Vibration amplitudes and fatigue life in multistage turbomachinery are commonly estimated by an investigation of the individual stages. Research is currently extending the scope to include strucural and aeroelastic inter-stage coupling. Both effects have been shown to significantly influence blade vibrations. For safe operation of modern blisk blading with its lower structural damping due to the elimination of frictional contacts at the blade roots, an accurate prediction of the vibration behavior with mistuning is necessary to avoid high cycle fatigue failures. In this paper, a cyclic Craig-Bampton reduction method with a-priori interface reduction for multistage rotors is extended to handle aeroelastic effects. This reduced order model efficiently predicts forced response in multistage applications. Aeroelastic multistage simulations are carried out using the harmonic balance method to account for the stage interactions and yield damping and stiffness coefficients, as well as excitation forces. Small structural mistuning is projected onto the tuned system modes of the rotor. The approach is applied to a two-stage compressor configuration. Monte Carlo simulations show the sensitivity of vibration amplitudes to the aeroelastic coupling for mistuning. The aeroelastic inter-stage coupling is found to originate mainly from acoustic mode propagation between the stages. The fatigue of rotor blades is significantly affected by multistage interactions since vibration amplitudes increase due to the superposition of the responses of multiple modes. This leads to the conclusion that aeroelastic multistage effects need to be incorporated in future design procedures to allow for an accurate prediction of fatigue life.

A harmonic mistuning concept for bladed disks is analyzed in order to intentionally reduce the forced response of specific modes below their tuned amplitude level. By splitting a mode pair associated with a specific nodal diameter pattern, the lightly damped traveling wave mode of the nominally tuned blisk is superposed with its counter-rotating complement. Consequently, a standing wave is formed in which the former wave train benefits from an increase in aerodynamic damping. Unlike previous analyses of randomly perturbed configurations, the mode-specific stabilization is intentionally promoted through adjusting the harmonic content of the mistuning pattern (MT). Through a reorientation of the localized mode shapes in relation to the discrete blades, the response is additionally attenuated by an amount of up to 7.6%. The achievable level of amplitude reduction is analytically predicted based on the properties of the tuned system. Furthermore, the required degree of mistuning for a sufficient separation of a mode pair is derived.

Reduced order models (ROMs) are widely used to enable efficient simulation of mistuned bladed disks. ROMs based on projecting the system dynamics into a subspace spanned by the modes of the tuned structure work well for small amounts of mistuning. When presented with large mistuning, including changes of geometry and number of finite element mesh nodes, advanced methods such as the the pristine-rogue-interface modal expansion (PRIME) are necessary. PRIME builds a reduced model from two full cyclic symmetric analyses, one for the nominal and one for the modified type of sector. In this paper a new reduced order model suitable for large mistuning with arbitrary mesh modifications is presented. It achieves higher accuracy than PRIME, while saving approximately 25% computational effort during the reduction process, when using the same number of cyclic modes. The new method gains its efficiency by recognizing that large modifications from damage or repair are unlikely to be exactly the same for multiple blades. It works by building a partially reduced intermediate model: All nominal sectors are reduced using cyclic modes of the tuned structure. The single modified sector is kept as the full model. For this reason, the new reduction method is called Partially Reduced Intermediate System Model (PRISM) method. The accuracy of the PRISM method is demonstrated on an axial compressor blisk and an academic blisk geometry.

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A model order reduction method based on the component mode synthesis for mistuned bladed disks is introduced, with one component for the disk and one component for each blade. The interface between the components at the blade roots is reduced using the wave-based substructuring (WBS) method, which employs tuned system modes. These system modes are calculated first, and used subsequently during the reduction of the individual components, which eliminates the need to build a partially reduced intermediate model with dense matrices. For the disk, a cyclic Craig–Bampton (CB) reduction is applied. The deviations of the stiffness and mass matrices of individual disk sectors are then projected into the cyclic basis of interior and interface modes of the disk substructure. Thereby, it is possible to model small disk mistuning in addition to large mistuning of the blades.