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Research Papers

Vibration Absorbers for a Mistuned Bladed Disk

[+] Author and Article Information
Alok Sinha

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: axs22@psu.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 15, 2016; final manuscript received February 27, 2018; published online April 16, 2018. Assoc. Editor: John Judge.

J. Vib. Acoust 140(5), 051002 (Apr 16, 2018) (8 pages) Paper No: VIB-16-1400; doi: 10.1115/1.4039539 History: Received August 15, 2016; Revised February 27, 2018

Mistuning refers to variations in modal properties of blades due to manufacturing tolerances and material defects. This can result in the amplification of a blade vibratory amplitude. This paper deals with the design of vibration absorbers for a mistuned bladed disk. First, the basic theory is established for undamped vibration absorbers using a single-mode model for each blade. Then, it is extended to include a multiple mode model of each blade and disk dynamics. The impact of mistuning on the bladed disk vibration is examined in the presence of undamped absorbers via Monte Carlo simulations. It is found that vibration absorbers can be an effective method to counter the detrimental effects of mistuning.

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References

Sinha, A. , 2017, Vibration of Nearly Periodic Structures and Mistuned Bladed Rotors, Cambridge University Press, Cambridge, UK. [CrossRef]
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Murthy, R. , and Mignolet, M. P. , 2012, “ Decreasing Bladed Disk Response With Dampers on a Few Blades—Part I: Optimization Algorithms and Blade-Only Dampers Applications,” ASME Paper No. GT2012-69789.
Den Hartog, J. P. , 1984, Mechanical Vibrations, Dover Publication, Mineola, NY.
Sinha, A. , 2010, Vibration of Mechanical Systems, Cambridge University Press, New York. [CrossRef]
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Gozen, S. , Olson, B. J. , Shaw, S. W. , and Pierre, C. , 2012, “ Resonance Suppression in Multi-Degree-of-Freedom Rotating Flexible Structures Using Order-Tuned Absorbers,” ASME J. Vib. Acoust., 134(6), p. 061016. [CrossRef]
Sinha, A. , 2008, “ Mistuning Analyses of a Bladed Disk: Pole-Zero and Modal Approaches,” ASME Paper No. GT2008-50191.
Kenyon, J. A. , Griffin, J. H. , and Kim, N. E. , 2005, “ Sensitivity of Tuned Bladed Disk Response to Frequency Veering,” ASME J. Eng. Gas Turbines Power, 127(4), pp. 835–842. [CrossRef]
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MathWorks, 2015, “Matlab Toolbox,” The MathWorks Inc., Natick, MA.
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Figures

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Fig. 1

One degree-of-freedom per sector model with vibration absorbers

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Fig. 2

Equivalent sector model for Fig. 1 without mistuning

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Fig. 3

Two degrees-of-freedom per sector model with vibration absorbers

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Fig. 4

Equivalent single sector model for Fig. 3 without mistuning

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Fig. 5

Nondimensional peak maximum amplitude without vibration absorber (model# 1, r = 1, std. dev. = 10,000)

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Fig. 6

Nondimensional peak maximum amplitude with vibration absorber (model# 1, r = 1, std. dev. = 10,000)

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Fig. 7

Nondimensional peak maximum absorber amplitude with vibration absorber (model# 1, r = 1, std. dev. = 10,000)

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Fig. 8

Pole-zero map of perfectly tuned transfer function (model# 1)

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Fig. 9

Nondimensional natural frequencies for each of 6 tuned systems with optimal absorber stiffness (model# 1)

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Fig. 10

Nodal diameter map for model# 2

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Fig. 11

Nondimensional peak maximum amplitude without vibration absorber (model# 2, r = 4, lower natural frequency)

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Fig. 12

Nondimensional peak maximum amplitude with vibration absorber (model# 2, r = 4, lower natural frequency)

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Fig. 13

Nondimensional peak maximum absorber amplitude with vibration absorber (model# 2, r = 4, lower natural frequency)

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Fig. 14

Nondimensional resonant amplitudes for absorber designed on the basis of each of 13 tuned natural frequency (model# 2, ma=0.1m1)

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Fig. 15

Tuned absorber stiffness for each of 13 nodal diameters and optimal absorber stiffness (model# 2)

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Fig. 16

Nondimensional resonant amplitude for optimal absorber (model# 2, ma=0.1m1, x1:×, x2:  o)

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Fig. 17

Equivalent sector model with vibration absorbers without mistuning (three degrees-of-freedom per sector model of bladed disk)

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