Analysis of Nonlinear Modal Damping due to Friction at Blade Roots in Mistuned Bladed Discs

2020 ◽  
Author(s):  
Junjie Chen ◽  
Chaoping Zang ◽  
Biao Zhou ◽  
E. P. Petrov
Keyword(s):  
Reduction Method ◽  
Mode Shapes ◽  
Dissipated Energy ◽  
Damping Factor ◽  
Nodal Diameter ◽  
Modal Damping ◽  
Engine Order ◽  
The Time Domain ◽  
Energy Dissipated ◽  
Small Parts

Abstract A method is proposed to analyse the modal damping in mistuned bladed-disc 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-disc 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 micro-slip are simulated by multitude of surface-to-surface elements modelling 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 disc sectors. The dependency of modal damping factor on blade mode shapes, engine-order excitation numbers, nodal diameter numbers and vibration amplitudes are studied and the distributions of amplitude and dissipated energy on the mistuned bladed-disc are investigated using a realistic blade disc model.

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

2021 ◽  
Vol 143 (3) ◽  
Author(s):  
Junjie Chen ◽  
Chaoping Zang ◽  
Biao Zhou ◽  
E. P. Petrov
Keyword(s):  
Reduction Method ◽  
Mode Shapes ◽  
Dissipated Energy ◽  
Damping Factor ◽  
Disk Model ◽  
Bladed Disk ◽  
Modal Damping ◽  
Engine Order ◽  
The Time Domain ◽  
Energy Dissipated

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.

Analysis of Nonlinear Modal Damping due to Friction at Blade Roots Using High-Fidelity Modelling

2018 ◽  
Author(s):  
Junjie Chen ◽  
Chaoping Zang ◽  
Biao Zhou ◽  
E. P. Petrov
Keyword(s):  
Finite Element ◽  
Direct Calculation ◽  
Surface Friction ◽  
Mode Shapes ◽  
Finite Element Models ◽  
High Fidelity ◽  
Three Dimension ◽  
Blade Vibration ◽  
Modal Damping ◽  
Energy Dissipated

In this paper, a methodology is developed for analysis of modal damping in root joints of bladed discs using large finite element models and detailed description of friction contacts at contact interfaces of the joints. The methods allows the analysis of: (i) a single blade vibration and (ii) a bladed-disc assembly for any family of modes (lower and higher modes) calculating the modal damping factors for different levels of vibrations. Three-dimension solid finite element models are used in the calculations. The analysis is performed in time domain through the transient dynamics analysis. The methodology allows the use of widely available finite element packages and based on the direct calculation of the energy dissipated at root joints due to micro-slip over the multitude of contact elements modelling the surface-to-surface friction contact interactions. The numerical studies of the dependency of modal damping factors on the vibration amplitudes are performed for simplified and realistic bladed disc models for different blade mode shapes, engine-order excitation numbers and nodal diameter numbers using high-fidelity models.

Investigation of Alternate Mistuned Turbine Blades Non-Linear Coupled by Underplatform Dampers

2013 ◽  
Author(s):  
S. Tatzko ◽  
L. Panning-von Scheidt ◽  
J. Wallaschek ◽  
A. Kayser ◽  
G. Walz
Keyword(s):  
Turbine Blades ◽  
Forced Response ◽  
Mode Shapes ◽  
Nodal Diameter ◽  
Frictional Contacts ◽  
Bladed Disk ◽  
Engine Order ◽  
Bladed Disk Assembly ◽  
Last Stage ◽  
Software Code

Freestanding turbine blades have typically low structural damping and thus require additional friction damping devices, such as underplatform dampers. The friction coupling between neighboring blades reduces response amplitude and increases resonance frequency. Along with forced response excitation large blades, especially of last stage, could be excited by fluid structural interaction (flutter). To prevent such excitation alternate mistuned blade patterns are beneficial disturbing traveling waves in the stage. In this paper the influence of alternate mistuning is investigated with a simplified oscillator chain as well as a bladed disk assembly coupled by frictional contacts. It is pointed out that the performance of friction coupling can be improved by alternate mistuning as long as the engine order of the excitation is below quarter of the number of blades. Alternate mistuning causes a mode coupling between two nodal diameter vibration mode shapes allowing for energy transfer. The in-house developed software code DATAR is enhanced and alternate mistuning can be applied to the blades as well as to the damping elements. For validation the DATAR code was applied to an alternate mistuned last stage blade of a Siemens gas turbine and compared with available field engine measurement.

Double Nodal Diameter Spectrum Method and its Application in Quantification of Vibration Localization of Impellers With Splitter Blades

2017 ◽  
Author(s):  
Kaicheng Liu ◽  
Jianjun Wang
Keyword(s):  
Travelling Wave ◽  
Mode Shapes ◽  
Response Analysis ◽  
Nodal Diameter ◽  
Mode Localization ◽  
Vibration Localization ◽  
Engine Order ◽  
Vibration Pattern ◽  
Harmonic Response Analysis ◽  
Definition Of

Double nodal diameter spectrum (DNDS) method which is used to analyze nodal diameter (ND) components of the vibration modes of impellers with splitters is proposed and its application in quantification of mode localization has been studied. Firstly, ND characteristics of the typical impeller with splitter blades are analyzed by mode shapes and representative subeigenvectors. Secondly, DNDS method is proposed and DNDSs of the representative modes indicate that the tuned modes of impellers with splitter blades contain two ND components. By applying the simplified engine order (EO) excitation in the form of a travelling wave, harmonic response analysis has been carried out by which double nodal diameter vibration characteristics of the structure and the effectiveness of the DNDS method are both validated. Lastly, in terms of quantifying mode localization, the definition of mode localization factor (MLF) is improved based on DNDS. The numerical example proves that the pairing process of choosing the tuned mode corresponding to the mistuned one by utilizing both DNDS and the vibration pattern of blades when calculating the improved MLF could pick out the closest tuned mode to the mistuned one, which has a more explicit physical meaning.

scholarly journals Investigation of Modal Behaviour of Resonance Spruce Wood Samples (Picea abies L.)

2017 ◽  
Vol 42 (1) ◽  
pp. 23-28 ◽  
Author(s):  
Przemysław Mania ◽  
Ewa Fabisiak ◽  
Ewa Skrodzka
Keyword(s):  
Picea Abies ◽  
Modal Analysis ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Pulse Excitation ◽  
Damping Factor ◽  
The North ◽  
Spruce Wood ◽  
Modal Damping ◽  
Resonance Wood

AbstractResults of experimental modal analysis of a resonance and non-resonance spruce wood (Picea abies L.) are presented. The resonance wood came from a tree from Poland and Bosnia and Herzegovina, while the non-resonance wood came from the vicinity of Olsztyn from the north-eastern Poland. The modal parameters (modal frequency, modal damping and mode shapes) of the wood samples were determined for the samples of 8 mm in thickness. Modal analysis was made by pulse excitation. The resonance and non-resonance wood differ in the fundamental modal parameters as well as in the number of potential modes. Additionally, calculated values of damping factor are presented. The values are much bigger for a non-resonance wood than for good quality resonance spruce.

Effect of Bass Bar Tension on Modal Parameters of a Violin's Top Plate

2015 ◽  
Vol 39 (1) ◽  
pp. 145-149 ◽  
Author(s):  
Ewa B. Skrodzka ◽  
Bogumił B.J. Linde ◽  
Antoni Krupa
Keyword(s):  
Modal Analysis ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Normal Value ◽  
Modal Damping

Abstract Experimental modal analysis of a violin with three different tensions of a bass bar has been performed. The bass bar tension is the only intentionally introduced modification of the instrument. The aim of the study was to find differences and similarities between top plate modal parameters determined by a bass bar perfectly fitting the shape of the top plate, the bass bar with a tension usually applied by luthiers (normal), and the tension higher than the normal value. In the modal analysis four signature modes are taken into account. Bass bar tension does not change the sequence of mode shapes. Changes in modal damping are insignificant. An increase in bass bar tension causes an increase in modal frequencies A0 and B(1+) and does not change the frequencies of modes CBR and B(1-).

scholarly journals Comparison of Two Numerical Algorithms for Computing the Effects of Mistuning of Fan Flutter

2016 ◽  
Author(s):  
L. Salles ◽  
M. Vahdati
Keyword(s):  
Numerical Models ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Mode Shapes ◽  
Minimal Amount ◽  
Aeroelastic System ◽  
Cpu Time ◽  
Influence Coefficients ◽  
Non Linear ◽  
The Time Domain

The aim of this paper is to study the effects of mistuning on fan flutter and to compare the prediction of two numerical models of different fidelity. The high fidelity model used here is a three-dimensional, whole assembly, time-accurate, viscous, finite-volume compressible flow solver. The Code used for this purpose is AU3D, written in Imperial College and validated for flutter computations over many years. To the best knowledge of authors, this is the first time such computations have been attempted. This is due to the fact that, such non-linear aeroelastic computations with mistuning require large amount of CPU time and cannot be performed routinely and consequently, faster (low fidelity) models are required for this task. Therefore, the second model used here is the aeroelastic fundamental mistuning model (FMM) and it based on an eigenvalue analysis of the linearized modal aeroelastic system with the aerodynamic matrix calculated from the aerodynamic influence coefficients. The influence coefficients required for this algorithm are obtained from the time domain non-linear Code by shaking one blade in the datum (tuned) frequency and mode. Once the influence coefficients have been obtained, the computations of aero damping require minimal amount of CPU time and many different mistuning patterns can be studied. The objectives of this work are to: 1. Compare the results between the two models and establish the capabilities/limitations of aeroelastic FMM, 2. Check if the introduction of mistuning would bring the experimental and computed flutter boundaries closer, 3. Establish a relationship between mistuning and damping. A rig wide-chord fan blade, typical of modern civil designs, was used as the benchmark geometry for this study. All the flutter analyses carried out in this paper are with frequency mistuning, but the possible consequences of mistuned mode shapes are briefly discussed at the end of this paper. Only the first family of modes (1F, first flap) is considered in this work. For the frequency mistuning analysis, the 1F frequency is varied around the annulus but the 1F mode shapes remain the same for all the blades. For the mode shape mistuning computations, an FE analysis of the whole assembly different mass blades is performed. The results of this work clearly show the importance of mistuning on flutter. It also demonstrates that when using rig test data for aeroelastic validation of CFD codes, the amount mistuning present must be known. Finally, it should be noted that the aim of this paper is the study of mistuning and not steady/unsteady validation of a CFD code and therefore minimal aerodynamic data are presented.

FERMION PERTURBATIONS IN HIGHER-DIMENSIONAL STRING-THEORY BLACK HOLES

2013 ◽  
Vol 22 (10) ◽  
pp. 1350073
Author(s):  
OWEN PAVEL FERNÁNDEZ PIEDRA ◽  
JOSE BERNAL CASTILLO ◽  
YULIER JIMENEZ SANTANA ◽  
LEOSDAN FIGUEREDO NORIS
Keyword(s):  
Black Hole ◽  
Damping Factor ◽  
Test Field ◽  
Perfect Agreement ◽  
Massless Fermion ◽  
Time Domain Data ◽  
Fermion Fields ◽  
Dimensional Spacetime ◽  
Higher Dimensional ◽  
The Time Domain

In this paper, we report the results of a detailed investigation of the complete time evolution of massless fermion fields propagating in spacetimes of higher-dimensional stringy black hole solutions, obtained from intersecting branes in string/M theory. We write the Dirac equation in D-dimensional spacetime in a form suitable to perform a numerical integration of it, and using a Prony fitting of the time domain data, we determine the quasinormal frequencies that characterize the test field evolution at intermediary times. We also present the results obtained for the quasinormal frequencies using a sixth-order WKB approximation, that are in perfect agreement with the numerical results. The power-law exponents that describe the field relaxation at very late-times are also determined, and we show that they depends upon the dimensionality of spacetime, and are identical to that associated with the relaxation of boson fields for odd dimensions. The dependence of the frequencies and damping factor of the spinor field with the charges of the stringy black hole are studied.

Modal Analyses of an Axial Turbine Blisk With Intentional Mistuning

2017 ◽  
Author(s):  
Bernd Beirow ◽  
Felix Figaschewsky ◽  
Arnold Kühhorn ◽  
Alfons Bornhorn
Keyword(s):  
Aerodynamic Performance ◽  
Forced Response ◽  
Mode Shapes ◽  
Axial Turbine ◽  
The Real ◽  
Operational Conditions ◽  
Aerodynamic Damping ◽  
Optimization Study ◽  
Engine Order ◽  
Turbine Blisk

The potential of intentional mistuning to reduce the maximum forced response is analyzed within the development of an axial turbine blisk for ship diesel engine turbocharger applications. The basic idea of the approach is to provide an increased aerodynamic damping level for particular engine order excitations and mode shapes without any significant distortions of the aerodynamic performance. The mistuning pattern intended to yield a mitigation of the forced response is derived from an optimization study applying genetic algorithms. Two blisk prototypes have been manufactured a first one with and another one without employing intentional mistuning. Hence, the differences regarding the real mistuning and other modal properties can be experimentally determined and evaluated as well. In addition, the experimental data basis allows for updating structural models which are well suited to compute the forced response under operational conditions. In this way, the real benefit achieved with the application of intentional mistuning is demonstrated.

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