# Vibration Parameters Identification of Rotating Blades Based on Blade Tip-Timing Sensor Waveforms
## 1 Introduction  
As the key component of aero-engine, the rotor blade is subjected to loads such as high speed, high temperature, high pressure and various complex forces, which make it the most easily vibration parts. In order to reduce the risk of high cycle fatigue failure of blade vibration, the real-time monitoring of blade vibration is applied to ensure the safe operation of aero-engine. The blade tip-timing method is one of the research hotspots in non-contact vibration monitoring of rotating blades. It develops on the basis of discontinuous phase method and pulse modulation method. Compared with other measurement methods, the blade tip-timing method is not only simple in structure and convenient in use, but also can measure the vibration of all blades at the same time. The basic principle of the blade tip-timing method is to install the blade tip-timing sensors on the casing at the top of the blade and use the sensors to sense the arrival time of the blade. Due to the vibration of the blade, the arrival time of the blade would be ahead or behind. Through the use of different blade tip-timing processing algorithms to process the time series, the blade vibration information can be obtained [1]. The AMERICAN ALLIANCE for ADVANCING TEST WORK has regarded blade tip-timing measurement technology as an important online monitoring technology [2]. In recent years, the extensive research has been carried out on blade tip-timing vibration measurement technology abroad, such as the UNIVERSITY of MANCHESTER in the UNITED KINGDOM, HOOD COMPANY in the UNITED STATES, FOGALE COMPANY in FRANCE, ROTADATA COMPANY in the UNITED KINGDOM and MTU COMPANY in GERMANY [3; 4; 5; 6]. This technology can be used to measure blade flutter, blade stress, blade fatigue and other abnormal blade vibration. In China, TIANJIN UNIVERSITY has firstly carried out research on the measurement of vibration parameters of non-contact rotating blades based on tip-timing [7; 8; 9]. In addition, the NATIONAL UNIVERSITY of DEFENSE TECHNOLOGY, BEJING UNIVERSITY of CHEMICAL TECHNOLOGY and LIAONING UNIVERSITY of TECHNOLOGY have also conducted in-depth research on this technology [10; 11; 12; 13; 14; 15]. According to the different number and distribution of sensors, different blade vibration forms and different test conditions, a variety of blade tip-timing vibration signal analysis algorithms are proposed. The velocity vector end trace method is also called the single-sensor method; only one blade tip-timing sensor is needed to obtain blade synchronous vibration information [16]. In this method, the rotating speed is changed gradually; that is, the exciting frequency of the blade is changed, and the amplitude and phase of synchronous vibration of the blade are also changed accordingly, so the vibration displacement curve obtained is also changed according to certain rules. The basic principle of the two parameter method, also known as the double-sensor method, is to obtain two groups of blade vibration displacement signals by using two blade tip-timing sensors distributed according to a certain angle on the basis of the velocity vector end trace method [17; 18]. Taking these two groups of displacement signals as the horizontal and longitudinal coordinates, an elliptic curve can be obtained. According to the relevant parameters of the ellipse (major and minor axis, inclination angle, etc. ), the synchronous vibration amplitude and frequency doubling of the blade can be calculated. The autoregressive method is based on the principle of autoregression and the single-mode single degree of freedom model, at least four blade tip-timing sensors are needed to identify the blade vibration parameters, and the angle distribution between sensors is equal as far as possible. Four vibration displacements at different times of the blade are obtained, and every revolution and the vibration frequency, vibration amplitude and the other parameters of the blade are obtained through the autoregressive linear equations [19].