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Research Papers: Gas Turbines: Structures and Dynamics

Rotational Speed-Dependent Contact Formulation for Nonlinear Blade Dynamics Prediction

[+] Author and Article Information
Torsten Heinze

Institute of Dynamics and Vibration Research,
Leibniz Universität,
Hannover 30167, Germany
e-mail: heinze@ids.uni-hannover.de

Lars Panning-von Scheidt, Jörg Wallaschek

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

Andreas Hartung

MTU Aero Engines AG,
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 25, 2018; final manuscript received July 3, 2018; published online December 5, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(4), 042503 (Dec 05, 2018) (11 pages) Paper No: GTP-18-1332; doi: 10.1115/1.4040843 History: Received June 25, 2018; Revised July 03, 2018

Considering rotational speed-dependent stiffness for vibrational analysis of friction-damped bladed disk models has proven to lead to significant improvements in nonlinear frequency response curve computations. The accuracy of the result is driven by a suitable choice of reduction bases. Multimodel reduction combines various bases, which are valid for different parameter values. This composition reduces the solution error drastically. The resulting set of equations is typically solved by means of the harmonic balance method. Nonlinear forces are regularized by a Lagrangian approach embedded in an alternating frequency/time domain method providing the Fourier coefficients for the frequency domain solution. The aim of this paper is to expand the multimodel approach to address rotational speed-dependent contact situations. Various reduction bases derived from composing Craig–Bampton, Rubin–Martinez, and hybrid interface methods will be investigated with respect to their applicability to capture the changing contact situation correctly. The methods validity is examined based on small academic examples as well as large-scale industrial blade models. Coherent results show that the multimodel composition works successfully, even if multiple different reduction bases are used per sample point of variable rotational speed. This is an important issue in case that a contact situation for a specific value of the speed is uncertain forcing the algorithm to automatically choose a suitable basis. Additionally, the randomized singular value decomposition is applied to rapidly extract an appropriate multimodel basis. This approach improves the computational performance by orders of magnitude compared to the standard singular value decomposition, while preserving the ability to provide a best rank approximation.

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References

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Figures

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Fig. 1

Widening effect for rotational speed-dependent stiffness

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Fig. 3

Craig–Bampton and Rubin–Martinez reduction

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Fig. 4

Multimodel reduction

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Fig. 5

Large-scale model 1

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Fig. 6

Reductions for contact and free boundaries

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Fig. 7

Hybrid interface reduction for contact boundaries

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Fig. 8

Hybrid interface conditions (a) and various contact situations per rotational speed (b)

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Fig. 9

Singular values for various reductions

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Fig. 10

Large-scale model 2

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Fig. 11

Error of (randomized) singular value decomposition of T; top: T∈C1563×222, middle: T∈C19710×378, bottom: T∈C19710×528

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Fig. 12

Relative computational time of randomized singular value decomposition of T

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Fig. 13

Absolute computational time of randomized singular value decomposition of T

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Fig. 14

Mechanism of multiresonance

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Fig. 15

Friction coefficient interpolation

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Fig. 16

Campbell-diagram of model 1 for fixed and free shroud contact

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Fig. 17

Preload transition 1 of model 1

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Fig. 18

Preload transition 1 of model 1 in detail

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Fig. 19

Preload transition 2 of model 1

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Fig. 20

Preload transition 2 of model 1 in detail

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Fig. 21

Preload transition 3 of model 1

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Fig. 22

Campbell diagram of model 2 for fixed and free shroud contact; damper always in contact

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Fig. 23

Preload transition 1 of model 2

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Fig. 24

Preload transition 1 of model 2 in detail

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Fig. 25

Preload transition 1 of model 2 in detail

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Fig. 26

Preload transition 2 of model 2

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Fig. 27

Craig–Bampton and Rubin–Martinez reduction under contact boundary conditions

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