Blade Tip Timing Research Articles

Dynamic Strain Reconstruction of Rotating Blades Based on Tip Timing and Response Transmissibility

Abstract Dynamic strain of rotating blades is critical in turbomachinery health monitoring and residual life evaluation. Though the blade tip timing (BTT) technique is promising to replace traditional strain gages, the lack of effective strain transformation through BTT hinders the implementation. In this paper, a noncontact dynamic strain reconstruction method of rotating blades is proposed based on the BTT technique and response transmissibility. First, the displacement-to-strain transmissibility (DST) considering rotational speed is derived from the frequency response functions based on blade mode shapes. A quadratic polynomial function of DST with respect to the rotational speed is provided to calibrate DST in blade rotational state. Second, the blade-tip displacement in resonance is obtained by BTT measurement and the Circumferential Fourier Fit processing method. Third, the dynamic strains of critical points on blades are calculated using the DST in conjunction with the tip displacement amplitude. In this paper, to validate the proposed method, acceleration and deceleration experiments, including both BTT and strain gages, are conducted on a spinning rotor rig. Experimental results demonstrate that the reconstructed dynamic strains of different positions on the rotating blades correspond well to the results measured by strain gages. The mean relative error between the reconstructed and measured results is generally within 8%.

Development of blade tip timing signal simulator based on a novel model reduction method of bladed disks

In order to improve the calculation efficiency of high fidelity finite element model (FEM) and solve the problem of the high BTT test cost, a blade tip timing (BTT) data simulator of rotating bladed disk based on reduced order model (ROM) is developed in this paper. Firstly, the ROM of rotating mistuned bladed disk is constructed by using the proper orthogonal decomposition (POD) method. Then, a construction method of BTT data simulator based on the ROM is proposed, which considers the influence of rotation effect, mistuned and speed fluctuation. Finally, the simulator is constructed based on an academic bladed disk, and the vibration parameters are identified by using the traditional vibration parameter identification methods to verify the effectiveness of the simulator. This study provides a new data generation method for effectively verifying the effectiveness of vibration parameter identification algorithm.

Experimental validation of FEM-computed stress to tip deflection ratios of aero-engine compressor blade vibration modes and quantification of associated uncertainties

Blade Tip Timing (BTT) technology is concerned with the estimation of turbomachinery blade stresses. The stresses are determined from BTT data by relating the measured tip deflection to the stresses via Finite Element (FE) models. The correlation of BTT measurements with FE predictions involves a number of uncertainties. This paper presents the process for validating the FE stress and deflection predictions of aero-engine compressor blades under non-rotation conditions as a critical preliminary step towards the complete understanding of their dynamic behaviour under rotating conditions when using BTT measurements. The process steps are described in detail, including the FE modelling and analysis of the blades and the blade-disk assembly, and the measurements of the blade tip deflection and blade stress. Furthermore, the uncertainties associated with the FE modelling and the measurement processes are quantified. The results show that the FE model is valid considering the control of most uncertainties. The experimental validation of the FE-computed stress-to-tip deflection calibration factors in the present study provides the basis for the determination of the calibration factors under rotational conditions using a previously presented BTT data simulator, and for the design of corresponding rotating experiments using BTT.

A novel method to improve the precision of BTT under rapid speed fluctuation conditions

It is ultra-important to evaluate the turbine machine blade dynamic stress under abnormal conditions such as rapid rotating speed fluctuation result from surge, rub and foreign object impact. The blade tip timing (BTT) based non-contact dynamic stress measurement method is the most promising technology to replace rotating blade strain gauge. However, there are great challenges to precisely monitor the blade vibration as the rotating speed rapidly fluctuated. It limits the application of BTT considerably. Here, a novel BTT method is proposed to achieve high-precision blade vibration measurement under rapid speed fluctuation conditions. The influence of speed fluctuation on the theoretical arrival time is investigated based on the relationship between blade theoretical arrival time and installation angle. Further, using of the SG filter greatly reduces the computational complexity. The effectiveness of the method is verified by numerical simulation, academic test rig and large industrial turbo fan. The results indicate that the speed measurement error is not more than 0.6 rpm as the accelerating speed as high as 1200 rpm/s. The blade vibration displacement error caused by the rapid speed change can be less than 10 μm. Comparing with existing BTT methods, the average and standard deviation of the blade vibration measurement error are greatly reduced. The method has great value for the application of the blade health monitor and predictive maintenance in turbomachines.

Rotating blade frequency identification by single-probe blade tip timing

The rotating blade is a key turbomachinery component with a high failure risk. Therefore, monitoring the rotating blade is urgently required. Blade tip timing (BTT) is regarded as an efficient technique for blade vibration monitoring as it reflects the condition of blades. However, the identification process from under-sampled data and probe layout optimization hinder the application of BTT. Most of the existing parameter identification methods have strict probe layout requirements; thus, an inappropriate probe layout may fail BTT measurements. An increased number of probes and optimal probe positions are considered essential for frequency identification. However, an optimal probe layout is usually restricted by arrangement. In this work, a novel frequency identification method via a single BTT probe is proposed by considering arrangement, cost, and safety restrictions. The proposed method focuses on the relationship between sampling and aliasing frequencies, which can be summarized in two steps: obtaining a Sampling–Aliasing Frequency (SAFE) map and identifying the resonance center and corresponding engine order (EO). Obtaining the SAFE map of the BTT signal recorded by a single probe is difficult because of low and variable sampling frequency. To overcome this problem, the adaptive window length short-time Fourier transform is proposed. Based on the SAFE and EO, the natural frequency can be accurately extracted from a single BTT measurement. Uniformly and nonuniformly variable speed conditions were investigated, and the results were compared with those obtained using multiple probes. The proposed method has been verified to provide blade natural frequency from a single-probe BTT measurement.

Blind interpolation for multi-frequency blade tip timing signals

Blade tip timing (BTT) is a promising non-contact on-line monitoring technique for rotor blades. Although various analytical methods for BTT signals have been developed, their accuracy and stability still need to be improved for subsequent blade damage detection. This paper derives and validates a blind interpolation method for multi-frequency BTT signals (BIMF). It is an integration of two novel algorithms proposed by this paper: (1) the multi-band interpolation (MBI) algorithm breaks the single-band limitation of established interpolation methods, and is capable of accurate and stable spectrum identification and waveform reconstruction when the approximate frequency distribution is known; (2) the real signal-based multiple signal classification (RSMUSIC) algorithm provides reliable prior knowledge of frequency for MBI. Simulation results verify the accuracy of the proposed methods and the advantages of BIMF over the BTT-based compressed sensing algorithms. Experimental results also validate the accuracy and stability of BIMF in spectrum identification.

Optimization and assessment of blade tip timing probe layout with concrete autoencoder and reconstruction error

Blade tip timing (BTT) is a promising non-contact measurement method for blade vibration monitoring. The limited number of probes leads to the inherent under-sampled problem of BTT signal. The quality of the analysis result of under-sampled signal depends on the probe layout. However, the application of existing probe layout optimization methods requires domain knowledge about blade vibration. Additionally, the lack of comparisons of probe layouts generated by different probe layout optimization methods makes it difficult to evaluate the performance of different methods. In this paper, we proposed a new probe layout optimization method based on a concrete autoencoder to reduce the reliance on the domain knowledge. The probe layouts were compared using an independently trained reconstructor in the time domain. And the spectral distance was defined to evaluate the performance of different probe layouts in the frequency domain. The validation results showed that the proposed method has superior time domain reconstruction performance and decent frequency domain reconstruction performance compared to other methods. The most informative and representative probe layout can be effectively selected by the proposed method.

A hybrid framework for remaining useful life estimation of turbomachine rotor blades

Hybrid methods for prognosis of mechanical components have the potential of improving remaining useful life (RUL) estimations. Hybrid methods combine physics-based and data-driven methods to diagnose faults and predict when failures will occur. In this work, we propose a hybrid framework that estimates the RUL from routine maintenance inspection data and condition monitoring data.This hybrid framework is applied to turbomachine rotor blades. Blade tip timing (BTT) measurements are used for condition monitoring. The least squares spectral analysis (LSSA) method is used to find the natural frequency. The natural frequency is a function of the blade's health state and is used to infer the crack length in the blade’s root. To accommodate for artificial rotational stiffening, an interpolation model of the blade's Campbell diagram, generated from a finite element model, is used.In the proposed methodology, we use an ensemble physics-based model that serves as a prior probability density function for a Gaussian process regression (GPR) model. The predictive distribution of the GPR model is constructed by conditioning the physics-based model on the observed data from routine maintenance inspections. We also compare this hybrid diagnosis model to the physics-based technique and other data-driven methods. The hybrid diagnosis model outperformed the physics-based method and data-driven methods.The unscented Kalman filter (UKF) is used to estimate and forecast the evolution of the crack length over time. Paris’ law coefficients are used as hidden latent variables in a hybrid degradation model. In the diagnosis and prognosis phases, we use the unscented transform to efficiently approximate the probability density functions of the crack length and the crack growth law parameters.Finally, we compare the applied hybrid model to a purely physics-based model and show that the hybrid model outperforms the physics-based model in predicting the length of a crack. We demonstrate that the hybrid model increases the accuracy and precision of RUL prediction from physics-based models with 60% on average.

Blade Tip Timing Signal Filtering Method Based on Sampling Aliasing Frequency Map

The rotor blade is the core turbomachinery component with high failure risk. Thus, condition monitoring of blades is critical to ensure engine safety. Blade tip timing (BTT) is one of the most promising approaches to measure vibration, which is used for monitoring the health of blades. In reality, blade displacement contains several unwanted components that cause measurement uncertainty. However, because undersampling leads to spectrum aliasing, and the aliasing frequency changes with speed fluctuation, conventional filtering techniques fail to remove the portion of the signal that causes uncertainty. In this work, two filtering methods for the BTT signal are proposed based on sampling aliasing frequency (SAFE) map, namely, single-probe data detrending and tracking sliding bandpass filtering, which can extract synchronous vibration and denoise the reserved signal (asynchronous vibration) due to the clear distribution of different components in the SAFE map. The former eliminates the rotation frequency and its harmonic components by detrending of the BTT signal, whereas the latter effectively reduces the noise of the BTT signal by bandpass filters whose limit frequencies are adjusted according to sampling frequency and the trajectory in the SAFE map. Furthermore, the time-domain signal and the spectrum obtained by the orthogonal matching pursuit (OMP) algorithm are used to show the filtering effect. The effectiveness and interpretability of the proposed method are verified by simulation and experimental data.

Study on identification of modal parameters of mistuned bladed disks

To develop turbomachinery blades with high reliability, it is indispensable to verify the natural frequency, damping, resonant stress, etc. under operating condition, and utilize these data in the mechanical design of a new blade. BTT (Blade Tip Timing) and the telemetry system have been widely used to measure the modal parameters of turbomachinery blades. In measurement of the modal parameters of blades under rotation, it is pointed out that the mistuning phenomena make the identification of modal parameters difficult. Namely, because, in a mistuned bladed disk, responses of many vibration modes are superimposed, it becomes difficult to correctly identify the natural frequency and damping of an individual blade. This is one of the critical issues to be overcome for developing blades with high reliability. In this study, a novel identification method of modal parameters of a mistuned system is proposed, where the modal parameters of a mistuned bladed disk are identified using the frequency responses consisting of many vibration modes. To verify the validity of the identification method proposed, typical mistuned systems of a turbocharger are analyzed, and the modal parameters are identified. The effect of the noise included in the measured frequency response on the accuracy of the identification is examined in detail.

A Modal Estimation Method for Evaluating Rotating Blades Based on Compressed Sensing and Blade Tip Timing

A Modal Estimation Method for Evaluating Rotating Blades Based on Compressed Sensing and Blade Tip Timing

Research on Running Status Monitoring and Rotating Blade Crack Detection of Large-Scale Centrifugal Compressor Based on Blade Tip Timing Technique

Research on Running Status Monitoring and Rotating Blade Crack Detection of Large-Scale Centrifugal Compressor Based on Blade Tip Timing Technique

Flow and Vibration in the Small Steam Turbine Last Stage

The paper deals with evaluation of experimental data obtained from the real-size 30 MW output Waste to Energy steam turbine. For many turbine regimes pressures in the last stage area were obtained. At the same time amplitudes of blade tips vibrations were measured of last rotor blades using the blade tip timing system and axial velocity of the steam at the last stage outlet. The obtained data are mutually correlated and relations are analysed between increased vibration values and pressure ratios at the last stage. Increased tip vibrations occur mainly in the area when the pressure ratio over the last blade tip and root is higher than one. In this case there is no expansion, but compression in the last stage of the turbine. The presented results contribute to understanding of processes in the last stage of the steam turbine, mainly for those regimes of turbine operation when its output is lower than 20 % of the nominal output, e.g. during the island regime.

Error Revising of Blade Tip-Timing Parameter Identification Caused by Frequency Sweep Rate

Error Revising of Blade Tip-Timing Parameter Identification Caused by Frequency Sweep Rate

Measurement of multiple physical quantities based on blade tip timing

Novel methods are proposed to expand the capability of a blade tip timing (BTT) system. Simultaneously measurement of blade tip clearance (BTC) and blade tip velocity (BTV) is realized. In terms of hardware, a convex lens is used at the emitting end of the laser fiber to adjust the optical path. In the software part, a new BTT protocol is designed where both the time-of-arrival and time-of-leaving as a blade sweeps across the detecting region are recorded. Meanwhile, new algorithms are developed to process the data. The methods are studied experimentally from various aspects. It is demonstrated that when a speed sensor is not available, the BTC and BTV can be measured by a double-lens sensor. The random error of BTC on a steady operational occasion is within 30 μm. Subtle dynamic responses during accelerations can be accurately captured. When a speed sensor is available, a single-lens sensor can be used to measure the BTC. Besides, a double-lens sensor can be automatically calibrated using a Kalman-filter-based algorithm to maintain high precision during long-time online measurement. All the methods have been validated on a compressor rig.

Blade tip characteristics of turbine disks with cracks

Crack detection of turbine disks is of great significance in aero-engine health monitoring. The traditional non-destructive testing (NDT) methods are not applicable for in-situ or online monitoring of crack propagation. In order to monitor the crack propagation via measured signals, it is necessary to investigate the dynamic characteristics of cracked turbine disks first. In this paper, finite element analysis (FEA) is carried out to study the blade tip characteristics of turbine disks with different types and size of cracks. Three observation parameters, i.e., blade tip clearance change, blade spacing and blade twist angle, are proposed as crack indicators. The effects of different crack types (e.g., circumferential crack, radial crack, crack at the center hole and crack at the bottom of the mortise) on the observation parameters are discussed qualitatively. Then the circumferential crack is selected as an example for the quantitative analysis. The circumferential cracks with different length, width, location and number are studied and compared systematically. The qualitative analysis results show that the three observation parameters can be used to detect different crack types except the crack at the center hole. The quantitative analysis results show that blade spacing is most sensitive to size parameters without crack width. The conclusions can provide proofs for the blade tip timing (BTT) of cracked turbine disks.

An Improved Blade Vibration Parameter Identification Method considering Tip Clearance Variation

Blade tip timing (BTT) technology is the most effective means for real-time monitoring of blade vibration. Accurately extracting the time of blade tip reaching the sensors is the key to ensure the accuracy of the BTT system. The tip clearance changes due to various complex forces during high-speed rotation. The traditional BTT signal extraction method does not consider the influence of tip clearance change on timing accuracy and introduces large timing errors. To solve this problem, a quadratic curve fitting timing method was proposed. In addition, based on the measurement principle of the eddy current sensors, the relationship among the output voltage of the eddy current sensor, tip clearance, and the blade cutting magnetic line angle was calibrated. A multisensor vibration parameter identification algorithm based on arbitrary angular distribution was introduced. Finally, the experiments were conducted to prove the effectiveness of the proposed method. The results show that in the range of 0.4 to 1.05 mm tip clearance change, the maximum absolute error of the timing values calculated by the proposed method is 26.0359 us, which is much lower than the calculated error of 203.7459 us when using the traditional timing method. When the tip clearance changed, the constant speed synchronous vibration parameters of No. 0 blade were identified. The average value of the vibration amplitude is 1.0881 mm. Compared with the identification results without changing tip clearance, the average value error of the vibration amplitude is 0.0017 mm. It is proved that within the blade tip clearance variation of 0.4 to 0.9 mm, the timing values obtained by the proposed timing method can accurately identify the vibration parameters of the blade.

Tip-timing accuracy improvement using optical fiber bundle probe with GRIN lens under varying blade tip clearance

The blade tip-timing (BTT) method has become the industry standard in blade vibration measurement. It monitors blade vibration based on the different times of arrival (ToAs) between blade vibration and not. The optical fiber bundle (OFB) probe is widely used to obtain ToA because of its small size, fast response, and high tip-timing accuracy. ToA is usually obtained by comparing the received signal with a fixed threshold level. However, the varying blade tip clearance (BTC) will affect the received signal, which directly causes the tip-timing error. We propose an optical fiber probe with GRIN lens, which eliminates the tip-timing error caused by varying BTC through the constant-fraction discrimination (CFD) method. The model of the OFB probe with GRIN lens is first established. Model analysis indicates that ToA obtained by the proposed method is constant no matter how BTC changes. Finally, the accuracy of the model and the effectiveness of the method are verified by two experiments. When BTC varied from 1.5 to 3.5 mm, the maximum tip-timing errors of OFB probe without and with GRIN lens were 181.12 μs and 10.44 μs, respectively.

An improved multiple per revolution-based blade tip timing method and its applications on large-scale compressor blades

Blade Tip Timing (BTT) is one of the most effective technologies for blade vibration measurement of turbomachinery. The blade vibration measurement indicates the operational status of the blades, which is of great significance for blade health management and fault diagnosis. However, the approaches and applications of BTT technologies are still facing enormous challenges. This study, based on the traditional once per revolution (OPR) methods, the measurement error of blade vibration induced by the speed fluctuation per revolution (SFPR) is investigated. Considering the effect of the SFPR, an improved multiple per revolution-based BTT method (MPR) for calculating the blade vibration is proposed. Furthermore, numerical simulation and experimental work of the MPR method are executed. Compared with the results of different technologies, the feasibility and reliability of the MPR method are verified by theoretical analysis and experimental verification. The MPR technology is also applied to blade vibration measurement of a large-scale Centrifugal Compressor and a large-scale Axial-Centrifugal Compressor. The conclusions of applications are well practical.

Key-Phase-Free Blade Tip-Timing for Nonstationary Test Conditions: An Improved Algorithm for the Vibration Monitoring of a SAFRAN Turbomachine from the Surveillance 9 International Conference Contest

A turbomachine is a fundamental engineering apparatus meant to transfer energy between a rotor and a fluid. Turbomachines are the core of power generation in many engineering applications such as electric power generation plants, aerospace, marine power, automotive etc. Their relevance makes them both mission critical and safety critical in many fields. To foster reliability and safety, then, continuous monitoring of the rotor is more than desirable. One promising monitoring technique is, with no doubt, the Blade Tip-Timing, which, being simple and non-invasive, can be easily implemented on many different rotors. Blade Tip-Timing is based on the recording of the time of arrival of the blades passing in front of a probe located at a fixed angular position. The non-contact nature of the measurement prevents influences on the measured vibration, that can be recovered for all the blades simultaneously, possibly even online. In this regard, a novel algorithm is presented in this paper for obtaining a good estimate of the vibration of the blades with minimum system complexity (i.e., only one Blade Tip-Timing probe) and minimum computational effort, so to create a simple vibration monitoring system, potentially implementable online. The methodology was tested on a dataset from a SAFRAN turbomachine made available during the Surveillance 9 international conference for a diagnostic contest.