Forced Response Analysis of Mistuned Turbine Bladings

2010 ◽  
Author(s):  
Christian Siewert ◽  
Heinrich Stu¨er
Keyword(s):  
Natural Frequency ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Forced Response ◽  
Response Analysis ◽  
Vibrational Behavior ◽  
Bladed Disk ◽  
Fundamental Model ◽  
Mechanical Models ◽  
Number Of Publications

It is well-known that the vibrational behavior of a mistuned bladed disk differs strongly from that of a tuned bladed disk. A large number of publications dealing with the dynamics of a mis-tuned bladed disk is available in the literature. Nearly all published mechanical models for a mistuned bladed disk consider the mistuning in terms of a perturbation of the mass and/or the stiffness matrix or in terms of a perturbation of the tuned system natural frequencies. Therefore, the possible effect of a damping mistuning is neglected in these models. In this paper, a model of a mistuned bladed disk with a combined damping and natural frequency mistuning is presented. This model is based on the well-known Fundamental Model of Mistuning with a novel extension to include the damping mistuning in a straight-forward way.

Transient Forced Response Analysis of Mistuned Steam Turbine Blades During Startup and Coastdown

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Christian Siewert ◽  
Heinrich Stüer
Keyword(s):  
Mechanical Model ◽  
Turbine Blades ◽  
Forced Vibrations ◽  
Forced Response ◽  
The Self ◽  
Response Analysis ◽  
Computationally Efficient ◽  
Bladed Disk ◽  
Steam Turbine Blades ◽  
Number Of Publications

It is well known that the vibrational behavior of a mistuned bladed disk differs strongly from that of a tuned bladed disk. A large number of publications dealing with the dynamics of mistuned bladed disks are available in the literature. The vibrational phenomena analyzed in these publications are either forced vibrations or self-excited flutter vibrations. Nearly, all published literature on the forced vibrations of mistuned blades disks considers harmonic, i.e., steady-state, vibrations, whereas the self-excited flutter vibrations are analyzed by the evaluation of the margin against instabilities by means of a modal, or rather than eigenvalue, analysis. The transient forced response of mistuned bladed disk is not analyzed in detail so far. In this paper, a computationally efficient mechanical model of a mistuned bladed disk to compute the transient forced response is presented. This model is based on the well-known fundamental model of mistuning (FMM). With this model, the statistics of the transient forced response of a mistuned bladed disk is analyzed and compared to the results of harmonic forced response analysis.

Transient Forced Response Analysis of Mistuned Steam Turbine Blades During Start-Up and Coast-Down

2014 ◽  
Author(s):  
Christian Siewert ◽  
Heinrich Stüer
Keyword(s):  
Mechanical Model ◽  
Turbine Blades ◽  
Forced Vibrations ◽  
Forced Response ◽  
Response Analysis ◽  
Computationally Efficient ◽  
Bladed Disk ◽  
Start Up ◽  
Steam Turbine Blades ◽  
Number Of Publications

It is well-known that the vibrational behavior of a mistuned bladed disk differs strongly from that of a tuned bladed disk. A large number of publications dealing with the dynamics of mistuned bladed disks is available in the literature. The vibrational phenomena analyzed in these publications are either forced vibrations or self-excited flutter vibrations. Nearly all published literature on the forced vibrations of mistuned blades disks considers harmonic, i. e. steady-state, vibrations, whereas the self-excited flutter vibrations are analyzed by the evaluation of the margin against instabilities by means of a modal, or rather than eigenvalue, analysis. The transient forced response of mistuned bladed disk is not analyzed in detail so far. In this paper, a computationally efficient mechanical model of a mistuned bladed disk to compute the transient forced response is presented. This model is based on the well-known Fundamental Model of Mistuning. With this model, the statistics of the transient forced response of a mistuned bladed disk is analyzed and compared to the results of harmonic forced response analysis.

Mistuning Identification of Bladed Disks Utilizing Neural Networks

2010 ◽  
Author(s):  
M. Ersin Yu¨mer ◽  
Ender Cig˘erog˘lu ◽  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Neural Networks ◽  
Mathematical Model ◽  
Case Studies ◽  
Natural Frequencies ◽  
Forced Response ◽  
Response Analysis ◽  
Bladed Disks ◽  
Data Set ◽  
Bladed Disk ◽  
New Methods

Mistuning affects forced response of bladed disks drastically; therefore, its identification plays an essential role in the forced response analysis of realistic bladed disk assemblies. Forced response analysis of mistuned bladed disk assemblies has drawn wide attention of researchers but there are a very limited number of studies dealing with identification of mistuning, especially if the component under consideration is a blisk (integrally bladed disk). This paper presents two new methods to identify mistuning of a rotor from the assembly modes via utilizing neural networks. It is assumed that a tuned mathematical model of the rotor under consideration is readily available, which is always the case for today’s realistic bladed disk assemblies. In the first method, a data set of selected mode shapes and natural frequencies is created by a number of simulations performed by mistuning the tuned mathematical model randomly. A neural network created by considering the number of modes, is then trained with this data set. Upon training the network, it is used to identify mistuning of the rotor from measured data. The second method further improves the first one by using it as starting point of an optimization routine and carries out an optimization to identify mistuning. To carry out identification analysis by means of the proposed methods, there are no limitations on the number of modes or natural frequencies to be used. Thus, they are suitable for incomplete data as well. Moreover, since system modes are used rather than blade alone counterparts, the techniques are ready to be used for analysis of blisks. Case studies are performed to demonstrate the capabilities of the new methods, using two different mathematical models to create training data sets; a lumped-parameter model and a relatively realistic reduced order model. Throughout the case studies, the effects of using incomplete mode families and random errors in assembly modes are investigated.

Mistuning Identification of Integrally Bladed Disks With Cascaded Optimization and Neural Networks

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Mehmet Ersin Yumer ◽  
Ender Cigeroglu ◽  
H. Nevzat Özgüven
Keyword(s):  
Neural Networks ◽  
Mathematical Model ◽  
Case Studies ◽  
Natural Frequencies ◽  
Forced Response ◽  
Response Analysis ◽  
Bladed Disks ◽  
Data Set ◽  
Bladed Disk ◽  
New Methods

Mistuning affects forced response of bladed disks drastically; therefore, its identification plays an essential role in the forced response analysis of bladed disk assemblies. Forced response analysis of mistuned bladed disk assemblies has drawn wide attention of researchers but there are a very limited number of studies dealing with identification of mistuning, especially if the component under consideration is an integrally bladed disk (blisk). This paper presents two new methods to identify mistuning of a bladed disk from the assembly modes via utilizing cascaded optimization and neural networks. It is assumed that a tuned mathematical model of the blisk under consideration is readily available, which is always the case for today’s realistic bladed disk assemblies. In the first method, a data set of selected mode shapes and natural frequencies is created by a number of simulations performed by mistuning the tuned mathematical model randomly. A neural network created by considering the number of modes, is then trained with this data set. Upon training the network, it is used to identify mistuning of the rotor from measured data. The second method further improves the first one by using it as a starting point of an optimization routine and carries out an optimization to identify mistuning. To carry out identification analysis by means of the proposed methods, there are no limitations on the number of modes or natural frequencies to be used. Thus, unlike existing mistuning identification methods they are suitable for incomplete data as well. Moreover, since system modes are used rather than blade alone counterparts, the techniques are ready to be used for analysis of blisks. Case studies are performed to demonstrate the capabilities of the new methods by using two different mathematical models to create training data sets a lumped-parameter model and a relatively realistic reduced order model. Throughout the case studies, the effects of using incomplete mode families and random errors in assembly modes are investigated. The results show that, the proposed method utilizing cascaded optimization and neural networks can identify mistuning parameters of a realistic blisk system with an exceptional accuracy even in the presence of incomplete and noisy test data.

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.

scholarly journals Vibrational Response Analysis of Mistuned Bladed Disk System of Grouped Blades

1998 ◽  
Author(s):  
Y. Kaneko ◽  
K. Mori ◽  
H. Ohyama ◽  
E. Watanabe
Keyword(s):  
Synthesis Method ◽  
Forced Response ◽  
Response Analysis ◽  
Analysis Method ◽  
Disk System ◽  
Vibrational Response ◽  
Bladed Disk ◽  
System A ◽  
Vibrational Characteristics ◽  
Grouped Blades

For the purpose of the efficient analysis of a mistuned bladed disk system, a new analysis method which applies the substructure synthesis method and the modal analysis method is proposed. Using the proposed method, the vibrational characteristics of the grouped blades structure are studied. From the results, it is found that the grouped blades structure is very sensitive to the mistuning. It is also found that the mixed grouped blades structure (a bladed disk system consisting of some different types of grouped blades relating to the number of blades contained) has an undesirable effect on the forced response. Moreover, by comparing the vibrational characteristics of the integral shroud blades (ISB) structure with those of the grouped blades structure, it is clarified that the reliability of the ISB structure is superior to other structures also from the viewpoint of the mistuning.

Vibration localization for a rotating mistuning bladed disk with the Coriolis effect by a state-space decoupling method

2017 ◽  
Vol 233 (3) ◽  
pp. 1011-1020 ◽  
Author(s):  
Xuanen Kan ◽  
Zili Xu
Keyword(s):  
State Space ◽  
Natural Frequency ◽  
Coriolis Force ◽  
High Speed ◽  
Forced Response ◽  
Coriolis Effect ◽  
Decoupling Method ◽  
Resonant Amplitude ◽  
Bladed Disk ◽  
Localization Factor

Slight deviations of blades due to manufacturing tolerances can cause mistuning of bladed disk leading to localized vibration, which can accelerate fatigue. Moreover, the rotating blades are subjected to the Coriolis effect and the influence of the Coriolis force on the natural frequencies of high-speed rotational bladed disks such as those of an aero-engine become more apparent. In this paper, the effect of Coriolis force on the forced response localization of a mistuned bladed disk are investigated, for conditions where the natural frequency located in the first and second modal families of the bladed disk. Mistuning is introduced by varying the Young’s modulus of each blade. Due to the asymmetric Coriolis matrix, it is not possible to directly decouple the system. A state-space decoupling method is developed to decouple the system to effectively calculate the forced response of bladed disk with the consideration of the Coriolis effect. The results show that response localization factor is increased by 13.09% considering the Coriolis force compared to the system without considering the Coriolis effect, in the case of where the first modal family is considered. In addition, the response localization factor with the consideration of the Coriolis force is decreased by 30.85% compared to the system without considering the Coriolis force, when the second modal family is considered. It indicates that the forced response localization with the consideration of the Coriolis effect will be changed obviously with the rotational speed increasing, when the concerning natural frequency is located in the first and second modal families. Furthermore, the effect of Coriolis force causes changes in the resonant frequencies and resonant amplitude, but does not introduce additional resonant peaks for the case of the mistuned bladed disk.

Natural Frequencies of Rotating Bladed Disks Using Clamped-Free Blade Modes

1983 ◽  
Vol 105 (4) ◽  
pp. 416-424
Author(s):  
S. J. Wildheim
Keyword(s):  
Periodic Structure ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Calculation Procedure ◽  
Dynamic Stiffness Matrix ◽  
Bladed Disk ◽  
Count Method ◽  
Dynamic Substructuring ◽  
Bladed Disk Assembly

The problem of calculating the natural frequencies of a practical rotating bladed disk assembly is solved by use of a new dynamic substructuring method employing the free modes of the disk and the clamped-free modes of the blade. The bladed disk may have lacing-wires at any radius. The lacing-wire, or any other general elastic connection element, is assumed to extend around the whole circumference. Hence, the assembly fulfills the requirements for a circumferentially periodic structure. Centrifugal effects are included. The free modes of the disk are used to describe the dynamics of the disk by a 4 × 4 receptance matrix. The row of blades is described by a dynamic stiffness matrix of order 4 + 10l, where l is the number of lacing-wires. The dynamic stiffness matrix of the blading is formed directly from the modes of one single clamped-free blade without any lacing-wire. The lacing-wires are treated as elastic and massless. The zeroes of the resulting transcendental frequency determinant of order 4 + 10l are solved by the sign-count method. The calculation procedure has proved to be very efficient. Further, it enjoys the precious property of being automatic and infallible in the sense that there is no risk of missing any frequency whatever the spacing of natural frequencies. Experimentally found frequencies are compared to calculated ones.

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 On Antiresonance in the Forced Response of Mistuned Bladed Disks

2003 ◽  
Vol 10 (2) ◽  
pp. 135-146 ◽  
Author(s):  
Keith Jones ◽  
Charles Cross
Keyword(s):  
Natural Frequencies ◽  
Critical Factor ◽  
Forced Response ◽  
Turbine Engines ◽  
Response Functions ◽  
Local Response ◽  
Bladed Disks ◽  
Important Conclusion ◽  
Bladed Disk ◽  
Lower Maximum

Mistuning in bladed disks usually increases the forced response of the maximum responding blade leading to shortened component life in turbine engines. This paper investigates mistuning using a transfer function approach where the frequency response functions (FRFs) are described by natural frequencies and antiresonant frequencies. Using this approach, antiresonant frequencies are shown to be a critical factor in determining the maximum blade response. Two insights are gained by formulating antiresonant frequencies as the eigenvalues of reduced system matrices: 1) Mistuning a particular blade has no effect on that blade's antiresonant frequencies. 2) Engine orders N and N/2, where N is the number of blades on the disk, tend to produce the highest maximum local response. Numerical examples are given using a spring-mass-oscillator model of a bladed disk. Pole-zero loci of mistuned bladed disks show that increased maximum blade response is often due to the damping of antiresonant frequencies. An important conclusion is that antiresonant frequencies can be arranged such that a mistuned bladed disk has a lower maximum blade response than a tuned bladed disk.

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