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Research Papers: Hydrodynamic Lubrication

Design of Tilting-Pad Journal Bearings Considering Bearing Clearance Uncertainty and Reliability Analysis

[+] Author and Article Information
Heitor Antonio Pereira da Silva

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

Rodrigo Nicoletti

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

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received March 5, 2018; final manuscript received July 25, 2018; published online August 31, 2018. Assoc. Editor: Alan Palazzolo.

J. Tribol 141(1), 011703 (Aug 31, 2018) (11 pages) Paper No: TRIB-18-1103; doi: 10.1115/1.4041021 History: Received March 05, 2018; Revised July 25, 2018

The dynamic characteristics of tilting-pad journal bearings (TPJBs) are strongly related to their geometric parameters, most importantly the bearing clearance. In turn, the bearing clearance in TPJBs is strongly dependent on the machining tolerances of the bearing parts and their assembling. Considering that, the machining tolerances of the pads can be of the same magnitude order of the oil film thickness in the bearing, it is uncertain that the TPJB will have the originally designed geometry after assembling. Therefore, the resultant dynamic characteristics of the TPJB also become uncertain. In this work, we present an investigation of tilting-pad bearings and their equivalent dynamic coefficients when subjected to dimensional variability. First, we perform a stochastic analysis of the system using a thermo-hydrodynamic (THD) model of the tilting-pad bearing and considering the bearing clearance in each pad as an independent random variable (varying between minimum and maximum values). We show that the scattering of the results of the dynamic coefficients is limited by the values obtained from TPJBs with all pads with maximum or minimum possible clearances. Second, we apply the concepts of reliability analysis to develop a design procedure for tilting-pad bearings. This design methodology considers the results obtained in the stochastic analysis and it allows the Engineer to appropriately design the bearing for a given probability of success or, inversely, a given probability of failure. Such approach assures a level of reliability to the dynamic coefficients of designed TPJBs in face of their dimensional variability.

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References

Lund, J. W. , 1964, “ Spring and Damping for the Tilting-Pad Journal Bearings,” ASLE Trans., 7(4), pp. 342–352. [CrossRef]
Dimond, T. , Younan, A. , and Allaire, P. E. , 2011, “ A Review of Tilting-Pad Bearing Theory,” Int. J. Rotating Mach., 2011(908469), pp. 1–23. [CrossRef]
Jones, G. J. , and Martin, F. A. , 1979, “ Geometry Effects in Tilting-Pad Journal Bearings,” ASLE Trans., 22(3), pp. 227–244. [CrossRef]
Fillon, M. , Dmochowski, W. , and Dadouche, A. , 2007, “ Numerical Study of the Sensitivity of Tilting-Pad Journal Bearing Performance Characteristics to Manufacturing Tolerances: Steady-State Analysis,” Tribol. Trans., 50(3), pp. 387–400. [CrossRef]
Dmochowski, W. , Dadouche, A. , and Fillon, M. , 2008, “ Numerical Study of the Sensitivity of Tilting-Pad Journal Bearing Performance Characteristics to Manufacturing Tolerances: Dynamic Analysis,” Tribol. Trans., 51(5), pp. 573–580. [CrossRef]
Cha, M. , Isaksson, P. , and Glavatskih, S. , 2013, “ Influence of Pad Compliance on Nonlinear Dynamic Characteristics of Tilting-Pad Journal Bearings,” Tribol. Int., 57, pp. 46–53. [CrossRef]
Saruhan, H. , Rouch, K. E. , and Roso, C. A. , 2004, “ Design Optimization of Tilting-Pad Journal Bearing Using a Genetic Algorithm,” Int. J. Rotating Mach., 10(4), pp. 301–307. [CrossRef]
Angantyr, A. , and Aidanpää, J. O. , 2006, “ Constrained Optimization of Gas Turbine Tilting Pad Bearing Designs,” ASME J. Eng. Gas Turbines Power, 128(4), pp. 873–878. [CrossRef]
Untaroiu, C. D. , and Untaroiu, A. , 2010, “ Constrained Design Optimization of Rotor-Tilting Pad Bearing Systems,” ASME J. Eng. Gas Turbines Power, 132(12), p. 122502. [CrossRef]
Dang, P. V. , Chatterton, S. , Pennachi, P. , and Vania, A. , 2016, “ Effect of the Load Direction on Non-Nominal Five-Pad Tilting-Pad Journal Bearings,” Tribol. Int., 98, pp. 197–211. [CrossRef]
Viveros, H. P. , and Nicoletti, R. , 2013, “ Lateral Vibration Attenuation of Shafts Supported by Tilting-Pad Journal Bearing With Embedded Electromagnetic Actuators,” ASME J. Eng. Gas Turbines Power, 136(4), p. 042503. [CrossRef]
Gomez, J. L. , Pineda, S. , and Diaz, S. E. , 2013, “ On the Effect of Pad Clearance and Preload Manufacturing Tolerances on Tilting-Pad Bearings Rotordynamic Coefficients,” ASME Paper No. GT2013-95214.
Quintini, J. C. R. , Pineda, S. , Matute, J. A. , Medina, L. U. , and Gomez, J. L. , and Diaz, S. E. , 2014, “ Determining the Effect of Bearing Clearance and Preload Uncertainties on Tilting-Pad Bearings Rotordynamic Coefficients,” ASME Paper No. GT2014-26773.
Ruiz, R. O. , and Diaz, S. E. , 2016, “ Effect of Uncertainties in the Estimation of Dynamic Coefficients on Tilting-Pad Journal Bearings,” ASME Paper No. IMECE2016-67252.
Cavalini , A. A., Jr. , Dourado, A. G. S. , Lara-Molina, F. A. , and Steffen, V., Jr. , 2016, “ Uncertainty Analysis of a Tilting-Pad Journal Bearing Using Fuzzy Logic Techniques,” ASME J. Vib. Acoust., 138(6), p. 061016. [CrossRef]
Melchers, R. E. , 1999, Structural Reliability Analysis and Prediction, 2nd ed., Wiley, New York.
Brockwell, K. , and Dmochowski, W. , 1992, “ Thermal Effects in the Tilting-Pad Journal Bearing,” J. Phys.—Part D: Appl. Phys., 25(3), pp. 384–392. [CrossRef]
Monmousseau, P. , Fillon, M. , and Frêne, J. , 1997, “ Transient Thermoelastohydrodynamic Study of Tilting-Pad Journal Bearings—Comparison Between Experimental Data and Theoretical Results,” ASME J. Tribol., 119(3), pp. 401–407. [CrossRef]
Santos, I. F. , and Nicoletti, R. , 1999, “ THD Analysis in Tilting-Pad Journal Bearings Using Multiple Orifice Hybrid Lubrication,” ASME J. Tribol., 121(4), pp. 892–900. [CrossRef]
Allaire, P. E. , Parsell, J. K. , and Barrett, L. E. , 1981, “ A Pad Perturbation Method for the Dynamic Coefficients of Tilting-Pad Journal Bearings,” Wear, 72(1), pp. 29–44. [CrossRef]
Rubinstein, R. Y. , 1981, Simulation and the Monte Carlo Method, Wiley, New York.

Figures

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Fig. 1

TPJB with resultant asymmetric geometry due to manufacturing tolerances [10]: (a) five-pad TPJB and (b) bearing profile: nominal, actual, and estimated (fitted)

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Fig. 2

TPJB with resultant asymmetric geometry due to manufacturing tolerances: (a) four-pad TPJB with embedded electromagnetic actuators [11] and (b) bearing profile: nominal and real

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Fig. 3

Tilting-pad bearing in load-on-pad configuration: asymmetric geometry due to variation of bearing assembled clearances in each pad

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Fig. 4

Local coordinate system fixed on the surface of the ith pad (Ly is the pad length and Lz is the pad width)

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Fig. 5

PDF of the adopted variation of bearing assembled clearances in the bearing

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Fig. 6

Convergence analysis of the randomly created values of bearing clearances: second moment of the distribution as a function of the number of samples

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Fig. 7

Adimensional stiffness coefficients of the rotor-bearing system as a function of the Sommerfeld number: (a) Kxx, (b) Kyy, (c) Kxy, (d) Kyx

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Fig. 8

Adimensional damping coefficients of the rotor-bearing system as a function of the Sommerfeld number: (a) Dxx, (b) Dyy, (c) Dxy, and (d) Dyx

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Fig. 9

PDF of the adimensional dynamic coefficients for different Sommerfeld numbers: (a) direct stiffness (So = 0.5), (b) direct stiffness (So = 11.0), (c) direct damping (So = 0.5), and (d) direct damping (So = 11.0)

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Fig. 10

PDF of a Gamma distribution fitted to the stochastic results of dynamic coefficients as a function of the minimum, the nominal, and the maximum dynamic coefficients

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Fig. 11

Maximum probability of failure: (a) domains of failure and success in the operating range of the TPJB and (b) probability of failure at So = Sof

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Fig. 12

Flow diagram of the design procedure

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Fig. 13

Adimensional stiffness Kxx (perpendicular to load) for different nominal bearing clearances (symmetric bearing): (a) stiffness as a function of the Sommerfeld number in the operating range and (b) PDF of the stiffness values at So = Sof

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Fig. 14

Adimensional stiffness Kyy (load direction) for different nominal bearing clearances (symmetric bearing): (a) stiffness as a function of the Sommerfeld number in the operating range and (b) PDF of the stiffness values at So = Sof

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Fig. 15

Adimensional damping Dxx (perpendicular to load) for different nominal bearing clearances (symmetric bearing): (a) damping as a function of the Sommerfeld number in the operating range and (b) PDF of the damping values at So = Sof

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Fig. 16

Adimensional damping Dyy (load direction) for different nominal bearing clearances (symmetric bearing): (a) damping as a function of the Sommerfeld number in the operating range and (b) PDF of the damping values at So = Sof

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