Probabilistic Analysis of Geometric Uncertainty Effects on Blade Modal Response

Abstract

This paper investigates the effect of manufacturing variations on the modal response of a transonic low aspect ratio fan. A simulated set of coordinate measurement machine measurements from a single rotor, representative of actual manufacturing variations, are used to investigate geometric effects. Principal component analysis is used to statistically model spatial geometry variations and reduce variable space dimensionality. Statistics from this analysis are used with Monte Carlo sampling to generate random blades realizations that are used to predict response distributions for a simulated fleet of 1000 blades. An existing approach to approximate blade frequency response is extended to include modal displacement and stress. These approximations are based on eigensensitivity analysis and first order Taylor series approximations. An approximation error analysis is conducted to quantify accuracy. The effect of small geometry variations on blade natural frequency, mode shape, and modal stress is investigated with results showing that small variations on the order of mils can cause significant variations in both scale and location of free and forced response.