Mistuned Bladed Research Articles

Experimental Investigation on a Bladed Disk with Traveling Wave Excitation.

Bladed disks are key components of turbomachines and their dynamic behavior is strongly conditioned by their small accidental lack of symmetry referred to as blade mistuning. The experimental identification of mistuned disks is complicated due to several reasons related both to measurement and data processing issues. This paper describes the realization of a test rig designed to investigate the behavior of mistuned disks and develop or validate data processing techniques for system identification. To simplify experiments, using the opposite than in the real situation, the disk is fixed, while the excitation is rotating. The response measured during an experiment carried out in the resonance-crossing condition is used to compare three alternative techniques to estimate the frequency-response function of the disk.

Tabu Genetic Cat Swarm Algorithm Analysis of Optimization Arrangement on Mistuned Blades Based on CUDA

Tabu genetic cat swarm optimization algorithm is proposed for optimization arrangement on mistuned blades. Furthermore, it is improved to be an innovative parallel algorithm based on Compute Unified Device Architecture (CUDA), whose performance is analyzed both in continuous and discrete solution space. The lumped parameter model and finite element model of the bladed-disk system are established for dynamics analysis and optimization verification. The complete mistuned parameter identification method and the improved mixed-interface prestressed substructure modal synthesis method are two other highlights. The results indicate that the algorithm in this paper has the advantages of low cost and high efficiency. The vibration localization and amplitude of the mistuned bladed-disk system are both reduced significantly. The optimization analysis method is proved to be applicable to the mistuned bladed-disk system of the aeroengine in engineering practice.

A New Method of Reducing the Vibration Localization of the Multi-packet Whole Mistuned Bladed Disk System Using Bladed Packets

Multi-packet whole bladed disks are found in some turbo engines. At the same time, mistuning of blades is inevitable and it will lead to the vibration localization in which vibration energy mainly locates in some blades in the bladed disk system. It can accelerate the high cycle fatigue of the bladed disk. It is critical to search for an efficient way to control the level of vibration localization of the mistuned bladed disk system. Therefore, in this paper, a new method of reducing the vibration localization of the mistuned bladed disk system using bladed packets is studied. A mathematical model is developed in which a coupling stiffness is introduced to describe the coupling relationship due to bladed packets. The effect of bladed packets on the vibration localization of the whole mistuned bladed disk is discussed. The results indicate that the bladed packet can really reduce the degree of the vibration localization of bladed disk. The relationship between the coupling strength of blade to blade and the vibration localization is researched. Moreover, different number of bladed packets of the mistuned bladed disk on the vibration localization of the mistuned bladed disk is investigated for researching the optimal multi-packet structures.

Blade vibration measurement and numerical analysis of a mistuned industrial impeller in a single-stage centrifugal compressor

Understanding and predicting the dynamical behavior of the impeller structure under realistic condition is vital for resonance-free and reliable design. This paper presents a novel method for high fidelity measurement and efficient modeling of impeller blade vibration considering realistic operating environment and mistuning effect. To clarify the blade forced vibration, strain gauge and blade tip timing (BTT) measurement have been conducted. Measurement introduced mistuning and flow disturbance from strain gauges are further excluded with tip-timing. The blade mistuning is then identified and quantified with the help of parameter estimation method and updates the numerical mistuned forced response model. Aerodynamic forcing function due to downstream diffuser vanes is also numerically evaluated based on a decoupled two row configuration and time transformation method. Results shown that BTT system is well applied to capture the blade resonance response and shows a promising way for monitoring individual blade component. The aerodynamic forcing is also found to be well captured and presents a wave decay trend along the flow path towards the upstream. Finally, based on the proposed BTT parameter driven vibration prediction method, the blade mistuned forced response shows a good agreement with measurement results. Improvement also implies variations of parameters and mistuning pattern should be considered as a critical part and uncertainty source in the numerical prediction. This work is of scientific significance to enrich the knowledge of blade vibration in centrifugal compressor using tip-timing and of industrial application value to consider mistuning problems with efficient reduce-order modeling method.

Analysis of Nonlinear Modal Damping Due to Friction at Blade Roots in Mistuned Bladed Disks

Abstract A method is proposed to analyze the modal damping in mistuned bladed-disk with root joints using large finite element models and the detailed description of frictional interactions at contact interfaces. The influence of mistuning on the dissipated energy for different blades on a bladed-disk and the modal damping factors for different vibration levels for any family of modes can be investigated. The dissipated energy and damping factors due to microslip are simulated by multitude of surface-to-surface elements modeling the friction contact interactions at root joints. The analysis is performed in the time domain, and an original reduction method is developed to obtain the results with acceptable computational times. The model reduction method allows the calculation of the modal damping of the mistuned assembly by evaluation of the energy dissipated at root joint of each individual blade using small parts of bladed disk sectors. The dependency of modal damping factor on blade mode shapes, engine-order excitation numbers, nodal diameter numbers, and vibration amplitudes is studied and the distributions of amplitude and dissipated energy on the mistuned bladed-disk are investigated using a realistic blade disk model.

Key Features of the Transient Amplification of Mistuned Systems

Abstract The dynamic behavior of bladed disks in resonance crossing has been intensively investigated in the community of turbomachinery, addressing the attention to (1) the transient-type response that appear when the resonance is crossed with a finite sweep rate and (2) the localization of the vibration in the disk due to the blade mistuning. In real conditions, the two mentioned effects coexist and can interact in a complex manner. This paper investigates the problem by means of analytic solutions obtained through asymptotic expansions, as well as numerical simulations. The mechanical system is assumed as simple as possible: a 2DOF linear system defined through the three parameters: damping ratio ξ, frequency mistuning Δ, rotor acceleration Ω̇. The analytic solutions are calculated through the multiple-scale method.

Mistuning Identification Technique Based on Blisk Detuning

The structural dynamics of turbomachinery bladed disks is of paramount importance to ensure safety and reliability. Due to their sensitivity to mistuning (that is, any deviation from nominal properties), bladed disk vibrations encountered in practical applications can be significantly amplified. Thus, it is important to identify mistuning of as-manufactured blisks so that computational models can be updated to include mistuning and used to accurately characterize the behavior of blisks in operating conditions. Several mistuning identification techniques based on bench tests have been developed. This paper focuses on the techniques based on blade isolation through mass detuning and modal testing: methods that require a simple experimental setup. The typical shortcoming of these methods is that they rely on measured blade frequencies as a proxy for blade mistuning. However, as presented in this study, it is often impossible to completely isolate a blade from the neighboring ones using mass detuning; as a result, the measured frequencies do not represent the cantilevered blade frequencies that many reduced-order models use to model mistuning. This is especially true for blisks in which the blade-to-disk stiffness ratio is not negligible: a scenario that could become more and more prevalent as the trend to design thinner disks to reduce blisk mass continues. A technique based on modal testing that is able to accurately identify mistuning by appropriately capturing the effect of residual blade-to-blade and blade-to-disk coupling is introduced in this paper. A validation is carried out using an academic blisk model and surrogate data, and the results demonstrate that the proposed method outperforms the direct use of blade frequencies as proxies for mistuning.

Mode localization in linear and periodically time‐varying mistuned wind rotor

AbstractRotor blades are the most important and most expensive part of a wind turbine; their dynamic behavior is of great significance for maintenance planning and safe operation. In this study, the effect of mistuning on the vibration modes of rotor blades was investigated, with a focus on the mode localization of linear time‐varying wind turbine rotors. And the significance of the work lies in finding that the mode localization may aggravate the blade damage and potentially reduced fatigue life of the blade. The rotating blades were approximated as cantilever Bernoulli–Euler beams, and the flapwise and edgewise modes of each blade were considered. The Lagrangian method was employed to derive the linear time‐varying dynamic equations of the wind turbine rotor. A wind turbine rotor was mistuned because of slight fluctuations in the blade stiffness; subsequently, Floquet analysis was employed for modal decomposition of a mistuned wind turbine rotor, and the mechanism of mode localization was examined in depth. Numerical simulation results indicated that slight mistuning of a single blade is sufficient for triggering mode localization. The effects of the magnitude of the blade mistuning and rotor speed on the severity of mode localization were analyzed. Finally, different quantitative measures were considered for characterizing the degree of mode localization in mistuned wind turbine rotors.

Vibration response prediction of coated blisks under multi-point non-contact excitations using mistuning identification data

The mistuning and excitations of the real engineering coated blisk are very complex and it is difficult to predict the vibration response. In this study, a numerical method of response prediction for coated blisks under multi-point non-contact excitations is proposed. The purpose of applying multi-point non-contact excitations to the blades is to get closer to the actual excitations condition of coated blisks. A non-rotating coated academic blisk is used as the research object, the component mode mistuning (CMM) reduced-order technique focusing on blade mistuning is improved to establish the response prediction model of the coated blisk, which includes quantized parameters of the blade substrate mistuning and the mistuning caused by coating. Meanwhile, the effects of the mass, stiffness and damping mistuning of the blisk substrate and the coating on the response are comprehensively considered in the model. In order to preserve the simulation accuracy of the response prediction model, the blade substrate mistuning and the mistuning caused by coating are identified, and the reduced-order model (ROM) is updated by the identification results of mass and stiffness mistuning. The response predictions of the numerical case and actual case of the non-rotating simplified coated academic blisk are carried out respectively. For the numerical case, the results of response prediction are in good agreement with the response calculation results of the high fidelity finite element model (FEM). Compared with the numerical case, the error between the predicted response and the tested response is larger, but this error level is sufficient to meet the requirements of engineering applications. All the results show that the proposed method is effective for predicting the response of the non-rotating coated academic blisks under multi-point excitations.

Acoustic Identification of Turbocharger Impeller Mistuning—A New Tool for Low Emission Engine Development

At present, exhaust gas turbochargers not only form the basis for the economical operation of petrol, diesel or gas engines of all power categories, but also have an irreplaceable role on reducing their emissions. In order to reduce emissions from internal combustion engines, various systems are being developed, all of which have a turbocharger as an important component. Demands on turbocharger system durability and reliability keep growing, which requires the application of increasingly advanced computational and experimental methods at the development beginning of these systems. The design of turbochargers starts with a mathematical description of their rotationally cyclic impellers. However, mistuning, i.e., a slight individual blade property deviation from the intended design parameters, leads to a disturbance of the rotational cyclic symmetry. This article deals with the effects of manufacturing-related deviations on the structural dynamic behaviour of real turbine rotors. As opposed to methods exploiting expensive scanning vibrometers for experimental modal analysis or time-consuming accurate measurement of the geometry of individual blades using 3D optical scanners. A suitable microphone and a finite element rotor wheel model are the basis of this new method. After comparing the described acoustic approach with the laser vibrometer procedure, the results seemed to be practically identical. In comparison with the laser technique the unquestionable added value of this new method is the fact that it brings a significant reduction in the financial requirements for laboratory equipment. Another important benefit is that the measuring process of bladed wheel mistuning is significantly less time-consuming.

Vibration Parameters Estimation by Blade Tip-Timing in Mistuned Bladed Disks in Presence of Close Resonances

The present paper is focused on the post processing of the data coming from the Blade Tip-Timing (BTT) sensors in the case where two very close peaks are present in the frequency response of the vibrating system. This type of dynamic response with two very close peaks can occur quite often in bladed disks. It is related to the fact that the bladed disk is not perfectly cyclic symmetric and the so called “mistuning” is present. A method based on the fitting of the BTT sensors data by means of a 2 degrees of freedom (2DOF) dynamic model is proposed. Nonlinear least square optimization technique is employed for identification of the vibration characteristics. A numerical test case based on a lump parameter model of a bladed disk assembly is used to simulate different response curves and the corresponding sensors signals. The Frequency Response Function (FRF) constructed at the resonance region is compared with the traditional Sine fitting results, the resonance frequencies and damping values estimated by the fitting procedure are also reported. Accurate predictions are achieved and the results demonstrate the considerable capacity of the 2DOF method to be used as a standalone or as a complement to the standard Sine fitting method.

Comparative Studies of Surrogate Models for Response Analysis of Mistuned Bladed Disks

The forced responses of bladed disks are highly sensitive to inevitable random mistuning. Considerable computational efforts are required for the sampling process to assess the statistical vibration properties of mistuned bladed disks. Therefore, efficient surrogate models are preferred to accelerate the process for probabilistic analysis. In this paper, four surrogate models are utilized to construct the relation between random mistuning and forced response amplitudes, which are polynomial chaos expansion (PCE), response surface method (RSM), artificial neural networks (ANN) and Kriging interpolation, respectively. A bladed disk with 2-degrees-of-freedom (2-DOF) each sector is used to validate the effectiveness of the surrogate models. The effects of number of training samples on the surrogate model accuracy are discussed. The responses results of one blade (single output) and maximum response of all blades (multi-output) indicate that PCE and Kriging interpolation could yield accurate and stable predictions of the statistical characteristics of the forced responses. PCE is recommended for the mistuned response predictions due to its accuracy and efficiency.

Response of large mistuned bladed disk assembly subjected to random excitations

In this study, the effects of large geometric mistuning on blade response are investigated considering the change of mistuning properties and excitation characteristics. The response variations because of large mistuning are negligible under white noise excitations and are highly significant under narrow band excitations. For the different excitation correlations, the responses are represented using non-dimensional variables in order for the results to be comparable to each other. It is shown that the ratio of the modal frequency between the tuned and large mistuned blades determines the propagation direction of the natural frequencies of the mistuned system, therefore, the responses of large mistuned blades depend primarily on their level of modal frequency.

Blade Arrangement Optimization for Mistuned Bladed Disk Based on Gaussian Process Regression and Genetic Algorithm

AbstractMistuning phenomena exist in the bladed disk due to the inevitable deviations among blades' properties, e.g., stiffness, mass, geometry, etc., leading to localization and response amplification. The dynamic performance of mistuned bladed disk is sensitive to the arrangement of blades. The blade arrangement optimization aims to obtain the optimal arrangement that minimizes the influence of mistuning. In this paper, a framework of high efficiency is raised to deal with the challenge of high computational cost this optimization. It comprehensively utilizes mixed-dimensional finite element model (MDFEM), Gaussian process (GP) regression, and genetic algorithm (GA). The MDFEM can perform mistuned modal analysis efficiently and provides the training set of GP regression rapidly. The GP model, as a surrogate model, predicts the desired dynamic performance directly without calculating the numerical model and can function as fitness function in optimization. GA has the capability to deal with combinatorial problems and is a good option for problems with large search domains and several local maxima/minima. The techniques and processes of three methods are illustrated in detail. Case studies, based on a real turbine, are concretely presented in a gradually progressive manner to test and verify the effectiveness, accuracy, and efficiency of methods and entire framework step by step. The results show the satisfactory optimal arrangement for a randomly chosen set of mistuned blades, and the influence of mistuning is reduced indeed. The time cost of the optimization has been reduced several orders of magnitude. This framework can be a promising approach for the blade arrangement optimization problem.

Accelerated Multifidelity Emulator Modeling for Probabilistic Rotor Response Study

Abstract This paper presents an efficient methodology to build a modal solution emulator for the probabilistic study of geometrically mistuned bladed rotors by using the newly developed localized-Galerkin multifidelity (LGMF) modeling and eigensolution reanalysis (ER) with the symmetric successive matrix inversion (SSMI) methods. The key idea of the mistuned blade emulator is to establish a reduced functional relationship between the stochastic geometric variations and the disturbed modal responses. The prediction accuracy of an emulator generally depends on how many training samples of modal solutions are available and how well the potential modal switching due to stochastic mistuning is captured. To reduce the computational costs of generating training samples without sacrificing accuracy, this paper introduces the collaborative framework of the new approaches of multifidelity (MF) modeling and ER. The proposed framework is demonstrated for its computational benefits with several numerical examples including the point-cloud scanned mistuned blade problem.

Calculation-and-Experimental Investigation on Natural Frequencies and Oscillation Modes of Pairwise-Shrouded Cooled Turbine Blades

The paper presents the results of simulations and experimental investigations on natural frequencies and oscillation modes of pairwise-shrouded cooled turbine blades and their rings with allowance for a possible frequency mistuning and the assured contact of mating surfaces of the root and shroud platform halves. As the research object, the high-pressure turbine wheel of an aircraft bypass turbojet engine has been selected. 3D finite element models of the turbine wheel blades/ period were developed as a system with structural rotational symmetry. The contact interaction between blades over the mating surfaces was modeled on basis of solving the stationary problem. The calculation-and-experimental investigations were performed for two operating conditions of the engine – the non-running engine and the steady-state maximum take-off condition. Results have been cited for individual, isolated blades. The results show a good agreement between calculated and experimental data. The frequency mistuning of those blades is found to be considerably dependent on oscillation mode number, but the mistuning value is practically not affected by the operating condition of the engine. It is confirmed that two oscillation modes are excited in the blade pair as a regular system in the presence of the mistuning of their frequencies, which are close to the inphase and antiphase frequencies. The ratio of natural frequencies of those oscillation modes is dependent on oscillation mode of isolated blades. It is shown that the frequency mistuning of paired blades due to excitation of two oscillation (inphase and antiphase) modes causes doubling of the number of resonant states of the turbine wheel what must be considered when developing methods to ensure their vibrational reliability.

Generalized SAFE Diagram for Mistuned Bladed Disks

Abstract The Singh's advanced frequency evaluation (SAFE) diagram is a design tool commonly used to find and thus prevent bladed disk resonances, allowing those modal combinations with no match in terms of angular harmonic shape to be neglected. In principle, the SAFE diagram is based on the assumption that the disk structure is perfectly cyclic; hence, any degree of mistuning would prevent its validity. However, each natural mode of a mistuned bladed disk can be expressed as a superimposition of angular harmonic components. The numbers of nodal diameters of these harmonics are extracted as the discrete Fourier transform of the eigenvector. In this paper, a new graphical representation is proposed to account for this complete harmonic content, instead of just a single (main or nominal) number of nodal diameters as in the conventional SAFE diagram. In addition, the relative intensities of the modal components are shown in this generalized SAFE diagram, for an indication of the induced vibrational magnitude of each possible resonance. Numerical and experimental cases are presented, obtaining significant examples of the proposed diagram. Analyzing the signals of an aeromechanical test, unexpected resonances were observed, which were not predicted by the conventional SAFE, but were detected with the proposed diagram.

Forced response characteristics of random mistuned blade disk based on weibull distribution and monte carlo simulation

This paper presents a method of mistuning identification of a random mistuned bladed parameter, to predict the forced vibration characteristics of random mistuned blade disk of aeroengine compressor, based on the prestress mode synthesis method, substructure finite element reduction model was adopted, the identification method combines Weibull distribution with Monte Carlo simulation to identify the random mistuned blade parameters. The vibration characteristics of mistuned bladed disks under different engine orders of excitation were calculated, and the vibration characteristics of mistuned bladed disk systems under different mistuning standard deviations were discussed. Vibration localization characteristics of mistuned bladed disk system were analysed by using localization factor. The correctness of the identification method was verified by calculating the vibration amplitude of mistuned bladed disk system under different mistuning standard deviations.

Mistuning sensitivity and optimization for bladed disks using high-fidelity models

Abstract An effective method is developed for efficient calculations of the sensitivity of the maximum forced response levels for mistuned bladed disks with respect to blade frequency mistuning. The expressions for 1st and 2nd order sensitivity coefficients are derived in an analytical form which provides high accuracy and computational efficiency. Then, the optimization methods are used for searching the best and worst mistuning patterns of bladed disks. Two major types of the mistuning optimization problems are considered: (i) a continuous optimization problem when the blade mistuning can take any values from a prescribed range and (ii) a combinatorial optimization problem, when the set of mistuned blades is given and the optimization can be achieved by blade re-arrangement in a disk. For the first type of the optimization problem a set of sensitivity-based optimization algorithms is applied and for the second type a variant of a genetic algorithm is developed. The analysis of mistuning sensitivity coefficients and results of optimization searching are shown on an example of a realistic turbine bladed disk.

Model update and validation of a mistuned high-pressure compressor blisk

ABSTRACTIn order to prepare an advanced 4-stage high-pressure compressor rig test campaign, details regarding both accomplishment and analysis of preliminary experiments are provided in this paper. The superior objective of the research project is to contribute to a reliable but simultaneously less conservative design of future high pressure blade integrated disks (blisk). It is planned to achieve trend-setting advances based on a close combination of both numerical and experimental analyses. The analyses are focused on the second rotor of this research compressor, which is the only one being manufactured as blisk. The comprehensive test program is addressing both surge and forced response analyses e.g. caused by low engine order excitation. Among others the interaction of aeroelastics and blade mistuning is demanding attention in this regard. That is why structural models are needed, allowing for an accurate forced response prediction close to reality. Furthermore, these models are required to support the assessment of blade tip timing (BTT) data gathered in the rig tests and strain gauge (s/g) data as well. To gain the maximum information regarding the correlation between BTT data, s/g-data and pressure gauge data, every blade of the second stage rotor (28 blades) is applied with s/g. However, it is well known that s/g on blades can contribute additional mistuning that had to be considered upon updating structural models.Due to the relevance of mistuning, efforts are made for its accurate experimental determination. Blade-by-blade impact tests according to a patented approach are used for this purpose. From the research point of view, it is most interesting to determine both the effect s/g-instrumentation and assembling the compressor stages on blade frequency mistuning. That is why experimental mistuning tests carried out immediately after manufacturing the blisk are repeated twice, namely, after s/g instrumentation and after assembling. To complete the pre-test program, the pure mechanical damping and modal damping ratios dependent on the ambient pressure are experimentally determined inside a pressure vessel. Subsequently the mistuning data gained before is used for updating subset of nominal system mode (SNM) models. Aerodynamic influence coefficients (AICs) are implemented to take aeroelastic interaction into account for forced response analyses. Within a comparison of different models, it is shown for the fundamental flap mode (1F) that the s/g instrumentation significantly affects the forced response, whereas the impact of assembling the compressor plays a minor role.