A recursive calculation method of vibration displacements using blade tip timing in angular domain

Abstract

Blade tip timing (BTT) is a non-contact measurement technique that can be used to monitor blade vibration in turbomachinery. The raw data measured by BTT is the arrival time of all blades at the same stage. However, most blade vibration monitoring methods based on BTT require the use of blade vibration displacements, which are derived from the raw arrival time data, the blade rotation radius and speed. Conventional BTT methods calculate blade tip displacements by comparing the measured arrival time with the ideal arrival time. The ideal arrival time is obtained by assuming that the rotational speed is constant in a revolution, which is inconsistent with the fact, especially when the rotational speed changes rapidly. In this paper, a recursive calculation method called recursive BTT is proposed to reduce the influence of rotational speed fluctuation on the accuracy of blade tip displacement calculation. Recursive BTT calculates the displacements in the angular domain instead of the time domain. A recursive formula is constructed in the angular domain to calculate the blade vibration displacement by using the angle between the vibrating blades. Compared with the conventional BTT method, which relies on the once-per-revolution (OPR) signal, recursive BTT makes full use of the arrival time of all blades at the same stage to calculate the displacements. The advantage of recursive BTT is illustrated through a simulation, a laboratory test and a full-scale aeroengine test. To evaluate the reliability of the calculated displacements, strain signals are resampled to compare with the calculated displacements in the laboratory test. In the full-scale aeroengine test, due to the lack of strain signals, BTT displacements are used to track the blade natural frequency to qualitatively indicate the influence of displacements on blade vibration monitoring. The results of finite element analysis and modal test are used for verification in the full-scale aeroengine test. Simulation and experimental results demonstrate that compared with existing methods, recursive BTT is robust for calculating blade vibration displacements.