Abstract

Experimental modal analysis of multifrequency vibration requires a measurement system with appropriate temporal and spatial resolution to recover the mode shapes. To fully understand the vibration it is necessary to be able to measure not only the vibration amplitude but also the vibration phase. We describe a multipoint laser vibrometer that is capable of high spatial and temporal resolution with simultaneous measurement of 256 points along a line at up to 80kHz. The multipoint vibrometer is demonstrated by recovering modal vibration data from a simple test object subject to transient excitation. A practical application is presented in which the vibrometer is used to measure vibration on a squealing rotating disk brake.

© 2007 Optical Society of America

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References

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  1. S. Welaratna, "Vibration testing in the automotive industry," EE-Eval. Eng. 39, 132-140 (2000).
  2. D. Moreno, B. Barrientos, C. Perez-Lopez, and F. Mendoza Santoyo, "Modal vibration analysis of a metal plate by using a laser vibrometer and the POD method," J. Opt. A 7, S356-S363 (2005).
    [CrossRef]
  3. C. Huang, "Transverse vibration analysis and measurement for the piezoceramic annular plate with different boundary conditions," J. Sound Vib. 283, 665-683 (2005).
    [CrossRef]
  4. A. B. Stanbridge and D. J. Ewins, "Modal testing using a scanning laser Doppler vibrometer," Mech. Syst. Signal Process. 13, 255-270 (1999).
    [CrossRef]
  5. B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noel, Z. W. Shen, and C. S. Chin, "Two-axis-scanning laser Doppler vibrometer for microstructure," Opt. Commun. 182, 175-185 (2000).
    [CrossRef]
  6. A. F. Doval, "A systematic approach to TV holography (review article)," Meas. Sci. Technol. 11, R1-R36 (2000).
    [CrossRef]
  7. J. M. Huntley, G. H. Kaufmann, and D. Kerr, "Phase-shifted dynamic speckle pattern interferometry at 1 kHz," Appl. Opt. 38, 6556-6563 (1999).
    [CrossRef]
  8. J. M. Kilpatrick, A. J. Moore, J. S. Barton, J. D. C. Jones, M. Reeves, and C. Buckberry, "Measurement of complex surface deformation by high-speed dynamic phase-stepped digital speckle pattern interferometry," Opt. Lett. 25, 1068-1070 (2000).
    [CrossRef]
  9. P. Hariharan, Basics of Interferometry (Academic, 1992).
  10. P. Carré, "Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures," Metrologia 2, 13-23 (1966).
    [CrossRef]
  11. A. W. Leissa, Vibration of Plates, NASA SP-160 (U.S. National Technical Information Service, 1969).
  12. M. Reeves, N. Taylor, C. Edwards, D. Williams, and C. H. Buckberry, "A study of brake disc modal behaviour during squeal generation using high-speed electronic speckle pattern interferometry and near-field sound pressure measurements," Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.) 214, 285-296 (2000).
    [CrossRef]
  13. F. Chen, G. M. Brown, M. M. Marchi, and M. Dale, "Recent advances in brake noise and vibration engineering using laser metrology," Opt. Eng. 42, 1359-1369 (2003).
    [CrossRef]
  14. R. Krupka, T. Walz, and A. Ettemeyer, "Fast and full-field measurement of brake squeal using pulsed ESPI technique," Opt. Eng. 42, 1354-1358 (2003).
    [CrossRef]

2005 (2)

D. Moreno, B. Barrientos, C. Perez-Lopez, and F. Mendoza Santoyo, "Modal vibration analysis of a metal plate by using a laser vibrometer and the POD method," J. Opt. A 7, S356-S363 (2005).
[CrossRef]

C. Huang, "Transverse vibration analysis and measurement for the piezoceramic annular plate with different boundary conditions," J. Sound Vib. 283, 665-683 (2005).
[CrossRef]

2003 (2)

F. Chen, G. M. Brown, M. M. Marchi, and M. Dale, "Recent advances in brake noise and vibration engineering using laser metrology," Opt. Eng. 42, 1359-1369 (2003).
[CrossRef]

R. Krupka, T. Walz, and A. Ettemeyer, "Fast and full-field measurement of brake squeal using pulsed ESPI technique," Opt. Eng. 42, 1354-1358 (2003).
[CrossRef]

2000 (5)

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noel, Z. W. Shen, and C. S. Chin, "Two-axis-scanning laser Doppler vibrometer for microstructure," Opt. Commun. 182, 175-185 (2000).
[CrossRef]

A. F. Doval, "A systematic approach to TV holography (review article)," Meas. Sci. Technol. 11, R1-R36 (2000).
[CrossRef]

J. M. Kilpatrick, A. J. Moore, J. S. Barton, J. D. C. Jones, M. Reeves, and C. Buckberry, "Measurement of complex surface deformation by high-speed dynamic phase-stepped digital speckle pattern interferometry," Opt. Lett. 25, 1068-1070 (2000).
[CrossRef]

S. Welaratna, "Vibration testing in the automotive industry," EE-Eval. Eng. 39, 132-140 (2000).

M. Reeves, N. Taylor, C. Edwards, D. Williams, and C. H. Buckberry, "A study of brake disc modal behaviour during squeal generation using high-speed electronic speckle pattern interferometry and near-field sound pressure measurements," Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.) 214, 285-296 (2000).
[CrossRef]

1999 (2)

J. M. Huntley, G. H. Kaufmann, and D. Kerr, "Phase-shifted dynamic speckle pattern interferometry at 1 kHz," Appl. Opt. 38, 6556-6563 (1999).
[CrossRef]

A. B. Stanbridge and D. J. Ewins, "Modal testing using a scanning laser Doppler vibrometer," Mech. Syst. Signal Process. 13, 255-270 (1999).
[CrossRef]

1966 (1)

P. Carré, "Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures," Metrologia 2, 13-23 (1966).
[CrossRef]

Barrientos, B.

D. Moreno, B. Barrientos, C. Perez-Lopez, and F. Mendoza Santoyo, "Modal vibration analysis of a metal plate by using a laser vibrometer and the POD method," J. Opt. A 7, S356-S363 (2005).
[CrossRef]

Barton, J. S.

Brown, G. M.

F. Chen, G. M. Brown, M. M. Marchi, and M. Dale, "Recent advances in brake noise and vibration engineering using laser metrology," Opt. Eng. 42, 1359-1369 (2003).
[CrossRef]

Buckberry, C.

Buckberry, C. H.

M. Reeves, N. Taylor, C. Edwards, D. Williams, and C. H. Buckberry, "A study of brake disc modal behaviour during squeal generation using high-speed electronic speckle pattern interferometry and near-field sound pressure measurements," Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.) 214, 285-296 (2000).
[CrossRef]

Carré, P.

P. Carré, "Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures," Metrologia 2, 13-23 (1966).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, M. M. Marchi, and M. Dale, "Recent advances in brake noise and vibration engineering using laser metrology," Opt. Eng. 42, 1359-1369 (2003).
[CrossRef]

Chin, C. S.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noel, Z. W. Shen, and C. S. Chin, "Two-axis-scanning laser Doppler vibrometer for microstructure," Opt. Commun. 182, 175-185 (2000).
[CrossRef]

Dale, M.

F. Chen, G. M. Brown, M. M. Marchi, and M. Dale, "Recent advances in brake noise and vibration engineering using laser metrology," Opt. Eng. 42, 1359-1369 (2003).
[CrossRef]

Doval, A. F.

A. F. Doval, "A systematic approach to TV holography (review article)," Meas. Sci. Technol. 11, R1-R36 (2000).
[CrossRef]

Edwards, C.

M. Reeves, N. Taylor, C. Edwards, D. Williams, and C. H. Buckberry, "A study of brake disc modal behaviour during squeal generation using high-speed electronic speckle pattern interferometry and near-field sound pressure measurements," Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.) 214, 285-296 (2000).
[CrossRef]

Ettemeyer, A.

R. Krupka, T. Walz, and A. Ettemeyer, "Fast and full-field measurement of brake squeal using pulsed ESPI technique," Opt. Eng. 42, 1354-1358 (2003).
[CrossRef]

Ewins, D. J.

A. B. Stanbridge and D. J. Ewins, "Modal testing using a scanning laser Doppler vibrometer," Mech. Syst. Signal Process. 13, 255-270 (1999).
[CrossRef]

Hariharan, P.

P. Hariharan, Basics of Interferometry (Academic, 1992).

Huang, C.

C. Huang, "Transverse vibration analysis and measurement for the piezoceramic annular plate with different boundary conditions," J. Sound Vib. 283, 665-683 (2005).
[CrossRef]

Huntley, J. M.

Jones, J. D. C.

Kaufmann, G. H.

Kerr, D.

Kilpatrick, J. M.

Krupka, R.

R. Krupka, T. Walz, and A. Ettemeyer, "Fast and full-field measurement of brake squeal using pulsed ESPI technique," Opt. Eng. 42, 1354-1358 (2003).
[CrossRef]

Leissa, A. W.

A. W. Leissa, Vibration of Plates, NASA SP-160 (U.S. National Technical Information Service, 1969).

Marchi, M. M.

F. Chen, G. M. Brown, M. M. Marchi, and M. Dale, "Recent advances in brake noise and vibration engineering using laser metrology," Opt. Eng. 42, 1359-1369 (2003).
[CrossRef]

Moore, A. J.

Moreno, D.

D. Moreno, B. Barrientos, C. Perez-Lopez, and F. Mendoza Santoyo, "Modal vibration analysis of a metal plate by using a laser vibrometer and the POD method," J. Opt. A 7, S356-S363 (2005).
[CrossRef]

Ngoi, B. K. A.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noel, Z. W. Shen, and C. S. Chin, "Two-axis-scanning laser Doppler vibrometer for microstructure," Opt. Commun. 182, 175-185 (2000).
[CrossRef]

Noel, N.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noel, Z. W. Shen, and C. S. Chin, "Two-axis-scanning laser Doppler vibrometer for microstructure," Opt. Commun. 182, 175-185 (2000).
[CrossRef]

Perez-Lopez, C.

D. Moreno, B. Barrientos, C. Perez-Lopez, and F. Mendoza Santoyo, "Modal vibration analysis of a metal plate by using a laser vibrometer and the POD method," J. Opt. A 7, S356-S363 (2005).
[CrossRef]

Reeves, M.

J. M. Kilpatrick, A. J. Moore, J. S. Barton, J. D. C. Jones, M. Reeves, and C. Buckberry, "Measurement of complex surface deformation by high-speed dynamic phase-stepped digital speckle pattern interferometry," Opt. Lett. 25, 1068-1070 (2000).
[CrossRef]

M. Reeves, N. Taylor, C. Edwards, D. Williams, and C. H. Buckberry, "A study of brake disc modal behaviour during squeal generation using high-speed electronic speckle pattern interferometry and near-field sound pressure measurements," Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.) 214, 285-296 (2000).
[CrossRef]

Santoyo, F. Mendoza

D. Moreno, B. Barrientos, C. Perez-Lopez, and F. Mendoza Santoyo, "Modal vibration analysis of a metal plate by using a laser vibrometer and the POD method," J. Opt. A 7, S356-S363 (2005).
[CrossRef]

Shen, Z. W.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noel, Z. W. Shen, and C. S. Chin, "Two-axis-scanning laser Doppler vibrometer for microstructure," Opt. Commun. 182, 175-185 (2000).
[CrossRef]

Stanbridge, A. B.

A. B. Stanbridge and D. J. Ewins, "Modal testing using a scanning laser Doppler vibrometer," Mech. Syst. Signal Process. 13, 255-270 (1999).
[CrossRef]

Tan, B.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noel, Z. W. Shen, and C. S. Chin, "Two-axis-scanning laser Doppler vibrometer for microstructure," Opt. Commun. 182, 175-185 (2000).
[CrossRef]

Taylor, N.

M. Reeves, N. Taylor, C. Edwards, D. Williams, and C. H. Buckberry, "A study of brake disc modal behaviour during squeal generation using high-speed electronic speckle pattern interferometry and near-field sound pressure measurements," Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.) 214, 285-296 (2000).
[CrossRef]

Venkatakrishnan, K.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noel, Z. W. Shen, and C. S. Chin, "Two-axis-scanning laser Doppler vibrometer for microstructure," Opt. Commun. 182, 175-185 (2000).
[CrossRef]

Walz, T.

R. Krupka, T. Walz, and A. Ettemeyer, "Fast and full-field measurement of brake squeal using pulsed ESPI technique," Opt. Eng. 42, 1354-1358 (2003).
[CrossRef]

Welaratna, S.

S. Welaratna, "Vibration testing in the automotive industry," EE-Eval. Eng. 39, 132-140 (2000).

Williams, D.

M. Reeves, N. Taylor, C. Edwards, D. Williams, and C. H. Buckberry, "A study of brake disc modal behaviour during squeal generation using high-speed electronic speckle pattern interferometry and near-field sound pressure measurements," Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.) 214, 285-296 (2000).
[CrossRef]

Appl. Opt. (1)

EE-Eval. Eng. (1)

S. Welaratna, "Vibration testing in the automotive industry," EE-Eval. Eng. 39, 132-140 (2000).

J. Opt. A (1)

D. Moreno, B. Barrientos, C. Perez-Lopez, and F. Mendoza Santoyo, "Modal vibration analysis of a metal plate by using a laser vibrometer and the POD method," J. Opt. A 7, S356-S363 (2005).
[CrossRef]

J. Sound Vib. (1)

C. Huang, "Transverse vibration analysis and measurement for the piezoceramic annular plate with different boundary conditions," J. Sound Vib. 283, 665-683 (2005).
[CrossRef]

Meas. Sci. Technol. (1)

A. F. Doval, "A systematic approach to TV holography (review article)," Meas. Sci. Technol. 11, R1-R36 (2000).
[CrossRef]

Mech. Syst. Signal Process. (1)

A. B. Stanbridge and D. J. Ewins, "Modal testing using a scanning laser Doppler vibrometer," Mech. Syst. Signal Process. 13, 255-270 (1999).
[CrossRef]

Metrologia (1)

P. Carré, "Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures," Metrologia 2, 13-23 (1966).
[CrossRef]

Opt. Commun. (1)

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noel, Z. W. Shen, and C. S. Chin, "Two-axis-scanning laser Doppler vibrometer for microstructure," Opt. Commun. 182, 175-185 (2000).
[CrossRef]

Opt. Eng. (2)

F. Chen, G. M. Brown, M. M. Marchi, and M. Dale, "Recent advances in brake noise and vibration engineering using laser metrology," Opt. Eng. 42, 1359-1369 (2003).
[CrossRef]

R. Krupka, T. Walz, and A. Ettemeyer, "Fast and full-field measurement of brake squeal using pulsed ESPI technique," Opt. Eng. 42, 1354-1358 (2003).
[CrossRef]

Opt. Lett. (1)

Proc. Inst. Mech. Eng. (1)

M. Reeves, N. Taylor, C. Edwards, D. Williams, and C. H. Buckberry, "A study of brake disc modal behaviour during squeal generation using high-speed electronic speckle pattern interferometry and near-field sound pressure measurements," Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.) 214, 285-296 (2000).
[CrossRef]

Other (2)

P. Hariharan, Basics of Interferometry (Academic, 1992).

A. W. Leissa, Vibration of Plates, NASA SP-160 (U.S. National Technical Information Service, 1969).

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Figures (8)

Fig. 1
Fig. 1

Optical configuration for a line scan vibrometer. T, test object; SG, signal generator. The vibrometer consists of laser diode source (LD), beam splitters (BS1 and BS2), cylindrical lenses L1 and L3, and imaging lens L2. One-dimensional and full-field images are captured using CCD1 and CCD2, respectively. The stepped signal generater, SWG, modulated the phase modulator (WGM) and is synchronized to CCD1 frame capture.

Fig. 2
Fig. 2

Intensity measurement of disk vibrations, with four sequential phase steps illustrated in the inset.

Fig. 3
Fig. 3

Vibration measurement on the circular plate excited using a piezoelectric strip attached to the reverse of the disk, with 987 Hz excitation frequency (camera running at 80 kHz ). The vibration displacement is given in nanometers.

Fig. 4
Fig. 4

Displacement measurement from transient excitation of the circular plate supported in the center. Time is the vertical axis with an 80 kHz frame rate, with spatial measurement on the horizontal axis.

Fig. 5
Fig. 5

Frequency content of line scan data proportional to FFT amplitude.

Fig. 6
Fig. 6

Vibrational modes of the circular disk. Column 2 plots the experimental vibration amplitude (in micrometers) obtained from the multipoint vibrometer in comparison with the modeled amplitude for the same portion of the disk. Column 3 plots the phase (in radians) measured by the multipoint vibrometer in comparison with modeled phase data. Column 4 shows the modeled mode shape. Column 5 illustrates experimental measurement of the modes using full-field time averaged ESPI with single-frequency excitation.

Fig. 7
Fig. 7

Brake disk vibration measurement.

Fig. 8
Fig. 8

Modeled data (solid curve) fitted to experimental data (●) for counterpropagating modes for a brake disk. Plots show the vibration amplitude in micrometers (left) and vibration phase (right) for the brake disk.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

I = I 0 [ 1 + V cos ( ϕ + φ ) ] ,
ϕ n φ = tan 1 [ { [ 3 ( I n + 1 I n + 2 ) ( I n I n + 3 ) ] [ ( I n I n + 3 ) + ( I n + 1 I n + 2 ) ] } 1 / 2 ( I n + 1 + I n + 2 ) ( I n + I n + 3 ) ] .
p ( r , θ ) = A sin ( ω n t ) J n ( k r ) cos ( n θ ) ,
p ( r , θ ) = A sin ( ω n t + ϕ t ) J n ( k n r ) cos ( n θ + ϕ s ) ,
S ( θ , t ) = A sin ( ω t + ϕ t 1 ) sin ( n θ + ϕ s 1 ) + A sin ( ω t + ϕ t 2 ) cos ( n θ + ϕ s 2 ) ,

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