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Research Papers

Reduced Order Models for Blade-To-Blade Damping Variability in Mistuned Blisks

[+] Author and Article Information
Anish G. S. Joshi

Vibrations and Acoustics Laboratory, Department of Mechanical Engineering,  University of Michigan, Ann Arbor, MI 48109ajozi@umich.edu

Bogdan I. Epureanu

Vibrations and Acoustics Laboratory, Department of Mechanical Engineering,  University of Michigan, Ann Arbor, MI 48109epureanu@umich.edu

J. Vib. Acoust 134(5), 051015 (Sep 07, 2012) (9 pages) doi:10.1115/1.4006880 History: Received February 25, 2011; Revised April 25, 2012; Published September 07, 2012; Online September 07, 2012

A novel reduced order modeling methodology to capture blade-to-blade variability in damping in blisks is presented. This new approach generalizes the concept of component mode mistuning (CMM), which was developed to capture stiffness and mass mistuning (and did not include variability in damping among the blades). This work focuses on modeling large variability in damping. Such variability is significant in many applications and particularly important for modeling damping coatings. Similar to the CMM based studies, structural damping is used to capture the damping effects due to the mechanical energy dissipation caused by internal friction within the blade material. The steady state harmonic responses of the blades are obtained using the novel reduced order modeling methodology and are validated by comparison with simulation results obtained using a full order model in ANSYS with a maximum amplitude error of 0.3%. It is observed that there is no strong correlation between the engine order of excitation and both the variation in the response from blade to blade and the blade amplification factors. The effects of damping mistuning are studied statistically through Monte Carlo simulations. For this purpose, the blisk model is subjected to multiple traveling wave excitations. The uncertainty in the various mechanisms responsible for dissipation of energy and the uncontrollability of these dissipation mechanisms makes it difficult to assign a reliable value for the loss factor of each blade. Hence, large variations (up to ±80%) in the structural damping coefficients of the blades are simulated.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Finite element model of the blisk

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Figure 2

One of the blades, the node being forced, and the node at which displacement is calculated

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Figure 3

Natural frequencies versus nodal diameter for the tuned blisk (ANSYS results)

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Figure 4

Damping mistuning pattern

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Figure 5

Normalized amplitude of one node per blade versus corresponding structural damping coefficient for each blade using the novel ROM (*) and using ANSYS (O-) with damping mistuning. (a) Engine order excitation 2. (b) Engine order excitation 5.

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Figure 6

Normalized amplitude of one node per blade versus corresponding structural damping coefficient for each blade using novel ROM

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Figure 7

Variation in the normalized amplitude of all blades versus engine order excitation

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Figure 8

Comparison of results obtained using the novel ROM and the results obtained using ANSYS when both stiffness and damping mistuning are present. (a) Engine order excitation 2. (b) Engine order excitation 5.

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Figure 9

Stiffness mistuning pattern showing the stiffness mistuning fractions for each blade

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Figure 10

Results obtained using the novel ROM for statistical analysis. Results for engine order 2 are shown. The lines of mean value, standard deviation from the mean, and the 99th percentile of the blade amplification factor at all values of standard deviation are shown.

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Figure 11

Probability distribution functions for four different values of the standard deviation of blade damping

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Figure 12

Blisk with 24 blades: lines of median blade amplification factors versus standard deviation of mistuning pattern for all engine order excitations

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Figure 13

Blisk with 23 blades: lines of median blade amplification factors versus standard deviation of mistuning pattern for all engine order excitations

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