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Research Papers

Optimal Vibration Reduction of Flexible Rotor Systems By the Virtual Bearing Method

[+] Author and Article Information
Shibing Liu

Mem. ASME
Hyperloop One,
2159 Bay Street,
Los Angeles, CA 90021
e-mail: shibing@hyperloop-one.com

Bingen Yang

Fellow ASME
Department of Aerospace and
Mechanical Engineering,
University of Southern California,
Los Angeles, CA 90089
e-mail: bingen@usc.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 11, 2017; final manuscript received August 31, 2017; published online October 9, 2017. Assoc. Editor: Stefano Lenci.

J. Vib. Acoust 140(2), 021008 (Oct 09, 2017) (11 pages) Paper No: VIB-17-1315; doi: 10.1115/1.4037956 History: Received July 11, 2017; Revised August 31, 2017

This paper presents a new approach to optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. The thrust of the effort is the introduction of a virtual bearing method (VBM), by which a minimum number of bearings can be automatically determined in a rotor design without trial and error. This unique method is useful in dealing with the issue of undetermined number of bearings. In the development, the VBM and a distributed transfer function method (DTFM) for closed-form analytical solutions are integrated to formulate an optimization problem of mixed continuous-and-integer type, in which bearing locations and bearing index numbers (BINs) (specially defined integer variables representing the sizes and properties of all available bearings) are selected as design variables. Solution of the optimization problem by a real-coded genetic algorithm yields an optimal design that satisfies all the rotor design requirements with a minimum number of bearings. Filling a technical gap in the literature, the proposed optimal bearing placement approach is applicable to either redesign of an existing rotor system for improvement of system performance or preliminary design of a new rotor system with the number of bearings to be installed being unforeknown.

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References

Bhat, R. B. , Rao, J. S. , and Sankar, T. S. , 1982, “ Optimum Journal Bearing Parameters for Minimum Rotor Unbalance Response in Synchronous Whirl,” ASME J. Mech. Des., 104(2), pp. 339–344. [CrossRef]
Panda, K. C. , and Dutt, J. K. , 2003, “ Optimum Support Characteristics for Rotor-Shaft System With Preloaded Rolling Element Bearings,” J. Sound Vib., 260(4), pp. 731–755. [CrossRef]
Lin, Y. , Cheng, L. , and Huang, T. P. , 1998, “ Optimal Design of Complex Flexible Rotor-Support Systems Using Minimum Strain Energy Under Multi-Constraint Conditions,” J. Sound Vib., 215(5), pp. 1121–1134. [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]
Srinivasan, S. , Maslen, E. H. , and Barrett, L. E. , 1997, “ Optimization of Bearing Locations for Rotor Systems With Magnetic Bearings,” ASME J. Eng. Gas Turbines Power, 119(2), pp. 464–468. [CrossRef]
Zhong, W. , Palazzolo, A. , and Kang, X. , 2016, “ Multi-Objective Optimization Design of Nonlinear Magnetic Bearing Rotordynamic Systems,” ASME J. Vib. Acoust., 139(1), p. 011011. [CrossRef]
Yang, B. S. , Choi, S. P. , and Kim, Y. C. , 2005, “ Vibration Reduction Optimum Design of a Steam-Turbine Rotor-Bearing System Using a Hybrid Genetic Algorithm,” Struct. Multidiscip. Optim., 30(1), pp. 43–53. [CrossRef]
Lund, J. W. , 1980, “ Sensitivity of the Critical Speeds of a Rotor to Changes in Design,” ASME J. Mech. Des., 102(1), pp. 115–121. [CrossRef]
Rajan, M. , Rajan, S. D. , Nelson, H. D. , and Chen, W. J. , 1987, “ Optimal Placement of Critical Speeds in Rotor-Bearing Systems,” ASME J. Vib. Acoust. Stress Reliab. Des., 109(2), pp. 152–157. [CrossRef]
Chen, T.-Y. , and Wang, B. P. , 1993, “ Optimum Design of Rotor-Bearing Systems With Eigenvalue Constraints,” ASME J. Eng. Gas Turbines Power, 115(2), pp. 256–260. [CrossRef]
Huang, S.-C. , and Lin, C.-A. , 2002, “ Sensitivity Analysis and Optimization of Undamped Rotor Critical Speeds to Supports Stiffness,” ASME J. Vib. Acoust., 124(2), pp. 296–301. [CrossRef]
Lin, C. , 2014, “ Optimization of Bearing Locations for Maximizing First Mode Natural Frequency of Motorized Spindle-Bearing Systems Using a Genetic Algorithm,” Appl. Math., 5(14), pp. 2137–2152. [CrossRef]
Shiau, T. N. , and Chang, J. R. , 1993, “ Multi-Objective Optimization of Rotor-Bearing System With Critical Speed Constraints,” ASME J. Eng. Gas Turbines Power, 115(2), pp. 246–255. [CrossRef]
Choi, B.-K. , and Yang, B.-S. , 2001, “ Multiobjective Optimum Design of Rotor-Bearing Systems With Dynamic Constraints Using Immune-Genetic Algorithm,” ASME J. Eng. Gas Turbines Power, 123(1), pp. 78–81. [CrossRef]
Choi, B.-K. , and Yang, B.-S. , 2001, “ Optimal Design of Rotor-Bearing Systems Using Immune-Genetic Algorithm,” ASME J. Vib. Acoust., 123(3), pp. 398–401. [CrossRef]
Shiau, T. N. , Kang, C. H. , and Liu, D. S. , 2008, “ Interval Optimization of Rotor-Bearing Systems With Dynamic Behavior Constraints Using an Interval Genetic Algorithm,” Struct. Multidiscip. Optim., 36(6), pp. 623–631. [CrossRef]
Ribeiro, E. A. , Pereira, J. T. , and Bavastri, C. A. , 2015, “ Passive Vibration Control in Rotor Dynamics: Optimization of Composed Support Using Viscoelastic Materials,” J. Sound Vib., 351, pp. 43–56. [CrossRef]
Lin, C. W. , 2012, “ Simultaneous Optimal Design of Parameters and Tolerance of Bearing Locations for High-Speed Machine Tools Using a Genetic Algorithm and Monte Carlo Simulation Method,” Int. J. Precis. Eng. Manuf., 13(11), pp. 1983–1988. [CrossRef]
Liu, S. , and Yang, B. , 2016, “ Vibrations of Flexible Multistage Rotor Systems Supported by Water-Lubricated Rubber Bearings,” ASME J. Vib. Acoust., 139(2), p. 021016. [CrossRef]
Liu, S. , and Yang, B. , 2014, “ Modeling and Analysis of Flexible Multistage Rotor Systems With Water-Lubricated Rubber Bearings,” ASME Paper No. IMECE2014-39841.
Liu, S. , and Yang, B. , 2017, “ A Virtual Bearing Method for Optimal Bearing Placement of Flexible Rotor Systems,” ASME Paper No. DETC2017-67216.
Fang, H. , and Yang, B. , 1998, “ Modeling, Synthesis and Dynamic Analysis of Complex Flexible Rotor Systems,” J. Sound Vib., 211(4), pp. 571–592. [CrossRef]
Lewis, F. M. , 1932, “ Vibration During Acceleration Through a Critical Speed,” Trans. ASME, 54(1), pp. 253–261.
Millsaps, K. T. , and Reed, G. L. , 1998, “ Reducing Lateral Vibrations of a Rotor Passing Through Critical Speeds by Acceleration Scheduling,” ASME J. Eng. Gas Turbines Power, 120(3), pp. 615–620. [CrossRef]
Caramia, M. , and Dell'Olmo, P. , 2008, Multi-Objective Management in Freight Logistics, Springer-Verlag, London.
Deep, K. , Singh, K. P. , Kansal, M. L. , and Mohan, C. , 2009, “ A Real Coded Genetic Algorithm for Solving Integer and Mixed Integer Optimization Problems,” Appl. Math. Comput., 212(2), pp. 505–518.

Figures

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Fig. 1

Schematic of a flexible rotor system

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Fig. 2

A rotating shaft with a bearing: (a) physical bearing with finite length and (b) pointwise bearing model (pointwise springs and dampers)

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Fig. 3

A stepped flexible rotor system in design: (a) the bare system with mounted disks, (b) the bare system with nonbearing regions (shaded areas), (c) the bare system with virtual bearings, and (d) the virtual rotor system with pointwise bearings

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Fig. 4

Unbalanced mass response of a flexible rotor system versus its shaft rotation speed

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Fig. 5

Example I: (a) the bare system with virtual bearings and nonbearing regions and (b) the virtual rotor system with pointwise bearings

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Fig. 6

Example I: spatial distributions of vibration amplitude of the rotor system in the previous design and the proposed optimal design

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Fig. 7

A simply supported flexible rotor system in example II: (a) the bare system, (b) the bare system with virtual bearings, and (c) the virtual rotor system with pointwise bearings

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Fig. 8

Example II: the unbalanced mass response of the rotor system versus its rotation speed

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Fig. 9

The spatial distributions of vibration amplitude at operating speed (8000 rpm) in example II: dashed line—the optimally designed rotor system with three bearings, and the solid line—the virtual rotor system with nine bearings

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