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Research Papers: Gas Turbines: Structures and Dynamics

Optimization-Aided Forced Response Analysis of a Mistuned Compressor Blisk

[+] Author and Article Information
Bernd Beirow

Mem. ASME
Brandenburg University of Technology,
Siemens-Halske-Ring 14,
Cottbus D-03046, Germany
e-mail: beirow@tu-cottbus.de

Thomas Giersch

Brandenburg University of Technology,
Siemens-Halske-Ring 14,
Cottbus D-03046, Germany
e-mail: thomas.giersch@tu-cottbus.de

Arnold Kühhorn

Mem. ASME
Brandenburg University of Technology,
Siemens-Halske-Ring 14,
Cottbus D-03046, Germany
e-mail: kuehhorn@tu-cottbus.de

Jens Nipkau

Rolls-Royce Deutschland Ltd., & Co. KG,
Eschenweg 4,
Blankenfelde-Mahlow D-15827, Germany
e-mail: Jens.Nipkau@rolls-Royce.com

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 9, 2014; final manuscript received July 15, 2014; published online August 26, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(1), 012504 (Aug 26, 2014) (10 pages) Paper No: GTP-14-1335; doi: 10.1115/1.4028095 History: Received July 09, 2014; Revised July 15, 2014

The forced response of the first rotor of an engine 3E (technology program) (E3E)-type high pressure compressor (HPC) blisk is analyzed with regard to varying mistuning, varying engine order (EO) excitations and the consideration of aero-elastic effects. For that purpose, subset of nominal system modes (SNM)-based reduced order models are used in which the disk remains unchanged while the Young's modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient (AIC) technique is employed to model aero-elastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades' Young's modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aero-elastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the interblade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.

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References

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Figures

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Fig. 1

HPC of an E3E core engine demonstrator [20] with six rotors manufactured as blisks

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Fig. 2

FE-model, (a) whole blisk and (b) blisk sector

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Fig. 4

Experimental setup for mistuning ID

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Fig. 5

Additional masses and clamping device for the modal hammer

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Fig. 6

Experimentally determined frequency mistuning distribution (1F) [16]

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Fig. 7

Blade stiffness based mistuning pattern adjusted to blade by blade experiments

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Fig. 8

Amplification of maximum blade displacements due to measured mistuning (FSI neglected)

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Fig. 9

ODS of the worst forced response at EO 15 (FSI neglected)

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Fig. 10

Aerodynamic damping versus IBPA φ and ND, at MTO

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Fig. 11

Amplification of maximum blade displacements due to measured mistuning

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Fig. 12

ODS of the largest forced response at EO 26 (FSI included)

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Fig. 13

(a) Blade stiffness based mistuning pattern and (b) amplification of maximum blade displacements due to one blade mistuning

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Fig. 14

ODS at EO 28: (a) without AIC and (b) with AIC

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Fig. 15

(a) Blade stiffness based mistuning pattern and (b) amplification of maximum blade displacements due to alternating mistuning

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Fig. 16

(a) ODS at EO 12 (AIC included) and (b) DFT of ODS at EO 12 (alternating mistuning)

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Fig. 17

Resulting aerodynamic damping

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Fig. 18

(a) ODS at EO 25 (alias EO −4) with AIC included, (b) DFT of ODS at EO 25 (alternating mistuning)

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Fig. 19

Amplification of maximum blade displacements (maximum forced response optimization, FSI neglected)

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Fig. 20

(a) Optimized mistuning pattern according to maximized forced response at EO 19 (FSI not considered), (b) ODS, and (c) DFT of ODS

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Fig. 21

Maximized forced response amplification

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Fig. 22

(a) Optimized mistuning pattern according to maximized forced response at EO 12 (AIC included), (b) ODS, and (c) DFT of ODS

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Fig. 23

Resulting aerodynamic damping (maximized forced response)

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Fig. 24

Minimized forced response amplification

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Fig. 25

(a) Optimized mistuning pattern according to minimized forced response at EO 26 (alias EO −3), AIC included, (b) ODS, and (c) DFT of ODS

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Fig. 26

Resulting aerodynamic damping (minimized forced response)

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