Research Papers: Gas Turbines: Structures and Dynamics

Multivariate Response Rotordynamic Modeling and Sensitivity Analysis of Tilting Pad Bearings

[+] Author and Article Information
Leonardo Urbiola-Soto

Faculty of Engineering,
Center for Advanced Technology,
Universidad Nacional Autónoma
de México (UNAM),
Boulevard Juriquilla 3001,
Queretaro, MX 76230
e-mail: leourbiola@gmail.com

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received January 3, 2017; final manuscript received October 12, 2017; published online April 10, 2018. Assoc. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 140(7), 072502 (Apr 10, 2018) (10 pages) Paper No: GTP-17-1003; doi: 10.1115/1.4038549 History: Received January 03, 2017; Revised October 12, 2017

Achieving an optimal design of journal bearings is a very challenging effort due to the many input and output variables involved, including rotordynamic and tribological responses. This paper demonstrates the use of a multivariate response modeling approach based on response surface design of experiments (RSDOE) to design tilting pad bearings. It is shown that an optimal configuration can be achieved in the early stages of the design process while substantially reducing the amount of calculations. To refine the multivariate response model, statistical significance of the factors was assessed by examining the test's p-value. The effect coefficient calculation complemented the statistical hypothesis testing as an overall quantitative measure of the strength of factors, namely; main effects, quadratic effects, and interactions between variables. This provided insight into the potential nonlinearity of the phenomena. Once arriving at an optimized design, a sensitivity analysis was performed to identify the input variables whose variabilities have the greatest influence on the mean of a given response. Finally, an analysis of percent contribution of each input variable standard deviation to the actual response standard deviation was performed.

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Urbiola-Soto, L. , Santibañez-Santoscoy, R. , López-Parra, M. , Ramirez-Reivich, A. , and Yañez-Valdes, R. , 2016, “Rotordynamic Optimization of Fixed Pad Journal Bearings Using Surface Response Design of Experiments,” ASME J. Eng. Gas Turbines Power, 138(12), p. 122502. [CrossRef]
Hashimoto, H. , and Matsumoto, K. , 2000, “Improvement of Operating Characteristics of High-Speed Hydrodynamic Journal Bearings by Optimum Design—Part I: Formulation of Methodology and Its Application to Elliptical Bearing Design,” ASME J. Tribol., 123(2), pp. 305–312. [CrossRef]
Yang, B. S. , Lee, Y. H. , Choi, B. K. , and Kim, H. J. , 2001, “Optimum Design of Short Journal Bearings by Artificial Life Algorithm,” J. Tribol. Int., 34(7), pp. 427–435. [CrossRef]
Saruhan, H. , Rouch, K. E. , and Roso, C. A. , 2001, “Design Optimization of Fixed Pad Journal Bearing for Rotor System Using a Genetic Algorithm Approach,” International Symposium on Stability Control of Rotating Machinery (ISCORMA), Lake Tahoe, NV, Aug. 20–24, Paper No. 3001.
Saruhan, H. , Rouch, K. E. , and Roso, C. A. , 2004, “Design Optimization of Tilting-Pad Journal Bearing Using a Genetic Algorithm Approach,” Int. J. Rotating Mach., 10(4), pp. 301–307. [CrossRef]
Roso, C. A. , 1997, “Optimization of Rotor-Bearing Systems for Industrial Turbomachinery Applications,” Ph.D. thesis, University of Kentucky, Lexington, KY.
Saruhan, H. , 2006, “Optimum Design of Rotor-Bearing System Stability Performance Comparing an Evolutionary Algorithm versus a Conventional Method,” Int. J. Mech. Sci., 48(12), pp. 1341–1351. [CrossRef]
Angantyr, A. , and Aidanpää, J.-O. , 2004, “Optimization of a Rotor Bearing System With Evolutionary Algorithm,” Tenth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC), Honolulu, HI, Mar. 7–11.
Angantyr, A. , and Aidanpää, J.-O. , 2005, “Constrained Optimization of Gas Turbine Tilting Pad Bearing Designs,” ASME J. Eng. Gas Turbines Power, 128(4), pp. 873–878. [CrossRef]
Hirani, H. , and Suh, N. P. , 2005, “Journal Bearing Design Using Multiobjective Genetic Algorithm and Axiomatic Design Approaches,” J. Tribol. Int., 38(5), pp. 481–491. [CrossRef]
Song, J.-D. , Yang, B.-S. , Choib, B.-G. , and Kim, H.-J. , 2005, “Optimum Design of Short Journal Bearings by Enhanced Artificial Life Optimization Algorithm,” J. Tribol. Int., 38(4), pp. 403–412. [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]
Urbiola-Soto, L. , Aboites, F. , and De Santiago, O. , 2003, “Análisis Rotodinámico Lateral de Compresores Centrífugos para Proceso, Reinyección y Transmisión de Gas—Parte I: Objetivos,” Memorias del 7 °Congreso y Expo Internacional de Ductos, Puebla, México, pp. 1–11.
Urbiola-Soto, L. , Aboites, F. , De Santiago, O. , Bertín, G. , and García, R. , 2003, “Análisis Rotodinámico Lateral de Compresores Centrífugos para Proceso, Reinyección y Transmisión de Gas—Parte II: Metodología,” Memorias del 7 °Congreso y Expo Internacional de Ductos, Puebla, México, pp. 1–11.
XLRotorTM, 2016, “Spreadsheets for Rotordynamic Analysis, Version 3.945,” Rotating Machinery Analysis, Inc., Brevard, NC.
API, 2002, “Axial and Centrifugal Compressors and Expander-Compressors for Petroleum, Chemical, and Gas Industry Services,” American Petroleum Institute, Washington, DC, Standard No. 617.
Zeidan, F. Y. , and Herbage, B. S. , 1991, “Fluid Film Bearing Fundamentals and Failure Analysis,” 20th Turbomachinery Symposium, College Station, TX, pp. 161–186. https://pdfs.semanticscholar.org/676e/8d91559fc3a6275f2924b436767d957c73e3.pdf
Nicholas, J. C. , 1994, “Tilting Pad Bearing Design,” 23rd Turbomachinery Symposium, Dallas, TX, Sept. 13–15, pp. 179–194.
Nicholas, J. C. , and Kirk, R. G. , 1979, “Selection and Design of Tilting Pad and Fixed Lobe Journal Bearings for Optimum Turborotor Dynamics,” Eighth Turbomachinery Symposium, pp. 43–57. https://oaktrust.library.tamu.edu/handle/1969.1/163764
Montgomery, D. C. , 2012, Design and Analysis of Experiments, 8th ed., Wiley, New York.
Rao, C. R. , 1947, “Factorial Experiments Derivable From Combinatorial Arrangements of Arrays,” J. R. Stat. Soc., 9(1), pp. 128–139.
Minitab Inc., 2003, “Minitab 17, version 17.1.0,” Minitab Inc., State College, PA.
Derringer, G. , and Suich, R. , 1980, “Simultaneous Optimization of Several Response Variables,” J. Qual. Technol., 12(4), pp. 214–219. http://asq.org/qic/display-item/?item=5341
Chase, K. W. , and Parkinson, A. R. , 1991, “A Survey of Research in the Application of Tolerance Analysis to the Design of Mechanical Assemblies,” Res. Eng. Des., 3(1), pp. 23–37. [CrossRef]


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Fig. 1

Compressor rotor: geometry (top) and rotordynamic model (bottom)

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Fig. 2

Four tilting pad-LBP bearing

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Fig. 3

Response variables

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Fig. 4

Effects of significant factors on response variables, coded units

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Fig. 5

Response surface of the threshold speed of instability versus Cp and m, uncoded units

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Fig. 6

Contour plots of the threshold speed of instability versus (a) Cp and m and (b) m and T, uncoded units

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Fig. 7

Optimization output of the RSDOE, uncoded units

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Fig. 8

Overlaid contour plot, optimum solution depicted by ⊕, uncoded units




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