Models for blisks with large blends and small mistuning

Abstract Small deviations of the structural properties of individual sectors of blisks, referred to as mistuning, can lead to localization of vibration energy and drastically increased forced responses. Similar phenomena are observed in blisks with large damages or repair blends. Such deviations are best studied statistically because they are random. In the absence of cyclic symmetry, the computational cost to predict the vibration behavior of blisks becomes prohibitively high. That has lead to the development of various reduced-order models (ROMs). Existing approaches are either for small mistuning, or are computationally expensive and thus not effective for statistical analysis. This paper discusses a reduced-order modeling method for blisks with both large and small mistuning, which requires low computational effort. This method utilizes the pristine, rogue and interface modal expansion (PRIME) method to model large blends. PRIME uses only sector-level cyclic modes strategically combined together to create a reduction basis which yields ROMs that efficiently and accurately model large mistuning. To model small mistuning, nodal energy weighted transformation (NEWT) is integrated with PRIME, resulting in N-PRIME, which requires only sector-level calculations to create a ROM which captures both small and large mistuning with minimized computational effort. The combined effects of large blends and small mistuning are studied using N-PRIME for a dual flow path system and for a conventional blisk. The accuracy of the N-PRIME method is validated against full-order finite element analyses for both natural and forced response computations, including displacement amplitudes and surface stresses. Results reveal that N-PRIME is capable of accurately predicting the dynamics of a blisk with severely large mistuning, along with small random mistuning throughout each sector. Also, N-PRIME can accurately capture modes with highly localized motions. A statistical analysis is performed to study the effects of random mistuning on both natural frequencies and forced responses and reveals that 1) new clusters of mistuned natural frequencies exist and cannot be treated as small deviations from nominal frequencies, and 2) unexpectedly high amplifications of forced responses exist, showing 3–5 times higher responses compared to the nominal system.