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

[+] Author Affiliations
Torsten Heinze, Lars Panning-von Scheidt, Jörg Wallaschek

Leibniz Universität Hannover, Hannover, Germany

Andreas Hartung

MTU Aero Engines AG, München, Germany

Paper No. GT2016-56375, pp. V07AT32A005; 14 pages
  • ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition
  • Volume 7A: Structures and Dynamics
  • Seoul, South Korea, June 13–17, 2016
  • Conference Sponsors: International Gas Turbine Institute
  • ISBN: 978-0-7918-4983-5
  • Copyright © 2016 by ASME


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 re-construct 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.

Copyright © 2016 by ASME



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