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Research Papers: Gas Turbines: Structures and Dynamics

A Method to Reduce the Energy Localization in Mistuned Bladed Disks by Application-Specific Blade Pattern Arrangement

[+] Author and Article Information
Andreas Hohl

Institute for Dynamics and Vibration Research,
Gottfried Wilhelm Leibniz Universität Hannover,
Hannover 30167, Germany
e-mail: andreas.hohl@gmx.net

Jörg Wallaschek

Institute for Dynamics and Vibration Research,
Gottfried Wilhelm Leibniz Universität Hannover,
Hannover 30167, Germany

1Corresponding author.

2Present address: Baker Hughes Drilling Services, Celle 29221, Germany.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received November 27, 2015; final manuscript received January 15, 2016; published online March 22, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(9), 092502 (Mar 22, 2016) (10 pages) Paper No: GTP-15-1546; doi: 10.1115/1.4032739 History: Received November 27, 2015; Revised January 15, 2016

The focus of the paper is the analysis of mistuning, which are small deviations of the blade properties, e.g., due to manufacturing tolerances. The resonant amplitudes of turbine blades are very sensitive to these deviations which can lead to significantly increased vibratory response of some blades with the increased risk of high cycle fatigue. The main part of the paper discusses about the methods that can be used to find blade patterns which are insensitive to energy localization. The sensitivity of the forced response against harmonic mistuning, which is a harmonic alignment of the blades respective to the mistuning factors of the single blades, is examined. A previously developed reduced order model (ROM) is used to efficiently conduct Monte Carlo simulations (MCSs). Especially the influence of the variance of the harmonically mistuned blade patterns is discussed. On the basis of this analysis, rules are developed to suppress the energy localization. The rules are mainly focused on the alignment of the blades around the bladed disk. The approach also takes advantage of the special properties of harmonic mistuning patterns. An assignment of the blades to insensitive harmonic mistuning patterns with a specific variance and number of periods is used to reduce the maximum of the amplification factor of the forced response. A similar approach uses intentional mistuning patterns with different blade types which are aligned harmonically and are insensitive to an additional stochastic mistuning. In case of specific combinations of the dependent parameters, especially the variance of the mistuning factors and the number of periods, the energy localization can be reduced considerably.

Copyright © 2016 by ASME
Topics: Disks , Blades , Resonance
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References

Figures

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Fig. 1

Finite element model of a full bladed disk

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Fig. 2

Finite element models of the substructures of the disk and the blades and the coupling DOF

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Fig. 3

Flow diagram to derive the ROM of the bladed disk

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Fig. 4

Disk segment with cyclic symmetry constraints and blade substructure

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Fig. 5

Nodal diameter diagram of bladed disk (Fig. 1)

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Fig. 6

FRF for the three blades ABC for the dominant excited modes (ND = 5) of the first family of modes (first bending) and different variances of the mistuning pattern

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Fig. 7

Maximum resonance amplitudes of the three blades ABC as function of the variance of the mistuning pattern

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Fig. 8

Comparison between the mistuning pattern with H = 2 ⋅ EO = 10 harmonics and the worst case amplitude determined with an optimization approach as function of the variance of the mistuning pattern

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Fig. 9

Maximum resonance amplitude for uneven harmonics H = 1 to H = 13 as a function of the variance of the mistuning pattern

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Fig. 10

Maximum resonance amplitude for even harmonics H = 8 to H = 14 as a function of the variance of the mistuning pattern

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Fig. 11

Lower and upper envelope of maximum resonance amplitudes of all harmonics H = 1 to H = 14

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Fig. 19

Quantiles calculated for different deterministic variances Var(δint)=sint2 and an additional constant variance with Var(δsto) = 10−4 by MCSs with and without assignment to a deterministic blade pattern with H = 9 harmonics and an excitation with EO = 5. Comparison to exact harmonic blade pattern.

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Fig. 18

Quantiles calculated for different deterministic variances Var(δint)=sint2 with H = 10 and an additional constant variance Var(δsto) = 10−6 and Var(δsto) = 10−4 by MCSs and an excitation with EO = 5. Comparison to exact harmonic blade pattern.

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Fig. 17

Quantiles calculated for different deterministic variances Var(δint)=sint2 with H = 10 and an additional constant variance Var(δsto) = 10−7 and Var(δsto) = 10−5 by MCSs and an excitation with EO = 5. Comparison to exact harmonic blade pattern.

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Fig. 16

Procedure for intentional mistuning of blades to reduce the amplitude amplification

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Fig. 15

Procedure for arrangement of blades to reduce the amplitude amplification due to mistuning

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Fig. 14

Quantiles calculated for different variances Var(δ) = s2 by MCSs with and without assignment to a deterministic blade pattern with H = 1 (top) and H = 2 (bottom) harmonics and an excitation with EO = 12. Comparison to exact harmonic blade pattern.

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Fig. 13

Quantiles calculated for different variances Var(δ) = s2 by MCSs with and without assignment to a deterministic blade pattern with H = 10 (three blades ABC, top) and H = 12 (bottom) harmonics and an excitation with EO = 5. Comparison to exact harmonic blade pattern.

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Fig. 12

Example of the assignment of a specific blade pattern (crosses) to a harmonic blade pattern with H = 10 harmonics (black curve)

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