Mistuned Bladed Research Articles

Resonant Response of Mistuned Bladed Disks Including Aerodynamic Damping Effects

Resonant Response of Mistuned Bladed Disks Including Aerodynamic Damping Effects

Numerical Investigations of Localized Vibrations of Mistuned Blade Integrated Disks (Blisks)

Blade-to-blade variations of bladed disk assemblies result in local zoning of vibration modes as well as amplitude magnifications, which primarily reduces the high cycle fatigue life of aeroengines. Criteria were introduced to determine the level of these mode localization effects depending on various parameters of a real high pressure compressor blisk rotor. The investigations show that blade vibration modes with lower interblade coupling, e.g., torsion modes or modes with high numbers of nodal diameter lines, have a significantly higher sensitivity to blade mistuning, which can be characterized by the higher percentage of blades on the total blisk strain energy.

Robustness Analysis of Mistuned Bladed Disk Using the Upper Bound of Structured Singular Value

Abstract This paper presents a method for the robustness analysis of the bladed disk with bounded random mistuning. The robust stability and performance are evaluated by the upper bound of the structured singular value. The robust control model of the bladed disk is established in virtue of linear fractional transformation. The influences of intentional stiffness mistuning in harmonic patterns on the robustness of the mistuned bladed disk are investigated. The numerical results indicate that the robust performance of the mistuned bladed disk could be effectively enhanced by appropriate harmonic intentional mistuning. The proposed method can help us design a bladed disk, which is insensitive to dangerous random mistuning.

Reduced-Order Model Construction Procedure for Robust Mistuning Identification of Blisks

The reduced-order modeling of integrally bladed disks (blisks) for predicting the mistuned vibration response has been well studied and understood. For solving a direct vibration problem, adding modes to the modeling basis improves the accuracy of the reducedorder model (ROM) with respect to the parent nite element model. In contrast, when solving an inverse problem for system identication, adding modes to the ROM while using the same measurements may actually reduce its accuracy. This is especially true for solving inverse problems related to identication of blade mistuning parameters, because the characteristics of the selected system modes for the ROM may not match well the assumptions used in the mistuning modeling approach. In this work, a procedure is introduced for constructing a ROM referred to as the inverse ROM (IROM) that is well suited for solving the mistuning identication inverse problem. First, a quantitative metric is dened to characterize and rank the tuned system modes with respect to their suitability for constructing IROMs. Then, the direct problem is solved using a larger direct ROM (or DROM) with prescribed mistuning in order to interrogate and validate the performance of various IROMs as modes are added. This enables the automated construction of suitable IROMs and improves the overall accuracy and robustness of mistuning identication.

Aeroelastic Analysis of Rotors With Flexible Disks and Alternate Blade Mistuning

A new reduced-order aeroelastic model using the principal shapes (AMPSs) of modes is presented. Rotors with flexible disks and alternate blade mistuning can challenge the fidelity of flutter prediction techniques that assume uniform blade-to-blade geometry and mode shape invariance with nodal diameter pattern. The AMPS method, however, accounts for alternating blade geometry as well as varying blade mode shapes, providing accurate flutter predictions for a large number of modes from a small number of computational fluid dynamics simulations. AMPS calculations on rotors with alternate blade mistuning are presented and compared to other prediction techniques. The results provide insight into how alternate blade mistuning affects aerodynamic coupling and the flutter characteristics of a rotor.

Vibration mechanism of a mistuned bladed-disk

For coupling vibration of the mistuned bladed-disk in aeroengine, the vibration differential equation of the system is established using component-mode synthesis methods. Experimental mode analysis and mode correction are used to calculate some low-order modes of tuned blade and the disk with cone-flange. The models of actual mistuned bladed-disk is constructed by exerting some small perturbation on the mode stiffness of blades. The forced vibration experimentation of an actual mistuned bladed-disk in non-rotating status is carried out to verify the vibration model and calculation formulae. The results show that excessive vibration response of a single blade is caused by blade mistuning, and the random mistuning distribution of a small frequency difference is more profitable than other arrangements for depressing the maximal vibration level of the hapless blade. In this study, the better natural frequency difference amplitude of blades and the right working frequency range of aeroengine are also suggested according to the result analysis of several numerical calculations.

Minimizing Maximum Modal Force in Mistuned Bladed Disk Forced Response

Amplitude magnification is defined as the maximum forced response amplitude of any blade on a mistuned bladed disk divided by the maximum response amplitude of any blade on a tuned bladed disk over a range of engine order excitation frequencies. This paper shows that amplitude magnification can be approximated as the maximum ratio of modal force divided by modal vector magnitude in an isolated family of turbine engine bladed disk modes. An infinite linear mistuning pattern, defined by a constant interblade stiffness increment between an infinite number of blades, is found to minimize the maximum modal force when subjected to engine order N/4 excitation. Linear mistuning, an approximation of the infinite linear mistuning pattern, approximately minimizes the maximum modal force for bladed disks with a finite number of blades when subjected to engine order N/4 excitation. From this theory, 2/N is proposed to be a lower boundary for amplitude magnification. The linear mistuning method is demonstrated to produce very low amplitude magnifications numerically and experimentally. The numerical examples suggest that linear mistuning may produce amplitude magnifications near the absolute minimum possible.

Analysis of Random Vibration for Mistuned Bladed Disk

When calculating the vibratory response of bladed turbine disks, it is assumed that all blades on a given disk are identical. This leads to the prediction that all blades experience the same amplitude. However, it has been shown experimentally that significant variations in these amplitudes occur for different blades on the same disk. These variations arise due to the effects of mistuning, which refers to small differences in blade characteristics. Although the mistuning effect on the resonant response has been studied systematically, few papers have researched the mistuning effect on the random vibration. This paper, first, presents the analysis method of the mistuning effect on the random vibration. Second, the mistuning analyses for the random vibration and the resonant vibration of the bladed turbine disk are carried out, and the both results are compared. From these results, the mistuning effect on the random vibration is clarified.

Stability Increase of Aerodynamically Unstable Rotors Using Intentional Mistuning

A new simple asymptotic mistuning model, which constitutes an extension of the well known fundamental mistuning model for groups of modes belonging to a modal family exhibiting a large variation of the tuned vibration characteristics, is used to analyze the effect of mistuning on the stability properties of aerodynamically unstable rotors. The model assumes that both the aerodynamics and the structural dynamics of the assembly are linear, and retains the first-order terms of a fully consistent asymptotic expansion of the tuned system where the small parameter is the blade mistuning. The simplicity of the model allows the optimization of the blade mistuning pattern to achieve maximum rotor stability. The results of the application of this technique to realistic welded-in-pair and interlock low-pressure-turbine rotors are also presented.

Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration

New techniques are presented for generating reduced-order models of the vibration of mistuned bladed disks from parent finite element models. A novel component-based modeling framework is developed by partitioning the system into a tuned bladed disk component and virtual blade mistuning components. The mistuning components are defined by the differences between the mistuned and tuned blade mass and stiffness matrices. The mistuned-system model is assembled with a component mode synthesis technique, using a basis of tuned-system normal modes and attachment modes. The formulation developed is general and can be applied to any mistuned bladed disk, including those with large geometric mistuning (e.g., severe blade damage). In the case of small (i.e., blade frequency) mistuning, a compact reduced-order model is derived by neglecting the attachment modes. For this component mode mistuning model, the blade mistuning is projected first onto the component modes of a tuned, cantilevered blade, and then projected again onto the tuned-system normal modes via modal participation factors. In this manner, several natural frequencies of each mistuned blade can be used to capture systematically the effects of the complex physical sources of mistuning. A numerical validation of the developed methods is performed for both large and small mistuning cases using a finite element model of an industrial rotor.

Piezoelectric Networks for Vibration Suppression of Mistuned Bladed Disks

Extensive investigations have been conducted to study the vibration localization phenomenon and the excessive forced response that can be caused by mistuning in bladed disks. Most previous researches have focused on analyzing∕predicting localization or attacking the mistuning issue via mechanical tailoring. Few have focused on developing effective vibration control methods for such systems. This study extends the piezoelectric network concept, which has been utilized for mode delocalization in periodic structures, to the control of mistuned bladed disks under engine order excitation. A piezoelectric network is synthesized and optimized to effectively suppress vibration in bladed disks. One of the merits of such an approach is that the optimum design is independent of the number of spatial harmonics, or engine orders. Local circuits are first formulated by connecting inductors and resistors with piezoelectric patches on the individual blades. Although these local circuits can function as conventional damped absorber when properly tuned, they do not perform well for bladed disks under all engine order excitations. To address this issue, capacitors are introduced to couple the individual local circuitries. Through such networking, an absorber system that is independent of the engine order can be achieved. Monte Carlo simulation is performed to investigate the effectiveness of the network for a bladed disk with a range of mistuning level of its mechanical properties. The robustness issue of the network in terms of detuning of the electric circuit parameters is also studied. Finally, negative capacitance is introduced and its effect on the performance and robustness of the network is investigated.

Fluid-Structural Coupling Effects on the Dynamics of Mistuned Bladed Disks

thehigh-fidelitystructuralmodelsistousethecantilever-bladenormalmodestocalculatetheunsteadyaerodynamic forces. In this paper, a new reduced-order modeling approach is developed by using the tuned system modes to calculate the unsteady aerodynamic forces directly. This new approach is applied to an industrial rotor. The results show that aerodynamic coupling has significant effects on the vibration of bladed disks for the case studied. Also, constraint modes are needed to yield accurate results if cantilever-blade normal modes are used to calculate the unsteadyaerodynamic forces.However,using the tunedsystemmodesto calculate theunsteadyaerodynamic forces saves a significant amount of computation time compared to the method using both cantilever-blade normal modes and constraint modes.

Forced Response of Harmonic Mistuned Blade Disks

In this paper, by adopting the continuous ring model and the perturbation analysis for free vibration, the authors showed the reason and the importance for the modes split phenomena and provided the qualitative relation between modes split and perturbation for the harmonic number of stiffness perturbation. Also through the modal analysis for forced vibration the authors showed possible ways to predict and prevent the worst case when blade will crack. That is, the harmonic number for stiffness distribution should be avoided to be twice the engine order.

The Influence of a Mistuned Blade’s Staggle Angle on the Vibration and Stability of a Shaft‐Disk‐Blade Assembly

The influence on coupling vibrations and stability among shaft‐torsion, disk‐transverse and blade‐bending of a rotor system with a mistuned blade′s staggle angle was investigated analytically. A shaft‐disk‐blade system has been found existing two types of coupling vibrations, disk‐blade (DB), and blade‐blade (BB) modes when the shaft was assumed rigid. If the shaft′s torsional flexibility was taken into account, an additional type of coupling modes, shaft‐disk‐blade (SDB), appeared. When an angle‐mistuned blade existed, the blades periodicity was destroyed and it was found to change not only the natural frequencies but also the types of modes. Due to blade′s mistune, the shaft torsion had to participate to balance such that DB modes vanished and replaced by SDB modes. A mistuned staggle angle was numerically found to alter the natural frequencies in an almost linear trend. At last, the rotational effects were found to merge frequency loci and eventually reached an instability point. Very interestingly, a mistuned blade diminished the possible instability caused by blade‐dominating modes, which existed in a perfect and periodic rotor. In words, the rotor might benefit from a mistuned blade from the stability viewpoint. The shaft‐dominating mode, yet, was unaffected by the mistune and retained a possible instability.

Coriolis Forces in Forced Response Analysis of Mistuned Bladed Disks

The problem of estimating the mutual interaction of the effects of Coriolis forces and of blade mistuning on the vibration characteristics of bladed disks is addressed in this paper. The influence of different degrees of mistuning on forced response and amplification factors are studied in the presence of Coriolis forces and then compared to their non-Coriolis counterparts using a computationally inexpensive, yet representative, model of a bladed disk. The primary objective of the study reported in this paper is to establish whether current mistuned bladed disk analyses should incorporate Coriolis effects in order to represent accurately all the significant factors that affect the forced response levels.

Modeling and Analysis of Mistuned Bladed Disk Vibration: Current Status and Emerging Directions

The literature on reduced-order modeling, simulation, and analysis of the vibration of bladed disks found in gas-turbine engines is reviewed. Applications to system identification and design are also considered. In selectively surveying the literature, an emphasis is placed on key developments in the last decade that have enabled better prediction and understanding of the forced response of mistuned bladed disks, especially with respect to assessing and mitigating the harmful impact of mistuning on blade vibration, stress increases, and attendant high cycle fatigue. Important developments and emerging directions in this research area are highlighted.

Predicting Blade Stress Levels Directly From Reduced-Order Vibration Models of Mistuned Bladed Disks

The forced vibration response of bladed disks can increase dramatically due to blade mistuning, which can cause major durability and reliability problems in turbine engines. To predict the mistuned forced response efficiently, several reduced-order modeling techniques have been developed. However, for mistuned bladed disks, increases in blade amplitude levels do not always correlate well with increases in blade stress levels. The stress levels may be computed by postprocessing the reduced-order model results with finite element analysis, but this is cumbersome and expensive. In this work, three indicators that can be calculated directly from reduced-order models are proposed as a way to estimate blade stress levels in a straightforward, systematic, and inexpensive manner. It is shown that these indicators can be used to predict stress values with good accuracy relative to finite element results, even for a case in which the displacement and stress levels show different frequency response trends.

Computation of the Statistics of Forced Response of a Mistuned Bladed Disk Assembly via Polynomial Chaos

The method of polynomial chaos has been used to analytically compute the statistics of the forced response of a mistuned bladed disk assembly. The model of the bladed disk assembly considers only one mode of vibration of each blade. Mistuning phenomenon has been simulated by treating the modal stiffness of each blade as a random variable. The validity of the polynomial chaos method has been corroborated by comparison with the results from numerical simulations.

블레이드 디스크의 International Mistuning 최적화 : 감쇠와 커플링효과

In turbomachinery rotor, there are small differences in the structural and/or geometrical properties of individual blades, which are referred to as blade mistuning. Mistuning effect of the forced response of bladed disks can be extremely large as often reported in many studies. In this paper, the pattern optimization of intentional mistuning for bladed disks considering with damping and coupling effect is the focus of the present investigation. More specifically, the class of intentionally mistuned disks considered here is limited, for cost reasons, to arrangements of two types of blades (A and B, say) and Genetic Algorithm and steepest descent method are used to optimize the arrangement of these blades around the disk to reduce the forced response of blade with different damping and coupling stiffness. Examples of application involving both simple bladed disk models and a 17-blade industrial rotor clearly demonstrate the significant benefits of using this class of intentionally mistuned disks.

Method for Analysis of Nonlinear Multiharmonic Vibrations of Mistuned Bladed Disks With Scatter of Contact Interface Characteristics

An efficient method for analysis of nonlinear vibrations of mistuned bladed disk assemblies has been developed. This development has facilitated the use of large-scale finite element models for realistic bladed disks, used hitherto in analysis of linear vibration, to be extended for the analysis of nonlinear multiharmonic vibration. The new method is based on a technique for the exact condensation of nonlinear finite element models of mistuned bladed disks. The model condensation allows the size of the nonlinear equations to be reduced to the number of degrees of freedom where nonlinear interaction forces are applied. The analysis of nonlinear forced response for simplified and realistic models of mistuned bladed disks has been performed. For a practical high-pressure bladed turbine disk, several types of nonlinear forced response have been considered, including mistuning by (i) scatter of underplatform dampers, (ii) shroud gap scatter, and (iii) blade frequency scatter in the presence of nonlinear shroud interactions.