Reduced Order Modeling Techniques for Dynamic Analysis of Mistuned Multi-Stage Turbomachinery Rotors

Abstract

Recent findings indicate that structural interstage (stage-to-stage) coupling in multi-stage rotors can have a critical impact on bladed disk dynamics by altering significantly the flexibility of the disk. This affects local eigenfrequency veering characteristics, and thus a design’s sensitivity to mistuning. In response to these findings, two reduced order modeling techniques are presented that accurately capture structural interstage coupling effects, while keeping model sizes at practical levels. Both free and forced responses of an example two-stage rotor are examined using novel component-mode-based reduced order modeling techniques for mistuned multi-stage assemblies. Both techniques employ an intermediate multi-stage model constructed by component mode synthesis (CMS), which is further reduced by either: (a) partial secondary modal analyses on constraint-mode partitions; or (b) a full-scale secondary modal analysis on the entire multi-stage CMS model. The introduced techniques are evaluated using finite element results as a benchmark. The proposed reduced order modeling techniques are shown to facilitate accurate multi-stage modeling and analyses with or without blade mistuning, using only computationally inexpensive modal data from a cyclic disk sector and a single blade per stage. It is concluded that the most promising and practically feasible approach may be a combination of approaches (a) and (b), in which secondary modal analyses and truncations are first carried out on disk-blade constraint-mode partitions, followed by a tertiary modal analysis on the resulting multi-stage model. In conclusion, by alleviating the restriction to single-stage analyses, the presented multi-stage modeling techniques will enable engineers to analyze the dynamics of mistuned turbomachinery rotor assemblies with greater confidence.