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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.

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Figures

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Fig. 1

Clamped beam with nonlinear element

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Fig. 2

Eigenfrequency of a clamped beam with friction nonlinearity

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Fig. 3

Modal damping of a clamped beam with friction nonlinearity

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Fig. 4

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

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Fig. 5

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

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Fig. 6

Resonance amplitude of a clamped beam with friction versus normal preload

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Fig. 7

Limit cycle oscillation amplitude and frequency versus flutter intensity

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Fig. 8

Limit cycle oscillation amplitude and frequency versus the limiting friction force

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Fig. 9

Finite element model of a bladed disk with shroud contact

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Fig. 10

Eigenfrequency of a bladed disk with shroud contact

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Fig. 11

Modal damping of a bladed disk with shroud contact

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Fig. 12

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

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Fig. 13

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

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Fig. 14

Limit cycle oscillation amplitude and frequency versus the flutter intensity

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