On the Foundation of Blade Tip Timing Measurement: Necessary and Sufficient Sampling for Aliasing-Free Sensing

Blade tip timing (BTT) is a promising vibration measurement for rotating blades owing to its non-contact feature, high measurement efficiency, and long service life. However, due to the measurement principle and installation restrictions, BTT signal is severely undersampled and thus hinders subsequent signal processing. Although many BTT analysis methods have sprung up like mushrooms, the performance of parameter identification or spectral analysis heavily depends on the probe layout and there is a lack of an intuitive and fundamental theory for BTT measurement. In this paper, we propose the necessary and sufficient sampling conditions for BTT measurement based on our previous delay sampling theorem, which provides fundamental insights for BTT measurement. By reviewing the existing BTT analysis methods, we demonstrate the correctness of the proposed theory. Finally, the high consistency between the theoretical inferences and simulation results verifies the correctness of the proposed theory.