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Research Papers: Gas Turbines: Structures and Dynamics

Estimation of Forcing Functions on a Mistuned Bladed Rotor From Harmonic Response

[+] Author and Article Information
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 August 9, 2017; final manuscript received August 18, 2017; published online November 28, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(5), 052503 (Nov 28, 2017) (7 pages) Paper No: GTP-17-1446; doi: 10.1115/1.4038183 History: Received August 09, 2017; Revised August 18, 2017

This paper deals with the estimation of forcing functions on a mistuned bladed rotor from measurements of harmonic response via Kalman filter (KF) in time domain. An unique feature of this approach is that the number of estimated variables can be far greater than the number of measurements. The robustness of this method to measurement errors is shown. It is also shown that direct prediction of amplitude and phase of sinusoidal force vector from input/output frequency response function has a large amount of errors in the presence of unavoidable measurement noise. Numerical examples contain both frequency mistuning and geometric mistuning.

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References

Sinha, A. , 2009, “ Reduced-Order Model of a Bladed Rotor With Geometric Mistuning,” ASME J. Turbomach., 131(3), p. 031007. [CrossRef]
Bhartiya, Y. , and Sinha, A. , 2013, “ Reduced Order Model of a Bladed Rotor With Geometric Mistuning Via Estimated Deviations in Mass and Stiffness Matrices,” ASME J. Eng. Gas Turbines Power, 135(5), p. 052501. [CrossRef]
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 [CrossRef]
Ekici, K. , and Hall, K. , 2008, “ Nonlinear Frequency Domain Analysis of Unsteady Flows in Turbomachinery With Multiple Excitation Frequencies,” AIAA J., 46(8), pp. 1912–1920. [CrossRef]
Schonenborn, H. , and Ashcroft, G. , 2014, “Comparison of Non-Linear Linearized CFD Analysis of the Stator-Rotor Interaction of a Compressor Stage,” ASME Paper No. GT2014-25256.
Besem, F. M. , Kielb, R. E. , and Key, N. L. , 2015, “ Forced Response Sensitivity of a Mistuned Rotor From an Embedded Compressor Stage,” ASME J. Turbomach., 138(3), p. 031002. [CrossRef]
Besem, F. M. , Kielb, R. E. , Galpin, P. , Zori, L. , and Key, N. L. , 2016, “ Mistuned Forced Response Predictions of an Embedded Rotor in a Multistage Compressor,” ASME J. Turbomach., 138(6), p. 061003. [CrossRef]
Warren, C. , Niezrecki, C. , and Avitabile, P. , 2010, “Optical Non-Contacting Vibration Measurement of Rotating Turbine Blades II,” A Conference on Structural Dynamics (IMAC-XXVIII), Jacksonville, FL, Feb. 1–4, pp. 39–44. http://www.am.chalmers.se/~thab/IMAC/2010/PDFs/Papers/s08p004.pdf
Vishwakarma, V. , and Sinha, A. , 2015, “ Estimation of Forcing Function for a Geometrically Mistuned Bladed Rotor Via Modified Modal Domain Analysis,” ASME J. Eng. Gas Turbines Power, 138(4), p. 042507. [CrossRef]
Sinha, A. , 2007, Linear Systems: Optimal and Robust Control, CRC Press, Boca Raton, FL.
Kielb, R. E. , Feiner, D. M. , Griffin, J. H. , and Miyakozawa , 2004, “Flutter of Mistuned Bladed Disks and Blisks With Aerodynamic and FMM Structural Coupling,” ASME Paper No. GT2004-54315.
Kielb, R. E. , 2015, private communication.
Ralston, A. , and Rabinowitz, P. , 1978, A First Course in Numerical Analysis, McGraw-Hill, New York.
Sinha, A. , Hall, B. , Cassenti, B. , and Hilbert, G. , 2008, “ Vibratory Parameters of Blades From Coordinate Measurement Machine Data,” ASME J. Turbomach., 130(1), p. 011013. [CrossRef]

Figures

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Fig. 1

Mistuned blade frequencies (model #1)

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Fig. 2

Modal coefficients of (measured) harmonic response (model #1)

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Fig. 3

Estimated modal coefficients of blade forces (model #1)

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Fig. 4

Time-domain estimation of 5-ND coefficient of blade forces (model #1)

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Fig. 5

Time-domain estimation of 8-ND (backward traveling wave) coefficient of blade forces (model #1)

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Fig. 6

Measured harmonic displacements (model #2)

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Fig. 7

Estimated modal coefficients of blade forces by direct method (model #2)

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Fig. 8

Time domain KF-estimated forces on blades 1 and 4 without measurement noise (model #2)

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Fig. 9

Time-domain KF estimated forces on blades 1 and 4 with measurement noise (model #2)

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Fig. 10

Time-domain KF estimation of 3-ND coefficient of blade forces with measurement noise (model #2)

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Fig. 11

Time-domain KF estimation of 7-ND coefficient of blade forces with measurement noise (model #2)

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Fig. 12

Time-domain KF estimation of 3 ND coefficient of blade forces with increased measurement noise (model #2)

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Fig. 13

Time domain KF estimation of 7-ND coefficient of blade forces with increased measurement noise (model #2)

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