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

Abstract

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 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 data collected during the mistuning ID, the overall procedure is integrated and efficient.

Measurement point selection and modal damping identification for bladed disks

“…The EIDV-based procedure presented by Holland et al 2 uses the full tuned system modes to calculate the optimal measurement locations. When the model of interest has many sectors with many candidate measurement locations, the matrices involved can become prohibitively large.…”

“…Such forcing is obtained in many cases where the applied forcing is only known to be the same as a reference forcing, whereas the actual magnitude of the reference forcing is unknown. An example of such a case is the forcing calibrated by using the procedure proposed by Holland et al 2 In that case α k = 1. Rearranging, Eq.…”

“…Conceptually, the effective independence distribution vector (EIDV) method 1 determines the amount of modal information for each point in a candidate set of measurement locations. Holland et al 2 extended the EIDV method to determine the minimum number and the best locations of the necessary measurements. Those approaches used whole system models which required a heavy computational effort.…”

“…Such forcing is obtained in many cases where the applied forcing is only known to be the same as a reference forcing, whereas the actual magnitude of the reference forcing is unknown. An example of such a case is the forcing calibrated by using the procedure proposed by Holland et al 2 Griffin et al 17 found that slightly mistuned system modes can be well represented as a linear combination of tuned system modes. This relationship has been used in studying the effects of crack propagation, [18][19][20] and multi-stage phenomena.…”

Collocation-based Stochastic Modeling of Uncertain Geometric Mistuning in Bladed Rotor

“…The unavoidable mistuning, in practical cases, destroys the cyclic symmetry and increases the vibration amplitudes. This implies that the vibrational energy in bladed rotor becomes restricted to one or few blades rather than being uniformly distributed throughout the whole rotor 5,6 . Consequently, certain blades may experience large vibration amplitudes and stresses which sometimes over the allowable values.…”