Blade tip timing for multi-mode identification based on the blade vibration velocity

Blade Tip Timing (BTT) is a widely employed non-contact measurement technique for monitoring turbomachinery blade vibrations. The conventional BTT method typically involves computing the expected time of arrival (TOA) and subtracting it from the actual TOA to derive the time difference, subsequently used to calculate blade-tip displacement. However, calculating the expected TOA introduces computational errors. Moreover, obtaining blade-tip vibration displacement under variable rotational speeds necessitates pre-processing to remove trend terms caused by speed fluctuations. To address these challenges, this study introduces a paradigm shift by replacing the traditional displacement-based blade-tip timing (D-BTT) with velocity-based blade-tip timing (V-BTT). Specifically, this approach utilizes the angular information between adjacent sensors and the measured TOA to extract the blade-tip vibration velocity through a Taylor series expansion, thus eliminating the calculating of the expected TOA and improving the computational efficiency. Building upon this methodology, a compressed sensing model for undersampled vibration velocity is established and solved using the Block-OMP algorithm, enabling vibration parameter identification without relying on prior information. By providing a superior representation of mid-frequency components of blade-tip vibration, V-BTT facilitates precise identification of higher-order vibration parameters in multi-mode blade motion. Finally, the efficacy of the proposed method is confirmed through numerical simulations and experiments involving multi-mode blades. The experimental results reveal that the relative errors of the first two modal frequencies for the five blades identified using vibration velocity are all below 0.5%, affirming the method's accuracy. Compared to the traditional D-BTT method, the V-BTT approach reduces the need for trend removal, eliminates calculation errors associated with the expected TOA, and, most importantly, enhances the accuracy of multi-mode frequency identification.