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Research Papers: Gas Turbines: Structures and Dynamics

Estimation of Forcing Function for a Geometrically Mistuned Bladed Rotor Via Modified Modal Domain Analysis

[+] Author and Article Information
Vinod Vishwakarma

Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: vinod.vish@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 June 29, 2015; final manuscript received September 3, 2015; published online October 28, 2015. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(4), 042507 (Oct 28, 2015) (8 pages) Paper No: GTP-15-1225; doi: 10.1115/1.4031563 History: Received June 29, 2015; Revised September 03, 2015

Modified modal domain analysis (MMDA) is a method to generate an accurate reduced-order model (ROM) of a bladed disk with geometric mistuning. An algorithm based on the MMDA ROM and a state observer is developed to estimate forcing functions for synchronous (including integer multiples) conditions from the dynamic responses obtained at few nodal locations of blades. The method is tested on a simple spring-mass model, finite element model (FEM) of a geometrically mistuned academic rotor, and FEM of a bladed rotor of an industrial-scale transonic research compressor. The accuracy of the forcing function estimation algorithm is examined by varying the order of ROM and the number of vibration output signals.

Copyright © 2016 by ASME
Topics: Rotors , Blades
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References

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Kammerer, A. , and Abhari, R. S. , 2010, “ Blade Forcing Function and Aerodynamic Work Measurements in a High Speed Centrifugal Compressor With Inlet Distortion,” ASME J. Eng. Gas Turbines Power, 132(9), p. 092504. [CrossRef]
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Vishwakarma, V. , Sinha, A. , Bhartiya, Y. , and Brown, J. M. , 2015, “ Modified Modal Domain Analysis of a Bladed Rotor Using Coordinate Measurement Machine Data on Geometric Mistuning,” ASME J. Eng. Gas Turbines Power, 137(4), p. 042502.
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Mercadel, M. , vonFlotow, A. , and Tappert, P. , 2001, “ Damage Identification by NSMS Blade Resonance Tracking in Mistuned Rotors,” IEEE Aerospace Conferences (AERO), Big Sky, MT, Mar. 10–17, pp. 7-3263–7-3277.
Salhi, B. , Lardies, J. , Berthillier, M. , Voinis, P. , and Bodel, C. , 2007, “ A Subspace Approach for the Analysis of Blade Tip Timing Data,” 12th IFToMM World Congress, Besancon, France, June 18–21, pp. 885–906.
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Figures

Grahic Jump Location
Fig. 1

Three degrees-of-freedom per sector rotor model

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Fig. 2

Three degrees-of-freedom model force estimation, force applied on m1i, nodal displacements of m1i are observed (nn=1,no=1,nf=1)

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Fig. 3

Three degrees-of-freedom model force estimation, force applied on m1i and m2, nodal displacements of m1i are observed (nn=2,no=1,nf=1)

Grahic Jump Location
Fig. 4

Three degrees-of-freedom model force estimation, force applied on m1i and m2, nodal displacements of m1i and m2 are observed (nn=2,no=2,nf=2)

Grahic Jump Location
Fig. 5

Three degrees-of-freedom model force estimation, force applied on m1i, m2, and m3, nodal displacements of m1i, m2, and m3 are observed (nn=3,no=3,nf=2)

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Fig. 6

Three degrees-of-freedom model force estimation, force applied on m1i, m2 and m3, nodal displacements of m1i, m2, and m3 are observed (nn=3,no=3,nf=3)

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Fig. 7

Academic rotor and POD features

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Fig. 8

Academic rotor force estimation, force applied on one location at the tip of each blade, displacements of three nodes for each blade are observed, and one POD feature is used in the ROM (nn=1,no=3,nf=5,np=1)

Grahic Jump Location
Fig. 9

Academic rotor force estimation, force applied on one location at the tip of each blade, displacements of four nodes for each blade are observed, and one POD feature is used in ROM (nn=1,no=4,nf=5,np=1)

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Fig. 10

Academic rotor force estimation, force applied on one location at the tip of each blade, displacement of one node of each blade is observed, and two POD features are used in ROM (nn=1,no=1,nf=5,np=2)

Grahic Jump Location
Fig. 11

Academic rotor force estimation, force applied on one location at tip of each blade, displacements of four nodes for each blades are observed and two POD features are used in ROM (nn=1,no=4,nf=5,np=2)

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Fig. 12

Transonic rotor force estimation, force applied on one location at the tip of each blade, axial displacements of eight nodes for each blade are observed and 17 POD feature are used in ROM (nn=1,no=8,nf=5,np=17)

Grahic Jump Location
Fig. 13

Transonic rotor force estimation, force applied on one location at the tip of each blade, axial displacements of eight nodes of each blade are observed, and 15 POD feature are used in ROM (nn=1,no=8,nf=5,np=15)

Grahic Jump Location
Fig. 14

Transonic rotor force estimation, force applied on one location at the tip of each blade, axial displacements of eight nodes for each blade are observed, and nine POD feature are used in ROM (nn=1,no=8,nf=5,np=9)

Grahic Jump Location
Fig. 15

Transonic rotor force estimation, force applied on one location at the tip of each blade, axial displacements of eight nodes are observed of each blade, and 12 POD feature are used in ROM (nn=1,no=8,nf=5,np=12)

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