Representation and analysis of geometric uncertainties in rotor blades

Geometric uncertainties involved in the rotor blade manufacturing process are a major concern for designers. The deviation of the produced components from their nominal geometry have an impact on the Natural Frequencies (NF) that, under certain circumstances, may have negative effects on the dynamic forced response in operative conditions. Geometric defects are usually limited by imposing dimensional tolerances based on empirical considerations, simplified approach that may lead to costly manufacturing requirements that still may not guarantee safe results. This paper proposes a probabilistic representation of the geometric uncertainties for rotor blades and defines a procedure to evaluate their effects on the blade NFs. The deviation from nominal geometry is represented through the Principal Component Analysis (PCA) where it is expressed as a sum of characteristic geometric shapes (GUMs) modulated by mutually uncorrelated random variables (Principal Components, PC). The effect of each GUM is then linearly propagated on the blade NFs and a sensitivity matrix is finally defined. The procedure is applied to a case-study that concerns a set of 50 nominally identical compressor blades and the ability of GUMs to represent the effects of geometric uncertainties is tested.