Nodal energy weighted transformation: A mistuning projection and its application to FLADE™ turbines

• A new technique to construct ROMs of mistuned bladed disks is proposed.
• This new technique is easily applied to dual path systems.
• ROM projection modes are logically related to modal families.
• Resulting ROMs are more accurate and smaller than established methods.

In recent years, several researchers have developed reduced-order models (ROMs) to efficiently and accurately calculate the forced response of blisks with known small mistuning. Small mistuning consists of the small blade-to-blade structural differences which destroy the inherent cyclic symmetry of the structure. This paper presents a nodal energy weighted transformation (NEWT) which can be used to construct ROMs of mistuned blisks and dual flow path systems, such as FLADE™FLADE™ turbines. The NEWT approach can be interpreted as a hybrid of two existing techniques: component mode mistuning (CMM) and the subset of nominal modes (SNM). Similar to the previous methods, NEWT assumes that the mistuned modes of the system are a linear combination of tuned modes. However, NEWT differs from its predecessors in the blisk substructuring and in the mistuning projection. Numerical results obtained using full order models, CMM, and NEWT are presented and compared over multiple frequency ranges for a finite element model of a blisk and that of a FLADE™FLADE™ turbine. These results show that ROMs based on NEWT have several attractive features: (a) the accuracy of the ROMs is comparable to ROMs based on CMM, and can be improved by increasing the size of the projection mode subset; (b) no necessary modifications are needed to analyze FLADE™FLADE™ turbines; and (c) the response of all modes can be predicted well even if they are not blade dominated.