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Research Papers: Hydrodynamic Lubrication

Analytical Evaluation of the Static and Dynamic Characteristics of Three-Lobe Journal Bearings With Finite Length

[+] Author and Article Information
Athanasios Chasalevris

Mem. ASME
CSBPP—Core Science Bearings
Preventive Acoustics,
BorgWarner Turbo Systems Engineering GmbH,
Marnheimer Strasse 85/87,
Kirchheimbolanden 67292, Germany
e-mail: chasalevris@sdy.tu-darmstadt.de

1Present address: ALSTOM Power/Industrial Steam Turbine Engineering, Rugby CV1 2UE, UK.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received October 7, 2014; final manuscript received March 9, 2015; published online May 6, 2015. Assoc. Editor: Bugra Ertas.

J. Tribol 137(4), 041701 (Oct 01, 2015) (16 pages) Paper No: TRIB-14-1251; doi: 10.1115/1.4030023 History: Received October 07, 2014; Revised March 09, 2015; Online May 06, 2015

The three-lobe bearings widely used in rotating machinery follow the design data evaluated using numerical methods for the solution of the Reynolds equation. This paper defines exact and approximate analytical solutions of the Reynolds equation for the case of three-lobe bearings with finite length. Dynamic characteristics are provided analytically with closed-form expressions for laminar regimes of operation, using an approximate analytical solution that proves to be reliable and of low cost of evaluation time. The results for eccentricity ratio, equilibrium locus, stiffness and damping coefficients are presented for a range of Sommerfeld number and different cases of load orientation and compared with theoretical and experimental data from the literature.

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Figures

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Fig. 1

Definition of the geometric properties of a three-lobe journal bearing

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Fig. 2

Fluid film thickness function hi/cb as a function of circumferential coordinate θ

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Fig. 3

Analytically estimated pressure profile in a three-lobe bearing with finite length for various eccentricities and attitude angles

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Fig. 4

Evaluated pressure distribution of the bearing for ɛ=0.25 and ϕ=135 deg and for static condition ɛ· = 0 using analytical and numerical solution under different solution parameters: (a) through the entire circumference, (b) lobe 1, (c) lobe 2, and (d) lobe 3

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Fig. 5

Evaluated pressure distribution at each lobe of the bearing for ɛ = 0.75 and ϕ = 135 deg and for static condition ɛ· = 0 using analytical and numerical solution under different solution parameters: (a) through the entire circumference, (b) lobe 1, (c) lobe 2, and (d) lobe 3

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Fig. 6

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m=0.878 and L/D=0.667

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Fig. 7

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m=0.879 and L/D=0.500

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Fig. 8

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m=0.898 and L/D=0.333

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Fig. 9

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m=0.706 and L/D=0.667

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Fig. 10

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m = 0.725 and L/D = 0.500

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Fig. 12

Stiffness coefficients Kij as a function of eccentricity ratio ɛ for: (a) L/D=0.25, (b) L/D=0.5, (c) L/D=0.75, and (d) L/D=1.0

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Fig. 11

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m = 0.727 and L/D = 0.333

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Fig. 13

Damping coefficients Cij as a function of eccentricity ratio ɛ for: (a) L/D=0.25, (b) L/D=0.5, (c) L/D=0.75, and (d) L/D=1.0

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