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Journal of Mechanical Science and Technology

, Volume 33, Issue 9, pp 4183–4190 | Cite as

Rotordynamic analysis and operation test of the power turbine with the concept of the Lee diagram

  • Donghyun LeeEmail author
  • Yun-Ho Seo
  • Hyungsoo Lim
  • Jongho Seo
Article
  • 8 Downloads

Abstract

Rotordynamic analysis in complex coordinates has many advantages. Especially, the Lee diagram, with the concept of the infinity norm in directional frequency response matrix, can an effective design tool for rotating machinery, because the severity of the mode is clearly identified, and it also includes the concept of the worst case response prediction. However, it is not widely used in the field because most of the previous studies and commercial software are based on the real coordinate system. Our objective was to apply the Lee diagram to analyze rotordyanmic characteristics of the power turbine, which is a typical example of turbomachinery. We show that this could be a useful design tool for rotating machinery. The power turbine in this study was used for the super critical carbon dioxide power generation system and the rotor was supported by tilting pad bearings. The equation of motion of the rotor and bearing system was derived in the complex coordinate system. The Lee diagram was calculated with the concept of the infinity norm and unbalance response was predicted. The operation test of the power turbine was done with compressed air, and the rotor vibration was measured with the proximity probes. The results of the analysis show that the resonance speed can be effectively estimated with the Lee diagram and the degree of the anisotropy of the system can be identified. The operation test was done successfully and the measured maximum rotor vibration was about 5 μm. In addition, the measured rotor vibration shows that the anisotropy of the power turbine is very small as predicted, and the predicted vibration amplitude shows good agreement with the test data.

Keywords

Lee diagram Rotordynamic Complex coordinate 

Nomenclature

A,B

System matrix in generalized state-space form

C

Damping matrix

f(t)

Force vector

fx(t), fy(t)

Force components in the real coordinates

G()

Fourier transformation of g(t)

g(t)

Force vector in the complex coordinates

H()

Frequency response matrix

K

Stiffness matrix

M

Mass matrix

P()

Fourier transformation of p(t)

p(t)

Response vector in the complex coordinates

q(t)

Response vector

r

Eigen vector in state-space form

u

Modal vector

v

Adjoint vector

w

State vector

x(t), y(t)

Displacement components in the real coordinates

λ

Eigen value

η

Principal coordinates

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Notes

Acknowledgments

This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) Grants No. 20182010106640 (Development of an energy saving 1,000 HP VSD turbo air compressor) and 20163030024510 (Development of a condition monitoring and diagnosis system for wind turbine generator system) funded by the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea.

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Copyright information

© KSME & Springer 2019

Authors and Affiliations

  • Donghyun Lee
    • 1
    Email author
  • Yun-Ho Seo
    • 1
  • Hyungsoo Lim
    • 2
  • Jongho Seo
    • 1
  1. 1.Department of System DynamicsKorea Institute of Machinery and MaterialsDaejeonKorea
  2. 2.Department of Energy Conversion SystemKorea Institute of Machinery and MaterialsDaejeonKorea

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