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Research Papers

Harmonic Transfer Function to Measure Translational and Rotational Velocities With Continuous-Scan Laser Doppler Vibrometry

[+] Author and Article Information
Shifei Yang

Graduate Research Assistant
Department of Engineering Physics,
University of Wisconsin-Madison,
535 Engineering Research Building,
1500 Engineering Drive,
Madison, WI 53706
e-mail: syang66@wisc.edu

Matthew S. Allen

Assistant Professor
Department of Engineering Physics,
University of Wisconsin-Madison,
535 Engineering Research Building,
1500 Engineering Drive,
Madison, WI 53706
e-mail: msallen@engr.wisc.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 4, 2013; final manuscript received December 9, 2013; published online February 5, 2014. Assoc. Editor: Jeffrey F. Rhoads.

J. Vib. Acoust 136(2), 021025 (Feb 05, 2014) (11 pages) Paper No: VIB-13-1309; doi: 10.1115/1.4026350 History: Received September 04, 2013; Revised December 09, 2013

A laser Doppler vibrometer measures the translational velocity at a point along the direction of incident light. It has been shown that rotational velocities can also be recovered when the laser scans continuously along a short line or small circular path around that point. This work uses the harmonic transfer function to relate the measured translational and rotational velocities to the input force. With this concept, the continuous-scan approach can be combined with the conventional point-by-point scheme, acquiring three dimensional velocities under various types of excitation conditions in the same amount of time that is required for obtaining only the translational velocity. The proposed approach is validated on a downhill ski under free-free boundary conditions with a circular scan pattern. The influence of the circle size, the scan rate and the surface quality on the noise level is evaluated. It is found that the circular-scan approach provides smoother and more reliable mode shapes than the conventional point-by-point approach given appropriate parameters. Local slopes at the measurement locations are then computed from the identified rotational velocities, providing additional information for model validation and damage detection.

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References

Figures

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Fig. 1

Scheme of measuring translational and rotational velocity using CSLDV

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Fig. 2

Circular scan pattern (dots represent laser measurement locations)

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Fig. 3

Spectrum of measured CSLDV signal with a 150 Hz scan frequency

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Fig. 4

Experimental set up. (a) Testing scheme; (b) load cell; and (c) retro-reflective tape.

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Fig. 5

Noise level with an 8 mm circle size. Blue line-measured velocity signal, red line-noise in measured signal. (a) 40 Hz scan frequency; and (b) 200 Hz scan frequency.

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Fig. 6

Noise level and standard deviation on retro-reflective tape. (a) Noise level; and (b) standard deviation.

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Fig. 7

Noise level and standard deviation on black bottom surface of the ski. (a) Noise level; and (b) standard deviation.

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Fig. 8

Noise level and standard deviation on yellow top surface of the ski. (a) Noise level; and (b) standard deviation.

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Fig. 9

Identified mode shapes using fast scan. (a) 1st bending mode at 19 Hz; (b) 2nd bending mode at 42 Hz; and (c) 3rd bending mode at 75 Hz.

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Fig. 10

Identified mode shapes of half-ski (vertical axis is amplitude). (a) Mode at 42 Hz by point measurement; (b) mode at 42 Hz by circular-scan; (c) mode at 75 Hz by point measurement; and (d) mode at 75 Hz by circular-scan.

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Fig. 11

Harmonic transfer functions of circular-scan at the same point: (a) on black bottom surface; and (b) on retro-reflective tape

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Fig. 12

AMI fit of the harmonic transfer function

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Fig. 13

Translational and rotational velocities for the mode at 42 Hz; (a) 3-D view; and (b) X-Y view

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Fig. 14

Measured deflection shape and local slope using the circular-scan approach. (a) Mode at 42 Hz; and (b) mode at 75 Hz.

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