Parametric Dynamics of Mistuned Bladed Disk

2014 ◽  
Author(s):  
Peiyi Wang ◽  
Lin Li
Keyword(s):  
Coupling Strength ◽  
Amplification Factor ◽  
Dynamic Properties ◽  
Forced Response ◽  
Design Parameters ◽  
Classical Dynamic ◽  
Mode Localization ◽  
Bladed Disk ◽  
Saddle Surface ◽  
Wear And Tear

The mistuning of bladed disk comes from manufacturing tolerances and in-service wear and tear. Consequently the cyclic symmetry has been destroyed by mistuning, even small mistuning levels could result in drastic changes in the dynamics of bladed disks. Specifically, mistuning can cause mode localization and an increase of the maximum forced response. It has been known that frequency veering, modal localization and magnification of response are three most classical dynamic properties of bladed disk. However few researches has focused on the relationships between dynamic characters and design parameters, because the proper variation ranges of the design parameters are difficult to be determined. The aim of this paper is to investigate the relationship between designed parameters and dynamic properties of mistuned bladed disk. Based on a lumped parametric model of bladed disk and utilizing parameterized eigenvalue solution, a reasonable range of designed parameter corresponding to specific nodal diameter index was provided. The numerical results showed that the curves of the gap of frequency veering versus coupling strength or blade stiffness have bowel-style. It was also found that there exists a quasi-saddle-surface while the vibration amplification factor varies with coupling strength and mistuning strength. The quasi-saddle-surface reveals that the existence of threshold of vibration amplification factor depends on the value of coupling strength. The result means that a proper choice of combination of coupling strength and mistuning strength could lead to a suppression of mistuned vibration amplification.

Investigation of Damping Potential of Strip Damper on a Real Turbine Blade

2016 ◽  
Author(s):  
M. Afzal ◽  
I. Lopez Arteaga ◽  
L. Kari ◽  
V. Kharyton
Keyword(s):  
Boundary Conditions ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Element Model ◽  
Forced Response ◽  
Contact Forces ◽  
Response Analysis ◽  
Bladed Disk ◽  
Different Types

This paper investigates the damping potential of strip dampers on a real turbine bladed disk. A 3D numerical friction contact model is used to compute the contact forces by means of the Alternate Frequency Time domain method. The Jacobian matrix required during the iterative solution is computed in parallel with the contact forces, by a quasi-analytical method. A finite element model of the strip dampers, that allows for an accurate description of their dynamic properties, is included in the steady-state forced response analysis of the bladed disk. Cyclic symmetry boundary conditions and the multiharmonic balance method are applied in the formulation of the equations of motion in the frequency domain. The nonlinear forced response analysis is performed with two different types of boundary conditions on the strip: (a) free-free and (b) elastic, and their influence is analyzed. The effect of the strip mass, thickness and the excitation levels on the forced response curve is investigated in detail.

Alternate Mistuning of Turbine Bladings Coupled by Underplatform Dampers

2012 ◽  
Author(s):  
S. Tatzko ◽  
L. Panning-von Scheidt ◽  
J. Wallaschek ◽  
A. Kayser
Keyword(s):  
Turbine Blades ◽  
Steady State Solution ◽  
Computational Effort ◽  
Forced Response ◽  
Nonlinear Coupling ◽  
Cyclic Symmetry ◽  
Periodic Excitation ◽  
Blade Vibration ◽  
Mode Localization ◽  
Bladed Disk

In turbo machinery design it is important to avoid vibrations that can destroy the turbine in the last resort. The rotating structure is exposed to periodic excitation forces. Two main types of periodic excitation can be distinguished. Flutter is the effect when mass flow forces couple with a natural vibration mode. The result is a negative damping coefficient and amplitudes will rise up to malfunction of the structure. The engine order excitation is a periodic excitation where the force signal is directly related to the speed of the rotor. A forced response calculation gives information about the blade vibration. Nonlinear coupling, i.e. friction coupling, between blades is used to increase damping of the bladed disk. Dynamic analysis of turbine blades with nonlinear coupling is a complex task and computer simulations are inevitable. Various techniques have been developed to reduce computational effort. The cyclic symmetry approach assumes each blade around the disk to be identical. Thus only one sector of the disk is sufficient to compute the steady state solution of the whole turbine blading. However, it has been observed that mistuning of blades reduces the flutter instability. On the other hand statistical mistuning can lead to dangerously high forced response amplitudes due to mode localization. A compromise is intentional mistuning. The simplest approach is alternate mistuning with every other blade exhibiting identical mechanical properties. This work explains in detail how a turbine bladed disk can be modeled when alternate mistuning is applied intentionally. Cyclic symmetry is used and each sector comprises two blades. This untypical choice of the sector size has significant impact on results of a cyclic modal analysis. Simulation results show the influence of alternate mistuned turbine bladings which are coupled by underplatform damper elements.

Experimental Investigation of Mode Localization and Forced Response Amplitude Magnification for a Mistuned Bladed Disk

2000 ◽  
Author(s):  
John Judge ◽  
Christophe Pierre ◽  
Oral Mehmed
Keyword(s):  
Experimental Investigation ◽  
Traveling Wave ◽  
Forced Response ◽  
Response Amplitude ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Element Analysis ◽  
Mode Localization ◽  
Bladed Disk ◽  
Out Of Plane

The results of an experimental investigation on the effects of random blade mistuning on the forced dynamic response of bladed disks are reported. The primary aim of the experiment is to gain understanding of the phenomena of mode localization and forced response blade amplitude magnification in bladed disks. A stationary, nominally periodic, twelve-bladed disk with simple geometry is subjected to a traveling-wave, out-of-plane, “engine order” excitation delivered via phase-shifted control signals sent to piezo-electric actuators mounted on the blades. The bladed disk is then mistuned by the addition of small, unequal weights to the blade tips, and it is again subjected to a traveling wave excitation. The experimental data is used to verify analytical predictions about the occurrence of localized mode shapes, increases in forced response amplitude, and changes in resonant frequency due to the presence of mistuning. Very good agreement between experimental measurements and finite element analysis is obtained. The out-of-plane response is compared and contrasted with the previously reported in-plane mode localization behavior of the same test specimen. This work also represents an important extension of previous experimental study by investigating a frequency regime in which modal density is lower but disk-blade interaction is significantly greater.

Finite-Element Modelling of an Experimental Mistuned Bladed Disk and Experimental Validation

2013 ◽  
Author(s):  
Jean de Cazenove ◽  
Scott Cogan ◽  
Moustapha Mbaye
Keyword(s):  
Finite Element ◽  
Model Building ◽  
Numerical Models ◽  
Dynamic Properties ◽  
Forced Response ◽  
Operating Conditions ◽  
Machining Process ◽  
Fe Model ◽  
Bladed Disk ◽  
Full Disk

Integrally bladed rotors dynamic properties are known to be particularly sensitive to small geometric discrepancies due to the machining process or in-service wear. In this context, it is straightforward that setting up accurate numerical models which take into account real mistuning patterns is a key issue in the prediction of forced response amplitudes under operating conditions. The present study focuses on an experimental bladed disk. Due to strong inter-blade coupling, the geometric mistuning is supposed to result in severe mode localization for the studied bladed disk, thus emphasizing the need of a realistic, predictive finite-element model. This paper describes the procedure which leads to the development and validation of a high-fidelity FE model for a realistic bladed disk, based on coordinate measurements by means of fringe projection. After giving an overview of the coordinate measurement and model building for the studied bladed disk, the comparison of cantilevered-blade and full disk calculated eigenfrequencies to individual blade and full disk in quasi-vacuum measurements are presented.

Resonant Response of Mistuned Bladed Disk Expressed by Vibratory Stress

2016 ◽  
Author(s):  
Yasutomo Kaneko ◽  
Kazushi Mori ◽  
Hiroharu Ooyama
Keyword(s):  
Stress Response ◽  
Amplification Factor ◽  
Forced Response ◽  
Response Analysis ◽  
Flat Plates ◽  
Bladed Disks ◽  
Displacement Response ◽  
Bladed Disk ◽  
Excited Vibration ◽  
Blade Flutter

Although bladed disks of turbomachinery are nominally designed to be cyclically symmetric (tuned system), the vibration characteristics of all blades on a disk are slightly different due to the manufacturing tolerance, the deviation of the material property, the wear during operation, and so on. These small variations break the cyclic symmetry, and split the eigenvalue pairs. The actual bladed disks with the small variations are referred to a mistuned system. In the forced response of a mistuned bladed disk, the responses of all blades become different, and the response of a certain blade may become extremely large due to the split of the duplicated eigenvalues, the distortion of the vibration modes, and so on. On the other hand, many researchers suggest that the mistuning suppresses the blade flutter, because the complete travelling wave mode is not formed in a disk. In other words, the main conclusions of researches on mistuning are that while mistuning has an undesirable effect on the forced response, it has a beneficial (stabilizing) effect on the blade flutter (the self-excited vibration). Although such mistuning phenomena of bladed disks have been studied since 1980s, almost all studies focused on the amplification factor of the displacement response, and few studies researched the amplification factor of the vibratory stress response. In this study, first, the frequency response analysis of the mistuned simple bladed disk consisting of flat plates is carried out. Comparing the amplification factor of the displacement response with that of the vibratory stress response, the amplification factor expressed by the vibratory stress is studied in detail. Second, the mistuning analysis of the actual bladed disk used in a steam turbine is carried out. From these results, the mistuning effect expressed by the vibratory stress is clarified.

scholarly journals Asymptotic Description of Maximum Mistuning Amplification of Bladed Disk Forced Response

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Carlos Martel ◽  
Roque Corral
Keyword(s):  
Upper Bound ◽  
Amplification Factor ◽  
Forced Response ◽  
Spring Model ◽  
Bladed Disk ◽  
Mass Spring Model ◽  
Amplification Process ◽  
Simple Mass ◽  
Response Amplification ◽  
Mass Spring

The problem of determining the maximum forced response vibration amplification that can be produced just by the addition of a small mistuning to a perfectly cyclical bladed disk still remains not completely clear. In this paper we apply a recently introduced perturbation methodology, the asymptotic mistuning model (AMM), to determine which are the key ingredients of this amplification process and to evaluate the maximum mistuning amplification factor that a given modal family with a particular distribution of tuned frequencies can exhibit. A more accurate upper bound for the maximum forced response amplification of a mistuned bladed disk is obtained from this description, and the results of the AMM are validated numerically using a simple mass-spring model.

Reduction of Forced Response Levels for Bladed Disks by Mistuning: Overview of the Phenomenon

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Amplification Factor ◽  
Forced Response ◽  
Statistical Properties ◽  
Combined Effect ◽  
Practical Significance ◽  
Structural Damping ◽  
Design Decisions ◽  
Bladed Disk ◽  
Reduction Effect ◽  
Optimization Search

The newly revealed phenomenon of reduction of forced response levels in a mistuned bladed disk to levels significantly (e.g., by a factor of 2 and more) lower than that of its tuned counterpart is studied in detail on an example of a realistic bladed disk. Statistical properties of the amplification factor of the mistuned forced response calculated with aero-effects included have been studied for cases of random blade mistuning and for mistuned blade rearrangements. The optimization search for the best mistuning patterns providing maximum forced response reduction effect have been performed and the robustness of the optimum mistuning patterns has been demonstrated. The combined effect of the aerodynamic and structural damping on the response reduction is assessed. It is shown that the new phenomenon is of major practical significance and has to be taken into account in analysis of the forced response and design decisions.

Study on Vibration Response Characteristics of Mistuned Bladed Disk Expressed by Vibratory Stress

2019 ◽  
Author(s):  
Yasutomu Kaneko ◽  
Toshio Watanabe ◽  
Tatsuya Furukawa ◽  
Saiji Washio
Keyword(s):  
Amplification Factor ◽  
Harmonic Excitation ◽  
Forced Response ◽  
Von Mises Stress ◽  
Bladed Disks ◽  
Resonant Amplitude ◽  
Response Characteristics ◽  
Bladed Disk ◽  
Disk Structure ◽  
Von Mises

Abstract Although bladed disks of turbomachinery are nominally designed to be cyclically symmetric (tuned system), the vibration characteristics of individual blades on a disk differ slightly owing to manufacturing tolerance, deviation of material properties, wear during operation, etc. These small variations break cyclic symmetry and split eigenvalue pairs. Actual bladed disks with small variations are called mistuned systems. Many researchers have studied mistuning and the main conclusion is that while mistuning has an undesirable effect on forced response, it has a beneficial effect on blade flutter. Although mistuning phenomena have been studied since the 1980s, studies on forced response are mostly related to increase in the resonant amplitude due to harmonic excitation force. In addition, because few papers have treated the amplification factor expressed in terms of vibratory stress, the mistuning phenomena of bladed disks expressed in terms of vibratory stress are not fully understood. In this study, the mistuning effect expressed in terms of vibratory stress is examined using the reduced-order model SNM (Subset of Nominal Modes) without any assumptions. By comparing the amplification factor expressed in terms of displacement response with that expressed in terms of vibratory stress response, including synthesized stress (von Mises stress and principal stress), the mistuning phenomena expressed in terms of vibratory stress are clarified. The effect of bladed disk structure on amplification factor is examined in detail as well.

High Fidelity Transient Forced Response Analysis of Mistuned Bladed Disks Under Complex Excitation and Variable Rotation Speeds

2020 ◽  
Author(s):  
Jing Tong ◽  
Chaoping Zang ◽  
Evgeny Petrov
Keyword(s):  
Large Scale ◽  
Rotation Speed ◽  
Dynamic Properties ◽  
Spectral Composition ◽  
Forced Response ◽  
Mode Shapes ◽  
Response Analysis ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Amplitude Amplification

Abstract An effective method is developed for the efficient calculation of the transient vibration response for mistuned bladed disks under complex excitation and varying rotation speeds. The method uses the large-scale finite element modelling of the bladed disks allowing the accurate description of the dynamic properties of the mistuned bladed disks. The realistic distributions of the excitation forces are considered, which resulted in the multiharmonic excitation loads. The transient response calculation is based on the analytically derived expressions for the transient forced response and the effective method used for the model reduction. The effects of the varying rotation speed on the natural frequencies and mode shapes of the mistuned bladed disk and its effects on the amplitude and the spectral composition of the loading are allowed for. The different functions of the rotation speed variation can be analyzed. Numerical studies of the transient forced response and the amplitude amplification in mistuned bladed disks are performed when the resonance regimes are passed during gas-turbine engine acceleration or deceleration. The effects of different types of excitation force and mistuning on transient amplitude amplification are illustrated by a large number of the computational results and comparative analysis. These results and analysis of transient forced response are shown on an example of a realistic mistuned bladed disk.

scholarly journals Response of Bladed Disks With Mistuned Blade-Disk Interfaces

2009 ◽  
Author(s):  
Javier Avalos ◽  
Marc P. Mignolet ◽  
Christian Soize
Keyword(s):  
Stochastic Modeling ◽  
Amplification Factor ◽  
Forced Response ◽  
Interface Properties ◽  
Physical Behavior ◽  
Disk Interface ◽  
Bladed Disk ◽  
Modeling Approach ◽  
Local Modeling

This paper focuses on the determination of the effects on the bladed disk forced response of small variations (mistuning) in the blade-disk interface properties as may result from blade seating. A blade-interface-disk mean model is first developed that relies on both the Craig-Bampton approach and a local modeling of the interface. Then, both model and data uncertainties are introduced in this model using the nonparametric stochastic modeling approach. An example of application is presented that indicates a difference in physical behavior of a bladed disk with mistuned interfaces as compared to one with mistuned blade alone frequencies. Most notably, it is shown that at equal variability on the blade frequencies, the variations in blade-disk interface properties lead to a higher amplification factor.

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