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Research Papers

Reduced-Order Modeling for Stability and Steady-State Response Analysis of Asymmetric Rotor Using Three-Dimensional Finite Element Model

[+] Author and Article Information
Zhaoli Zheng

Key Laboratory of Thermo-Fluid
Science and Engineering,
Ministry of Education,
School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an, Shaanxi Province 710049, China
e-mail: 18974267525@163.com

Yonghui Xie

Shaanxi Engineering Laboratory of
Turbomachinery and Power Equipment,
School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an, Shaanxi Province 710049, China
e-mail: yhxie@mail.xjtu.edu.cn

Di Zhang

Key Laboratory of Thermo-Fluid
Science and Engineering,
Ministry of Education,
School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an, Shaanxi Province 710049, China
e-mail: zhang_di@mail.xjtu.edu.cn

1Corresponding author.

Manuscript received June 25, 2019; final manuscript received June 28, 2019; published online July 22, 2019. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(10), 101001 (Jul 22, 2019) (9 pages) Paper No: GTP-19-1328; doi: 10.1115/1.4044217 History: Received June 25, 2019; Revised June 28, 2019

A generalized and efficient technique of reduced-order model (ROM) is proposed in this paper for stability and steady-state response analysis of an asymmetric rotor based on three-dimensional (3D) finite element model. The equations of motion of the asymmetric rotor-bearing system are established in the rotating frame. Therefore, the periodic time-variant coefficients only exist at a tiny minority of degrees-of-freedom (DOFs) of bearings. During the model reduction process, the asymmetric rotor-bearing system is divided into rotor and bearings. Only the rotor was reduced. And the physical coordinates of bearings are kept in the reduced model during reduction. Then, the relationship between the rotor and bearings is established by inserting periodic time-variant stiffness and damping matrix of bearings into the reduced model of rotor. There is no reduction to the matrices of bearings, which guarantees the accuracy of the calculation. This technique combined with fixed-interface component mode synthesis (CMS) and free-interface CMS is compared with other existing modal reduction method on an off-center asymmetric rotor and shows good performance.

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References

Huang, S. , Liu, Z. , and Su, J. , “ On Double Frequency Vibration of a Generator-Bearing System With Asymmetrical Stiffness,” ASME Paper No. IMECE2002-39229.
Sayed, M. , and Kamel, M. , 2011, “ Stability Study and Control of Helicopter Blade Flapping Vibrations,” Appl. Math. Modell., 35(6), pp. 2820–2837. [CrossRef]
Sanches, L. , Michon, G. , Berlioz, A. , and Alazard, D. , 2011, “ Instability Zones for Isotropic and Anisotropic Multibladed Rotor Configurations,” Mech. Mach. Theory, 46(8), pp. 1054–1065. [CrossRef]
Al-Shudeifat, M. A. , 2013, “ On the Finite Element Modeling of the Asymmetric Cracked Rotor,” J. Sound Vib., 332(11), pp. 2795–2807. [CrossRef]
Han, Q. , and Chu, F. , 2012, “ Parametric Instability of a Rotor-Bearing System With Two Breathing Transverse Cracks,” Eur. J. Mech.—A/Solids, 36, pp. 180–190. [CrossRef]
Ebrahimi, A. , Heydari, M. , and Behzad, M. , 2014, “ A Continuous Vibration Theory for Rotors With an Open Edge Crack,” J. Sound Vib., 333(15), pp. 3522–3535. [CrossRef]
Boru, F. E. , 2010, Numerical and Experimental Response and Stability Investigations of Anisotropic Rotor-Bearing Systems, Kassel University Press GmbH, Kassel, Germany.
Nandi, A. , and Neogy, S. , 2005, “ An Efficient Scheme for Stability Analysis of Finite Element Asymmetric Rotor Models in a Rotating Frame,” Finite Elem. Anal. Des., 41(14), pp. 1343–1364. [CrossRef]
Kang, Y. , Shih, Y. P. , and Lee, A. C. , 1992, “ Investigation on the Steady-State Responses of Asymmetric Rotors,” ASME J. Vib. Acoust., 114(2), pp. 194–208. [CrossRef]
Brosens, P. J. , and Crandall, S. H. , 1961, “ Whirling of Unsymmetrical Rotors,” ASME J. Appl. Mech., 28(3), pp. 355–362. [CrossRef]
Crandall, S. H. , and Brosens, P. J. , 1961, “ On the Stability of Rotation of a Rotor With Rotationally Unsymmetric Inertia and Stiffness Properties,” ASME J. Appl. Mech., 28(4), pp. 567–849. [CrossRef]
Yamamoto, T. , and Ōta, H. , 1964, “ On the Unstable Vibrations of a Shaft Carrying an Unsymmetrical Rotor,” ASME J. Appl. Mech., 31(3), pp. 515–522. [CrossRef]
Yamamoto, T. , and Ota, H. , 1967, “ The Damping Effect on Unstable Whirlings of a Shaft Carrying an Unsymmetrical Rotor,” Memoirs of the Faculty of Engineering Nagoya University, 19(2), pp. 197–215.
Bishop, R. E. D. , and Parkinson, A. G. , 1965, “ Second Order Vibration of Flexible Shafts,” Philos. Trans. R. Soc. B Biol. Sci., 259(1095), pp. 1–31. [CrossRef]
Inagaki, T. , Kanki, H. , and Shiraki, K. , 1980, “ Response Analysis of a General Asymmetric Rotor-Bearing System,” ASME J. Mech. Des., 102(1), pp. 147–157. [CrossRef]
Kang, Y. , Lee, A. C. , and Shih, Y. P. , 1994, “ A Modified Transfer Matrix Method for Asymmetric Rotor-Bearing Systems,” ASME J. Appl. Mech., 58(3), pp. 309–317.
Kang, Y. , Lee, Y. G. , and Chen, S. C. , 1997, “ Instability Analysis of Unsymmetrical Rotor-Bearing Systems Using the Transfer Matrix Method,” J. Sound Vib., 199(3), pp. 381–400. [CrossRef]
Genta, G. , 1988, “ Whirling of Unsymmetrical Rotors: A Finite Element Approach Based on Complex Co-Ordinates,” J. Sound Vib., 124(1), pp. 27–53. [CrossRef]
Jei, Y. G. , and Lee, C. W. , 1988, “ Finite Element Model of Asymmetrical Rotor-Bearing Systems,” Ksme J., 2(2), pp. 116–124. [CrossRef]
Jei, Y. G. , and Lee, C. W. , 1992, “ Modal Analysis of Continuous Asymmetrical Rotor Bearing Systems,” J. Sound Vib., 152(2), pp. 245–262. [CrossRef]
Rao, J. , and Sreenivas, R. , 2003, “ Dynamics of Asymmetric Rotors Using Solid Models,” International Gas Turbine Congress, Tokyo, Japan, Nov. 2–7, pp. 2–7.
Zuo, Y. , Wang, J. , and Ma, W. , 2017, “ Quasimodes Instability Analysis of Uncertain Asymmetric Rotor System Based on 3D Solid Element Model,” J. Sound Vib., 390, pp. 192–204. [CrossRef]
Lee, C.-W. , Han, D.-J. , Suh, J.-H. , and Hong, S.-W. , 2007, “ Modal Analysis of Periodically Time-Varying Linear Rotor Systems,” J. Sound Vib., 303(3–5), pp. 553–574. [CrossRef]
Ma, W. M. , Wang, J. J. , and Wang, Z. , 2015, “ Frequency and Stability Analysis Method of Asymmetric Anisotropic Rotor-Bearing System Based on Three-Dimensional Solid Finite Element Method,” ASME J. Eng. Gas Turbines Power, 137(10), p. 102502. [CrossRef]
Nandi, A. , 2004, “ Reduction of Finite Element Equations for a Rotor Model on Non-Isotropic Spring Support in a Rotating Frame,” Finite Elem. Anal. Des., 40(9–10), pp. 935–952. [CrossRef]
Lazarus, A. , Prabel, B. , and Combescure, D. , 2010, “ A 3D Finite Element Model for the Vibration Analysis of Asymmetric Rotating Machines,” J. Sound Vib., 329(18), pp. 3780–3797. [CrossRef]
Wang, S. , Wang, Y. , Zi, Y. , and He, Z. , 2015, “ A 3D Finite Element-Based Model Order Reduction Method for Parametric Resonance and Whirling Analysis of Anisotropic Rotor-Bearing Systems,” J. Sound Vib., 359, pp. 116–135. [CrossRef]
Bampton, M. C. C. , and Craig, R. R., Jr. , 1968, “ Coupling of Substructures for Dynamic Analyses,” AIAA J., 6(7), pp. 1313–1319. [CrossRef]
Hintz, R. M. , 1975, “ Analytical Methods in Component Modal Synthesis,” AIAA J., 13(8), pp. 1007–1016. [CrossRef]
Rubin, S. , 1975, “ Improved Component-Mode Representation for Structural Dynamic Analysis,” AIAA J., 13(8), pp. 995–1006. [CrossRef]

Figures

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Fig. 1

The eight-coefficient journal bearing model

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Fig. 2

Three-dimensional finite element model of an off-center asymmetric rotor

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Fig. 3

The real part of the eigenvalues versus rotational speed: (a) isotropic system and (b) anisotropic system

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Fig. 4

The transverse amplitudes of anisotropic system versus the number of harmonics in Hill's method

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Fig. 5

The transverse amplitudes versus rotational speed: (a) isotropic system and (b) anisotropic system

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Fig. 6

The amplitudes of each harmonic component versus rotational speed: (a) isotropic system and (b) anisotropic system

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Fig. 7

The relative error of amplitudes of each harmonic component versus rotational speed: (a) 1 × harmonics, (b) 2 × harmonics, (c) 3 × harmonics, and (d) 4 × harmonics

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