Generalized SAFE Diagram for Mistuned Bladed Disks

The Singh's advanced frequency evaluation (SAFE) diagram is a design tool commonly used to find and thus prevent bladed disk resonances, allowing those modal combinations with no match in terms of angular harmonic shape to be neglected. In principle, the SAFE diagram is based on the assumption that the disk structure is perfectly cyclic; hence, any degree of mistuning would prevent its validity. However, each natural mode of a mistuned bladed disk can be expressed as a superimposition of angular harmonic components. The numbers of nodal diameters of these harmonics are extracted as the discrete Fourier transform of the eigenvector. In this paper, a new graphical representation is proposed to account for this complete harmonic content, instead of just a single (main or nominal) number of nodal diameters as in the conventional SAFE diagram. In addition, the relative intensities of the modal components are shown in this generalized SAFE diagram, for an indication of the induced vibrational magnitude of each possible resonance. Numerical and experimental cases are presented, obtaining significant examples of the proposed diagram. Analyzing the signals of an aeromechanical test, unexpected resonances were observed, which were not predicted by the conventional SAFE, but were detected with the proposed diagram.