Abstract

We put forward a plan of improving the oblique-incidence optical interferometric system applied in the measurement of tooth flanks of an involute spur gear in order to expand its capability to measure an involute helical gear. On the basis of the features of an involute helical tooth flank, we discuss how to realize the parallelism between the optical axis of the object arm of the optical system and the straight lines constructing the involute helical tooth flank. This parallelism helps the optical system produce an interference fringe pattern as clear as the one of an involute spur gear [Appl. Opt. 49, 6409 (2010).]. A numerical simulation is then performed to examine the correctness of the improvement. During simulating, we unify the equation of difference tooth flanks by means of importing two parameters in relation to the left or right side of a tooth flank and the helical direction of teeth, respectively. Finally, the actual experiment is fulfilled through the real optical system built on an optical table. The simulation and experiment results verify the correctness and feasibility of the proposed improvement.

© 2011 Optical Society of America

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References

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  1. P. Carré, “Installation et utilisation du comparateur photoélectrique et interferentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
    [CrossRef]
  2. R. Crane, “New developments in interferometry. V. Interference phase measurement,” Appl. Opt. 8, 538–542 (1969).
  3. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef] [PubMed]
  4. H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley-Interscience, 2007), pp. 547–666.
    [CrossRef]
  5. C. Meneses-Fabian, G. Rodriguez-Zurita, and V. Arrizon, “Optical tomography of transparent objects with phase-shifting interferometry and stepwise-shifted Ronchi ruling,” J. Opt. Soc. Am. A 23, 298–305 (2006).
    [CrossRef]
  6. Y. P. Kumar and S. Chatterjee, “Thickness measurement of transparent glass plates using a lateral shearing cyclic path optical configuration setup and polarization phase shifting interferometry,” Appl. Opt. 49, 6552–6557 (2010).
    [CrossRef] [PubMed]
  7. S. Chatterjee and Y. P. Kumar, “Measurement of surface profile of a long-radius optical surface with wedge phase shifting lateral shear interferometer,” Opt. Eng. 49, 103602 (2010).
    [CrossRef]
  8. S. Chatterjee, “Measurement of surface figure of plane optical surfaces using Fizeau interferometer with wedge phase-shifter,” Opt. Laser Technol. 37, 43–49 (2005).
    [CrossRef]
  9. N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
    [CrossRef]
  10. S. H. Wang, C. G. Quan, C. J. Tay, I. Reading, and Z. P. Fang, “Measurement of a fiber-end surface profile by use of phase-shifting laser interferometry,” Appl. Opt. 43, 49–56 (2004).
    [CrossRef] [PubMed]
  11. Z. T. Ge and F. Kobayashi, “High-precision measurement of a fiber connector end face by use of a Mirau interferometer,” Appl. Opt. 45, 5832–5839 (2006).
    [CrossRef] [PubMed]
  12. H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996).
    [CrossRef]
  13. S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI, 1996), Vol.  1230, pp. 1111–1123.
  14. S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995).
    [CrossRef]
  15. S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998).
    [CrossRef]
  16. S.-P. Fang, L.-J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik (to be published).
    [CrossRef]
  17. S. Fang, L. Wang, M. Komori, and A. Kubo, “Simulation method for interference fringe patterns in measuring gear tooth flanks by laser interferometry,” Appl. Opt. 49, 6409–6415(2010).
    [CrossRef] [PubMed]
  18. F. L. Litvin and A. Fuentes, Gear Geometry and Applied Theory, 2nd ed. (Cambridge University, 2004).
    [CrossRef]
  19. J. R. Colbourne, The Geometry of Involute Gears (Springer, 1987).
    [CrossRef]
  20. S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45, 170–177 (2009).
    [CrossRef]
  21. S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45, 244–252(2009).
    [CrossRef]

2010

2009

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45, 170–177 (2009).
[CrossRef]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45, 244–252(2009).
[CrossRef]

2006

2005

S. Chatterjee, “Measurement of surface figure of plane optical surfaces using Fizeau interferometer with wedge phase-shifter,” Opt. Laser Technol. 37, 43–49 (2005).
[CrossRef]

2004

2003

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

1998

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998).
[CrossRef]

1996

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996).
[CrossRef]

1995

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995).
[CrossRef]

1974

1969

R. Crane, “New developments in interferometry. V. Interference phase measurement,” Appl. Opt. 8, 538–542 (1969).

1966

P. Carré, “Installation et utilisation du comparateur photoélectrique et interferentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Arrizon, V.

Brangaccio, D. J.

Bruning, J. H.

Carré, P.

P. Carré, “Installation et utilisation du comparateur photoélectrique et interferentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Chatterjee, S.

Y. P. Kumar and S. Chatterjee, “Thickness measurement of transparent glass plates using a lateral shearing cyclic path optical configuration setup and polarization phase shifting interferometry,” Appl. Opt. 49, 6552–6557 (2010).
[CrossRef] [PubMed]

S. Chatterjee and Y. P. Kumar, “Measurement of surface profile of a long-radius optical surface with wedge phase shifting lateral shear interferometer,” Opt. Eng. 49, 103602 (2010).
[CrossRef]

S. Chatterjee, “Measurement of surface figure of plane optical surfaces using Fizeau interferometer with wedge phase-shifter,” Opt. Laser Technol. 37, 43–49 (2005).
[CrossRef]

Colbourne, J. R.

J. R. Colbourne, The Geometry of Involute Gears (Springer, 1987).
[CrossRef]

Crane, R.

R. Crane, “New developments in interferometry. V. Interference phase measurement,” Appl. Opt. 8, 538–542 (1969).

Fang, S.

S. Fang, L. Wang, M. Komori, and A. Kubo, “Simulation method for interference fringe patterns in measuring gear tooth flanks by laser interferometry,” Appl. Opt. 49, 6409–6415(2010).
[CrossRef] [PubMed]

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI, 1996), Vol.  1230, pp. 1111–1123.

Fang, S. P.

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45, 170–177 (2009).
[CrossRef]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45, 244–252(2009).
[CrossRef]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996).
[CrossRef]

Fang, S.-P.

S.-P. Fang, L.-J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik (to be published).
[CrossRef]

Fang, Z. P.

Fuentes, A.

F. L. Litvin and A. Fuentes, Gear Geometry and Applied Theory, 2nd ed. (Cambridge University, 2004).
[CrossRef]

Fujio, H.

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998).
[CrossRef]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI, 1996), Vol.  1230, pp. 1111–1123.

Gallagher, J. E.

Ge, Z. T.

Herriott, D. R.

Hui, W. K.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Kobayashi, F.

Komori, M.

S. Fang, L. Wang, M. Komori, and A. Kubo, “Simulation method for interference fringe patterns in measuring gear tooth flanks by laser interferometry,” Appl. Opt. 49, 6409–6415(2010).
[CrossRef] [PubMed]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45, 244–252(2009).
[CrossRef]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45, 170–177 (2009).
[CrossRef]

S.-P. Fang, L.-J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik (to be published).
[CrossRef]

Kubo, A.

S. Fang, L. Wang, M. Komori, and A. Kubo, “Simulation method for interference fringe patterns in measuring gear tooth flanks by laser interferometry,” Appl. Opt. 49, 6409–6415(2010).
[CrossRef] [PubMed]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45, 244–252(2009).
[CrossRef]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45, 170–177 (2009).
[CrossRef]

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998).
[CrossRef]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI, 1996), Vol.  1230, pp. 1111–1123.

S.-P. Fang, L.-J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik (to be published).
[CrossRef]

Kumar, Y. P.

S. Chatterjee and Y. P. Kumar, “Measurement of surface profile of a long-radius optical surface with wedge phase shifting lateral shear interferometer,” Opt. Eng. 49, 103602 (2010).
[CrossRef]

Y. P. Kumar and S. Chatterjee, “Thickness measurement of transparent glass plates using a lateral shearing cyclic path optical configuration setup and polarization phase shifting interferometry,” Appl. Opt. 49, 6552–6557 (2010).
[CrossRef] [PubMed]

Litvin, F. L.

F. L. Litvin and A. Fuentes, Gear Geometry and Applied Theory, 2nd ed. (Cambridge University, 2004).
[CrossRef]

Mei, X. S.

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45, 170–177 (2009).
[CrossRef]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45, 244–252(2009).
[CrossRef]

Meneses-Fabian, C.

Nakai, T.

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998).
[CrossRef]

Ngoi, B. K. A.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Oyama, K.

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI, 1996), Vol.  1230, pp. 1111–1123.

Quan, C. G.

Reading, I.

Rodriguez-Zurita, G.

Rosenfeld, D. P.

Saitoh, Y.

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998).
[CrossRef]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI, 1996), Vol.  1230, pp. 1111–1123.

Schreiber, H.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley-Interscience, 2007), pp. 547–666.
[CrossRef]

Sivakumar, N. R.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Suzuki, M.

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998).
[CrossRef]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI, 1996), Vol.  1230, pp. 1111–1123.

Tay, C. J.

Venkatakrishnan, K.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Wang, L.

Wang, L.-J.

S.-P. Fang, L.-J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik (to be published).
[CrossRef]

Wang, S. H.

White, A. D.

Yatagai, T.

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996).
[CrossRef]

Appl. Opt.

Chin. J. Mech. Eng.

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45, 170–177 (2009).
[CrossRef]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45, 244–252(2009).
[CrossRef]

J. Opt. Soc. Am. A

Metrologia

P. Carré, “Installation et utilisation du comparateur photoélectrique et interferentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Opt. Eng.

S. Chatterjee and Y. P. Kumar, “Measurement of surface profile of a long-radius optical surface with wedge phase shifting lateral shear interferometer,” Opt. Eng. 49, 103602 (2010).
[CrossRef]

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Opt. Laser Technol.

S. Chatterjee, “Measurement of surface figure of plane optical surfaces using Fizeau interferometer with wedge phase-shifter,” Opt. Laser Technol. 37, 43–49 (2005).
[CrossRef]

Optik

S.-P. Fang, L.-J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik (to be published).
[CrossRef]

Trans. Jpn. Soc. Mech. Eng. C

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996).
[CrossRef]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995).
[CrossRef]

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998).
[CrossRef]

Other

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI, 1996), Vol.  1230, pp. 1111–1123.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley-Interscience, 2007), pp. 547–666.
[CrossRef]

F. L. Litvin and A. Fuentes, Gear Geometry and Applied Theory, 2nd ed. (Cambridge University, 2004).
[CrossRef]

J. R. Colbourne, The Geometry of Involute Gears (Springer, 1987).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a), (b) Simulation interference fringe patterns for tooth flanks of an involute spur gear and an involute helical gear, respectively. They are binary (i.e., black and white) to be observed clearly. (c), (d) Positioning relationship between the simulated gears and the pair of wedge prisms, respectively, corresponding to (a) and (b). The simulated helical gear has the same main parameters as the simulated spur one, except that the helical gear has a helix angle 20 ° .

Fig. 2
Fig. 2

(a) Model of a tooth of an involute helical gear, (b) forming process of a tooth flank of an involute helical gear, i.e., a scanning surface of a mother straight line in a plane tangent to the base cylinder when it rolls over the base cylinder.

Fig. 3
Fig. 3

(a) Mother involute curve screws along the helices on the base or pitch cylinder, which forms a tooth flank of an involute helical gear, and (b) the two helices on the base and pitch cylinders are developed on a plane. β g and β p are the helix angles of the base and pitch cylinder, respectively, and H is the lead of the helicoid, which is same for the base and pitch cylinders.

Fig. 4
Fig. 4

Relationship between the measured helical gear and the pair of wedge prisms in the (a) OXY plane and (b) OXZ plane. The OXY plane exists in the middle of the face width of the measured gear.

Fig. 5
Fig. 5

Simulation interference fringe pattern when the angle 20 ° of Fig. 1d is changed into 18.75 ° . The helical gear has following main parameters: module of 3.0, 60 teeth, helix angle of 20 ° , pressure angle of 20 ° , and face width of 15 mm .

Fig. 6
Fig. 6

Comparison of the optical length differences among the object arm, before and after changing the installation angle between the axis of the measured gear and the axis of the pair of wedge prisms.

Fig. 7
Fig. 7

Schematic of the measuring machine used in the measurement of tooth flanks of gears.

Fig. 8
Fig. 8

Actual interference fringe pattern collected in the experiment for the involute helical gear.

Equations (6)

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

β g = arcsin ( sin β p · cos α n ) ,
hel = { 1 0 1 right helical gear spur gear left helical gear .
{ x 0 = r g · cos ( side · tan α n + Φ ) side · r g · tan α n · sin ( side · tan α n + Φ ) y 0 = r g · cos ( side · tan α n + Φ ) + side · r g · tan α n · sin ( side · tan α n + Φ ) z 0 = hel · r g · Φ / tan β g ,
{ n 0 x = side · cos β g · cos ( side · tan α n + Φ ) n 0 y = side · cos β g · sin ( side · tan α n + Φ ) n 0 z = side · hel · sin β g .
{ x = r g · cos ( side · tan α n + Φ + γ ) side · r g · tan α n · sin ( side · tan α n + Φ + γ ) y = r g · cos ( side · tan α n + Φ + γ ) + side · r g · tan α n · sin ( side · tan α n + Φ + γ ) z = hel · r g · Φ / tan β g ,
{ n x = side · cos β g · cos ( side · tan α n + Φ + γ ) n y = side · cos β g · sin ( side · tan α n + Φ + γ ) n z = side · hel · sin β g ,

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