0
Research Papers

Rotor Dynamics Behavior of Tilting Pad Bearing Supported Turbo-Expander Considering Temperature Gradient

[+] Author and Article Information
Ming Li, Xiaohu Wang, Huiyu Bai, Fucai Li, Guang Meng

State Key Laboratory of Mechanical System
and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China

Xingxing Liu

AVIC Commercial Aircraft Engine Co., Ltd.,
Shanghai 200241, China

Rui Zhu

School of Energy
and Environment Engineering,
Shanghai University of Electric Power,
Shanghai 200090, China;
State Key Laboratory of Mechanical System
and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China

Hongguang Li

State Key Laboratory of Mechanical System
and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: hgli@sjtu.edu.cn

1Corresponding author.

Manuscript received December 15, 2014; final manuscript received March 6, 2015; published online August 26, 2015. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 11(2), 021004 (Aug 26, 2015) (16 pages) Paper No: CND-14-1315; doi: 10.1115/1.4030831 History: Received December 15, 2014

This paper dedicates on the rotor dynamics behavior analysis on a tilting pad bearing supported turbo-expander rotor system considering temperature gradient. Both numerical and experimental investigations are conducted intensively. The influence of the temperature gradient is modeled as the change of the lubrication oil viscosity and the length variation of the clearance due to the cryogenic thermal expansion of the journal. The analytical expressions of the tilting pad bearing oil-film force are then amended and substitute into the lumped parameter model of the turbo-expander rotor dynamics. Linear analysis based on this model indicates that the existence of the temperature gradient can stabilize the turbo-expander rotor system to an extent, while the nonlinear analyses reveal that the temperature gradient will advance the occurrence of the quasi-periodic motion and break the equilibrium of the vibration between the expander side and the compressor side. Furthermore, an experimental system is established and the experimental results show that the temperature of the tilting pad bearing is influenced by the environment temperature greatly; the spectrum of the displacement of the rotor is dominated by the synchronous frequency of the impellers and bearings. The experiment results also observe the vibration amplitude decreases when the environment temperature gets down and grows when the rotating speed increases. At the same time, the sensitivity of the vibration amplitude versus rotating speed decreases as the environment temperature rises, and vice versa.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Smith, A. R. , and Klosek, J. , 2001, “A Review of Air Separation Technologies and Their Integration With Energy Conversion Processes,” Fuel Process. Technol., 70(2), pp. 115–134. [CrossRef]
Bloch, H. P. , and Soares, C. , 2001, Turboexpanders and Process Applications, Gulf Professional Publishing, Houston, TX.
Rayleigh, L. , 1898, “Liquid Air at One Operation,” Nature, 58(1946), p. 199. [CrossRef]
Xiong, L.-Y. , Wu, G. , Hou, Y. , Liu, L.-Q. , Ling, M.-F. , and Chen, C.-Z. , 1997, “Development of Aerodynamic Foil Journal Bearings for a High Speed Cryogenic Turboexpander,” Cryogenics, 37(4), pp. 221–230. [CrossRef]
Walton, J. F. , and Hesmat, H. , 2002, “Application of Foil Bearings to Turbomachinery Including Vertical Operation,” ASME J. Eng. Gas Turbines Power, 124(4), pp. 1032–1041. [CrossRef]
Zhu, Q. , and Zhang, W. J. , 2003, “A Preliminary Nonlinear Analysis of the Axial Transient Response of the Sector-Shaped Hydrodynamic Thrust Bearing-Rotor System,” ASME J. Tribol., 125(4), pp. 854–858. [CrossRef]
Hou, Y. , Zhu, Z. H. , and Chen, C. Z. , 2004, “Comparative Test on Two Kinds of New Compliant Foil Bearing for Small Cryogenic Turbo-Expander,” Cryogenics, 44(1), pp. 69–72. [CrossRef]
Wang, X. , Zhuang, M. , Zhang, Q. , Li, S. , and Fu, B. , 2011, “Dynamic Stability Study of Static Gas Bearing for Small Cryogenic Turbo-Expander,” Plasma Sci. Technol., 13(4), pp. 506–512. [CrossRef]
Herzog, R. , Buhler, P. , Gahler, C. , and Larsonneur, R. , 1996, “Unbalance Compensation Using Generalized Filters in the Multivariable Feedback of Magnetic Bearings,” IEEE Trans. Control Syst. Technol., 4(5), pp. 580–586. [CrossRef]
Qiu, J. , Tani, J. , and Kwon, T. , 2003, “Control of Self-Excited Vibration of a Rotor System With Active Gas Bearings,” ASME J. Vib. Acoust., 125(3), pp. 328–334. [CrossRef]
Gjika, K. , San Andres, L. , and Larue, G. D. , 2010, “Nonlinear Dynamic Behavior of Turbocharger Rotor-Bearing Systems With Hydrodynamic Oil Film and Squeeze Film Damper in Series: Prediction and Experiment,” ASME J. Comput. Nonlinear Dyn., 5(4), p. 041006. [CrossRef]
Ying, G. , Meng, G. , and Jing, J. , 2009, “Turbocharger Rotor Dynamics With Foundation Excitation,” Arch. Appl. Mech., 79(4), pp. 287–299. [CrossRef]
Tian, L. , Wang, W. , and Peng, Z. , 2011, “Dynamic Behaviours of a Full Floating Ring Bearing Supported Turbocharger Rotor With Engine Excitation,” J. Sound Vib., 330(20), pp. 4851–4874. [CrossRef]
Lee, J. G. , and Palazzolo, A. , 2013, “Morton Effect Cyclic Vibration Amplitude Determination for Tilt Pad Bearing Supported Machinery,” ASME J. Tribol., 135(1), p. 011701. [CrossRef]
Schmied, J. , Pozivil, J. , and Walch, J. , 2008, “Hot Spots in Turboexpander Bearings: Case History, Stability Analysis, Measurements and Operational Experience,” ASME Paper No. GT2008-51179.
Li, M. , Li, C. , Liu, X. , Li, H. , Li, F. , and Meng, G. , 2015, “Nonlinear Rotor Dynamics on Turbo Expander With Unbalanced Bearing Force Caused by Temperature Difference,” J. Vibroeng., 17(1), pp. 33–46.
Munson, B. R. , Young, D. F. , and Okiishi, T. H. , 1990, Fundamentals of Fluid Mechanics, Wiley, New York.
Doolittle, A. K. , 1951, “Studies in Newtonian Flow. I. The Dependence of the Viscosity of Liquids on Temperature,” J. Appl. Phys., 22(8), pp. 1031–1035. [CrossRef]
Kittel, C. , and McEuen, P. , 1976, Introduction to Solid State Physics, Wiley, New York.
Nix, F. , and MacNair, D. , 1941, “The Thermal Expansion of Pure Metals: Copper, Gold, Aluminum, Nickel, and Iron,” Phys. Rev., 60(8), pp. 597–605. [CrossRef]
Pagano, S. , Rocca, E. , Russo, M. , and Russo, R. , 1995, “Dynamic Behaviour of Tilting-Pad Journal Bearings,” Proc. Inst. Mech. Eng., Part J, 209(4), pp. 275–285. [CrossRef]
Brancati, R. , Rocca, E. , and Russo, R. , 1996, “Non-Linear Stability Analysis of a Rigid Rotor on Tilting Pad Journal Bearings,” Tribol. Int., 29(7), pp. 571–578. [CrossRef]
Okabe, E. P. , and Cavalca, K. L. , 2009, “Rotordynamic Analysis of Systems With a Non-Linear Model of Tilting Pad Bearings Including Turbulence Effects,” Nonlinear Dyn., 57(4), pp. 481–495. [CrossRef]
Adams, M. , and Payandeh, S. , 1983, “Self-Excited Vibration of Statically Unloaded Pads in Tilting-Pad Journal Bearings,” J. Lubr. Technol., 105(3), pp. 377–383. [CrossRef]
Liu, X. , 2013, “Study on Nonlinear Dynamics of Double Cantilever Rotor-Bearing System,” Master thesis, Shanghai Jiao Tong University, Shanghai, China (in Chinese).
Bai, H. , Liu, X. , Li, H. , Zhang, W. , Meng, G. , Li, M. , and Wang, X. , 2014, “Nonlinear Dynamic Characteristics of Large-Scale Tilting Pad Journal Bearing-Rotor Systems,” J. Vibroeng., 16(8), pp. 4045–4064.
Campbell, W. , 1924, “Protection of Steam Turbine Disk Wheels From Axial Vibration,” ASME Spring Meeting, Cleveland, OH, Paper No. 1920.

Figures

Grahic Jump Location
Fig. 1

Couette flow model of sliding bearing

Grahic Jump Location
Fig. 2

Viscosity-temperature diagram of ISO32 turbine oil

Grahic Jump Location
Fig. 3

Sketch map of tilting pad bearing with four pads

Grahic Jump Location
Fig. 4

Logarithm linear relationship between temperature and Sommerfeld ratio

Grahic Jump Location
Fig. 5

Campbell diagram, temperature of expander bearing journal: (a) 40 °C, (b) 0 °C, (c) −50 °C, and (d) −100 °C

Grahic Jump Location
Fig. 6

Bifurcation diagram and zoomed bifurcation diagram at 40 °C: (a) expander impeller and (b) compressor impeller

Grahic Jump Location
Fig. 7

Waterfall diagram and zoomed waterfall diagram at 40 °C: (a) expander impeller and (b) compressor impeller

Grahic Jump Location
Fig. 8

Response of expander impeller at 40 °C and 580 Hz: (a) time signal, (b) frequency spectrum, (c) trajectory of rotor axis, and (d) Poincaré diagram

Grahic Jump Location
Fig. 9

Trajectories of rotor axis at 40 °C and 580 Hz

Grahic Jump Location
Fig. 10

Bifurcation diagram and zoomed bifurcation diagram at 0 °C: (a) expander impeller and (b) compressor impeller

Grahic Jump Location
Fig. 11

Waterfall diagram and zoomed waterfall diagram at 0 °C: (a) expander impeller and (b) compressor impeller

Grahic Jump Location
Fig. 12

Response of expander impeller at 0 °C and 400 Hz: (a) time signal, (b) frequency spectrum, (c) trajectory of rotor axis, and (d) Poincaré diagram

Grahic Jump Location
Fig. 13

Response of expander impeller at 0 °C and 615 Hz: (a) time signal, (b) frequency spectrum, (c) trajectory of rotor axis, and (d) Poincaré diagram

Grahic Jump Location
Fig. 14

Trajectories of rotor axis at 0 °C and 400 Hz

Grahic Jump Location
Fig. 15

Trajectories of rotor axis at 0 °C and 615 Hz

Grahic Jump Location
Fig. 16

Bifurcation diagram and zoomed bifurcation diagram at −50 °C: (a) expander impeller and (b) compressor impeller

Grahic Jump Location
Fig. 17

Waterfall diagram and zoomed waterfall diagram at −50 °C: (a) expander impeller and (b) compressor impeller

Grahic Jump Location
Fig. 18

Response of expander impeller at −50 °C and 585 Hz: (a) time signal, (b) frequency spectrum, (c) trajectory of rotor axis, and (d) Poincaré diagram

Grahic Jump Location
Fig. 19

Trajectory of rotor axis at −50 °C and 585 Hz

Grahic Jump Location
Fig. 20

Response of expander impeller at −50 °C and 648 Hz: (a) time signal, (b) frequency spectrum, (c) trajectory of rotor axis, and (d) Poincaré diagram

Grahic Jump Location
Fig. 21

Trajectories of rotor axis at −50 °C and 648 Hz

Grahic Jump Location
Fig. 22

Bifurcation diagram and zoomed bifurcation diagram at −100 °C: (a) expander impeller and (b) compressor impeller

Grahic Jump Location
Fig. 23

Waterfall diagram and zoomed waterfall diagram at −100 °C: (a) expander impeller and (b) compressor impeller

Grahic Jump Location
Fig. 24

Response of expander impeller at −100 °C and 648 Hz: (a) time signal, (b) frequency spectrum, (c) trajectory of rotor axis, and (d) Poincaré diagram

Grahic Jump Location
Fig. 25

Trajectories of rotor axis at −100 °C and 648 Hz

Grahic Jump Location
Fig. 26

Experimental system

Grahic Jump Location
Fig. 27

Serial number of tilting pads

Grahic Jump Location
Fig. 28

Eddy current sensors arrangement

Grahic Jump Location
Fig. 29

Temperatures of tilting pads under different environment temperatures

Grahic Jump Location
Fig. 30

Experimental result of trajectories at 63 Hz and −50 °C

Grahic Jump Location
Fig. 31

Waterfall diagram on (a) temperature and (b) rotating speed

Grahic Jump Location
Fig. 32

Vibration amplitude versus (a) environment temperature and (b) rotating speed

Grahic Jump Location
Fig. 33

2D diagram of rotating speed and environment temperature versus vibration amplitude: (a) expander impeller, (b) compressor impeller, (c) expander bearing, and (d) compressor bearing

Grahic Jump Location
Fig. 34

Sketch map of tilting pad bearing

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In