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Research Papers

Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Bulk-Flow Analysis: Influence of Static Eccentricity and Whirling Amplitude

[+] Author and Article Information
Koya Yamada

Mem. ASME
Department of Mechanical Systems Engineering,
Nagoya University,
Furo-cho, Chikusa-ku,
Nagoya 464-8603, Japan
e-mail: k_yamada@nuem.nagoya-u.ac.jp

Atsushi Ikemoto

Department of Mechanical Systems Engineering,
Nagoya University,
Furo-cho, Chikusa-ku,
Nagoya 464-8603, Japan

Tsuyoshi Inoue

Mem. ASME
Department of Mechanical Systems Engineering,
Nagoya University,
Furo-cho, Chikusa-ku,
Nagoya 464-8603, Japan
e-mail: inoue.tsuyoshi@nagoya-u.jp

Masaharu Uchiumi

Mem. ASME
Muroran Institute of Technology,
27-1 Mizumoto-cho,
Muroran 050-8585, Hokkaido, Japan
e-mail: uchiumi@mmm.muroran-it.ac.jp

1Corresponding author.

Manuscript received July 2, 2018; final manuscript received July 17, 2018; published online October 4, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(2), 021017 (Oct 04, 2018) (8 pages) Paper No: GTP-18-1412; doi: 10.1115/1.4041128 History: Received July 02, 2018; Revised July 17, 2018

Rotor-dynamic fluid force (RD fluid force) of turbomachinery is one of the causes of the shaft vibration problem. Bulk flow theory is the method for analyzing this RD fluid force, and it has been widely used in the design stage of machine. The conventional bulk flow theory has been carried out under the assumption of concentric circular shaft's orbit with a small amplitude. However, actual rotating machinery's operating condition often does not hold this assumption, for example, existence of static load on the machinery causes static eccentricity. In particular, when such a static eccentricity is significant, the nonlinearity of RD fluid force may increase and become non-negligible. Therefore, conventional bulk flow theory is not applicable for the analysis of the RD fluid force in such a situation. In this paper, the RD fluid force of the annular plain seal in the case of circular whirling orbit with static eccentricity is investigated. The case with both the significant static eccentricity and the moderate whirling amplitude is considered, and the perturbation analysis of the bulk-flow theory is extended to investigate the RD fluid force in such cases. In this analysis, the assumption of the perturbation solution is extended to both static terms and whirling terms up to the third order. Then, the additional terms are caused by the coupling of these terms through nonlinearity, and these three kinds of terms are considered in the extended perturbation analysis of the bulk flow theory. As a result, a set of nonlinear analytical equations of the extended perturbation analysis of the bulk flow theory, for the case with both the significant static eccentricity and the moderate whirling amplitude, is deduced. The RD fluid force for such cases is analyzed, and the occurrence of constant component, backward synchronous component, and super-harmonic components in the RD fluid force is observed in addition to the forward synchronous component. The representation of RD fluid force coefficients (RD coefficients) are modified for the case with significant static eccentricity, and the variation of RD fluid force coefficients for the magnitude of static eccentricity is analyzed. These analytical results of RD fluid force and its RD coefficients are compared with the numerical results using finite difference analysis and experimental results. As a result, the validity of the extended perturbation analysis of the bulk-flow theory for the case with both the significant static eccentricity and the moderate whirling amplitude is confirmed.

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References

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Ikemoto, A. , Inoue, T. , Sakamoto, K. , and Uchiumi, M. , 2018, “ Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Perturbation Analysis of the Bulk-Flow Theory (Influence of Whirling Amplitude in the Case With Concentric Circular Whirl),” ASME J. Tribol., 140(4), p. 041708. [CrossRef]
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Figures

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Fig. 1

Theoretical model of the annular plain seal

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Fig. 2

Perturbation components

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Fig. 3

RD fluid force on case 1A: (a) xy diagram and (b) frequency spectrum

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Fig. 4

RD fluid force on case 1B: (a) xy diagram and (b) frequency spectrum

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Fig. 5

RD fluid force on case 1C: (a) xy diagram and (b) frequency spectrum

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Fig. 6

Comparisons of RD coefficients between analytical results and experimental results [11]: (a) direct inertia, (b) cross coupled inertia (no experimental results were shown in Ref. [11]), (c) direct damping, (d) cross coupled damping, (e) direct stiffness, and (f) cross coupled stiffness

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Fig. 7

The effect of inlet loss coefficient on RD coefficients: (a) direct inertia, (b) cross coupled inertia, (c) direct damping, (d) cross coupled damping, (e) direct stiffness, and (f) cross coupled stiffness

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