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Research Papers: Gas Turbines: Structures and Dynamics

A Taylor Series Expansion Approach for Nonlinear Blade Forced Response Prediction Considering Variable Rotational Speed

[+] Author and Article Information
Torsten Heinze

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

Lars Panning-von Scheidt

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

Jörg Wallaschek

Institute of Dynamics and Vibration Research,
Leibniz Universität Hannover,
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 September 26, 2016; final manuscript received October 6, 2016; published online January 24, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(6), 062503 (Jan 24, 2017) (10 pages) Paper No: GTP-16-1466; doi: 10.1115/1.4035286 History: Received September 26, 2016; Revised October 06, 2016

In the field of turbomachinery, great efforts are made to enhance computational tools to obtain reliable predictions of the vibrational behavior of friction-damped bladed disks. As a trade-off between computational burden and level of simplification, numerous methods were developed to reduce the nonlinear systems dimension. Using component mode synthesis methods (CMS), one is capable to describe the systems motion by interface and modal coordinates. Subsequently or alternatively, the dynamic compliance matrix can be evaluated efficiently by means of modal superposition to avoid the inversion of the dynamic stiffness matrix. Only the equations corresponding to the degrees-of-freedom (DOF) subject to localized nonlinear contact forces need to be solved simultaneously, whereas the solution of the linear DOF is obtained by exploiting the algebraic character of the set of equations. In this paper, an approach is presented to account for rotational speed-dependent stiffness in the subset of nonlinear DOF without the need to re-evaluate the associated eigenvalue problem (EVP) when rotational speed is changed. This is done by means of a Taylor series expansion of the eigenvalues and eigenvectors used for the modal superposition to reconstruct the dynamic compliance matrix. In the context of forced response predictions of friction-damped blisks, the expansion is performed up to different order for a simplified blisk model with nonlinear contact interfaces. The results are compared to the solution obtained by direct evaluation of the EVP at selected rotational speeds and the solution when dynamic compliance matrix is built up by direct inversion of the dynamic stiffness matrix. Finally, the proposed methods computational performance is analyzed.

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Figures

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Fig. 1

Relative computational time for inversion related to EVP versus dimension of matrix

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Fig. 2

Single-DOF model of a cyclic blisk segment for first flapwise bending mode

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Fig. 3

Campbell diagram of single-DOF model at different engine order excitations

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Fig. 4

Forced response of single-DOF model at engine order 1

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Fig. 5

Forced response of single-DOF model at engine order 3

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Fig. 6

Multi-DOF model of a blisk with shroud interfaces

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Fig. 10

Forced responses of multi-DOF model for variable increasing damping

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Fig. 11

Linearized and nonlinear forced responses of multi-DOF model for constant and interpolated stiffness

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Fig. 12

Nonlinear forced responses of multi-DOF model for constant and interpolated stiffness and higher harmonic order

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Fig. 13

Nonlinear forced responses of multi-DOF model for various constant and interpolated stiffnesses

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Fig. 7

Campbell diagram of multi-DOF model at engine order 5

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Fig. 8

Linearized forced response of multi-DOF model at engine order 5

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Fig. 9

Forced responses of multi-DOF model for constant and interpolated stiffness

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Fig. 14

Nonlinear forced responses of multi-DOF model using Taylor series expansion

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Fig. 15

Nonlinear forced responses of multi-DOF model using Taylor series expansion, small frequency range

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Fig. 16

Relative amplitude error of nonlinear forced responses of multi-DOF model using Taylor series expansion

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Fig. 17

Campbell diagram of multi-DOF model at engine order 14

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Fig. 18

Nonlinear forced responses of multi-DOF model using Taylor series expansion during veering

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Fig. 19

Campbell diagram of multi-DOF model at engine order 6

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Fig. 20

Nonlinear forced responses of multi-DOF model using Taylor series expansion during tangency region

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Fig. 21

Nonlinear forced responses of multi-DOF model using Taylor series expansion during tangency region, small frequency range

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Fig. 22

Nonlinear forced responses of multi-DOF model using Taylor series expansion during tangency region, varying operation points

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Fig. 23

Normalized preprocessing time

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Fig. 24

Normalized solving time

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