Analysis of Deformation of Mistuned Bladed Disks With Friction and Random Crystal Anisotropy Orientation Using Gradient-Based Polynomial Chaos Expansion

Abstract

Single crystal blades used in high pressure turbine bladed disks of modern gas-turbine engines exhibit material anisotropy. In this paper, the sensitivity analysis is performed to quantify the effects of blade material anisotropy orientation on deformation of a mistuned bladed disk under static centrifugal load. For a realistic, high fidelity model of a bladed disk both: (i) linear and (ii) nonlinear friction contact conditions at blade roots and shrouds are considered. The following two kinds of analysis are performed: (i) local sensitivity analysis (LSA), based on first-order derivatives of system response with respect to design parameters, and (ii) statistical analysis using polynomial chaos expansion (PCE). The PCE is used to transfer the uncertainty in random input parameters to uncertainty in static deformation of the bladed disk. An effective strategy, using gradient information, is proposed to address the “curse of dimensionality” problem associated with statistical analysis of realistic bladed disk.

Polynomial chaos expansion for permutation and cyclic permutation invariant systems: Application to mistuned bladed disks

“…PCE has been applied to many different types of applications [40,41]. However, for sophisticated engineering applications, potentially exhibiting a nonlinear mechanical behavior, one may consider two types of limitations of this methodology.…”

“…Nonetheless, in the field of turbomachinery, when modeling mistuning or blade specific parameters on a large bladed disk-that may easily feature more than twenty blades-a very large number of random variables must be considered which severely constrains the degree of the polynomial interpolation to low values [41,2]. This comes at the cost of less accurate results and thus constitutes a bottleneck for a widespread application of PCE in the field of turbomachinery.…”