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Research Papers: Hydrodynamic Lubrication

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)

[+] Author and Article Information
Atsushi Ikemoto

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

Tsuyoshi Inoue

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

Kazukiyo Sakamoto

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

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.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 16, 2017; final manuscript received November 7, 2017; published online April 3, 2018. Assoc. Editor: Alan Palazzolo.

J. Tribol 140(4), 041708 (Apr 03, 2018) (15 pages) Paper No: TRIB-17-1017; doi: 10.1115/1.4039370 History: Received January 16, 2017; Revised November 07, 2017

The bulk-flow theory for the rotordynamic (RD) fluid force has been investigated for many years. These conventional bulk-flow analyses were performed under the assumption and restriction that the whirl amplitude was very small compared to the seal clearance while actual turbomachinery often causes the large amplitude vibration, and these conventional analyses may not estimate its RD fluid force accurately. In this paper, the perturbation analysis of the bulk-flow theory is extended to investigate the RD fluid force in the case of concentric circular whirl with relatively large amplitude. A set of perturbation solutions through third-order perturbations are derived explicitly. It relaxes the restriction of conventional bulk flow analysis, and it enables to investigate the RD fluid force for the whirl amplitude up to about a half of the clearance. Using derived equations, the nonlinear analytical solutions of the flow rates and pressure are deduced, and the characteristics of the RD fluid force are investigated in both radial and tangential directions. The influence of the whirl amplitude on the RD fluid force is explained and validated by comparing with computational fluid dynamics (CFD) analysis. These results are useful for the analysis and prediction of frequency response of the vibration of the rotating shaft system considering the RD fluid forces.

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Figures

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Fig. 1

Theoretical model of the annular seal

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Fig. 4

Variation of velocities for the circumferential position at inlet and outlet. Large eccentricities q=q̂/Ĉr=0.5: (a) at inlet and (b) at outlet.

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Fig. 5

y+ contours on both the stator and the rotor: (a) stator and (b) rotor

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Fig. 2

Dependency of flow rate, radial, and tangential forces to the grid size

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Fig. 3

Comparison of radial, tangential, and axial velocities at the midpoint axial position along the seal. Case with large eccentricities q=q̂/Ĉr=0.5: (a) variation of velocities for the circumferential position, (b) velocity profiles at four circumferential positions, 0, 90, 180, and 270 deg, (c) velocity profiles at 0 deg, and (d) velocity profiles at 90 deg.

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Fig. 6

Relationship between the whirl amplitude and the magnitude of perturbation variables (5000 rpm). Ordinates show nondimensionalized variables h1=ĥ1/Ĉr, uz1(z)=ûz1(z)/ûz0(0), uθ1(z)=ûθ1(z)/(R̂ω/2), and p1(z)=p̂1(z)/p̂0(0).

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Fig. 11

Damping coefficients: (a) Ĉ(q̂) and (b) ĉ(q̂)

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Fig. 12

Stiffness coefficients: (a) K̂(q̂) and (b) k̂(q̂)

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Fig. 7

Comparisons of the RD fluid force between linear analysis and nonlinear analysis at 5000 rpm: (a) radial force and (b) tangential force

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Fig. 8

Comparisons of the RD fluid force for different whirling amplitude, q = 0.1, 0.3, and 0.5, at 5000 rpm: (a) radial force and (b) tangential force

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Fig. 9

Comparisons between bulk flow analysis and CFD at 5000 rpm (a) radial force and (b) tangential force

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Fig. 10

Inertia coefficients: (a) M̂(q̂) and (b) m̂(q̂)

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Fig. 13

Rotordynamic coefficients at 1000 rpm: (a) M̂(q̂), (b) m̂(q̂), (c) Ĉ(q̂), (d) ĉ(q̂), (e) K̂(q̂), and (f) k̂(q̂)

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Fig. 14

Rotordynamic coefficients at 5000 rpm: (a) M̂(q̂), (b) m̂(q̂), (c) Ĉ(q̂), (d) ĉ(q̂), (e) K̂(q̂), and (f) k̂(q̂)

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