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Research Papers

[+] Author and Article Information
Paul L. Mikrut

Hessert Laboratory,
Department of Aerospace and
Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: Paul.Mikrut@cummins.com

Scott C. Morris

Hessert Laboratory,
Department of Aerospace and
Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: s.morris@nd.edu

Joshua D. Cameron

Hessert Laboratory,
Department of Aerospace and
Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: j.cameron@nd.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 24, 2014; final manuscript received April 20, 2015; published online July 23, 2015. Assoc. Editor: Mary Kasarda.

J. Vib. Acoust 137(6), 061007 (Jul 23, 2015) (8 pages) Paper No: VIB-14-1027; doi: 10.1115/1.4030423 History: Received January 24, 2014

## Abstract

This paper discusses the application of a novel vibration measurement technique, termed blade image velocimetry (BIV), to a high-speed axial compressor. Measurements of compressor blade vibration can be difficult to obtain and are critical to aeromechanical design validation. The measurement technique discussed in this paper used a commercial particle image velocimetry (PIV) system and was developed as an alternative to conventional measurement techniques such as strain gages and blade tip timing (BTT). The measurement principles and error analysis are reviewed. Methods for estimating the magnitude of random noise corrupting the measurement and validating the vibration amplitude estimates are presented. The technique was validated using a 1.5 stage axial compressor operating at low shaft speed, where it measured the tip velocity to within 0.02% of the true value. The technique was then used to investigate blade vibration at high shaft speed. Low amplitude vibrations in first bending and first torsion were discovered when the compressor was operated at design air-mass flow rate. These vibrations had a maximum tip deflection of $15μm$ for bending and $7μm$ for torsion. The vibration amplitude for first bending and first torsion tripled when the compressor was operated at low air mass-flow rate, corresponding to deep stall. Furthermore, excitation of the third eigenmode was also measured. The maximum tip deflections of the first three eigenmodes when the compressor was operated at deep stall were $47μm$, $27μm$, and $15μm$, respectively.

## References

Al-Bedoor, B. , 2002, “Blade Vibration Measurement in Turbomachinery: Current Status,” Shock Vib. Dig., 34(6), pp. 455–461.
Kielb, J. , Abhari, R. , and Dunn, M. , 2001, “Experimental and Numerical Study of Forced Response in a Full-Scale Rotating Turbine,” ASME Paper No. 2001-GT-263.
Heath, S. , and Imregun, M. , 1998, “A Survey of Blade Tip-Timing Measurement Techniques for Turbomachinery Vibration,” ASME J. Eng. Gas Turbines Power, 120(4), pp. 784–791.
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Carrington, I. , Wright, J. , Cooper, J. , and Dimitriadis, G. , 2001, “A Comparison of Blade Tip Timing Data Analysis Methods,” Proc. Inst. Mech. Eng., Part G, 125(6), pp. 301–312.
Mikrut, P. , Bennington, M. , Cameron, J. , and Morris, S. , 2010, “Blade Image Velocimetry: Development and Uncertainty Analysis,” Meas. Sci. Technol., 21(1), p. 015109.
Feeny, B. , and Kappagantu, R. , 1998, “On the Physical Interpretation of Proper Orthogonal Modes in Vibrations,” J. Sound Vib., 211(4), pp. 607–616.
Cameron, J. D. , Bennington, M. , Ross, M. H. , Morris, S. C. , Du, J. , Lin, F. , and Chen, J. , 2013, “The Influence of Tip Clearance Momentum Flux on Stall Inception in a High-Speed Axial Compressor,” ASME J. Turbomach., 35(5), p. 051005.
Raffel, M. , Willert, C. , Wereley, S. , and Kompenhans, J. , 2007, Particle Image Velocimetry: A Practical Guide, 2nd ed., Springer, Berlin.
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Lin, W. K. , Lee, K. H. , Lu, P. , Lim, S. P. , and Abd Liang, Y. C. , 2002, “The Relationship Between Eigenfunctions of Karhunen–Loéve Decomposition and the Modes of Distributed Parameter Vibration System,” J. Sound Vib., 256(4), pp. 791–799.

## Figures

Fig. 1

Sketch of a cantilevered rotor blade and tip velocity measurement points

Fig. 2

Cross section of the rotor blade at four locations along the span. Note that the hub had a large thickness to chord ratio and high stagger angle, whereas the tip had a low thickness to chord ratio and low stagger angle.

Fig. 3

First three eigenmodes of the rotor blade: (a)[f]1 = 2148 Hz, (b)[f]2 = 2698 Hz, and (c)[f]3 = 4025 Hz

Fig. 4

Schematic of the experimental setup used to demonstrate BIV

Fig. 5

(a) Image of a blade tip used for BIV measurements. The shaft speed was 2881 rpm. (b) Tip velocity estimated from the BIV technique.

Fig. 6

Chordwise distribution of error in ensemble-averaged circumferential tip velocity for a shaft speed of 2886 rpm. ▷ blade 1; blade 4; blade 5; and blade 5, camera operated using single-frame double-exposure.

Fig. 7

Chordwise distribution of rms error in axial tip velocity for a shaft speed of 2886 rpm. ▷ blade 1; blade 4; blade 5; and blade 5, camera operated using single-frame double-exposure.

Fig. 8

Phase-averaged axial velocity versus reference time. The shaft speed was 2886 rpm and the axial velocity was induced by the magnetic bearings. BIV measurement and axial velocity from axial position sensor.

Fig. 9

A comparison of the chord-normal fluctuating tip velocity as determined from POD and BIV analyses. The compressor was operated at 13,551 rpm and at design air mass flow. FEM mode 1; FEM mode 2; FEM mode 3; first POD eigenmode; second POD eigenmode; and third POD eigenmode. Note that the FEM mode shapes were identical to those shown in Fig. 3. The gray box denotes the BIV estimated noise level, ±ση.

Fig. 10

A comparison of the chord-normal fluctuating tip velocity as determined from POD and BIV analyses. The compressor was operated at 13,551 rpm and in deep stall. FEM mode 1; FEM mode 2; FEM mode 3; first POD eigenmode; second POD eigenmode; and third POD eigenmode. Note that the FEM mode shapes were identical to those shown in Fig. 3. The gray box denotes the BIV estimated noise level, ±ση.

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