strong interaction encountered in the system response, effectively solves the huge error problem caused by the univariate dimensionality reduction method [36], and provides important application potential for uncertainty analysis. In addition, an important advantage of PCE is that the mean and variance of the responses can be easily obtained from the surrogate model, and the sensitivity analysis based on variance can also be performed: Sobol analysis [35,37]. Therefore, sensitivity analysis will be used in this study.…”

Propagation of friction parameter uncertainties in the nonlinear dynamic response of turbine blades with underplatform dampers

“…The PCE has also been coupled with multi-harmonic balance methods to investigate the effects of the uncertainties in nonlinear systems [44,45]. One of the main advantages of the PCE is that it can be exploited without any additional simulation to directly determine the mean and the variance of the process, but also to perform a variance-based sensitivity analysis based: Sobol analysis [46,47] and for this reason has been used in the present study.…”