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Research Papers

Reduced-Order Models of Blisks With Small Geometric Mistuning

[+] Author and Article Information
Seunghun Baek

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48104
e-mail: baeksh@umich.edu

Bogdan Epureanu

Professor
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: epureanu@umich.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 7, 2016; final manuscript received February 16, 2017; published online May 30, 2017. Assoc. Editor: John Yu.

J. Vib. Acoust 139(4), 041003 (May 30, 2017) (10 pages) Paper No: VIB-16-1071; doi: 10.1115/1.4036105 History: Received February 07, 2016; Revised February 16, 2017

A technique for generating reduced-order models (ROMs) of bladed disks with small geometric mistuning is proposed. Discrepancies in structural properties (mistuning) from blade to blade can cause a significant increase in the maximum vibratory stress. The effects of mistuning have been studied over the past few decades. Many researchers have studied the dynamic behavior of mistuned bladed disks by using ROMs. Many of these techniques rely on the fact that the modes of a mistuned system can be approximated by a linear combination of modes of the corresponding tuned system. In addition, the tuned system modes have been modeled in component mode mistuning by using modal participation factors of cantilevered blade modes. Such techniques assume that mistuning can be well modeled as variations in blade-alone frequencies. However, since geometric deformations contain stiffness and mass variations, mistuning can no longer be captured by cantilevered blade modes alone. To address this, several studies have focused on large and small geometric mistuning. These studies exploited the difference between tuned (with perturbed geometry) and nominal tuned mode shapes. In this work, we extend on that approach and devote particular attention to the development of ROMs of bladed disks with small geometric mistuning. The methodology requires only sector-level calculations and therefore can be applied to highly refined, realistic models of industrial size.

Copyright © 2017 by ASME
Topics: Disks , Blades , Modeling
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References

Figures

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Fig. 1

A finite element model of a blisk with geometric mistuning in blade numbers 3, 5, 9, 20, and 24

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Fig. 2

System frequencies of tuned and cyclic mistuned bladed disk system

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Fig. 3

Residuals at each transformation matrix

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Fig. 4

Top plots show full wheel modes (tuned left and cyclic mistuned right); bottom plots show axial direction, blade portion modes from two different sector models without phase alignment (left) and with phase alignment (right) (n = 1)

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Fig. 5

FE model of the academic blisks and the blade model at sector l

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Fig. 6

Tuned blade (left) and geometrically mistuned blade (right)

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Fig. 7

The first cantilevered blade frequency of each mistuned blade

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Fig. 8

The system frequencies (left) and the system frequency errors (right)

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Fig. 9

The ratio of the error in deviation calculated from the ROM (ΔfROM − ΔfAct) to the actual deviation (ΔfAct)

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Fig. 10

MAC plot (k, r = 1–100)

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Fig. 11

Mistuned response at the natural frequency of the sixth mode (1284.98 Hz), obtained by using full-order model, an ROM with four additional ΔΦ modes at each mistuned sector, and an ROM with eight additional ΔΦ modes at each mistuned sector

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Fig. 12

Forced responses predicted by the ROM and by the full-order FE model: (a) engine order one excitation, (b) six excitations, and (c) eight excitations

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Fig. 13

Young's modulus mistuning value along blade number

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Fig. 14

Frequency relative difference between the tuned and mistuned system (top), and system frequency errors (bottom)

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Fig. 15

Schematic of ROM procedure

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