On the Determination of Nodal Diameter Spectrum and Mistuning Quantification of Synchronous Blade Vibrations Through Blade-Tip-Timing Measurements

Synchronous vibrations can severely impact the service life of impellers. Previous studies have demonstrated that mistuning significantly influences the nodal diameter of these vibrations. Specifically, mistuned impellers exhibit forced vibration responses comprising multiple nodal diameters, leading to asymmetric vibration expression among the impeller sectors and substantial amplitude overshoots. Blade-Tip-Timing (BTT) is a promising technique for monitoring synchronous vibrations due to its non-intrusive nature and capability to monitor all blades simultaneously. This paper presents a novel method for calculating the Nodal Diameter Spectrum (NDS) of synchronous blade vibrations through BTT measurements. The method utilizes the vibration properties, which are estimated via BTT through the Circumferential Fourier Fit method, to reconstruct the blade vibrations. Since the vibration properties of the blades are not determined at the same time, the vibrations are synchronized to acquire the impeller Operational Deflection Shape (ODS), which can be associated with the mistuned impeller modes at the resonance crossings. Subsequently, the NDS is determined by performing Discrete Fourier Transform (DFT) analysis on the impeller ODS. Simulated data are used to assess the effect of the vibration sample point on the DFT results and the impact of noise. Based on these results a strategy for the determination of the NDS in a revolution is derived. Next, the method is applied to experimental data acquired from a turbocharger test bench. To investigate the consistency of the proposed method, the results of multiple datasets of the same vibration are presented. In addition, the method is validated by comparing the experimental results with those acquired by forced response simulations. Finally, by employing the experimentally determined impeller ODS and the NDS, mistuning quantification factors are calculated.