Post correcting for gyroscopic effects via dynamic substructuring

Frequency response functions (FRFs) often serve as a basis for predicting sound and vibration levels at a receiver position, with a known excitation at a source position. Within the dynamic substructuring framework it is possible to build the FRFs of a complex assembly from the known FRFs of its subcomponents. However, in the case of subcomponents with revolving parts the task is further complicated due to gyroscopic effects. These components are changing their dynamic behavior depending on the operating speed. A correct approach would require measuring the FRFs of the rotating machinery at each operating speed, which is a difficult and tedious task. Thus, the unmeasured gyroscopic effects are often neglected (but not always negligible) in practice. We propose a dynamic substructuring based approach, for analytically coupling the gyroscopic reaction moments to an FRF matrix, measured on the idling subcomponent. Gyroscopic terms only influence subcomponent motions that are tilting the rotation axis. The proposed method will thus be interpreted and derived as a coupling in the subspace of this tilting motion. An analytical testcase is used to exemplify and validate the proposed method. We show how the tilting angles can be determined from an overdetermined set of measured sensor motions, based on a kinematic assumption. The validity of this kinematic assumption certainly influences the solution, which will also be shown on the example.