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Research Papers: Gas Turbines: Structures and Dynamics

# Geometric Mistuning Identification of Integrally Bladed Rotors Using Modified Modal Domain Analysis

[+] Author and Article Information
Yasharth Bhartiya

ANSYS, Inc.,
Canonsburg, PA 15317
e-mail: yasharth@gmail.com

Alok Sinha

Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: axs22@psu.edu

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received April 15, 2014; final manuscript received May 23, 2014; published online July 2, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 136(12), 122504 (Jul 02, 2014) (8 pages) Paper No: GTP-14-1199; doi: 10.1115/1.4027762 History: Received April 15, 2014; Revised May 23, 2014

## Abstract

Modified modal domain analysis (MMDA) is a novel method for the development of a reduced order model of a bladed rotor with geometric mistuning. This method utilizes proper orthogonal decomposition (POD) of coordinate measurement machine (CMM) data on blades' geometries, and sector analyses using ansys and solid modeling. In a recent paper, MMDA has been extended to use second order Taylor series approximations of perturbations in mass and stiffness matrices ($δM$ and $δK$) instead of exact $δM$ and $δK$. Taylor series expansions of deviations in mass and stiffness matrices due to geometric mistuning give a direct approach for generating the reduced order model from the components of POD features of spatial variations in blades' geometries. Reversing the process, algorithms for mistuning identification based on MMDA are presented in this paper to calculate the geometric mistuning parameters. Two types of algorithm, one based on modal analyses and the other on the forced responses, are presented. The validity of these methods are then verified through a mistuned academic rotor.

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## Figures

Fig. 1

Finite element model of a bladed disk [7]

Fig. 2

POD features #1 and #2 [8]

Fig. 3

Mistuning parameter ξ1 estimated using modal analysis (true mean geometry)

Fig. 4

Mistuning parameter ξ2 estimated using modal analysis (true mean geometry)

Fig. 5

Mistuning parameter ξ1 estimated using modal analysis (approx. mean geometry)

Fig. 6

Mistuning parameter ξ2 estimated using modal analysis (approx. mean geometry)

Fig. 7

Mistuning parameter ξ1 estimated using harmonic analysis (true mean geometry and true damping coefficient)

Fig. 8

Mistuning parameter ξ2 estimated using harmonic analysis (true mean geometry and true damping coefficient)

Fig. 9

Mistuning parameter ξ1 estimated using harmonic analysis (approx. mean geometry and 80% error in damping coefficient)

Fig. 10

Mistuning parameter ξ2 estimated using harmonic analysis (approx. mean geometry and 80% error in damping coefficient)

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