A Keyphasor-Free Traveling Waves Analysis Method Based on Blade Tip Timing and Experimental Validation

Vibration-induced high-cycle fatigue of blades is a prevalent issue in turbomachinery. Blade tip timing (BTT) emerges as a nonintrusive, promising method for assessing blade vibration. Despite its potential, BTT's inherent measurement limitations often result in the undersampling of individual blade data. Assuming that the bladed-disk assembly vibrates in nodal diameter modes, traveling wave analysis (TWA) can overcome the limitations of undersampling and identify the nodal diameter modes associated with the frequency components. Traditional TWA methods rely on a keyphasor or once-per-revolution sensor to provide accurate reference signals. However, such a sensor could be damaged during operation or challenging to install due to limited space in field tests. In this paper, a new keyphasor-free TWA (KF-TWA) method is introduced, which is capable of measuring the order and nodal diameter of nodal diameter vibrations with as few as two sensors. Theoretical derivations reveal the method's resilience to the steady-state displacement of blades. The feasibility and effectiveness of the KF-TWA method are validated through numerical experiments and compressor tests. In the numerical experiments, blade detuning and nodal diameter vibration responses are simulated, leading to the development of a criterion for identifying nodal diameter vibrations. A compressor test rig, equipped with a 64-keyphasor disk and a sufficient number of circumferentially distributed sensors, is designed to provide blade vibration benchmark. In the experiments, the KF-TWA method successfully identified nodal diameter vibrations with amplitudes as low as 0.014 mm, consistently yielding identical results across multiple sensor pairs, which demonstrates a higher robustness compared to the traditional TWA method. The results presented offer valuable insights into the engineering application of this technology.