Testing and Calibration Procedures for Mistuning Identification and Traveling Wave Excitation of Blisks

In this work, an integrated testing and calibration procedure is presented for performing mistuning identification (ID) and traveling wave excitation (TWE) of one-piece bladed disks (blisks). The procedure yields accurate results while also being highly efficient and is comprised of three basic phases. First, selected modes from a tuned blisk finite element model are used to determine a minimal set of measurement degrees of freedom (and locations) that will work well for mistuning ID. Second, a testing procedure is presented that allows the mistuning to be identified from relatively few vibration response measurements. A numerical validation is used to investigate the convergence of the mistuning ID results to a prescribed mistuning pattern using the proposed approach and alternative testing strategies. Third, a method is derived to iteratively calibrate the excitation applied to each blade so that differences among the blade excitation magnitudes can be minimized for a single blade excitation, and also the excitation phases can be accurately set to achieve the desired traveling wave excitation. The calibration algorithm uses the principle of reciprocity and involves solving a least-squares problem to reduce the effects of measurement noise and uncertainty. Because the TWE calibration procedure re-uses the data collected during the mistuning ID, the overall procedure is integrated and efficient.