A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Discs

2003 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Nonlinear Structure ◽  
Sector Model ◽  
Symmetry Properties ◽  
Symmetric Structures

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disc using a periodic sector model without any loss of accuracy in calculations and modelling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disc forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disc model: (i) using sector finite element matrices; (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disc with shrouds have demonstrated the high efficiency of the method.

Sensitivity of Tuned Bladed Disk Response to Frequency Veering

2004 ◽  
Author(s):  
J. A. Kenyon ◽  
J. H. Griffin ◽  
N. E. Kim
Keyword(s):  
Forced Response ◽  
Mode Interaction ◽  
Mode Shapes ◽  
Disk Model ◽  
Bladed Disk ◽  
Modal Response ◽  
Generalized Force ◽  
Cyclic Symmetric ◽  
Fixed Reference ◽  
Interblade Phase Angle

A continuous method is presented for representing the mode interaction that occurs in frequency veering in terms of the nominal sector modes of a cyclic symmetric bladed disk model constrained at a fixed reference interblade phase angle. Using this method, the effect of frequency veering on the mode shapes can be considered in the context of the generalized forces exciting the system and the modal response of the bladed disk. It is shown that in a blade-dominated family of modes, the transfer of modal energy to the disk in the veering results in a lower generalized force exciting the mode as well as reduced response amplitude in the blade. For the disk-dominated modes, the sharing of modal energy with the blades can lead to the disk being excited by aerodynamic loading. These effects can have important implications for predicting and interpreting forced response in bladed disks. Numerical examples are provided to illustrate these concepts.

Sensitivity of Tuned Bladed Disk Response to Frequency Veering

2004 ◽  
Vol 127 (4) ◽  
pp. 835-842 ◽  
Author(s):  
J. A. Kenyon ◽  
J. H. Griffin ◽  
N. E. Kim
Keyword(s):  
Forced Response ◽  
Mode Interaction ◽  
Mode Shapes ◽  
Disk Model ◽  
Bladed Disk ◽  
Aerodynamic Loading ◽  
Modal Response ◽  
Generalized Force ◽  
Cyclic Symmetric ◽  
Interblade Phase Angle

A continuous method is presented for representing the mode interaction that occurs in frequency veering in terms of the nominal sector modes of a cyclic symmetric bladed disk model constrained at a reference interblade phase angle. Using this method, the effect of frequency veering on the mode shapes can be considered in the context of the generalized forces exciting the system and the modal response of the bladed disk. It is shown that in a blade-dominated family of modes, the transfer of modal energy to the disk in the veering results in a lower generalized force exciting the mode as well as reduced response amplitude in the blade. For the disk-dominated modes, the sharing of modal energy with the blades can lead to the disk being excited by aerodynamic loading. These effects can have important implications for predicting and interpreting forced response in bladed disks. Numerical examples are provided to illustrate these concepts.

Blade Root Joint Modelling and Analysis of Effects of Their Geometry Variability on the Nonlinear Forced Response of Tuned and Mistuned Bladed Disks

2020 ◽  
Author(s):  
Adam Koscso ◽  
E. P. Petrov
Keyword(s):  
Harmonic Balance Method ◽  
Forced Response ◽  
High Fidelity ◽  
Contact Interactions ◽  
Bladed Disks ◽  
Element Mesh ◽  
Disk Model ◽  
Bladed Disk ◽  
Nonlinear Contact ◽  
Manufacturing Tolerances

Abstract One of the major sources of the damping of the forced vibration for bladed disk structures is the micro-slip motion at the contact interfaces of blade-disk joints. In this paper, the modeling strategies of nonlinear contact interactions at blade roots are examined using high-fidelity modelling of bladed disk assemblies and the nonlinear contact interactions at blade-disk contact patches. The analysis is performed in the frequency domain using multiharmonic harmonic balance method and analytically formulated node-to-node contact elements modelling frictional and gap nonlinear interactions. The effect of the number, location and distribution of nonlinear contact elements are analyzed using cyclically symmetric bladed disks. The possibility of using the number of the contact elements noticeably smaller than the total number of nodes in the finite element mesh created at the contact interface for the high-fidelity bladed disk model is demonstrated. The parameters for the modeling of the root damping are analysed for tuned and mistuned bladed disks. The geometric shapes of blade roots and corresponding slots in disks cannot be manufactured perfectly and there is inevitable root joint geometry variability within the manufacturing tolerances. Based on these tolerances, the extreme cases of the geometry variation are defined and the assessment of the possible effects of the root geometry variation on the nonlinear forced response are performed based on a set of these extreme cases.

Steady-State Characteristics of a Dual-Rotor System With Intershaft Bearing Subjected to Mass Unbalance and Base Motions

2018 ◽  
Author(s):  
Xi Chen ◽  
Mingfu Liao
Keyword(s):  
Steady State ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Axial Rotation ◽  
Rotor System ◽  
Mode Shapes ◽  
Mass Unbalance ◽  
Moving Base ◽  
Lateral Rotation ◽  
Force Vectors

A dual-rotor system with an intershaft bearing subjected to mass unbalance and base motions is established. Using Lagrange’s principle, equations of motion for dual-rotor system relative to moving base are derived. Rotary inertia, gyroscopic inertia, transverse shear deformation, mass unbalance, and six components of deterministic base motions are taken into account. Using state-space vector, steady-state characteristics of dual-rotor system are analyzed through dual-rotor critical speed map, mode shapes, unbalance responses considering base rotations, frequency responses due to base motions, and shaft orbits. The results show that base translations just add external force vectors, while base rotations bring on parametric system matrices and additional force vectors. Base rotations not only change natural frequencies of dual-rotor system, but also break the symmetry of dynamic characteristics in the case of base lateral rotation. Excited by base harmonic translation, resonant frequencies correspond to whirl frequencies. The orbit remains circular under base axial rotation, while it becomes elliptical with a static offset under lateral rotation and then a complicated curve due to harmonic translation. When harmonic frequency of base translation gets close to dual-rotor excitation frequencies, obvious beat vibration appears. Overrall, this flexible approach can ensure calculation accuracy with high efficiency and good expandability.

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 Forced Vibration of Delaminated Timoshenko Beams under the Action of Moving Oscillatory Mass

2013 ◽  
Vol 20 (1) ◽  
pp. 79-96 ◽  
Author(s):  
M.H. Kargarnovin ◽  
M.T. Ahmadian ◽  
R.A. Jafari-Talookolaei
Keyword(s):  
Dynamic Response ◽  
Forced Vibration ◽  
Equations Of Motion ◽  
Mode Shapes ◽  
Solution Technique ◽  
Timoshenko Beams ◽  
Modal Expansion ◽  
Forced Vibration Analysis ◽  
First Time ◽  
Moving Oscillator

This paper presents the dynamic response of a delaminated composite beam under the action of a moving oscillating mass. In this analysis the Poisson's effect is considered for the first time. Moreover, the effects of rotary inertia and shear deformation are incorporated. In our modeling linear springs are used between delaminated surfaces to simulate the dynamic interaction between sub-beams. To solve the governing differential equations of motion using modal expansion series, eigen-solution technique is used to obtain the natural frequencies and their corresponding mode shapes necessary for forced vibration analysis. The obtained results for the free and forced vibrations of beams are verified against reported similar results in the literatures. Moreover, the maximum dynamic response of such beam is compared with an intact beam. The effects of different parameters such as the velocity of oscillating mass, different ply configuration and the delamination length, its depth and spanwise location on the dynamic response of the beam are studied. In addition, the effects of delamination parameters on the oscillator critical speed are investigated. Furthermore, different conditions under which the detachment of moving oscillator from the beam will initiate are investigated.

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.

scholarly journals An Experimental Investigation of Vibration Localization in Bladed Disks: Part II — Forced Response

1997 ◽  
Author(s):  
Marlin J. Kruse ◽  
Christophe Pierre
Keyword(s):  
Experimental Investigation ◽  
Forced Response ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Structural Coupling ◽  
Vibration Localization ◽  
Bladed Disk ◽  
Engine Order ◽  
Localized Mode ◽  
The Impact

The results of an experimental investigation on the effects of random blade mistuning on the forced dynamic response of bladed disks are reported. Two experimental specimens are considered: a nominally periodic twelve-bladed disk with equal blade lengths, and the corresponding mistuned bladed disk, which features slightly different blades of random lengths. Both specimens are subject to traveling-wave excitations delivered by piezo-electric actuators. The primary aim of the experiment is to demonstrate the occurrence of an increase in forced response blade amplitudes due to mistuning, and to verify analytical predictions about the magnitude of these increases. In particular, the impact of localized mode shapes, engine order excitation, and disk structural coupling on the sensitivity of forced response amplitudes to blade mistuning is reported. This work reports one of the first systematic experiments carried out to demonstrate and quantify the effect of mistuning on the forced response of bladed disks.

Vibration Analysis of Shrouded Turbine Blades for a 30 MW Gas Turbine

2013 ◽  
Author(s):  
Ryoji Tamai ◽  
Ryozo Tanaka ◽  
Yoshichika Sato ◽  
Karsten Kusterer ◽  
Gang Lin ◽  
...  
Keyword(s):  
Contact Force ◽  
Vibration Analysis ◽  
Turbine Blades ◽  
Forced Response ◽  
Experimental Results ◽  
Mode Shapes ◽  
Contact Friction ◽  
The Real ◽  
Bladed Disk ◽  
Resonance Frequencies

Turbine blades are subjected to high static and dynamic loads. In order to reduce the vibration amplitude means of friction damping devices have been developed, e.g. damping wires, interblade friction dampers and shrouds. This paper presents both numerical and experimental results for investigating the dynamical behavior of shrouded turbine blades. The studies are focused on the lowest family of the bladed disk. The aspect of experimental studies, the effect of the shroud contact force on the resonance frequency of the blade was examined by using the simplified blade test stand. Based on the result of the simplified blade studies, the shroud contact force of the real blade was determined in order to stabilize the resonance frequencies of the bladed disk system. The resonance frequencies and mode shapes of the real bladed disk assembly were measured in no rotation and room temperature condition. Finally, the dynamic strains were measured in the actual engine operations by using a telemetry system. The aspect of analytical studies, a non-linear vibration analysis code named DATES was applied to predict vibration behavior of a shrouded blade model which includes contact friction surfaces. The DATES code is a forced response analysis code that employs a 3-dimensional friction contact model. The Harmonic Balance Method (HBM) is applied to solve resulting nonlinear equations of motion in frequency domain. The simulated results show a good agreement with the experimental results.

Sign in / Sign up

Export Citation Format

Share Document