Blade Tip Timing Measurement Research Articles

Forced Response of Rotating Blisks: Prediction and Correlation to Blade Tip-Timing Measurements

Abstract This paper explores two different blisk dynamic models for resonant vibration prediction of a rotating blisk test piece, i.e., the Model-BDTID and geometrically mistuned models (GMM). The former represents a mistuned blisk model with blade mistuning pattern experimentally retrieved by a recently proposed blade mistuning identification method based on blade detuning tests (BDTID). It falls into the scope of the frequency-mistuning modeling approach. The latter refers to a geometrically mistuned model constructed upon high-precision blisk geometry data by leveraging the advanced optical geometry measurement technology. A specifically developed “Sector Mode Assembling Reduction Technique” is exploited for efficient dynamic analyses of the large-sized GMM. Forced response tests are performed in a spinning rig under well-controlled laboratory condition. The blade tip-timing (BTT) technique is employed to give all-blade vibration measurements of the rotating blisk. Correlation results between the forced response predictions to BTT measurements demonstrate that both the Model-BDTID constructed upon the identified blade mistuning of the blisk at rest and the GMM, can predict the resonant vibration of the rotating blisk with satisfactory accuracy.

Statistical blade tip timing measurement, Part II: High-order cumulant architecture

Blade tip timing (BTT) is a potential non-contact vibration measurement technique for rotating blades owing to its high efficiency and long service life. However, probe layout design and vibration parameter identification are critical challenges in BTT due to its inherent undersampling. To address this issue, we have proposed the concept of statistical BTT measurement which promotes efficient layouts and parameter identification methods by shifting the recovery target from the signal to itself to its statistics. In the first paper of series papers, we have developed covariance architecture for BTT measurement and signal post-processing. In this second part of series papers, we set out to develop BTT measurement from a higher-order statistic perspective. Specifically, we find that the 2qth-order cumulant retains the vibration information (frequency and amplitude) of the signal itself and it can be recovered at lower sampling rates than what is prescribed by the covariance architecture. On this basis, we propose a higher-order cumulant architecture for BTT measurement, which contains two aspects: higher-order difference layout (HODL) and higher-order cumulant-based parameter identifications. HODL is a special family of layouts that physically guarantee the availability of consecutive higher-order cumulant estimations and thus leads to a satisfactory parameter identification. To facilitate application, a series of concrete HODLs are provided for users, including a four-level nested layout and its enhanced version, and optimal fourth-order difference layout. The quantitative comparison in the simulations and experiments shows the effectiveness of the proposed higher-order cumulant architecture. Compared with the architectures developed from covariance and signal itself perspective, the proposed higher-order cumulant architecture is not only more robust to noise but also further reduces the number of required probes.

Compressed covariance sensing for blade tip timing measurement

Due to harsh working conditions, rotating blades are prone to failures. Thus, it is urgently needed to monitor blade health. Blade tip timing (BTT) is a promising non-contact vibration technique for rotating blades owing to its high efficiency and long service time. However, due to severe undersampling, traditional spectrum analysis methods are ineffective in identifying characteristic parameters and recovering the power spectrum of vibrations for condition monitoring. To address this issue, this paper proposes a compressed covariance sensing-based BTT (CCS-BTT) method for power spectrum estimation. Specifically, we build a compressed covariance sensing representation model for BTT signal, where the covariance representation can be non-underdetermined owing to the Hermitian Toeplitz structure of the covariance matrix. Then, a universal covariance sampling pattern (UCSP) is derived to ensure the complete covariance information can be efficiently recovered without sparsity constraint. By utilizing the inherent periodicity, the derived UCSP significantly improves the efficiency of BTT measurement. Moreover, for practicality, we present a series of optimized layouts based on UCSP that cover almost all possible cases of probe numbers in BTT measurement. Finally, extensive simulations and experiments validate the effectiveness and performance of CCS-BTT. By shifting the perspective from the signal itself to its covariance, CCS-BTT opens many avenues for the development of BTT signal processing. In addition, the proposed method is expected to be used in deterministic compressive sampling of wide-sense stationary signals.

Time delay-based spectrum reconstruction for nonuniform and sub-Nyquist sampling in blade tip timing

Rotating blades play a functional role during the working process of turbomachinery, but they are prone to failure due to harsh working conditions. Blade tip timing (BTT) is a potential technique for operational blade health monitoring due to its noncontact feature and efficiency. The critical issue in the application of BTT is extracting vibration parameters or reconstructing the spectrum for subsequent fault diagnosis. However, the nonuniform and undersampling characteristics of the BTT signal challenge signal processing. In this work, we developed an effective and efficient time delay-based spectrum reconstruction method. On this basis, we proposed the conditions (minimal probe number and delay sampling criterion) for the spectrum reconstruction. The proposed reconstruction conditions apply to most BTT methods for parameter identification or spectrum reconstruction and provide guidance for BTT measurement. Finally, the effectiveness of the proposed method and the correctness of the reconstruction conditions were demonstrated by a series of simulations and experiments.

Analytical method “Anmena” for blade tip timing measurement systems – Principle of the method

The paper describes further ongoing work on a new complex system for measuring and calculating the vibrations of turbine blades which was introduced in previous publications. This new system uses an innovative approach consisting of precise separation of measured data. The following text relates to the method of calculating the pure blade vibration based on an analytical approach. It is an essential part of the complex system. For this purpose, the multiple analytical method was developed and named “Anmena” (it is an abbreviation of the Czech term “analytická metoda násobku”, meaning analytical method of multiple). This paper is focused on introducing the basic principle of method and analysis of its reliability and expected accuracy on theoretical aspects. In addition, the so-called zero deviation axis is introduced for solutions that are theoretically independent of the distortion of the measured data expected in practice.

OPR-free single probe blade tip timing for monitoring rotating blade

Condition monitoring is crucial for a rotating blade working in harsh conditions. Blade tip timing (BTT) is a potential technique for operational blade health monitoring owing to its non-contact and efficiency, which identifies the vibration parameters characterizing the blade condition. However, severe undersampling and difficult probe/sensor installation hinder its application. Moreover, minimizing probe number, including once per revolution (OPR) sensor, to reduce modifications to turbomachinery is advocated in the field of health monitoring, especially for high-end equipment, such as aero-engines. In this paper, we proposed a single probe OPR-free BTT based parameters identification method for both synchronous and asynchronous vibrations. To avoid the use of OPR signal, rotating including angle (RIA) replaced the tip displacement as a signal to be analyzed. In addition, a sampling aliasing frequency (SAFE) map was constructed using the RIA signal, which provided the guidelines for parameter identification. Finally, the effectiveness and robustness of the proposed method were validated by a series of simulations and experiments. By reducing installation and hardware costs, the proposed method significantly improved the practicability of BTT measurement.

Experimental Investigation on Hardware and Triggering Effect in Tip-Timing Measurement Uncertainty.

Non-destructive testing for structural health monitoring is becoming progressively important for gas turbine manufacturers. As several techniques for diagnostics and condition-based maintenance have been developed over the years, the tip-timing approach is one of the preferred approaches for characterizing the dynamic behavior of turbine blades using non-contact probes. This experimental work investigates the uncertainty of the time-of-arrival of a Blade Tip-Timing measurement system, a fundamental requirement for numerical and aeromechanical modeling validation. The study is applied to both the measurement setup and the data processing procedure of a generic commercial measurement system. The influence of electronic components and signal processing on the tip-timing uncertainty is determined under different operating conditions.

Blade Crack Diagnosis Based on Blade Tip Timing and Convolution Neural Networks

The diagnosis of blade crack faults is critical to ensuring the safety of turbomachinery. Blade tip timing (BTT) is a non-contact vibration displacement measurement technique, which has been extensively studied for blade vibration condition monitoring recently. The fault diagnosis methods based on deep learning can be summarized as studying the internal logical relationship of data, automatically mining features, and intelligently identifying faults. This research proposes a crack fault diagnostic method based on BTT measurement data and convolutional neural networks (CNNs) for the crack fault detection of blades. There are two main aspects: the numerical analysis of the rotating blade crack fault diagnosis and the experimental research in rotating blade crack fault diagnosis. The results show that the method outperforms many other traditional machine learning models in both numerical models and tests for diagnosing the depth and location of blade cracks. The findings of this study contribute to the real-time online crack fault diagnosis of blades.

Deep Learning for Compressed Sensing-Based Blade Vibration Reconstruction From Sub-Sampled Tip-Timing Signals

Blade tip-timing (BTT) signals are always seriously sub-sampled, so reconstruction is much necessary for vibration analysis. Blade vibration responses are sparse in order domain and classical compressed sensing (CS) algorithms are difficult to reconstruct vibration orders due to lack of prior sparse information under variable speeds. In order to deal with this issue, this paper proposes an end-to-end deep compressed sensing (DCS) method. Firstly, a Multi-coset BTT measurement model is built under variable speeds and the DCS model is derived in order domain, where a specific convolutional neural network (CNN) is designed. Next, a Simulink model is built to generate training and testing samples. The simulation results show that the convolution layer with the ReLU layer placed after the BN layer can improve the reconstruction performance and the proposed method has better reconstruction accuracy and speed than classical CS algorithms. In the end, experiments are done and the results demonstrate that blade vibration orders can be recovered accurately by the proposed method, which will provide a novel way of BTT signal analysis.

Uncovering the Root Causes of Stall Flutter in a Wide Chord Fan Blisk

Flutter was encountered at part speeds in a scaled wide chord fan blisk designed for a civil aeroengine during a rig test when the fan bypass flow was throttled toward its stall boundary. Analysis of the blade tip timing measurement data revealed that the fan blades vibrated at the first flap (1F) mode with nodal diameters of two and three. To facilitate a further rig test and ultimately eliminate the flutter problem, a numerical campaign was launched to help understand the root causes of the flutter. Both the influence coefficient method (ICM) and the traveling wave method (TWM) were employed in the numerical investigation to analyze unsteady flows due to blade vibration, with the intention to corroborate different numerical results and take advantage of each method. To eliminate nonphysical reflections, a sponge layer with an inflated mesh size was used for the extended inlet and outlet regions. Steady flow field and unsteady flow field were examined to relate them to the blade flutter. The influences of vibration frequency, mass flow rate, shock, boundary layer separation and acoustic mode propagation behaviors on the fan flutter stability were also investigated. Particular attention was paid to the acoustic mode propagation behaviors.

Spatial transformation of general sampling-aliasing frequency region for rotating-blade parameter identification with emphasis on single-probe blade tip-timing measurement

Blade-health monitoring is intensely required for turbomachinery because of the high failure risk of rotating blades. Blade-Tip Timing (BTT) is considered as the most promising technique for operational blade-vibration monitoring, which obtains the parameters that characterize the blade condition from recorded signals. However, its application is hindered by severe undersampling and stringent probe layouts. An inappropriate probe layout can make most of the existing methods invalid or inaccurate. Additionally, a general conflict arises between the allowed and required layouts because of arrangement restrictions. For the sake of economy and safety, parameter identification based on fewer probes has been preferred by users. In this work, a spatial-transformation-based method for parameter identification is proposed based on a single-probe BTT measurement. To present the general Sampling-Aliasing Frequency (SAFE) map definition, the traditional time–frequency analysis methods are extended to a time-sampling frequency. Then, a SAFE map is projected onto a parameter space using spatial transformation to extract the slope and intercept parameters, which can be physically interpreted as an engine order and a natural frequency using coordinate transformation. Finally, the effectiveness and robustness of the proposed method are verified by simulations and experiments under uniformly and nonuniformly variable speed conditions.

Tip-timing measurements of transient vibrations in mistuned bladed disks

Bladed disks are usually characterized by a rich dynamic response during service due to the occurrence of several mode shapes that vibrate at resonance within the operative range. In particular, during start-ups and shutdowns, the variable speed causes a temporary crossing of resonance that cannot be neglected to determine stress envelope and safety margins of the system during its whole mission. In fact, fluid flow induces fluctuating loads with variable frequencies (non-stationary regime) on the blades being responsible of a dynamic response which does not follow the so-called steady-state (stationary) response. This paper proposes a novel post-processing method for Blade Tip-Timing (BTT) measurements for the identification of the resonance parameters of mistuned bladed disks working in non-stationary operative conditions. The method is based on a two degrees of freedom model (2DOF) and focuses on transient resonances in which two mistuned modes with close resonance frequencies are involved in the dynamic response. In such circumstances, the identification method based on the single degree of freedom (1DOF) model usually fails.To verify the effectiveness of the method, numerical and experimental investigations have been performed. First, a mathematical simulator based on a lumped parameter model of a bladed disk system is used to generate the BTT simulated data. Experimental signals are measured using a commercial BTT system through a set of optical probes mounted circumferentially around a rotating dummy blisk. It is shown that the method produces accurate predictions for the numerical simulation, even in the presence of considerable noise levels. Moreover, experimental results confirm a successful implementation of the method on the actual BTT measurements.

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%.

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.

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.

Five dimensional movement measurement method for rotating blade based on blade tip timing measuring point position tracking

As a non-intrusive blade vibration measurement technology, Blade Tip Timing (BTT) has been widely studied and developed in recent years. However, there are still many potential uncertainties in BTT technique, which reduce the correlation of the BTT measurements against the Finite Element (FE) predictions and the Strain Gauge (SG) measurements. One of the main ones is that the BTT sensor only measures the displacement of the blade tip in the direction of rotation. But blade tip movements other than rotation direction including axial, lean, bend, untwist, and sweep will change the position of the measuring point relative to the blade tip. In this paper, a method for measuring the five dimensional blade tip movements is proposed. This method uses BTT data, blade tip profile equation, and the initial measuring point position to track the actual measuring point position relative to the blade tip during blade rotation, so as to determine the blade axial, lean, bend, untwist, and sweep. Simulation results have proven the effectiveness and accuracy of the proposed method. Experiments were carried out on the test rig, industrial axial fan, and engine fan, results show that the method can effectively and accurately measure these types of blade tip movements. The relative error of blade untwist angle measurement is 3.6%. The work in this paper can improve the reliability of BTT measurements, and is of great significance to the comprehensive perception of operation state and accurate evaluation of dynamic stress of rotating blades.

Multi-coset angular sampling-based compressed sensing of blade tip-timing vibration signals under variable speeds

Blade Tip-Timing (BTT) has been regarded as a promising way of on-line blade vibration monitoring. But blind multi-band BTT vibration reconstruction is a big challenge under variable speeds and under-sampling. In order to deal with it, a novel Compressed Sensing (CS) method is proposed based on Multi-Coset Angular Sampling (MCAS) in this paper. First, multi-coset sampling scheme of BTT vibration signals is presented. Then the CS model of BTT vibration signals is derived in order domain. A sufficient condition of the number of BTT sensors is derived for perfect reconstruction and optimal placement of BTT sensors is determined by minimizing the condition number. In the end, numerical simulations are done to validate the proposed method and the performances of four reconstruction algorithms are compared, i.e., Orthogonal Matching Pursuit (OMP), Multiple Signal Classification (MUSIC), Basis Pursuit Denoising (BPDN) and Modified Focal Underdetermined System Solver (MFOCUSS). Influences of the sensor placement, the number of BTT sensors and measurement noises on the reconstruction performances are also testified. The results demonstrate that the proposed method is feasible and the overall performance of the BPDN algorithm is the best among the four algorithms. Also the reconstruction performance decreases with the accelerations of rotating speed.

A new bladed assembly simulator and an improved two-parameter plot method for blade tip-timing numerical simulations

The blade tip-timing measurement technique is presently the most promising technique for monitoring the blades of axial turbines and aircraft engines in operating conditions. Due to the high cost of experimental simulations of blade tip-timing–based condition monitoring methods, a numerical simulator for the vibrational behavior of bladed assemblies can be helpful for researchers interested in this field. So far, in most of the numerical simulators, the centrifugal effect of rotational speed on the natural frequencies is neglected. In this study, a new bladed assembly considering the centrifugal effect of the rotational speed for blade tip-timing numerical simulations is proposed. Moreover, an improvement in the engine order estimation algorithm in a two-parameter plot method is accomplished. In the assembly, blades are assumed to be cantilevered Euler–Bernoulli beams coupled together using linear springs. The finite element method is used to extract mass and stiffness matrices from differential equations of the system. By using the two-parameter plot method, the engine order of the excitation is detected. To examine the performance of the algorithm, Monte–Carlo simulation is implemented. The new simulator fulfills both cyclic symmetry and increase in the natural frequencies with increase in rotational speed. Engine order estimation with the new formulation in the two-parameter plot method is accurate. Hence, the new simulator and formulation for two-parameter plot method are reliable for numerical simulations.

Robust sparse representation model for blade tip timing

Blade tip timing (BTT) is one of the most important non-contact monitoring methods for blade vibration estimation. BTT predominantly consists of two steps: 1) acquiring the original pulse signal generated by the rotating blade through optical probes. 2) Obtaining the arrival time of the original pulses through a high-precision counter and then transforming it to deflection. Multiple noise is involved in BTT measurement, which is further complicated by the variable operating environment owing to the complexity and multiplicity of blade vibration and the transmission path. With the introduction of prior knowledge, sparse representation has proved a promising tool for the reconstruction of blade vibration features. However, the classical sparse representation model applied in BTT, is mostly formulated and conducted based on the simple assumption that the noise follows a Gaussian distribution. The assumption, too idealized for real practices, restricts the performance promotion of sparse representation in BTT. To address this problem and to represent the unknown noise, a robust sparse representation model based on a mixture of Gaussians (MoG) is proposed in this work. The solution algorithm of the proposed model is then derived from the perspective of the expectation maximization (EM) algorithm. To validate the effectiveness of the present method, the performance of the developed methodology is discussed in terms of different regular items.

Interpolation method for wideband signal reconstruction based on blade tip timing measurement

Blade tip timing (BTT) technique has become a promising way of online damage diagnosis for compressor and turbine blades by monitoring their vibrations. However, there are some disadvantages in previous algorithms for BTT signals, including not high precision, strict sensor layout, signal bandwidth limit, and weak anti-noise ability. To solve these problems, a novel interpolation method for wideband signal reconstruction (IWSR) is presented. Simulations are conducted using a lumped parameter model, which shows that IWSR reconstructs noiseless signals with overall errors mainly below 1%, and identifies the exact frequencies of 5 dB noise signals. In addition, the results validate its signal separation function and verify that its sensor layout is almost arbitrary, and its maximum allowable bandwidth is half the product of sensor number and rotational frequency. Experimental results demonstrate its effectiveness in frequency identification. In conclusion, IWSR provides precise information for real-time blade damage diagnosis, which benefits turbomachinery safety.