Bladed Disk Research Articles

Investigation on the vibration localization of mistuned bladed disk with frictional contact

The mistuning phenomenon is commonly seen in the bladed assemblies of turbomachinery, leading to an unreasonably localized energy distribution that may increase the risk of high cycle fatigue and potentially cause blade failure. The friction coupling interaction is often introduced to attenuate the effect of excessive amplification on the structural vibration. To investigate the vibration localization of damped and mistuned bladed-disk system, a typical mistuning characterization is applied to an improved four-degree-of-freedom lumped parameter model to explicit the vibratory properties with coupled frictional contact. The statistical findings of natural frequency and modal localization factor are obtained by employing the Monte Carlo simulation to explore the influence of mistuned variance and coupled stiffness on the modal localization of free and damped bladed-disk system, respectively. The forced response sensitivity featured in the mistuned variance is quantitatively analyzed from the perspective of vibration localization and energy distribution by the nonlinear solution method. The influence of excitation order and normal load are further, respectively, discussed on the response localization level of the mistuned system. The results can provide fundamental knowledge of the impact of the mistuning pattern on vibration localization for the early design of the aeroengine.

Selective transmit modeling framework of complex system reliability analysis considering failure correlation

To improve the efficiency and accuracy of complex system reliability analysis considering failure correlation, a selective transmit modeling framework (STMF) is proposed by integrating multi-stage selective modeling (MSM) strategy with multi-failure transmit modeling (MTM) architecture. In MSM, the modeling quality of multi-learner is discussed to establish the optimal functional relationship between multi-variable and multi-response by considering the suitability of modeling samples, and the fitting performance of copula functions is quantified to construct the optimal correlation model between multi-failure through distance measure. For MTM, the correlation sequence measurement structure of multiple modes is established to construct the joint reliability analysis model of complex structure by updating iteratively the margin distribution functions with the strongest correlation. Taking the turbine bladed disk as study object, the validation of the proposed STMF is verified by comparing with other methods. The analytical results of study case can be expressed as that (i) STMF holds the superior performance in modeling accuracy and time-consuming, at 2.6308 × 10-2 and 0.4638 s respectively; (ii) STMF also has the best property in simulation, separately at 2.2123 s in simulation efficiency and at 99.9899 % in simulation precision; (iii) the reliability 0.9876 of study case obtained by STMF is higher than the reliability 0.9855 that depends on the mutual independence assumption. The effort of this work is prominent to promote effectively the quantification of multi-failure correlation and the improvement of reliability analysis performance for complex systems.

Aero Bladed Disk Assembly Evaluation Using Surface Matching With Contact Constraints

Aero Bladed Disk Assembly Evaluation Using Surface Matching With Contact Constraints

Technological scheme of wood resources utilization model development

In the present work the justification of the urgency of solving the issue of environmental friendliness of materials produced from wood resources is given. The analysis of the production technology of semifinished wood-fiber products is carried out at the current stage of development of the board industry. The estimation of board formation properties of the wood fiber mass produced in disk blade grinding machines is given, and the inefficiency of the used equipment is substantiated. The expediency of using the equipment with cavitation effect as the second grinding stage in the production of wood pulp was substantiated. As a result, the purpose of the present work was the development of the technology for the production of the semifinished wood fiber product with the use of a rotor-pulsation apparatus as the second stage of the wood pulp mill. To achieve the goal, an analysis of modern technologies used in the production of fiberboard was carried out. The model of technological scheme of production of wood fiberboards by wet method in the environment of AnyLogic program package was developed. Based on the technological scheme developed, a dynamic model of the fiberboard production process was built using a rotor-pulsation apparatus in the second stage of wood pulp milling. In the course of research, statistical analysis methods and simulation modelling of technological processes were applied. The results obtained can find application in the production of fiberboard, as well as in the improvement of technological processes at the enterprises of the forest complex.

Convergence-free mapping of non-linear damper-blade performance

In the bladed disks of turbomachinery, the problem arises of finding a damping device that reduces as much as possible the amplitude of the alternating stresses produced by the forced vibrations excited by the gas flow. Dry friction solid underplatform dampers are an established solution.The shape and size of the damper, in association with those of the platform, neck and airfoil, determine the non-linear response curves having as parameter the intensity of external excitation, here synthetically represented by a “proof” excitation force. Of greatest importance are the combinations (frequency, excitation force) that realise the maximum amplitude of forced oscillation (measured, for example, at the blade tip) and the maximum value of the amplitude of the variable stress produced by the vibrations at a critical point of the blade. Since the design of the damper-blade coupling is High-Cycle Fatigue driven, this stress amplitude is taken as a reference and related to the value of the excitation force. This can finally take the well-known form of the damper performance curve.Especially in the case of parametric explorations concerning shape, size and contact parameters, the current approach to this non-linear response problem, based on iterative convergence, is numerically prohibitive unless one uses special search techniques, such as the surrogate models of various types that are favoured today.An alternative computational process is presented here, that of integrating PCR (Platform Centred Reduction) with a new approach called Amplitude Layered (excitation) Force Mapping. This process reduces the amount of computation by up to three orders of magnitude compared to standard techniques and is a winning alternative to surrogate models.

Synchronous Vibration Parameter Recognition of Constant-Speed Blades Based on Blade Tip Clearance Measurement

A new method for the synchronous vibration parameter identification of constant-speed rotating blades based on blade tip clearance (BTC) measurement and blade tip timing (BTT) is introduced. A BTC sensor is used to measure the BTC when the blade tip passes through each sensor. The BTT method is used to determine whether the blade tip arrives in advance or lags. The geometric model between the BTC and the blade tip vibration displacement (BTVD) is established, and the BTVD of the blade tip passing through each sensor is obtained. Then, the nonlinear least squares method is used to determine the synchronous vibration parameters of the constant-speed rotating blade. The results show that with an increase in amplitude, the higher the accuracy of the vibration parameter identification proposed in this paper; with a decrease in the random error of the BTC measurement, the higher the accuracy of the vibration parameter identification proposed in this paper; with a decrease in the random error in the measurement of the blade disk dimensions, the higher the accuracy of the vibration parameter identification proposed in this paper. In addition, the smaller the ratio of the blade length to the blade disk radius, the higher the accuracy of the vibration parameter identification method introduced in this paper. Because the structure of the gas turbine compressor and turbine blade disk has a small blade disk ratio, the method proposed in this paper is suitable for the simultaneous vibration parameter identification of gas turbine compressor blades and turbine blades.

A novel non-intrusive ROM for randomly excited linear dynamical systems with high stochastic dimension using ANN

Analyzing large stochastic dynamical systems is computationally very expensive. A statistical simulation framework requires invoking the solver multiple times — ranging from thousands to millions. A non-intrusive reduced order model (ROM) serves as a computationally efficient alternative in this framework. Uncertainties in dynamical systems originate from two sources: system parameters and excitation. However, all the existing ROMs have been developed for uncertainty only in the system parameters. To the best of the authors’ knowledge, no ROM exists for dynamical systems under random excitation. A discretization of the input process increases the stochastic dimensionality, typically by a few hundred or thousand. This leads to a high dimensional interpolation or regression in the ROM, which is practically infeasible. This issue is addressed in this work by proposing a novel non-intrusive ROM that bypasses the need for such discretization. Accordingly, a regression is carried out directly on the random excitation using a neural network-based surrogate model. A principal component-based data compression is used in tandem to reduce the stochastic dimensionality of excitations. Detailed numerical studies are conducted to study the accuracy and efficiency of the proposed ROM using two examples: a mistuned bladed disk problem and a soil–structure interaction. The numerical results show that the proposed ROM is accurate and gains a significant speed-up of more than sixty for both examples. Using the proposed ROM, the cost of uncertainty quantification can be reduced significantly within the framework of Monte Carlo simulation.

Comparison of Subspace Identification Methods for Modal Estimation of Bladed Disks

Abstract Bladed disks are critical parts of aeronautic turbojet engines requiring numerous dynamic analysis tests to fully achieve their design process. This work presents subspace state-space identification techniques for estimation of modal parameters of bladed disks using realistic although numerically generated test case data. Indeed, modal testing of bladed disks can exhibit high modal density leading to modal estimation issues. This study focuses on subspace state-space identification framework as it is an efficient way to process vector valued time series and thus to estimate modal parameters in a context of high modal density. In order to evaluate the techniques of interest, a versatile modal model has been specifically implemented to simulate data representative of full scale rotating aeronautic fan modal tests. This model is easily adjustable allowing to evaluate the identification methods in a more or less severe estimation context. The performance of the investigated methods is discussed and compared with the prescribed parameters of the model. Moreover, different techniques to estimate the order of the associated state-space model are reviewed and tested over several simulated configurations. Finally, a method to evaluate the uncertainties over the model parameters using covariance of estimator results and pseudospectrum computation is proposed and discussed over the investigated test cases.

Research Progress on the Creep Resistance of High-Temperature Titanium Alloys: A Review

High-temperature titanium alloys are one of the most important research directions in the field of high-temperature aerospace alloys. They are mainly used in high-temperature-resistant components, such as blade disks, blades, and casings of aero-engines, and are key materials in a new generation of high thrust-to-weight ratio aero-engines. In the service environment of engineering applications, the creep resistance of high-temperature titanium alloys is one of the most important characteristic indicators. This paper reviews and analyzes the research status and progress on the creep properties of typical high-temperature titanium alloys in service in recent years. The effects of the creep parameters, alloy composition, and microstructure on the creep behavior of high-temperature titanium alloys are discussed, and various possible mechanisms for increasing the creep resistance of high-temperature titanium alloys are summarized.

Sensitivity Analysis of Transient Forced Response of Mistuned Bladed Disks Under Complex Excitation and Varying Rotation Speed

Abstract During accelerations and decelerations of gas-turbine engines, the transient vibration effects in bladed disk vibration become significant and the transient response needs to be efficiently and accurately assessed. This paper develops an effective method for efficient calculations of the sensitivity of the transient vibration response for a mistuned-bladed disk under varying rotation speeds. The sensitivities are calculated concerning two major factors: (i) the blade mistuning and (ii) the rotor acceleration/deceleration rates. The method uses the large-scale finite element modeling of the bladed disk to accurately describe the dynamic properties of the mistuned bladed disk. The method can be applied for a case when the loading is the transient load, with the amplitude and frequency spectrum changing with rotation speed. The dependency of the modal characteristics on the rotation speed is included in the formulation of the sensitivity analysis method. Efficient reduced order models are used to reduce the computational cost, which can adapt to the effects of the varying rotation speed on the natural frequencies and mode shapes of the mistuned bladed disk under transient conditions. The expressions for the sensitivities are derived analytically which provides high accuracy and speed of the calculations. The method has been implemented in a computer code and thoroughly verified using a set of test cases. The studies of transient forced response sensitivity have been performed for realistic bladed disk models.

Approximate symplectic approach for mistuned bladed disk dynamic problem

A blade disk system plays a crucial role in the energy conversion efficiency of turbomachinery. Generally, a bladed disk is designed as a tuned system, which implies that the dynamic behaviors of all the blades are identical. In practice, there are some differences between the blades, known as mistuning, that can result in localized vibration. Thus, in this study, an approximate symplectic method developed to reproduce the vibration localization in a mistuned bladed disk system, that can provide guidance for designing vibration control strategies for the system. Considering the morphological characteristics of the interface roughness and the dynamic/stickiness characteristics of the sliding joint surface, an improved dry friction model is established to describe the coupling effects between the blades. Considering the micro-dynamic behaviors of the multi-joint surfaces, the dynamic problem of the entire bladed disk system is formulated as a set of ordinary differential equations (ODEs). An approximate symplectic method is developed in the Hamiltonian framework to simulate the vibration of each blade in the mistuned bladed disk system. From the numerical results reported, the phenomenon of vibration localization in the mistuned bladed disk system is reproduced in the comparison with the results in the tuned bladed disk system. In addition, the influences of the initial positive pressure, contact angle, and roughness of the surfaces on the strength of the vibration localization are revealed in detail in the numerical simulations.

Damping and Stiffness Mistuning Effects in a Bladed Disk With Varied Disk Coupling

Abstract Component mode mistuning (CMM) is a well-known, well documented reduced order modeling technique that effectively models small variations in blade-to-blade stiffness for bladed disks. In practice, bladed disks always have variations, referred to as mistuning, and are a focus of a large amount of research. One element that is commonly ignored from small mistuning implementations is the variation within the blade-to-blade damping values. This work seeks to better understand the effects of damping mistuning by utilizing both structural and proportional damping formulations. This work builds from previous work that implemented structural damping mistuning reduced order models formulated based on CMM. A similar derivation was used to create reduced order models with a proportional damping formulation. The damping and stiffness mistuning values investigated in this study were derived using measured blade natural frequencies and damping ratios from high-speed rotating experiments on freestanding blades. The two separate damping formulations that are presented give very similar results, enabling the user to select their preferred method for a given application. A key parameter investigated in this work is the significance of blade-to-blade coupling. The blade-to-blade coupling study investigates how the level of coupling impacts damping mistuning effects versus applying average damping to the bladed disk model. Also, the interaction of stiffness and damping mistuning is studied. Monte Carlo simulations were carried out to determine amplification factors, or the ratio of mistuned blade responses to tuned blade responses, for various mistuning levels and patterns.

Dynamic characteristics of vibration localization of mistuned bladed disk due to shroud and blade damages

Dynamic behaviors of turbine blades are important for the dynamic design of whole-bladed disk systems. The bladed disk systems with shrouds are used to achieve advanced functions in operation. The shrouds are used to connect several blades as a bladed packet, and several bladed packets are assembled as a bladed disk. Previous researches mainly focus on the mistuning of the bladed disk. However, in operation, the shrouds often suffer damage and wear, and it will lead to shrouds mistuning. The shroud is a critical component for adjusting the coupling strength of the blade to the blade. The innovation of this paper is to study the coupling dynamics problem caused by blade mistuning and shroud damage. The localized vibration of the bladed disk is caused by the blade mistuning, and the shroud damage can also cause the localized vibration of the bladed disk. The coupling dynamic behaviors of bladed disk caused by blade mistuning and shroud damage are important. Therefore, the dynamic behaviors of a mistuned bladed disk with the shroud are important for the bladed disk. A numerical method is conducted to investigate the dynamic characteristics of the whole bladed disk with shroud. The coupling effect between shroud and blade mistuning on the dynamic behaviors of the bladed disk is researched. The numerical model is validated by assuming the shroud and blade mistuning is zero. The coupling effect of shroud and blade mistuning leads to the characteristics being more complicated. Bladed packet is the basic part of the bladed disk with shroud. In order to study the modal characteristics of bladed packets due to shroud, an experiment is conducted. It is worth noting that the first sub remains invariable with the increasing of stiffness ratio.

Effects of the Seal Wire on the Nonlinear Dynamics of the Aircraft Engine Turbine Blades

Abstract Complicated systems made of multiple components are known to be difficult to model, considering their solutions can change dramatically even with the slightest variations in conditions. Aircraft engines contain such complicated systems, and some components in aircraft engines' turbines can cause significant changes in the system's overall response. Hence, this study is focused on investigating the behavior of a turbine blade of an aircraft engine and the effects of the contact between the blade and the seal wire on the dynamics of the blade-disk system. The investigation is performed via various numerical simulations in time and frequency domains. One sector of the bladed disk is modeled using the finite element method with the lock plate and the seal wire imposing cyclic symmetry boundary conditions in the static, modal, and frequency domain forced response analyses. In time domain analyses, the cyclic symmetry is replaced with simplified displacement restricting boundary conditions. The time domain analysis contains steady-state forced responses of the system. The results show that contact with the seal wire is not a major source of nonlinearity and damping. The contacts with the lock plate contribute more to the vibration damping than the seal wire. However, compared to the contacts at the root of the blade, both components remain less significant with regard to frictional damping and nonlinearity.

FSI Application in the Parametric Analysis of Blade–Disk Connection of Turbojet Engine Compressor

The following paper evaluates the strength properties of the critical area of the turbine rotor stage of a jet engine. This is where the blade is attached to the rotor disk. Important aspects of this issue are characteristic geometrical dimensions and operating factors, e.g., changes in rotor speed. In the article, the strength properties of the rotor stage with a trapezoidal blade–disk connection were analyzed using parametric analysis considering fluid–structure interaction (FSI). Virtual models of the compressor rotor stages were developed, including parametric blade–disk connections and discrete models for FEM (finite element method) and CFD (computational fluid dynamics) analyses. The parametric analysis was aimed at assessing selected geometric parameters in terms of their impact on the maximum stresses in the blade root. The analysis performed shows that by changing the blade’s width and thickness angles at the root, we can influence the value of the maximum stresses in the rotor stage. It was noticed that some combinations of these two parameters may negatively affect the value of the stresses in the rim.

Numerical Investigation of Friction Induced Interaction of Flutter Modes in a Realistic Low Pressure Turbine Rotor

Abstract Flutter response of bladed disks is a quite an important problem in modern designs of low pressure turbines, but, even for tuned configurations, it is not fully understood yet. Some research work suggests that, in a tuned rotor, the flutter induced vibration state that sets in consists of just a single traveling wave mode, while others show flutter states composed of several traveling waves active at the same time. Many of these studies were performed using conceptual models, such as mass-spring systems or asymptotically reduced models. In this work, a high fidelity bladed disk model is integrated into the time domain for the case of a realistic aerodynamically unstable low pressure turbine. In this configuration, the only nonlinear effect is the friction present at the blade disk attachment, which is responsible for the saturation of the flutter growth, and it is also the only mechanism that allows the interaction among the different unstable traveling wave modes. A case with multiple unstable modes of the same modal family is studied first. After that, the study is extended to a case where modes of different modal families are unstable and have similar aerodynamic instability levels. The interaction of unstable modes from different modal families is studied, we believe, for the first time, as previous flutter analyses were restricted to the interaction of unstable modes from the same family.

Fatigue life prediction of mistuned steam turbine blades subjected to deviations in blade geometry

The blades of the steam turbine are subjected to bending of the steam flow, centrifugal loading, vibration response, and structural mistuning. These factors mentioned contribute significantly to the fatigue failure of steam turbine blades. Low pressure (LP) steam turbines experience premature blade and disk failures due to the stress concentrations in the root location of the blade of its bladed disk. This study of mistuned steam turbine blades subjected to variation in blade geometry will be of great significance to the electricity generation industry. A simplified, mistuned, scaled-down steam turbine bladed disk model was developed using ABAQUS finite element analysis (FEA) software. The acquisition of the vibration characteristics and steady-state stress response of the disk models was carried out through FEA. Such studies are very limited. Subsequently, numerical stress distributions were acquired and the model was subsequently exported to Fe-Safe software for fatigue life calculations based on centrifugal and harmonic sinusoidal pressure loading. Vibration characteristics and response of the variation of the geometric blade of the steam turbine were investigated. Natural FEA frequencies compared well with the published literature of real steam turbines, indicating the reliability of the developed FEA model. The study found that fatigue life is most sensitive to changes in blade length, followed by width and then thickness, in this order. Analytical life cycles and Fe-Safe software show a percentage difference of less than 4.86%. This concludes that the numerical methodology developed can be used for real-life mistuned steam turbine blades subjected to variations in blade geometry.

Transient Resonance Passage of a Mistuned Bladed Disk with and without Underplatform Dampers

In this work, the vibration response of an academic free-standing turbine blisk is analyzed in regard to transient resonance passages. Measurement data are recorded using strain gauges and tip timing to evaluate the blades first bending mode both linearly and with two different types of underplatform dampers. These results are validated against steady-state responses and show good agreement with each other. To examine the effects of a transient resonance passage, response functions of each blade are evaluated both with and without the underplatform dampers. It is shown that friction damping is able to inhibit any appearance of a transient ring-down. Additionally, a multi-mass oscillator model with frictional contacts is analyzed, which qualitatively exhibits the same dynamics as the measurements. Due to geometric mistuning, all blades exhibit different vibration responses. This can lead to a transient amplitude amplification, which is observed on several blades. Analogously, this phenomenon can be mitigated by friction damping.

Modal characteristics of a flexible dual-rotor coupling system with blade crack

Rotating blade is highly susceptible to cracking in harsh conditions, which seriously affects the dynamic characteristics of the power equipment. Existing research focuses primarily on the blade crack in a single blade or bladed disk, ignoring the flexibility and coupling factors of the shaft. This paper aims to present a theoretical framework for modeling a whole flexible dual-rotor system and investigate the effects of blade crack on the modal characteristics of the coupling system. The finite element and assumed modes (FE-AM) hybrid method is adopted to model the dual-rotor system. The crack-caused stiffness loss is determined based on the released strain energy. The accuracy of the developed model is verified by comparing it with the finite model and experimental results. After that, the influences of the rotating speed and crack parameters on the coupling system are systematically investigated. The results indicate that frequency veering and mode shift occur with increasing rotating speed due to the rotational effects affecting each flexible component differently. Blade bending and shaft torsion are coupled, and each affects the mode predominated by the other. The blade crack causes mode localization and mistuned distribution phenomenon in the disk. The shaft’s bending and torsion modes are coupled into the coupling modes associated with blade bending due to the blade crack as well. It is also demonstrated that the crack-caused disk’s localized mode is gradually transformed from the 2-nodal diameter mode. Furthermore, the natural frequencies associated with the disk’s low-nodal diameter and the mode shapes associated with the high-nodal diameter are sensitive to the blade crack. The proposed model can provide a theoretical foundation for fault diagnosis of blade crack in the rotating machine.

Prediction of fatigue life of mistuned steam turbine blades subjected to variations in blade geometry

There is a large number of power stations suffering from fatigue failures of the steam turbine blades. The steam turbine blades are also subjected to steam flow bending, centrifugal loading, vibration response, and structural mistuning. These mentioned factors significantly contribute to the fatigue failure of the steam turbine blades. Low-Pressure (LP) steam turbines experience premature blade and disk failures due to the stress concentrations at the blade root area of its bladed disk. Driven by the problems encountered by the steam power plant electricity generating utilities with regards to steam turbine blades fatigue failure, this study of the mistuned steam turbine blades subjected to variation in blade geometry will be of great significance to the electricity generation industry. A simplified, scaled-down mistuned steam turbine bladed disk model was developed using ABAQUS finite element analysis (FEA) software. Acquisition of the vibration characteristics and steady-state stress response of the disk models was performed through FEA. Thereafter, numerical stress distributions were acquired, and the model was subsequently exported to Fe-Safe software for fatigue life calculations based on centrifugal and harmonic sinusoidal pressure loading. The vibration characteristics and the response of the variation steam turbine geometric blade was conducted. The FEA natural frequencies compared well with published literature of the real steam turbines indicating reliability of the developed FEA model. The study found that the fatigue life is most sensitive to changes in blade length, followed by the width, and then the thickness, in this order. The analytical life cycles and Fe-Safe software shows the percentage difference of less than 4.86%. This concludes that the developed numerical methodology can be used for real-life mistuned steam turbine blades subjected to variations in blade geometry.