Research Papers: Hydrodynamic Lubrication

Nonlinear Dynamic Analysis of High Speed Oil-Free Turbomachinery With Focus on Stability and Self-Excited Vibration

[+] Author and Article Information
P. Bonello

School of Mechanical, Aerospace
and Civil Engineering,
University of Manchester,
Pariser Building,
Sackville Street,
Manchester M13 9PL, UK
e-mail: philip.bonello@manchester.ac.uk

H. M. Pham

School of Mechanical, Aerospace
and Civil Engineering,
University of Manchester,
Pariser Building,
Sackville Street,
Manchester M13 9PL, UK

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 6, 2014; final manuscript received June 3, 2014; published online July 15, 2014. Assoc. Editor: Daniel Nélias.

J. Tribol 136(4), 041705 (Jul 15, 2014) (10 pages) Paper No: TRIB-14-1003; doi: 10.1115/1.4027859 History: Received January 06, 2014; Revised June 03, 2014

This paper presents a generic technique for the transient nonlinear dynamic analysis (TNDA) and the static equilibrium stability analysis (SESA) of a turbomachine running on foil air bearings (FABs). This technique is novel in two aspects: (i) the turbomachine structural model is generic, based on uncoupled modes (rotor is flexible, nonsymmetric and includes gyroscopic effects; dynamics of support structure can be accommodated) and (ii) the finite-difference (FD) state equations of the air films are preserved and solved simultaneously with the state equations of the foil structures and the state equations of the turbomachine modal model, using a readily available implicit integrator (for TNDA) and a predictor-corrector approach (for SESA). An efficient analysis is possible through the extraction of the state Jacobian matrix using symbolic computing. The analysis is first applied to the finite-element model of a small commercial automotive turbocharger that currently runs on floating ring bearings (FRBs) and is slightly adapted here for FABs. The results of SESA are shown to be consistent with TNDA. The case study shows that, for certain bearing parameters, it is possible to obtain a wide speed range of stable static equilibrium operation with FABs, in contrast to the present installation with FRBs. Application of the method to a test rig reported in the literature reveals a reasonable degree of correlation between theory and experiment.

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Pham, H. M., and Bonello, P., 2013, “Efficient Techniques for the Computation of the Nonlinear Dynamics of a Foil-Air Bearing Rotor System,” ASME Paper No. GT2013-94389. [CrossRef]
Bonello, P., and Pham, H. M., 2014, “The Efficient Computation of the Nonlinear Dynamic Response of a Foil-Air Bearing Rotor System,” J. Sound Vib., 333(15), pp. 3459–3478. [CrossRef]
Le Lez, S., Arghir, M., and Frene, J., 2009, “Nonlinear Numerical Prediction of Gas Foil Bearing Stability and Unbalanced Response,” ASME J. Eng. Gas Turbine Power, 131(1), p. 012503. [CrossRef]
Wang, C.-C., and Chen, C.-K., 2001, “Bifurcation of Self-Acting Gas Journal Bearings,” ASME J. Tribol., 123(4), pp. 755–767. [CrossRef]
Zhang, J., Kang, W., and Liu, Y., 2009, “Numerical Method and Bifurcation Analysis of Jeffcott Rotor System Supported in Gas Journal Bearing,” ASME J. Comput. Nonlinear Dyn., 4(1), p. 011007. [CrossRef]
Kim, D., 2007, “Parametric Studies on Static and Dynamic Performance of Air Foil Bearings With Different Top Foil Geometries and Bump Stiffness Distributions,” ASME J. Tribol., 129(2), pp. 354–364. [CrossRef]
Song, J., and Kim, D., 2007, “Foil Gas Bearing With Compression Springs: Analyses and Experiments,” ASME J. Tribol., 129(3), pp. 628–639. [CrossRef]
Lee, D.-H., Kim, Y.-C., and Kim, K.-W., 2009, “The Dynamic Performance Analysis of Foil Bearings Considering Coulomb Friction: Rotating Unbalance Response,” Tribol. Trans., 52(2), pp. 146–156. [CrossRef]
Faria, M. T. C., and San Andrès, L., 2000, “On the Numerical Modeling of High-Speed Hydrodynamic Gas Bearings,” ASME J. Tribol., 122(1), pp. 124–130. [CrossRef]
Shampine, L. F., and Reichelt, M. W., 1997, “The matlab ODE Suite,” SIAM J. Sci. Comput., 18(1), pp. 1–22. [CrossRef]
Kim, D., Lee, A. S., and Choi, B. S., 2013, “Evaluation of Foil Bearing Performance and Nonlinear Rotordynamics of 120 kW Oil-Free Gas Turbine Generator,” ASME Paper No. GT2013-95800. [CrossRef]
Lee, D., and Kim, D., 2010, “Five Degrees of Freedom Nonlinear Rotor Dynamics Model of a Rigid Rotor Supported by Multiple Airfoil Bearings,” Proceedings of the 8th IFToMM International Conference on Rotor Dynamics, KIST, Seoul, Korea, Sept. 12–15, pp. 819–826.
Bonello, P., 2009, “Transient Modal Analysis of the Nonlinear Dynamics of a Turbocharger on Floating Ring Bearings,” Proc. Inst. Mech. Eng., Part J, 223(1), pp. 79–93. [CrossRef]
Peng, Z.-C., and Khonsari, M. M., 2004, “Hydrodynamic Analysis of Compliant Foil Bearings With Compressible Air Flow,” ASME J. Tribol., 126(3), pp. 542–546. [CrossRef]
Ewins, D. J., 2000, Modal Testing: Theory, Practice, and Application, 2nd ed., Research Studies, Baldock, UK.
Groves, K. H., and Bonello, P., 2010, “Improved Identification of Squeeze-Film Damper Models for Aeroengine Vibration Analysis,” Tribol. Int., 43(9), pp. 1639–1649. [CrossRef]
Dahlquist, G., 1974, Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ.
Seydel, R., 1994, Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos, Springer, New York.
Kirk, R. G., Alsaeed, A. A., and Gunter, E. J., 2007, “Stability Analysis of a High-Speed Automotive Turbocharger,” Tribol. Trans., 50(3), pp. 427–434. [CrossRef]
Holmes, R., Brennan, M. J., and Gottrand, B., 2004, “Vibration of an Automotive Turbocharger—A Case Study,” Proceedings of the 8th International Conference on Vibrations in Rotating Machinery, University of Wales, Swansea, UK, Sept. 7–9, IMechE Conference Transactions, pp. 445–455.
Heshmat, H., 1994, “Advancements in the Performance of Aerodynamic Foil Journal Bearings: High Speed and Load Capability,” ASME J. Tribol., 116(2), pp. 287–295. [CrossRef]


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Fig. 1

Turbocharger assembly with FABs: (a) turbocharger schematic and (b) cross section of FAB

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Fig. 2

Turbocharger rotor: (a) rotor FE model and (b) free–free rotor modes at zero rotor speed

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Fig. 3

FAB journal trajectories at 5000 rpm from default initial conditions over 20 revolutions, test 1: (a) FAB1 and (b) FAB2 (SS: steady-state)

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Fig. 4

SESA results for tests 1–3: (a) perturbation exponential growth factor and (b) ratio of perturbation frequency to rotor speed

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Fig. 5

Divergence of FAB journal trajectories at 6000 rpm from 1% perturbed static equilibrium over 200 revolutions, test 1: (a) FAB1 and (b) FAB2

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Fig. 6

Divergence of FAB journal trajectories at 100,000 rpm from 1% perturbed static equilibrium over 250 revolutions, test 1: (a) FAB1 and (b) FAB2

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Fig. 7

Frequency spectra of the test 1 limit cycles (FAB1, y-direction): (a) 6000 rpm and (b) 100,000 rpm

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Fig. 8

SESA results (perturbation exponential growth factor): tests 3–5 and tests 6–8

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Fig. 9

FAB journal trajectories at 100,000 rpm test 7 over last 50 rev/s out of 200 rev/s from 20% perturbed static equilibrium: (a) FAB1 and (b) FAB2

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Fig. 10

Foil journal bearing test apparatus [21]

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Fig. 11

Analyzer output for probe Ry at turbine end; coastdown from 2200 rev/s [21]

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Fig. 12

SESA results for experimental rig in Fig. 10: (a) perturbation exponential growth factor and (b) perturbation frequency

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Fig. 13

Frequency spectrum of limit cycle at 2200 rev/s of right-hand FAB in Fig. 10 (y vibration): (a) predicted and (b) measurement from Ref. [21]




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