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Research Papers

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

[+] Author and Article Information
T. Klauke

 BTU Cottbus, Siemens-Halske-Ring 14, 03046 Cottbus, Germanythomas.klauke@tu-cottbus.de

A. Kühhorn, B. Beirow, M. Golze

 BTU Cottbus, Siemens-Halske-Ring 14, 03046 Cottbus, Germany

Or integrated bladed rotor (IBR).

German research program aiming at new HPC technologies, 3E=efficiency, economy, and environment.

Diametric nodal lines: nodal diameters (ND), concentric nodal lines: nodes circles.

In case of the CSM 0, only a single eigenvalue occurs.

If the number of blades is even, the CSMmax has a single eigenvalue only.

If CSM=CSMmax, all blades oscillate in counter phase to each other.

If the disk displacement can be disabled (which means a complete decoupling of blades and disk), the blade alone frequency (also called as single blade frequency) can be determined for an infinite stiff clamping, respectively.

Blisk vibration modes with a low number of nodal diameters are often exceptional cases in cases of free boundary conditions.

In case of multishaft aeroengine with different rpm.

In case of 1<CSM<CSMmax.

Due to many restrictions, the maximum number of strain gauges on blades per rotor is limited to 69. Thus only blades with high blade amplitudes are suitable to achieve a sufficient signal-to-noise ratio during vibration monitoring.

Caused by the airflow around the blades.

In-phase and counter-phase-blade-vibrations of tuned and mistuned bladed disks result in additional aerodynamic forces and aerodynamic damping due to the compression of the flow between the vibrating blades.

In case of blisks, only the material damping occurs because of the missing blade-disk-connection.

J. Turbomach 131(3), 031002 (Apr 02, 2009) (11 pages) doi:10.1115/1.2985074 History: Received January 29, 2007; Revised August 15, 2008; Published April 02, 2009

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.

Copyright © 2009 by American Society of Mechanical Engineers
Topics: Vibration , Disks , Blades
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References

Figures

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Figure 8

Influence of different blade mistuning levels on vibration modes (first torsion modes, (M)CSMs 1; left: displacement amplitudes; right: normalized axial displacements at each leading edge blade tip)

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Figure 9

FRFs of blade No. 6 for different mistuning levels, EO 1, first torsion mode, magnitude amplification of axial displacements at leading edge blade tip, D=1.0%(Q=500)

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Figure 10

Left: normalized axial blade displacements at all leading edge blade tips of CSM 1 (tuned system, torsion mode); right: Fourier decomposition of the vibration mode

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Figure 11

Left: normalized axial blade diplacements at all leading edge blade tips (torsion mode, mistuned system); right: Fourier decomposition of the vibration mode σmistuning=0.68%

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Figure 12

Normalized axial blade displacements at all leading edge blade tips of CSM 1 (left) and MCSM 1 (right), first torsion modes

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Figure 13

Localization factors of natural vibrations depending on the blade mistuning standard deviation of first torsion modes 1-sine-wave mistuning distribution around blisk circumference

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Figure 14

Localization factors of natural vibrations depending on the blade mistuning standard deviation (first three blade modes) 1-sine-wave mistuning distribution around blisk circumference

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Figure 15

Maximum localization factors of the first three blade modes depending on the blade mistuning standard deviation; (⋯) first flap mode, (---) second flap mode, (—) first torsion mode, average of three artificial sine-wave blade mistuning distributions

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Figure 16

Localization factor versus mode fill factor of natural vibrations, 1-sine-wave mistuning distribution around blisk circumference, σmistuning=0.24%

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Figure 17

Localization factor versus mode fill factor of the first torsion mode depending on the mistuning level, 1-sine-wave mistuning distribution around blisk circumference

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Figure 18

Percentage of blades on total blisk strain energy of natural vibrations depending on the blade mistuning standard deviation of first torsion mode, 1-sine-wave mistuning distribution around blisk circumference

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Figure 19

Localization factor versus percentage of blades on total blisk strain energy of natural vibrations depending, 1-sine-wave mistuning distribution around blisk circumference, σmistuning=0.24%

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Figure 20

Percentage of blades on total blisk strain energy compared to the resulting averaged localization factor of natural vibrations depending on the disk stiffness; (⋯, white dotted) first flap mode, (---, grey dotted) second flap mode, (—, black dotted) first torsion mode, average of three artificial sine-wave mistuning distributions

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Figure 21

Localization factor versus percentage of blades on total blisk strain energy depending on the disk stiffness; (⋯) first flap mode, (---) second flap mode, (—) first torsion mode, average of three artificial sine-wave mistuning distributions

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Figure 22

Maximum localization factor (—) of first torsion modes versus maximum amplitude magnification factor (⋯) depending on the mistuning level, forced response analysis, D=0.1%(Q=500), EO CSMmax, 1 sine-wave mistuning distribution

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Figure 23

Maximum localization factor (—) and amplitude magnification (⋯) depending on the damping value, forced response analysis for EO 1, σmistuning=0.68%, 1 sine-wave mistuning, first torsion mode

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Figure 24

Maximum axial blade amplitude depending on the disk stiffness, first torsion mode, tuned system, D=0.1%(Q=500), (⋯) EO/CSM 1, (---) EO/CSM 4, (—) EO/CSM 12 (CSMmax)

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Figure 7

Measured blade eigenfrequency deviations of Engine 3E HPC Rotor 1, (⋯) first flap mode, (---) second flap mode, (—) first torsion mode

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Figure 6

Different artificial sinusoidal mistuning distributions caused by blade Young’s modulus modification of Engine 3E HPC Rotor 1

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Figure 5

Enlarged section of the coupling diagram compared to the blade’s contributions to the total blisk strain energy, first torsion modes, free boundary conditions

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Figure 4

Coupling diagram of Engine 3E HPC Stage 1, illustration of the first three blade modes, free boundary conditions

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Figure 3

Fundamental blade vibration modes (first flap mode (left), second flap mode (middle), first torsion mode (right)), fixed sector model, magnitude of displacements

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Figure 2

Disk-dominated vibration mode (CSM 2, 731.2Hz; displacement magnitude (left), normalized axial displacements at all blade tips (right), Engine 3E HPC Rotor 1)

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Figure 1

Vibration mode characterization using the blade’s contribution to the total blisk strain energy (mean value of double eigenmodes)

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Figure 26

Maximum amplitude magnification depending on the disk stiffness, mistuned system (σmistuning=0.68%), D=0.1%(Q=500), (⋯) first flap mode, (---) second flap mode, (—) first torsion mode, averaged values of EO 1, EO 4, EO 12 (CSMmax) excitation and three artificial sinusoidal mistuning distributions

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Figure 25

Maximum localization factor depending on the disk stiffness, mistuned system (σmistuning=0.68%), D=0.1%(Q=500), (⋯) first flap mode, (---) second flap mode, (—) first torsion mode, averaged values of EO 1, EO 4, EO 12 (CSMmax) excitation and three artificial sinusoidal mistuning distributions

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