Research Papers: Gas Turbines: Structures and Dynamics

Transient Analysis of Gas-Expanded Lubrication and Rotordynamic Performance in a Centrifugal Compressor

[+] Author and Article Information
Brian K. Weaver

Rotating Machinery and Controls Laboratory,
Department of Mechanical
and Aerospace Engineering,
University of Virginia,
122 Engineer's Way,
Charlottesville, VA 22904
e-mail: bkw3q@virginia.edu

Jason A. Kaplan

1000 Wright Way,
Cheswick, PA 15024
e-mail: jkaplan@curtisswright.com

Andres F. Clarens

Rotating Machinery and Controls Laboratory,
Department of Civil
and Environmental Engineering,
University of Virginia,
351 McCormick Road,
Charlottesville, VA 22904
e-mail: aclarens@virginia.edu

Alexandrina Untaroiu

Laboratory for Turbomachinery
and Components,
Department of Biomedical Engineering
and Mechanics,
Virginia Tech,
324 Norris Hall,
495 Old Turner Street,
Blacksburg, VA 24061
e-mail: alexu@vt.edu

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 12, 2015; final manuscript received August 30, 2015; published online October 21, 2015. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(4), 042504 (Oct 21, 2015) (8 pages) Paper No: GTP-15-1249; doi: 10.1115/1.4031527 History: Received July 12, 2015; Revised August 30, 2015

Gas-expanded lubricants (GELs) have the potential to increase bearing energy efficiency, long-term reliability, and provide for a degree of control over the rotordynamics of high-speed rotating machines. Previous work has shown that these tunable mixtures of synthetic oil and dissolved carbon dioxide could be used to maximize the stability margin of a machine during startup by controlling bearing stiffness and damping. This allows the user to then modify the fluid properties after reaching a steady operating speed to minimize bearing power loss and reduce operating temperatures. However, it is unknown how a typical machine would respond to rapid changes in bearing stiffness and damping due to changes in the fluid properties once the machine has completed startup. In this work, the time-transient behavior of a high-speed compressor was evaluated numerically to examine the effects of rapidly changing bearing dynamics on rotordynamic performance. Two cases were evaluated for an eight-stage centrifugal compressor: an assessment under stable operating conditions as well as a study of the instability threshold. These case studies presented two contrasting sets of transient operating conditions to evaluate, the first being critical to the viability of using GELs in high-speed rotating machinery. The fluid transitions studied for machine performance were between that of a polyol ester (POE) synthetic lubricant and a GEL with a 20% carbon dioxide content. The performance simulations were carried out using a steady-state thermoelastohydrodynamic (TEHD) bearing model, which provided bearing stiffness and damping coefficients as inputs to a time-transient rotordynamic model using Timoshenko beam finite elements. The displacements and velocities of each node were solved for using a fourth-order Runge–Kutta method and provided information on the response of the rotating machine due to rapid changes in bearing stiffness and damping coefficients. These changes were assumed to be rapid due to (1) the short lubricant residence times calculated for the bearings and (2) rapid mixing due to high shear rates in the machine bearings causing sudden changes in the fluid properties. This operating condition was also considered to be a worst-case scenario as an abrupt change in the bearing dynamics would likely solicit a more extreme rotordynamic response than a more gradual change, making this analysis quite important. The results of this study provide critical insight into the nature of operating a rotating machine and controlling its behavior using GELs, which will be vital to the implementation of this technology.

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Harangozo, A. V. , Stolarski, T. A. , and Gozdawa, R. J. , 1991, “ The Effect of Different Lubrication Methods on the Performance of a Tilting-Pad Journal Bearing,” Tribol. Trans., 34(4), pp. 529–536. [CrossRef]
Allaire, P. , Humphris, R. , and Barrett, L. , 1986, “ Critical Speeds and Unbalance Response of a Flexible Rotor in Magnetic Bearings,” European Turbomachinery Symposium, London, Oct. 27–28.
Allaire, P. , Humphris, R. , and Kasarda, M. , 1987, “ Magnetic Bearing/Damper Effects on Unbalance Response of Flexible Rotors,” 22nd Annual IECEC Conference, Philadelphia, PA, Aug. 10–14, pp. 824–828.
Humphris, R. , Allaire, P. , and Lewis, D. , 1986, “ Design and Testing of Magnetic Bearings for Vibration Reduction,” 41st Meeting of the Mechanical Failures Prevention Group, Naval Air Test Center, Patuxent River, MD, Oct. 28–30, pp. 92–100.
Maslen, E. , Hermann, P. , and Scott, M. , 1989, “ Practical Limits to the Performance of Magnetic Bearings: Peak Force, Slew Rate, and Displacement Sensitivity,” ASME J. Tribol., 111(2), pp. 331–336. [CrossRef]
Williams, R. D. , Keith, F. J. , and Allaire, P. E. , 1990, “ Digital Control of Active Magnetic Bearings,” IEEE Trans. Ind. Electron., 37(1), pp. 19–27. [CrossRef]
Knospe, C. R. , Hope, R. W. , and Fedigan, S. J. , 1995, “ Experiments in the Control of Unbalance Response Using Magnetic Bearings,” Mechatronics, 5(4), pp. 385–400. [CrossRef]
Hu, T. , Lin, Z. , and Jiang, W. , 2005, “ Constrained Control Design for Magnetic Bearing Systems,” ASME J. Dyn. Syst. Meas. Control, 127(4), pp. 601–616. [CrossRef]
Yoon, S. Y. , Lin, Z. , and Goyne, C. , 2010, “ Control of Compressor Surge With Active Magnetic Bearings,” 49th IEEE Conference on Decision and Control, Atlanta, GA, Dec. 15–17, pp. 4323–4328.
Wang, W. , Gao, J. , and Zhang, Y. , 2011, “ Numerical and Experimental Investigation on the Controlling for Rotor-to-Stationary Part Rubbing in Rotating Machinery,” ASME Paper No. GT2011-46250, pp. 425–434.
Dimond, T. , Allaire, P. , and Mushi, S. , 2012, “ Modal Tilt/Translate Control and Stability of a Rigid Rotor With Gyroscopics on Active Magnetic Bearings,” Int. J. Rotating Mach., 2012, p. 567670. [CrossRef]
Mushi, S. E. , Lin, Z. , and Allaire, P. E. , 2012, “ Design, Construction, and Modeling of a Flexible Rotor Active Magnetic Bearing Test Rig,” Mechatronics, 17(6), pp. 1170–1182. [CrossRef]
Bently, D. E. , Grant, J. W. , and Hanifan, P. C. , 2000, “ Active Controlled Hydrostatic Bearings for a New Generation of Machines,” ASME Paper No. 2000-GT-0354, pp. 1–9.
Bently, D. E. , Eldridge, T. , and Jensen, J. , 2001, “ Externally Pressurized Bearings Allow Rotor Dynamic Optimization,” VDI Berichte, 1640, pp. 49–62.
Santos, I. , and Watanabe, F. Y. , 2003, “ Feasibility of Influencing the Dynamic Fluid Film Coefficients of a Multirecess Journal Bearing by Means of Active Hybrid Lubrication,” J. Braz. Soc. Mech. Sci. Eng., 25(2), pp. 154–163. [CrossRef]
Santos, I. F. , Nicoletti, R. , and Scalabrin, A. , 2004, “ Feasibility of Applying Active Lubrication to Reduce Vibration in Industrial Compressors,” ASME J. Eng. Gas Turbines Power, 126(4), pp. 848–854. [CrossRef]
Santos, I. F. , 2011, “ Trends in Controllable Oil Film Bearings,” IUTAM Symposium on Emerging Trends in Rotor Dynamics, New Delhi, India, Mar. 23–26, pp. 185–199.
Jung, S. Y. , and Choi, S. , 1995, “ Analysis of a Short Squeeze-Film Damper Operating With Electrorheological Fluids,” Tribol. Trans., 38(4), pp. 857–862. [CrossRef]
Carmignani, C. , Forte, P. , and Rustighi, E. , 2006, “ Design of a Novel Magneto-Rheological Squeeze-Film Damper,” Smart Mater. Struct., 15(1), pp. 164–170. [CrossRef]
Kim, K. , Lee, C. , and Koo, J. , 2008, “ Design and Modeling of Semi-Active Squeeze Film Dampers Using Magneto-Rheological Fluids,” Smart Mater. Struct., 17(3), p. 035006. [CrossRef]
Goodwin, M. , Boroomand, T. , and Hooke, C. , 1989, “ Variable Impedance Hydrodynamic Journal Bearings for Controlling Flexible Rotor Vibrations,” Rotating Mach. Dyn., 18(1), pp. 261–267.
Roach, M. P. , and Goodwin, M. J. , 1992, “ Vibration Control in Rotating Machinery by the Use of Accumulators or Aerated Lubricants,” International Conference on Rotating Machine Dynamics, Venice, Italy, Apr. 28–30, pp. 367–375.
Deckler, D. , Veillette, R. , and Braun, M. , 2004, “ Simulation and Control of an Active Tilting-Pad Journal Bearing,” Tribol. Trans., 47(3), pp. 440–458. [CrossRef]
Sun, L. , and Krodkiewski, J. , 2000, “ Experimental Investigation of Dynamic Properties of an Active Journal Bearing,” J. Sound Vib., 230(5), pp. 1103–1117. [CrossRef]
Palazzolo, A. , Lin, R. , and Alexander, R. , 1991, “ Test and Theory for Piezoelectric Actuator-Active Vibration Control of Rotating Machinery,” ASME J. Vib. Acoust., 113(2), pp. 167–175. [CrossRef]
Palazzolo, A. , Jagannathan, S. , and Kascak, A. , 1993, “ Hybrid Active Vibration Control of Rotor Bearing Systems Using Piezoelectric Actuators,” ASME J. Vib. Acoust., 115(1), pp. 111–119. [CrossRef]
Osman, T. , Nada, G. , and Safar, Z. , 2001, “ Static and Dynamic Characteristics of Magnetized Journal Bearings Lubricated With Ferrofluid,” Tribol. Int., 34(6), pp. 369–380. [CrossRef]
Vance, J. M. , and Ying, D. , 2000, “ Experimental Measurements of Actively Controlled Bearing Damping With an Electrorheological Fluid,” ASME J. Eng. Gas Turbines Power, 122(2), pp. 337–344. [CrossRef]
Zhu, C. , 2005, “ A Disk-Type Magneto-Rheological Fluid Damper for Rotor System Vibration Control,” J. Sound Vib., 283(3), pp. 1051–1069. [CrossRef]
Heshmat, H. , Chen, H. M. , and Walton, J. , 2000, “ On the Performance of Hybrid Foil-Magnetic Bearings,” ASME J. Eng. Gas Turbines Power, 122(1), pp. 73–81. [CrossRef]
Swanson, E. E. , Heshmat, H. , and Walton, J. , 2002, “ Performance of a Foil-Magnetic Hybrid Bearing,” ASME J. Eng. Gas Turbines Power, 124(2), pp. 375–382. [CrossRef]
Clarens, A. , Younan, A. , and Wang, S. , 2010, “ Feasibility of Gas-Expanded Lubricants for Increased Energy Efficiency in Tilting-Pad Journal Bearings,” ASME J. Tribol., 132(3), p. 031802. [CrossRef]
Weaver, B. K. , Younan, A. A. , and Dimond, T. W. , 2013, “ Properties and Performance of Gas-Expanded Lubricants in Tilting Pad Journal Bearings,” Tribol. Trans., 56(4), pp. 687–696. [CrossRef]
Weaver, B. K. , Dimond, T. W. , and Kaplan, J. A. , 2014, “ Gas-Expanded Lubricant Performance and Effects on Rotor Stability in Turbomachinery,” ASME Paper No. GT2014-26980, pp. 1–13.
Weaver, B. K. , Zhang, Y. , and Clarens, A. F. , 2014, “ Nonlinear Analysis of Rub Impact in a Three-Disk Rotor and Correction via Bearing and Lubricant Adjustment,” ASME Paper No. IMECE201-40055.
Badgley, R. , and Booker, J. , 1969, “ Turborotor Instability: Effect of Initial Transients on Plane Motion,” ASME J. Tribol., 91(4), pp. 625–630.
Kirk, R. , and Gunter, E. , 1974, “ Transient Response of Rotor-Bearing Systems,” ASME J. Manuf. Sci. Eng., 96(2), pp. 682–690.
Lund, J. , 1976, “ Linear Transient Response of a Flexible Rotor Supported in Gas-Lubricated Bearings,” ASME J. Tribol., 98(1), pp. 57–65.
Adams, M. , 1980, “ Non-Linear Dynamics of Flexible Multi-Bearing Rotors,” J. Sound Vib., 71(1), pp. 129–144. [CrossRef]
Li, D. , Choy, K. , and Allaire, P. , 1980, “ Stability and Transient Characteristics of Four Multilobe Journal Bearing Configurations,” ASME J. Tribol., 102(3), pp. 291–298.
Li, C. , 1982, “ Dynamics of Rotor Bearing Systems Supported by Floating Ring Bearings,” ASME J. Tribol., 104(4), pp. 469–476.
Sakata, M. , Aiba, T. , and Ohnabe, H. , 1983, “ Transient Vibration of High-Speed, Lightweight Rotors Due to Sudden Imbalance,” ASME J. Eng. Gas Turbines Power, 105(3), pp. 480–486. [CrossRef]
Choy, F. , and Padovan, J. , 1987, “ Non-Linear Transient Analysis of Rotor-Casing Rub Events,” J. Sound Vib., 113(3), pp. 529–545. [CrossRef]
Palazzolo, A. , Lin, R. , and Kascak, A. , 1989, “ Active Control of Transient Rotordynamic Vibration by Optimal Control Methods,” ASME J. Eng. Gas Turbines Power, 111(2), pp. 264–270. [CrossRef]
Holl, H. J. , and Irschik, H. , 1994, “ A Substructure Method for the Transient Analysis of Nonlinear Rotordynamic Systems Using Modal Analysis,” 12th International Modal Analysis Conference (IMAC XII), Honolulu, HI, Jan. 31–Feb. 3, pp. 1638–1638.
Gadangi, R. , Palazzolo, A. , and Kim, J. , 1996, “ Transient Analysis of Plain and Tilt Pad Journal Bearings Including Fluid Film Temperature Effects,” ASME J. Tribol., 118(2), pp. 423–430. [CrossRef]
Castro, H. F. , Cavalca, K. L. , and Nordmann, R. , 2008, “ Whirl and Whip Instabilities in Rotor-Bearing System Considering a Nonlinear Force Model,” J. Sound Vib., 317(1), pp. 273–293. [CrossRef]
Hauk, A. , 2001, “ Thermo- Und Fluiddynamik Von Synthetischen Schmierstoffen Mit Kohlendioxid Als Kaültemittel in PKW-Klimaanlagen [Thermo and Fluid Dynamics of Synthetic Lubricants With Carbon Dioxide as Refrigerant in Air Conditioning],” Ph.D. thesis, Ruhr University, Bochum, Germany.
Grunberg, L. , and Nissan, A. H. , 1949, “ Mixture Law for Viscosity,” Nature, 164(4175), pp. 799–800. [CrossRef] [PubMed]
Totten, G. E. , Westbrook, S. R. , and Shah, R. J. , 2003, Fuels and Lubricants Handbook Technology, Properties, Performance, and Testing, ASTM International, West Conshokocken, PA.
Larsson, R. , and Andersson, O. , 2000, “ Lubricant Thermal Conductivity and Heat Capacity Under High Pressure,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 214(4), pp. 337–342. [CrossRef]
Jensen, M. , and Jackman, D. , 1984, “ Prediction of Nucleate Pool Boiling Heat-Transfer Coefficients of Refrigerant-Oil Mixtures,” ASME J. Heat Transfer, 106(1), pp. 184–190. [CrossRef]
He, M. , 2003, “ Thermoelastohydrodynamic Analysis of Fluid Film Journal Bearings,” Ph.D. thesis, University of Virginia, Charlottesville, VA.
He, M. , and Allaire, P. , 2002, “ Thermoelastohydrodynamic Analysis of Journal Bearings With 2D Generalized Energy Equation,” 6th International Conference on Rotor Dynamics (IFTOMM), Sydney, Australia, Sept. 30–Oct. 3.
He, M. , Allaire, P. , and Barrett, L. , 2002, “ TEHD Modeling of Leading Edge Groove Tilting Pad Bearings,” 6th International Conference on Rotor Dynamics (IFTOMM), Sydney, Australia, Sept. 30–Oct. 3.
Ng, C. , and Pan, C. , 1965, “ A Linearized Turbulent Lubrication Theory,” J. Basic Eng., 87(3), pp. 675–688. [CrossRef]
Elrod, Jr., H. , and Ng, C. , 1967, “ A Theory for Turbulent Fluid Films and its Application to Bearings,” J. Lubr. Technol., 89(3), pp. 346–362. [CrossRef]
Barrett, L. E. , 1978, “ Stability and Nonlinear Response of Rotor-Bearing Systems With Squeeze Film Bearings,” Ph.D. thesis, University of Virginia, Charlottesville, VA.
Nicholas, J. , Gunter, E. , and Barrett, L. , 1978, “ The Influence of Tilting Pad Bearing Characteristics on the Stability of High Speed Rotor-Bearing Systems,” Design Engineering Conference on Topics in Fluid Film Bearing and Rotor Bearing System Design and Optimization, Chicago, Apr. 17–20, pp. 55–78.
API, 2005, “API Standard Paragraphs Rotordynamic Tutorial: Lateral Critical Speeds, Unbalance Response, Stability, Train Torsionals, and Rotor Balancing,” 2nd ed., American Petroleum Institute, Washington, DC, API Standard No. 684.
Cao, J. , 2012, “ Transient Analysis of Flexible Rotors With Nonlinear Bearings, Dampers and External Forces,” Ph.D. thesis, University of Virginia, Charlottesville, VA.
API, 2002, “Axial and Centrifugal Compressors and Expander-Compressors for Petroleum, Chemical, and Gas Industry Service, Downstream Service,” 7th ed., American Petroleum Institute, Washington, DC, API Standard No. 617.


Grahic Jump Location
Fig. 1

GELs provide real-time control over lubricant viscosity

Grahic Jump Location
Fig. 2

Finite-element model of the eight-stage compressor

Grahic Jump Location
Fig. 3

Direct (a) stiffness and (b) damping coefficients as a function of lubricant viscosity

Grahic Jump Location
Fig. 4

Cross-coupled stiffness coefficients as a function of lubricant viscosity

Grahic Jump Location
Fig. 5

Transient (a) x and (b) y displacements of the compressor rotor at node 4

Grahic Jump Location
Fig. 6

A spectrum analysis of the first case shows the range of frequencies excited by the rapid changes in fluid properties

Grahic Jump Location
Fig. 7

Transient (a) x and (b) y displacements of the compressor rotor at node 17

Grahic Jump Location
Fig. 8

A spectrum analysis of the compressor vibration shows the destabilizing subsynchronous vibration

Grahic Jump Location
Fig. 9

Transient (a) x and (b) y displacements of the compressor rotor at node 4 at the instability threshold

Grahic Jump Location
Fig. 10

Whirl orbit shape at node 4 (a) as the rotor traverses the instability threshold and (b) relative to the bearing clearance

Grahic Jump Location
Fig. 11

Transient (a) x and (b) y displacements of the compressor rotor at node 17 at the instability threshold



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