0
Research Papers: Gas Turbines: Structures and Dynamics

Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and Its Application to Bladed Disks With Shroud Contact

[+] Author and Article Information
Malte Krack

e-mail: krack@ids.uni-hannover.de

Jörg Wallaschek

Institute of Dynamics and Vibration Research,
Leibniz Universität Hannover,
Hannover 30167, Germany

Christian Siewert

Siemens AG - Energy Sector,
Steam Turbine Engineering E F PR SU R&D BL2,
Mülheim an der Ruhr 45478, Germany

Andreas Hartung

MTU Aero Engines GmbH,
München 80995, Germany

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June 27, 2013; final manuscript received July 1, 2013; published online August 30, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 135(10), 102502 (Aug 30, 2013) (8 pages) Paper No: GTP-13-1187; doi: 10.1115/1.4025002 History: Received June 27, 2013; Revised July 01, 2013

The design of bladed disks with contact interfaces typically requires analyses of the resonant forced response and flutter-induced limit cycle oscillations. The steady-state vibration behavior can efficiently be calculated using the multiharmonic balance method. The dimension of the arising algebraic systems of equations is essentially proportional to the number of harmonics and the number of degrees of freedom (DOFs) retained in the model. Extensive parametric studies necessary, e.g., for robust design optimization are often not possible in practice due to the resulting computational effort. In this paper, a two-step nonlinear reduced order modeling approach is proposed. First, the autonomous nonlinear system is analyzed using the generalized Fourier-Galerkin method. In order to efficiently study localized nonlinearities in large-scale systems, an exact condensation approach as well as analytically calculated gradients are employed. Moreover, a continuation method is employed in order to predict nonlinear modal interactions. Modal properties such as eigenfrequency and modal damping are directly calculated with respect to the kinetic energy in the system. In a second step, a reduced order model is built based on the single nonlinear resonant mode theory. It is shown that linear damping and harmonic forcing can be superimposed. Moreover, similarity properties can be exploited to vary normal preload or gap values in contact interfaces. Thus, a large parameter space can be covered without the need for recomputation of nonlinear modal properties. The computational effort for evaluating the reduced order model is almost negligible since it contains a single DOF only, independent of the original system. The methodology is applied to both a simplified and a large-scale model of a bladed disk with shroud contact interfaces. Forced response functions, backbone curves for varying normal preload, and excitation level as well as flutter-induced limit cycle oscillations are analyzed and compared to conventional methods. The limits of the proposed methodology are indicated and discussed.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Cameron, T. M., Griffin, J. H., Kielb, R. E., and Hoosac, T. M., 1990, “An Integrated Approach for Friction Damper Design,” ASME J. Vib. Acoust., 112(2), pp. 175–182. [CrossRef]
Panning, L., 2002, Untersuchungen zum Schwingungsverhalten von Gasturbinenschaufeln mit asymmetrischen Reibelementen.
Petrov, E. P., and Ewins, D. J., 2004, “State-of-the-Art Dynamic Analysis for Non-Linear Gas Turbine Structures,” Proc. IMechE G: J. Aerosp. Eng., 218(3), pp. 199–211. [CrossRef]
Laxalde, D., Thouverez, F., Sinou, J. J., and Lombard, J. P., 2007, “Qualitative Analysis of Forced Response of Blisks With Friction Ring Dampers,” Eur. J. Mech. A Solids, 26(4), pp. 676–687. [CrossRef]
Siewert, C., Panning, L., Wallaschek, J., and Richter, C., 2010, “Multiharmonic Forced Response Analysis of a Turbine Blading Coupled by Nonlinear Contact Forces,” ASME J. Eng. Gas Turb. Power, 132(8), p. 082501. [CrossRef]
Petrov, E. P., and Ewins, D. J., 2003, “Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks,” ASME J. Turbomach., 125(2), pp. 364–371. [CrossRef]
Nacivet, S., Pierre, C., Thouverez, F., and Jezequel, L., 2003, “A Dynamic Lagrangian Frequency-Time Method for the Vibration of Dry-Friction-Damped Systems,” J. Sound Vib., 265(1), pp. 201–219. [CrossRef]
Poudou, O., Pierre, C., and Reisser, B., 2004, “A New Hybrid Frequency-Time Domain Method for the Forced Vibration of Elastic Structures With Friction and Intermittent Contact,” Proc. of the 10th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, HI, March 7–11, Paper No. ISROMAC10-2004-068.
Petrov, E. P., 2009, “Analysis of Sensitivity and Robustness of Forced Response for Nonlinear Dynamic Structures,” Mech. Syst. Sig. Process., 23(1), pp. 68–86. [CrossRef]
Nikolic, M., Petrov, E. P., and Ewins, D. J., 2008, “Robust Strategies for Forced Response Reduction of Bladed Disks Based on Large Mistuning Concept,” ASME J. Eng. Gas Turb. Power, 130(2), p. 022501. [CrossRef]
Krack, M., Panning-von Scheidt, L., Wallaschek, J., Siewert, C., and Hartung, A., 2012, “Robust Design of Friction Interfaces of Bladed Disks With Respect to Parameter Uncertainties,” Proc. of ASME Turbo Expo 2012, Copenhagen, Denmark, June 11–15, Paper No. GT2012-68578.
Bladh, R., Castanier, M. P., and Pierre, C., 1999, “Reduced Order Modeling and Vibration Analysis of Mistuned Bladed Disk Assemblies With Shrouds,” ASME J. Eng. Gas Turb. Power, 121(3), pp. 515–522. [CrossRef]
Craig, R. R., 2000, “Coupling of Substructures for Dynamic Analysis: An Overview,” AIAA Paper No. 2000-1573. [CrossRef]
Berthillier, M., Dhainhaut, M., Burgaud, F., and Garnier, V., 1997, “A Numerical Method for the Prediction of Bladed Disk Forced Response,” ASME J. Eng. Gas Turb. Power, 112(2), pp. 404–410. [CrossRef]
Siewert, C., Krack, M., Panning, L., and Wallaschek, J., 2008, “The Nonlinear Analysis of the Multiharmonic Forced Response of Coupled Turbine Blading,” Proc. of the 12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, HI, March 17–22, Paper No. ISROMAC12-2008-20219.
Pierre, C., Ferri, A. A., and Dowell, E. H., 1985, “Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method,” ASME J. Appl. Mech., 52(4), pp. 958–964. [CrossRef]
Petrov, E. P., 2006, “Direct Parametric Analysis of Resonance Regimes for Nonlinear Vibrations of Bladed Discs,” ASME Turbo Expo 2006: Power for Land, Sea and Air, Barcelona, Spain, May 8–11, ASME Paper No. GT2006-90147. [CrossRef]
Laxalde, D., and Thouverez, F., 2009, “Complex Non-Linear Modal Analysis for Mechanical Systems Application to Turbomachinery Bladings With Friction Interfaces,” J. Sound Vib., 322(4–5), pp. 1009–1025. [CrossRef]
Kerschen, G., Peeters, M., Golinval, J. C., and Vakakis, A. F., 2009, “Nonlinear Normal Modes, Part I: A Useful Framework for the Structural Dynamicist: Special Issue: Non-Linear Structural Dynamics,” Mech. Syst. Sig. Process., 23(1), pp. 170–194. [CrossRef]
Guillen, J., and Pierre, C., 1998, “An Efficient, Hybrid, Frequency-Time Domain Method for the Dynamics of Large-Scale Dry-Friction Damped Structural Systems,” Proc. of the IUTAM Symposium, Munich, Germany, August 3–7.
Krack, M., Panning-von Scheidt, L. and Wallaschek, J., 2013, “A High-Order Harmonic Balance Method for Systems With Distinct States,” J. Sound Vib., 332(21), pp. 5476–5488. [CrossRef]
Szemplinska-Stupnicka, W., 1979, “The Modified Single Mode Method in the Investigations of the Resonant Vibrations of Non-Linear Systems,” J. Sound Vib., 63(4), pp. 475–489. [CrossRef]
Chong, Y. H., and Imregun, M., 2000, “Development and Application of a Nonlinear Modal Analysis Technique for MDOF Systems,” J. Vib. Control, 7(2), pp. 167–179. [CrossRef]
Gibert, C., 2003, “Fitting Measured Frequency Response Using Non-Linear Modes,” Mech. Syst. Sig. Process., 17(1), pp. 211–218. [CrossRef]
Petrov, E. P., 2004, “Method for Direct Parametric Analysis of Nonlinear Forced Response of Bladed Discs With Friction Contact Interfaces,” ASME Turbo Expo 2004, Power for Land, Sea, and Air, Vienna, Austria, June 14–17, 2004, ASME Paper No. GT2004-53894. [CrossRef]
Petrov, E. P., 2012, “Analysis of Flutter-Induced Limit Cycle Oscillations in Gas-Turbine Structures With Friction, Gap, and Other Nonlinear Contact Interfaces,” ASME J. Turbomach., 134(6), p. 061018. [CrossRef]
Berthillier, M., Dupont, C., Mondal, R., and Barrau, J. J., 1998, “Blades Forced Response Analysis With Friction Dampers,” ASME J. Vib. Acoust., 120(2), pp. 468–474. [CrossRef]
Panning, L., Sextro, W., and Popp, K., 2000, “Optimization of Interblade Friction Damper Design,” ASME Turbo Expo 2000, Power for Land, Sea and Air, Munich, Germany, May 8–11, ASME Paper No. 2000-GT-0541.
Georgiades, F., Peeters, M., Kerschen, G., Golinval, J. C., and Ruzzene, M., 2008, “Nonlinear Modal Analysis and Energy Localization in a Bladed Disk Assembly,” ASME Turbo Expo 2008: Power for Land, Sea and Air, GT2008, Berlin, Germany, June 9–13, ASME Paper No. GT2008-51388. [CrossRef]
Krack, M., Herzog, A., Panning-von Scheidt, L., Wallaschek, J., Siewert, C., and Hartung, A., 2012, “Multiharmonic Analysis and Design of Shroud Friction Joints of Bladed Disks Subject to Microslip,” ASME 2012 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2012), Chicago, IL, August 12–15, ASME Paper No. DETC2012-70184.

Figures

Grahic Jump Location
Fig. 1

Clamped beam with nonlinear element

Grahic Jump Location
Fig. 2

Eigenfrequency of a clamped beam with friction nonlinearity

Grahic Jump Location
Fig. 3

Modal damping of a clamped beam with friction nonlinearity

Grahic Jump Location
Fig. 4

Forced response of a clamped beam with friction nonlinearity for varying excitation level

Grahic Jump Location
Fig. 5

Forced response of a clamped beam with friction nonlinearity for varying normal preload

Grahic Jump Location
Fig. 6

Resonance amplitude of a clamped beam with friction versus normal preload

Grahic Jump Location
Fig. 7

Limit cycle oscillation amplitude and frequency versus flutter intensity

Grahic Jump Location
Fig. 8

Limit cycle oscillation amplitude and frequency versus the limiting friction force

Grahic Jump Location
Fig. 9

Finite element model of a bladed disk with shroud contact

Grahic Jump Location
Fig. 10

Eigenfrequency of a bladed disk with shroud contact

Grahic Jump Location
Fig. 11

Modal damping of a bladed disk with shroud contact

Grahic Jump Location
Fig. 12

Forced response of a bladed disk with shroud contact for varying excitation level

Grahic Jump Location
Fig. 13

Forced response of a bladed disk with shroud contact for varying normal preload (solid lines: NMS, crosses: HBM)

Grahic Jump Location
Fig. 14

Limit cycle oscillation amplitude and frequency versus the flutter intensity

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