Multi-stage modeling of turbine engine rotor vibration

In this study, an efficient approach for modeling the vibration of multi-stage rotors is proposed in order to allow more realistic predictions of the free and forced response of bladed disks. The reduced-order modeling approach is based on component mode synthesis, with each stage (bladed disk) treated as a separate component. Thus, each component retains cyclic symmetry, and single-sector models may be used for calculating the component modes. Because adjacent stages typically have different numbers of blades, the single-stage models are synthesized by projecting the stage-to-stage interface motion onto a common basis of circumferentially harmonic shapes. In this manner, any mismatch between sector sizes and finite element meshes at the interface can be handled systematically and automatically, without requiring additional multi-point constraints. For further size reduction, secondary modal analysis is performed on the entire synthesized model. Therefore, only a small set of multi-stage modes are retained in the final reduced-order model, yielding an extremely compact model that retains high accuracy relative to the parent finite element model.