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Hydrodynamic Lubrication

Optimization of Journal Bearing Profile for Higher Dynamic Stability Limits

[+] Author and Article Information
Rodrigo Nicoletti

Department of Mechanical Engineering
School of Engineering of São Carlos
University of São Paulo
Trabalhador São-Carlense 400
13566-590 São Carlos, Brazil
e-mail: rnicolet@sc.usp.br

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received April 9, 2012; final manuscript received October 2, 2012; published online December 20, 2012. Assoc. Editor: Mihai Arghir.

J. Tribol 135(1), 011702 (Dec 20, 2012) (13 pages) Paper No: TRIB-12-1047; doi: 10.1115/1.4007885 History: Received April 09, 2012; Revised October 02, 2012

This work presents an optimization procedure to find bearing profiles that improve stability margins of rotor-bearing systems. The profile is defined by control points and cubic splines. Stability margins are estimated using bearing dynamic coefficients, and obtained solutions are analyzed as a function of the number of control points and of the Sommerfeld number at optimization. Results show the feasibility of finding shapes for the bearing that significantly improve the stability margins. Some of the obtained solutions overcome the stability margins of conventional bearings, such as the journal bearing and preloaded bearings with 0.5 and 0.67 preload. A time domain simulation of a flexible shaft rotating system supported by such bearings corroborates the results.

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References

Figures

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Fig. 1

Two lobe journal bearing in study

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Fig. 2

Coordinate system attached to the sliding surface of the bearing (ith lobe)

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Fig. 3

Equivalent dynamic coefficients of the journal bearing (constant bearing radius)

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Fig. 4

Rigid rotor stability threshold for the journal bearing (constant bearing radius)

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Fig. 5

Eccentricity and attitude angle of the rotor in the journal bearing (constant bearing radius)

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Fig. 6

Bearing radius as a function of θi: cubic spline interpolation of equally spaced control points

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Fig. 7

Flow chart of the algorithm for evaluating the objective function given the value of design variables

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Fig. 8

Flow chart of the algorithm for solving the optimization problem (matlab function fmincon)

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Fig. 9

Rigid rotor stability threshold for the bearings with optimized shape with different control points, calculated at S = 0.5

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Fig. 12

Sommerfeld number for unconditional stability and minimum stability threshold as a function of the Sommerfeld number at which optimization is performed

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Fig. 11

Rigid rotor stability threshold for the bearings with optimized shape calculated at different Sommerfeld numbers: (a) 10 control points; (b) 14 control points; (c) 18 control points; (d) 24 control points

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Fig. 10

Sommerfeld number for unconditional stability and minimum stability threshold as a function of the number of control points, calculated at S = 0.5

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Fig. 13

Rigid rotor stability threshold for the bearings with optimized shape: a comparison to conventional bearings

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Fig. 14

Shape of the optimized bearings in comparison to the original journal bearing shape (best results): (a) reference frame; (b) 10 points/S = 1.0; (c) 14 points/S = 2.0; (d) 24 points/S = 1.0

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Fig. 15

Rotor-bearing system and reference frames

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Fig. 16

Maximum amplitude of the unbalance response of the rotor-bearing system during run-up with conventional and optimized bearings

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Fig. 17

Stiffness coefficients of the optimized bearings in comparison to those of the journal bearing: (a) direct coefficients; (b) cross-coupling coefficients

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Fig. 18

Damping coefficients of the optimized bearings in comparison to those of the journal bearing: (a) direct coefficients; (b) cross-coupling coefficients

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Fig. 19

Percentage variation of the dynamic coefficients of the 10 pts./S = 1.0 optimized bearing from corrections of [20]

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Fig. 20

Percentage variation of the dynamic coefficients of the 14 pts./S = 2.0 optimized bearing from corrections of [20]

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