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Research Papers: Gas Turbines: Structures and Dynamics

Mistuning Forced Response Characteristics Analysis of Mistuned Bladed Disks

[+] Author and Article Information
Haitao Liao, Jianjun Wang, Jianyao Yao, Qihan Li

School of Jet Propulsion, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

J. Eng. Gas Turbines Power 132(12), 122501 (Aug 20, 2010) (11 pages) doi:10.1115/1.4001054 History: Received June 25, 2009; Revised January 04, 2010; Published August 20, 2010; Online August 20, 2010

The problem of determining the worst-case mistuning pattern and robust maximum mistuning forced response of a mistuned bladed rotor is formulated and solved as an optimization problem. This approach is exemplified on a two-degrees-of-freedom per blade disk model, two three-degrees-of-freedom per blade disk models, and a mistuned two-stage bladed rotor. The results of the optimum search of the worst-case mistuning patterns for the lumped parameter models are analyzed, which reveals that the maximum blade forced response in a mistuned bladed disk is associated with mistuning jump, which causes strong localization of the vibration response in a particular blade. The mistuning jump-localization phenomenon has been observed for all of the numerical examples, and it is also demonstrated that the highest response was always experienced by a blade of mistuning value jump. The two- and three-degrees-of-freedom per blade disk models are also for determination of its sensitivity coefficients with respect to mistuning variation. Studies show that there is not a threshold of mistuning beyond which the maximum forced response levels off, or even drops, as the degree of mistuning is increased further. The maximum magnification factor is found to increase as the mistuning level is increased and reaches a maximum value at the upper limit of the mistuning level. The influence of the multistage coupling is revealed by comparing the results of single-stage analysis with that of the multistage case. The computed results have been compared with the Monte Carlo simulation produced, and it is demonstrated that the accuracy and efficiency of the maximum amplitude magnification factor computed by the presented method can be better than that of Monte Carlo simulations.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 8

Forced response of the worst-case bladed disk when the blade mass and stiffness is mistuned: (a) stiffness mistuned; (b) mass mistuned

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Figure 12

Natural frequencies of tuned rotor nos. 1 and 2

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Figure 13

Blade response of tuned rotor nos. 1 and 2

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Figure 14

The worst-case mistuning pattern for the isolated rotor nos. 1 and 2

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Figure 15

Forced response for each blade of the worst-case mistuning pattern shown in Fig. 1 (isolated rotor no. 1)

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Figure 16

Forced response for each blade of the worst-case mistuning pattern shown in Fig. 1 (isolated rotor no. 2)

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Figure 17

Maximum amplitude magnification factor as a function of mistuning strength

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Figure 18

Frequency response of the tuned two-stage rotor

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Figure 19

The worst-case mistuning pattern for the two-stage bladed disk

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Figure 1

Geometrical interpretation of search spaces

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Figure 2

Flowchart of the GA-SQP hybrid algorithm

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Figure 3

Lumped-parametric model of a bladed disk

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Figure 4

Natural frequencies of the bladed disk

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Figure 5

Frequency response of the tuned bladed disk

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Figure 6

Maximum amplitude magnification progress with evaluations

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Figure 7

The worst-case mistuning pattern

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Figure 9

Statistical distribution of the peak maximum amplitude when the blade mass or stiffness is mistuned: (a) mass mistuned; (b) stiffness mistuned

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Figure 10

Maximum amplitude magnification as a function of mistuning strength

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Figure 11

Model of the two-stage rotor: (a) model of rotor stage no. 1; (b) model of rotor stage no. 2

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Figure 20

Forced response for each blade of the worst mistuning shown in Fig. 1 (stage no. 1)

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Figure 21

Forced response for each blade of the worst mistuning shown in Fig. 1 (stage no. 2)

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Figure 22

Statistical distribution of the peak maximum amplitude

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