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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June 2017
Research-Article
A Taylor Series Expansion Approach for Nonlinear Blade Forced Response Prediction Considering Variable Rotational Speed
Torsten Heinze,
Torsten Heinze
Institute of Dynamics and Vibration Research,
Leibniz Universität Hannover,
Hannover 30167, Germany
e-mail: heinze@ids.uni-hannover.de
Leibniz Universität Hannover,
Hannover 30167, Germany
e-mail: heinze@ids.uni-hannover.de
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Lars Panning-von Scheidt,
Lars Panning-von Scheidt
Institute of Dynamics and Vibration Research,
Leibniz Universität Hannover,
Hannover 30167, Germany
Leibniz Universität Hannover,
Hannover 30167, Germany
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Jörg Wallaschek,
Jörg Wallaschek
Institute of Dynamics and Vibration Research,
Leibniz Universität Hannover,
Hannover 30167, Germany
Leibniz Universität Hannover,
Hannover 30167, Germany
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Andreas Hartung
Andreas Hartung
MTU Aero Engines AG,
München 80995, Germany
München 80995, Germany
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Torsten Heinze
Institute of Dynamics and Vibration Research,
Leibniz Universität Hannover,
Hannover 30167, Germany
e-mail: heinze@ids.uni-hannover.de
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
Leibniz Universität Hannover,
Hannover 30167, Germany
Jörg Wallaschek
Institute of Dynamics and Vibration Research,
Leibniz Universität Hannover,
Hannover 30167, Germany
Leibniz Universität Hannover,
Hannover 30167, Germany
Andreas Hartung
MTU Aero Engines AG,
München 80995, Germany
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. Jun 2017, 139(6): 062503 (10 pages)
Published Online: January 24, 2017
Article history
Received:
September 26, 2016
Revised:
October 6, 2016
Citation
Heinze, T., Panning-von Scheidt, L., Wallaschek, J., and Hartung, A. (January 24, 2017). "A Taylor Series Expansion Approach for Nonlinear Blade Forced Response Prediction Considering Variable Rotational Speed." ASME. J. Eng. Gas Turbines Power. June 2017; 139(6): 062503. https://doi.org/10.1115/1.4035286
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