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Research Papers: Gas Turbines: Structures and Dynamics

Analysis of Bifurcations in Multiharmonic Analysis of Nonlinear Forced Vibrations of Gas Turbine Engine Structures With Friction and Gaps

[+] Author and Article Information
E. P. Petrov

School of Engineering and Informatics,
University of Sussex,
Brighton BN1 9QT, UK
e-mail: y.petrov@sussex.ac.uk

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received January 26, 2016; final manuscript received February 4, 2016; published online April 12, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(10), 102502 (Apr 12, 2016) (11 pages) Paper No: GTP-16-1033; doi: 10.1115/1.4032906 History: Received January 26, 2016; Revised February 04, 2016

An efficient frequency-domain method has been developed to analyze the forced response of large-scale nonlinear gas turbine structures with bifurcations. The method allows detection and localization of the design and operating conditions sets where bifurcations occur, calculation of tangents to the solution trajectory, and continuation of solutions under parameter variation for structures with bifurcations. The method is aimed at calculation of steady-state periodic solution, and multiharmonic representation of the variation of displacements in time is used. The possibility of bifurcations in realistic gas-turbine structures with friction contacts and with cubic nonlinearity has been shown.

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References

Sanliturk, K. Y. , Imregun, M. , and Ewins, D. J. , 1997, “ Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers,” ASME J. Vib. Acoust., 119(1), pp. 96–103. [CrossRef]
Chen, J. , and Menq, C. , 2001, “ Prediction of Periodic Response of Blades Having 3D Nonlinear Shroud Constraints,” ASME J. Eng. Gas Turbines Power, 123(4), pp. 901–909. [CrossRef]
Petrov, E. P. , and Ewins, D. J. , 2003, “ Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Discs,” ASME J. Turbomach., 125(2), pp. 364–371. [CrossRef]
Zucca, S. , Firrone, C. M. , and Gola, M. M. , 2012, “ Numerical Assessment of Friction Damping at Turbine Blade Root Joints by Simultaneous Calculation of the Static and Dynamic Contact Loads,” Nonlinear Dyn., 67(3), pp. 1943–1955. [CrossRef]
Laborenz, J. , Krack, M. , Panning, L. , Wallaschek, J. , Denk, M. , and Masserey, P.-A. , 2012, “ Eddy Current Damper for Turbine Blading: Electromagnetic Finite Element Analysis and Measurement Results,” ASME J. Eng. Gas Turbines Power, 134(4), p. 042504. [CrossRef]
Siewert, C. , Panning, L. , Wallaschek, J. , and Richter, C. , 2009, “ Multiharmonic Forced Response Analysis of a Turbine Blading Coupled by Nonlinear Contact Forces,” ASME Paper No. GT2009-59201.
Batailly, A. , Legrand, M. , et al. ., 2012, “ Numerical-Experimental Comparison in the Simulation of Rotor/Stator Interaction Through Blade-Tip/Abradable Coating Contact,” ASME J. Eng. Gas Turbines Power, 134(8), p. 082504. [CrossRef]
Cigeroglu, E. , An, N. , and Menq, C.-H. , 2007, “ Wedge Damper Modeling and Forced Response Prediction of Frictionally Constrained Blades,” ASME Paper No. GT2007-27963.
Cameron, T. M. , and Griffin, J. H. , 1989, “ An Alternating Frequency/Time Domain Method for Calculating Steady Response of Nonlinear Dynamic Systems,” ASME J. Appl. Mech., 56(1), pp. 149–154. [CrossRef]
Cardona, A. , Coune, T. , Lerusse, A. , and Geradin, M. , 1994, “ A Multiharmonic Method for Non-Linear Vibration Analysis,” Int. J. Numer. Methods Eng., 37(9), pp. 1593–1608. [CrossRef]
Petrov, E. P. , 2007, “ Direct Parametric Analysis of Resonance Regimes for Nonlinear Vibrations of Bladed Discs,” ASME J. Turbomach., 129(3), pp. 495–502. [CrossRef]
Petrov, E. P. , 2009, “ Method for Sensitivity Analysis of Resonance Forced Response of Bladed Disks With Nonlinear Contact Interfaces,” ASME J. Eng. Gas Turbines Power, 131(2), p. 022510. [CrossRef]
Petrov, E. P. , 2005, “ Sensitivity Analysis of Nonlinear Forced Response for Bladed Discs With Friction Contact Interfaces,” ASME Paper No. GT2005-68935.
Kuznetsov, Y. A. , 1998, Elements of Applied Bifurcation Theory, Springer-Verlag, New York.
Moore, G. , and Spence, A. , 1980, “ The Calculation of Turning Points of Nonlinear Equations,” SIAM J. Numer. Anal., 17(4), pp. 567–576. [CrossRef]
Geradin, M. , and Cardona, A. , 2001, Flexible Multibody Dynamics: A Finite Element Approach, Wiley, Chichester, UK, p. 327.
Felippa, C. A. , 1987, “ Traversing Critical Points by Penalty Springs,” NUMETA’87 Conference, Swansea, Wales, Nijhoff Publishers, Dordrecht, The Netherlands, pp. C2/1–C2/8.
Wriggers, P. , and Simo, J. C. , 1990, “ A General Procedure for the Direct Computation of Turning and Bifurcation Points,” Int. J. Numer. Methods Eng., 30(1), pp. 155–176. [CrossRef]
Riks, E. , 1979, “ An Incremental Approach to the Solution of the Snapping and Buckling Problems,” Int. J. Solids Struct., 15(7), pp. 529–551. [CrossRef]
Crisfield, M. , 1981, “ A Fast Incremental/Iterative Solution Procedure That Handles Snap-Through,” Comput. Struct., 13, pp. 55–62. [CrossRef]
Fried, I. , 1984, “ Orthogonal Trajectory Accession to the Nonlinear Equilibrium Curve,” Comput. Methods Appl. Mech. Eng., 47(3), pp. 283–297. [CrossRef]
Petrov, E. P. , 2014, “ Sensitivity Analysis of Multiharmonic Self-Excited Limit-Cycle Vibrations in Gas-Turbine Engine Structures With Nonlinear Contact Interfaces,” ASME Paper No. GT2014-26673.
Petrov, E. P. , 2012, “ Multiharmonic Analysis of Nonlinear Whole Engine Dynamics With Bladed Disc-Casing Rubbing Contacts,” ASME Paper No. GT2012-68474.
Huang, S. , Petrov, E. P. , and Ewins, D. J. , 2006, “ Comprehensive Analysis of Periodic Regimes of Forced Vibration for Structures With Nonlinear Snap-Through Springs,” 6th International Conference on Modern Practice in Stress and Vibration Analysis, Bath, UK, Sept. 5–7, pp. 443–453.
DaCunha, J. , and Davis, J. , 2011, “ A Unified Floquet Theory for Discrete, Continuous, and Hybrid Periodic Linear Systems,” J. Differ. Equations, 251(11), pp. 2987–3027. [CrossRef]
Von Groll, G. , and Ewins, D. J. , 2001, “ The Harmonic Balance Method With Arc-Length Continuation in Rotor/Stator Contact Problems,” J. Sound Vib., 241(2), pp. 223–233. [CrossRef]

Figures

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Fig. 1

A trajectory of maximum displacement calculated as a function of excitation frequency

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Fig. 2

A rotor with negative linear stiffness

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Fig. 3

Equilibrium configurations for the prestressed rotor support

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Fig. 4

Forced response of a simple rotor model: major solution curve and bifurcation points

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Fig. 5

Forced response of a simple rotor model with all the found bifurcation branches

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Fig. 6

Forced response of a simple rotor model with all the found bifurcation branches: a zoomed view for a low-frequency range

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Fig. 7

Comparison of the time-domain and frequency-domain solutions: a case of frequency increasing

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Fig. 8

Comparison of the time-domain and frequency-domain solutions: a case of frequency decreasing

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Fig. 9

Time-domain and frequency-domain solutions: the difference between displacements of bladed disk and casing

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Fig. 10

Contact interaction force at third rubbing contact for all the branching solutions

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Fig. 11

Contact interaction force at third rubbing contact for all the branching solutions: a zoomed view

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Fig. 12

Contact interaction force at first rubbing contact for all the branching solutions

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Fig. 13

Contact interaction force at fourth rubbing contact for all the branching solutions

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Fig. 14

Time- and frequency-domain solutions: contact force at first rubbing contact for rotor acceleration, case 1

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Fig. 15

Time- and frequency-domain solutions: contact force at first rubbing contact for rotor acceleration, case 2

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Fig. 16

Time- and frequency-domain solutions: contact force at first rubbing contact for rotor deceleration

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Fig. 17

Relative coefficient values of the tangents' equation

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Fig. 18

Convergence of the bifurcation localization: the simple rotor case

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Fig. 19

Convergence of the bifurcation localization: the gas turbine engine model

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