Abstract

A new technique is proposed for noncontact measurement of bending vibration directly from a rotating component. This notoriously difficult and previously unattained measurement is a further development of laser Doppler vibrometry. Simultaneously the technique provides an accurate measure of shaft torsional vibration in situations in which measurements of torsional vibration have shown significant sensitivity to bending vibration. Experimental results validate the theory developed, and a conservative estimate of the minimum measurable bending vibration is made at 20 millidegrees.

© 1996 Optical Society of America

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References

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  1. L. E. DrainThe Laser Doppler Technique (Wiley, Chichester, UK, 1980), pp. 222–225.
  2. S. J. Rothberg, N. A. HalliwellTrans. ASME: J. Vibration Acoust. 116, 326 (1994).
    [CrossRef]
  3. N. A. Halliwell, C. J. D. Pickering, P. G. EastwoodJ. Sound Vibratio 93, 588 (1984).
    [CrossRef]
  4. T. J. Miles, M. Lucas, S. J. Rothberg, presented at ASME 15th Biennial Conference on Vibration and Noise, Boston, Mass., September 17–21, 1995.
  5. M. Kinoshita, T. Sakamoto, H. Okamurain SAE Transactions, Section 3 (Society of Automotive Engineers, Warrendale, Pa., 1989), paper 891127, pp.1605–1615.

1994

S. J. Rothberg, N. A. HalliwellTrans. ASME: J. Vibration Acoust. 116, 326 (1994).
[CrossRef]

1989

M. Kinoshita, T. Sakamoto, H. Okamurain SAE Transactions, Section 3 (Society of Automotive Engineers, Warrendale, Pa., 1989), paper 891127, pp.1605–1615.

1984

N. A. Halliwell, C. J. D. Pickering, P. G. EastwoodJ. Sound Vibratio 93, 588 (1984).
[CrossRef]

Drain, L. E.

L. E. DrainThe Laser Doppler Technique (Wiley, Chichester, UK, 1980), pp. 222–225.

Eastwood, P. G.

N. A. Halliwell, C. J. D. Pickering, P. G. EastwoodJ. Sound Vibratio 93, 588 (1984).
[CrossRef]

Halliwell, N. A.

S. J. Rothberg, N. A. HalliwellTrans. ASME: J. Vibration Acoust. 116, 326 (1994).
[CrossRef]

N. A. Halliwell, C. J. D. Pickering, P. G. EastwoodJ. Sound Vibratio 93, 588 (1984).
[CrossRef]

Kinoshita, M.

M. Kinoshita, T. Sakamoto, H. Okamurain SAE Transactions, Section 3 (Society of Automotive Engineers, Warrendale, Pa., 1989), paper 891127, pp.1605–1615.

Lucas, M.

T. J. Miles, M. Lucas, S. J. Rothberg, presented at ASME 15th Biennial Conference on Vibration and Noise, Boston, Mass., September 17–21, 1995.

Miles, T. J.

T. J. Miles, M. Lucas, S. J. Rothberg, presented at ASME 15th Biennial Conference on Vibration and Noise, Boston, Mass., September 17–21, 1995.

Okamura, H.

M. Kinoshita, T. Sakamoto, H. Okamurain SAE Transactions, Section 3 (Society of Automotive Engineers, Warrendale, Pa., 1989), paper 891127, pp.1605–1615.

Pickering, C. J. D.

N. A. Halliwell, C. J. D. Pickering, P. G. EastwoodJ. Sound Vibratio 93, 588 (1984).
[CrossRef]

Rothberg, S. J.

S. J. Rothberg, N. A. HalliwellTrans. ASME: J. Vibration Acoust. 116, 326 (1994).
[CrossRef]

T. J. Miles, M. Lucas, S. J. Rothberg, presented at ASME 15th Biennial Conference on Vibration and Noise, Boston, Mass., September 17–21, 1995.

Sakamoto, T.

M. Kinoshita, T. Sakamoto, H. Okamurain SAE Transactions, Section 3 (Society of Automotive Engineers, Warrendale, Pa., 1989), paper 891127, pp.1605–1615.

J. Sound Vibratio

N. A. Halliwell, C. J. D. Pickering, P. G. EastwoodJ. Sound Vibratio 93, 588 (1984).
[CrossRef]

SAE Transactions, Section 3

M. Kinoshita, T. Sakamoto, H. Okamurain SAE Transactions, Section 3 (Society of Automotive Engineers, Warrendale, Pa., 1989), paper 891127, pp.1605–1615.

Trans. ASME: J. Vibration Acoust.

S. J. Rothberg, N. A. HalliwellTrans. ASME: J. Vibration Acoust. 116, 326 (1994).
[CrossRef]

Other

L. E. DrainThe Laser Doppler Technique (Wiley, Chichester, UK, 1980), pp. 222–225.

T. J. Miles, M. Lucas, S. J. Rothberg, presented at ASME 15th Biennial Conference on Vibration and Noise, Boston, Mass., September 17–21, 1995.

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Figures (7)

Fig. 1
Fig. 1

Optical configuration of the LTV.

Fig. 2
Fig. 2

Definition of instrument–target incidence angles.

Fig. 3
Fig. 3

Experimental arrangement of two LTV’s.

Fig. 4
Fig. 4

LTV outputs showing combined torsional and bending vibrations: (a) LTV1 (solid curve) and LTV2 (dashed curve); (b) spectrum of LTV1 output.

Fig. 5
Fig. 5

Processed time-domain signals: (a) resolved torsional vibration, (b) resolved bending vibration.

Fig. 6
Fig. 6

Torsional vibration spectra: (a) resolved data, (b) independently measured data.

Fig. 7
Fig. 7

Bending vibration spectra: (a) resolved data, (b) independently measured data.

Equations (7)

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f beat = ( 4 μ π d / λ ) N cos β sin α ,
f 1 = ( 4 μ π d / λ ) N sin [ α + Δ α ( t ) ] ,
f 2 = ( 4 μ π d / λ ) N sin [ α Δ α ( t ) ] .
f 1 = ( 4 μ π d / λ ) N [ sin α + Δ α ( t ) cos α ] ,
f 2 = ( 4 μ π d / λ ) N [ sin α Δ α ( t ) cos α ] .
f 1 + f 2 = ( 4 μ π d / λ ) 2 N sin α ,
( f 1 f 2 ) / ( f 1 + f 2 ) = Δ α ( t ) / tan α .

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