Abstract

In this work, we propose a new demodulation technique for three-dimensional (3-D) tip clearance measurements using the output signals acquired from three two-circle coaxial optical fiber bundles. This technique is based on the ratio of the difference in the signal intensities between any two sensing units of the optical fiber probe, and we derived the demodulation equations using the second-order Taylor expansion for a three-variable function. We verified the feasibility of the demodulation technique by experiments and demodulation error curves, which indicates that the method is viable for 3-D tip clearance measurements.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. D. Müller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to casing running clearance,” J. Eng. Gas Turbine. Power 119(4), 877–884 (1997).
    [Crossref]
  2. S. Heath and M. Imregun, “An improved single-parameter tip-timing method for turbo machinery blade vibration measurements using optical laser probes,” Int. J. Mech. Sci. 38(10), 1047–1058 (1996).
    [Crossref]
  3. F. Teng, X. D. Zhang, and S. Y. Xie, “Research on variation mechanism of three-dimensional blade tip clearance of aero-engine,” Proceedings of 13th International Conference on Ubiquitous Robots and Ambient Intelligence (Korea Robotics Society, 2016), 07734008.
    [Crossref]
  4. T. Schmitz and J. Ziegert, “A new sensor for the micro metre-level measurement of three-dimensional, dynamic contours,” Meas. Sci. Technol. 10(2), 51–62 (1999).
    [Crossref]
  5. H. J. Tiziani and H. M. Uhde, “Three-dimensional image sensing by chromatic confocal microscopy,” Appl. Opt. 33(10), 1838–1843 (1994).
    [Crossref] [PubMed]
  6. C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photo grammetry and fringe projection,” Opt. Eng. 39(1), 224–231 (2000).
    [Crossref]
  7. A. Anand, V. K. Chhaniwal, P. Almoro, G. Pedrini, and W. Osten, “Shape and deformation measurements of 3D objects using volume speckle field and phase retrieval,” Opt. Lett. 34(10), 1522–1524 (2009).
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  9. T. Mawatari and D. Nelson, “A multi-parameter Bragg grating fiber optic sensor and tri-axial strain measurement,” Smart Mater. Struct. 17(3), 035033 (2008).
    [Crossref]
  10. C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
    [Crossref]
  11. Q. Yang and C. Butler, “Three-dimensional fibre-optic position sensor,” Proceedings of SPIE-The International conference of Optical Fibre Sensors in China, 1572, 558–563 (1991).
    [Crossref]
  12. T. Oiwa and H. Nishitani, “Three-dimensional touch probe using three fibre optic displacement sensors,” Meas. Sci. Technol. 15(1), 84–90 (2004).
    [Crossref]
  13. S. Y. Xie and X. D. Zhang, “Design and modeling of three-dimensional tip clearance optical probe based on two-circle coaxial optical fiber bundle,” Proceedings of IEEE International Conference on Sensors, 16582224 (2016).
    [Crossref]
  14. D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using askewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).
  15. I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
    [Crossref] [PubMed]
  16. I. García, J. Beloki, and A. Berganza, “Different configurations of a reflective intensity-modulated optical sensor to avoid modal noise in tip clearance measurements,” J. Lightwave Technol. 33(12), 2663–2669 (2015).
    [Crossref]
  17. S. Y. Xie and X. D. Zhang, “Research on three-dimensional output behavior of displacement sensor of two-circle coaxial optical fiber bundle,” J. Vibr. Meas. Diagnosis 37(1), 174–181 (2017).
  18. S. Xie, X. Zhang, B. Wu, and Y. Xiong, “Output characteristics of two-circle coaxial optical fiber bundle with regard to three-dimensional tip clearance,” Opt. Express 26(19), 25244–25256 (2018).
    [Crossref] [PubMed]
  19. X. D. Zhang, B. Wu, and S. Y. Xie, “Optical fiber measurement system for 3-D variation of turbine blade tip clearance,” Optics and Precision Engineering 26, 1578–1587 (2018).
    [Crossref]
  20. E. Canbay, U. Ersoy, and T. Tankut, “A three component force transducer for reinforced concrete structural testing,” Eng. Struct. 26(2), 257–265 (2004).
    [Crossref]
  21. B. H. Jia, “Research on optical fiber based measurement and active control technology of turbine tip clearance,” Ph.D. thesis (Northwestern Polytechnical University, Xi’an, China, 2013). (in Chinese)
  22. Y. W. Xiong, X. D. Zhang, and S. Y. Xie, “Effect of thermal fatigue on three-dimensional blade tip clearance of aero-engine,” presented at 14th Conference on Test and Measurement Technology of Aero-engine, Xiamen, China, 5–7 Nov. 2018. (in Chinese)

2018 (2)

X. D. Zhang, B. Wu, and S. Y. Xie, “Optical fiber measurement system for 3-D variation of turbine blade tip clearance,” Optics and Precision Engineering 26, 1578–1587 (2018).
[Crossref]

S. Xie, X. Zhang, B. Wu, and Y. Xiong, “Output characteristics of two-circle coaxial optical fiber bundle with regard to three-dimensional tip clearance,” Opt. Express 26(19), 25244–25256 (2018).
[Crossref] [PubMed]

2017 (1)

S. Y. Xie and X. D. Zhang, “Research on three-dimensional output behavior of displacement sensor of two-circle coaxial optical fiber bundle,” J. Vibr. Meas. Diagnosis 37(1), 174–181 (2017).

2015 (2)

I. García, J. Beloki, and A. Berganza, “Different configurations of a reflective intensity-modulated optical sensor to avoid modal noise in tip clearance measurements,” J. Lightwave Technol. 33(12), 2663–2669 (2015).
[Crossref]

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

2013 (1)

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

2012 (1)

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using askewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

2010 (1)

2009 (1)

2008 (1)

T. Mawatari and D. Nelson, “A multi-parameter Bragg grating fiber optic sensor and tri-axial strain measurement,” Smart Mater. Struct. 17(3), 035033 (2008).
[Crossref]

2004 (2)

T. Oiwa and H. Nishitani, “Three-dimensional touch probe using three fibre optic displacement sensors,” Meas. Sci. Technol. 15(1), 84–90 (2004).
[Crossref]

E. Canbay, U. Ersoy, and T. Tankut, “A three component force transducer for reinforced concrete structural testing,” Eng. Struct. 26(2), 257–265 (2004).
[Crossref]

2000 (1)

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photo grammetry and fringe projection,” Opt. Eng. 39(1), 224–231 (2000).
[Crossref]

1999 (1)

T. Schmitz and J. Ziegert, “A new sensor for the micro metre-level measurement of three-dimensional, dynamic contours,” Meas. Sci. Technol. 10(2), 51–62 (1999).
[Crossref]

1997 (1)

D. Müller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to casing running clearance,” J. Eng. Gas Turbine. Power 119(4), 877–884 (1997).
[Crossref]

1996 (1)

S. Heath and M. Imregun, “An improved single-parameter tip-timing method for turbo machinery blade vibration measurements using optical laser probes,” Int. J. Mech. Sci. 38(10), 1047–1058 (1996).
[Crossref]

1994 (1)

Aldabaldetreku, G.

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Almoro, P.

Anand, A.

Beloki, J.

I. García, J. Beloki, and A. Berganza, “Different configurations of a reflective intensity-modulated optical sensor to avoid modal noise in tip clearance measurements,” J. Lightwave Technol. 33(12), 2663–2669 (2015).
[Crossref]

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Berganza, A.

Berghmans, F.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Butler, C.

Q. Yang and C. Butler, “Three-dimensional fibre-optic position sensor,” Proceedings of SPIE-The International conference of Optical Fibre Sensors in China, 1572, 558–563 (1991).
[Crossref]

Canbay, E.

E. Canbay, U. Ersoy, and T. Tankut, “A three component force transducer for reinforced concrete structural testing,” Eng. Struct. 26(2), 257–265 (2004).
[Crossref]

Chah, K.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Chhaniwal, V. K.

Degrieck, J.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Duan, F. J.

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using askewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

Ersoy, U.

E. Canbay, U. Ersoy, and T. Tankut, “A three component force transducer for reinforced concrete structural testing,” Eng. Struct. 26(2), 257–265 (2004).
[Crossref]

Eve, S.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

García, I.

I. García, J. Beloki, and A. Berganza, “Different configurations of a reflective intensity-modulated optical sensor to avoid modal noise in tip clearance measurements,” J. Lightwave Technol. 33(12), 2663–2669 (2015).
[Crossref]

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Geernaert, T.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Gomina, M.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Guo, H. T.

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using askewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

Heath, S.

S. Heath and M. Imregun, “An improved single-parameter tip-timing method for turbo machinery blade vibration measurements using optical laser probes,” Int. J. Mech. Sci. 38(10), 1047–1058 (1996).
[Crossref]

Illarramendi, M. A.

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Imregun, M.

S. Heath and M. Imregun, “An improved single-parameter tip-timing method for turbo machinery blade vibration measurements using optical laser probes,” Int. J. Mech. Sci. 38(10), 1047–1058 (1996).
[Crossref]

Jiménez, F.

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Johann, E.

D. Müller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to casing running clearance,” J. Eng. Gas Turbine. Power 119(4), 877–884 (1997).
[Crossref]

Li, Y.

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using askewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

Luyckx, G.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Mawatari, T.

T. Mawatari and D. Nelson, “A multi-parameter Bragg grating fiber optic sensor and tri-axial strain measurement,” Smart Mater. Struct. 17(3), 035033 (2008).
[Crossref]

Mergo, P.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Mozumdar, S.

D. Müller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to casing running clearance,” J. Eng. Gas Turbine. Power 119(4), 877–884 (1997).
[Crossref]

Müller, D.

D. Müller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to casing running clearance,” J. Eng. Gas Turbine. Power 119(4), 877–884 (1997).
[Crossref]

Nelson, D.

T. Mawatari and D. Nelson, “A multi-parameter Bragg grating fiber optic sensor and tri-axial strain measurement,” Smart Mater. Struct. 17(3), 035033 (2008).
[Crossref]

Nishitani, H.

T. Oiwa and H. Nishitani, “Three-dimensional touch probe using three fibre optic displacement sensors,” Meas. Sci. Technol. 15(1), 84–90 (2004).
[Crossref]

Oiwa, T.

T. Oiwa and H. Nishitani, “Three-dimensional touch probe using three fibre optic displacement sensors,” Meas. Sci. Technol. 15(1), 84–90 (2004).
[Crossref]

Osten, W.

Pedrini, G.

Reich, C.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photo grammetry and fringe projection,” Opt. Eng. 39(1), 224–231 (2000).
[Crossref]

Reza, S. A.

Ritter, R.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photo grammetry and fringe projection,” Opt. Eng. 39(1), 224–231 (2000).
[Crossref]

Riza, N. A.

Schmitz, T.

T. Schmitz and J. Ziegert, “A new sensor for the micro metre-level measurement of three-dimensional, dynamic contours,” Meas. Sci. Technol. 10(2), 51–62 (1999).
[Crossref]

Sheard, A. G.

D. Müller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to casing running clearance,” J. Eng. Gas Turbine. Power 119(4), 877–884 (1997).
[Crossref]

Sonnenfeld, C.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Sulejmani, S.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Tankut, T.

E. Canbay, U. Ersoy, and T. Tankut, “A three component force transducer for reinforced concrete structural testing,” Eng. Struct. 26(2), 257–265 (2004).
[Crossref]

Teng, F.

F. Teng, X. D. Zhang, and S. Y. Xie, “Research on variation mechanism of three-dimensional blade tip clearance of aero-engine,” Proceedings of 13th International Conference on Ubiquitous Robots and Ambient Intelligence (Korea Robotics Society, 2016), 07734008.
[Crossref]

Thesing, J.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photo grammetry and fringe projection,” Opt. Eng. 39(1), 224–231 (2000).
[Crossref]

Thienpont, H.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Tiziani, H. J.

Uhde, H. M.

Urbanczyk, W.

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Wang, K.

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using askewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

Wu, B.

X. D. Zhang, B. Wu, and S. Y. Xie, “Optical fiber measurement system for 3-D variation of turbine blade tip clearance,” Optics and Precision Engineering 26, 1578–1587 (2018).
[Crossref]

S. Xie, X. Zhang, B. Wu, and Y. Xiong, “Output characteristics of two-circle coaxial optical fiber bundle with regard to three-dimensional tip clearance,” Opt. Express 26(19), 25244–25256 (2018).
[Crossref] [PubMed]

Xie, S.

Xie, S. Y.

X. D. Zhang, B. Wu, and S. Y. Xie, “Optical fiber measurement system for 3-D variation of turbine blade tip clearance,” Optics and Precision Engineering 26, 1578–1587 (2018).
[Crossref]

S. Y. Xie and X. D. Zhang, “Research on three-dimensional output behavior of displacement sensor of two-circle coaxial optical fiber bundle,” J. Vibr. Meas. Diagnosis 37(1), 174–181 (2017).

F. Teng, X. D. Zhang, and S. Y. Xie, “Research on variation mechanism of three-dimensional blade tip clearance of aero-engine,” Proceedings of 13th International Conference on Ubiquitous Robots and Ambient Intelligence (Korea Robotics Society, 2016), 07734008.
[Crossref]

Xiong, Y.

Yang, Q.

Q. Yang and C. Butler, “Three-dimensional fibre-optic position sensor,” Proceedings of SPIE-The International conference of Optical Fibre Sensors in China, 1572, 558–563 (1991).
[Crossref]

Ye, D. C.

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using askewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

Zhang, X.

Zhang, X. D.

X. D. Zhang, B. Wu, and S. Y. Xie, “Optical fiber measurement system for 3-D variation of turbine blade tip clearance,” Optics and Precision Engineering 26, 1578–1587 (2018).
[Crossref]

S. Y. Xie and X. D. Zhang, “Research on three-dimensional output behavior of displacement sensor of two-circle coaxial optical fiber bundle,” J. Vibr. Meas. Diagnosis 37(1), 174–181 (2017).

F. Teng, X. D. Zhang, and S. Y. Xie, “Research on variation mechanism of three-dimensional blade tip clearance of aero-engine,” Proceedings of 13th International Conference on Ubiquitous Robots and Ambient Intelligence (Korea Robotics Society, 2016), 07734008.
[Crossref]

Ziegert, J.

T. Schmitz and J. Ziegert, “A new sensor for the micro metre-level measurement of three-dimensional, dynamic contours,” Meas. Sci. Technol. 10(2), 51–62 (1999).
[Crossref]

Zubia, J.

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Appl. Opt. (2)

Eng. Struct. (1)

E. Canbay, U. Ersoy, and T. Tankut, “A three component force transducer for reinforced concrete structural testing,” Eng. Struct. 26(2), 257–265 (2004).
[Crossref]

Int. J. Mech. Sci. (1)

S. Heath and M. Imregun, “An improved single-parameter tip-timing method for turbo machinery blade vibration measurements using optical laser probes,” Int. J. Mech. Sci. 38(10), 1047–1058 (1996).
[Crossref]

J. Eng. Gas Turbine. Power (1)

D. Müller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to casing running clearance,” J. Eng. Gas Turbine. Power 119(4), 877–884 (1997).
[Crossref]

J. Lightwave Technol. (1)

J. Vibr. Meas. Diagnosis (1)

S. Y. Xie and X. D. Zhang, “Research on three-dimensional output behavior of displacement sensor of two-circle coaxial optical fiber bundle,” J. Vibr. Meas. Diagnosis 37(1), 174–181 (2017).

Meas. Sci. Technol. (2)

T. Oiwa and H. Nishitani, “Three-dimensional touch probe using three fibre optic displacement sensors,” Meas. Sci. Technol. 15(1), 84–90 (2004).
[Crossref]

T. Schmitz and J. Ziegert, “A new sensor for the micro metre-level measurement of three-dimensional, dynamic contours,” Meas. Sci. Technol. 10(2), 51–62 (1999).
[Crossref]

Opt. Eng. (2)

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photo grammetry and fringe projection,” Opt. Eng. 39(1), 224–231 (2000).
[Crossref]

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using askewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

Opt. Express (1)

Opt. Lett. (1)

Optics and Precision Engineering (1)

X. D. Zhang, B. Wu, and S. Y. Xie, “Optical fiber measurement system for 3-D variation of turbine blade tip clearance,” Optics and Precision Engineering 26, 1578–1587 (2018).
[Crossref]

Sensors (Basel) (1)

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Smart Mater. Struct. (2)

T. Mawatari and D. Nelson, “A multi-parameter Bragg grating fiber optic sensor and tri-axial strain measurement,” Smart Mater. Struct. 17(3), 035033 (2008).
[Crossref]

C. Sonnenfeld, G. Luyckx, S. Sulejmani, T. Geernaert, S. Eve, M. Gomina, K. Chah, P. Mergo, W. Urbanczyk, H. Thienpont, J. Degrieck, and F. Berghmans, “Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates,” Smart Mater. Struct. 24(5), 55003–55015 (2015).
[Crossref]

Other (5)

Q. Yang and C. Butler, “Three-dimensional fibre-optic position sensor,” Proceedings of SPIE-The International conference of Optical Fibre Sensors in China, 1572, 558–563 (1991).
[Crossref]

F. Teng, X. D. Zhang, and S. Y. Xie, “Research on variation mechanism of three-dimensional blade tip clearance of aero-engine,” Proceedings of 13th International Conference on Ubiquitous Robots and Ambient Intelligence (Korea Robotics Society, 2016), 07734008.
[Crossref]

S. Y. Xie and X. D. Zhang, “Design and modeling of three-dimensional tip clearance optical probe based on two-circle coaxial optical fiber bundle,” Proceedings of IEEE International Conference on Sensors, 16582224 (2016).
[Crossref]

B. H. Jia, “Research on optical fiber based measurement and active control technology of turbine tip clearance,” Ph.D. thesis (Northwestern Polytechnical University, Xi’an, China, 2013). (in Chinese)

Y. W. Xiong, X. D. Zhang, and S. Y. Xie, “Effect of thermal fatigue on three-dimensional blade tip clearance of aero-engine,” presented at 14th Conference on Test and Measurement Technology of Aero-engine, Xiamen, China, 5–7 Nov. 2018. (in Chinese)

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Figures (8)

Fig. 1
Fig. 1 Attenuation characteristics of the light intensity received by the receiving fibers due to overlapping of the light spots for different values of the equivalent radius ri and radial displacement z0.
Fig. 2
Fig. 2 Measurement principle of 3-D tip clearance optical probe.
Fig. 3
Fig. 3 Photo of the probe, calibration table and processing circuit.
Fig. 4
Fig. 4 Simulation and experiment results of the 3-D output characters of the bundle.
Fig. 5
Fig. 5 Diagram of measurement scope and the approximate region of (z0, α, β).
Fig. 6
Fig. 6 Demodulation error curves of z0, α and β at the equivalent expansion point Oe of (ze, 0.5°,0.5°) and (ze, 0.6°,0.4°).
Fig. 7
Fig. 7 Demodulation error curves of z0, α and β at equivalent expansion point Oe(2.01mm, αe, βe) and (2.03mm, αe, βe).
Fig. 8
Fig. 8 Demodulation error curves of z0, α and β at equivalent expansion point Oe (ze, 1.7°, 0.8°).

Tables (5)

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Table 1 Demodulation Errors at the Nearby Points of (2 mm, 0.6°, 0.4°) with Same Value of z0 but Different Values of α and β

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Table 2 Demodulation Errors at the Nearby Points of (2 mm, 1°, 0.7°) with Same Value of z0 but Different Values of α and β

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Table 3 Demodulation Errors at the Nearby Points of (2 mm, 1°, 0.7°) with the Same Values of α and β but Different Value of z0

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Table 4 Expansion Coefficients Estimated Using Calibration Data and Calculated Using Output Function

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Table 5 Demodulation Errors at the Nearby Points of (2 mm, 1.6°, 2.5°) with the Same Value of z0 but Different Values of α and β

Equations (34)

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tan( α )x+tan( β )y+z z 0 =0.
z 0i ( z 0 ,α,β)= z 0 x i α y i β.
h i ( z 0 ,α,β)= 2 z 0i ( z 0 ,α,β) 1+ α 2 + β 2 .
r i ( z 0 ,α,β)= [ 2 z 0i ( z 0 ,α,β)α 1+ α 2 + β 2 + x i ] 2 + [ 2 z 0i ( z 0 ,α,β)β 1+ α 2 + β 2 + y i ] 2 .
I ti ( z 0 ,α,β)= exp[ r i 2 ( z 0 ,α,β)/ h i 2 ( z 0 ,α,β) ] h i ( z 0 ,α,β) .
ω r i = a 0 [1+ζ ( h i / a 0 ) 1.5 tan θ c ].
f 1i ( z 0 ,α,β)= 1 1+ ( r i ω r i ) 8 = 1 1+ { r i ( z 0 ,α,β) a 0 [1+ζ ( h i / a 0 ) 1.5 tan θ c ] } 8 .
f 2i ( z 0 ,α,β)= 1 1+ [ γ i ( z 0 ,α,β)/υ] 8 .
γ i =arccos( x si ( z 0 ,α,β)2α+ y si ( z 0 ,α,β)2β+ z si ( z 0 ,α,β) x si 2 ( z 0 ,α,β)+ y si 2 ( z 0 ,α,β)+ z si 2 ( z 0 ,α,β) 1+4 α 2 +4 β 2 ).
I i ( z 0 ,α,β)= I ti ( z 0 ,α,β) f 1i ( z 0 ,α,β) f 2i ( z 0 ,α,β).
I in ( z 0 ,α,β)= i=1 6 I ti ( z 0 ,α,β) f 1i ( z 0 ,α,β) f 2i ( z 0 ,α,β) .
I out ( z 0 ,α,β)= i=7 12 I ti ( z 0 ,α,β) f 1i ( z 0 ,α,β) f 2i ( z 0 ,α,β) .
z 1 = z 0 Ttan(α).
z 2 = z 0 Ttan(β).
z 1 = z 0 2tan(α).
z 2 = z 0 2tan(β).
I 0out ( z 0 ,α,β)= k 1o ( z 0 C z )+ k 2o ( z 0 C z ) 2 + k 3o ( z 0 C z )(α C α )+ k 4o ( z 0 C z )(β C β ) + f out (α,β).
I 0in ( z 0 ,α,β)= k 1i ( z 0 C z )+ k 2i ( z 0 C z ) 2 + k 3i ( z 0 C z )(α C α )+ k 4i ( z 0 C z )(β C β ) + f in (α,β).
I 1out ( z 1 ,α,β)= k 1o ( z 0 2α C z )+ k 2o ( z 0 2α C z ) 2 + k 3o ( z 0 2α C z )(α C α ) + k 4o ( z 0 2α C z )(β C β )+ f out (α,β).
I 1in ( z 1 ,α,β)= k 1i ( z 0 2α C z )+ k 2i ( z 0 2α C z ) 2 + k 3i ( z 0 2α C z )(α C α ) + k 4i ( z 0 2α C z )(β C β )+ f in (α,β).
I 2out ( z 2 ,α,β)= k 1o ( z 0 2β C z )+ k 2o ( z 0 2β C z ) 2 + k 3o ( z 0 2β C z )(α C α ) + k 4o ( z 0 2β C z )(β C β )+ f out (α,β).
I 2in ( z 1 ,α,β)= k 1i ( z 0 2β C z )+ k 2i ( z 0 2β C z ) 2 + k 3i ( z 0 2β C z )(α C α ) + k 4i ( z 0 2β C z )(β C β )+ f in (α,β).
D M 01 = I 0out I 1out I 0in I 1in = 4 k 2o z 0 +(2 k 3o 4 k 2o )α+2 k 4o β+(2 k 1o 4 k 2o C z 2 k 3o C α 2 k 4o C β ) 4 k 2i z 0 +(2 k 3i 4 k 2i )α+2 k 4i β+(2 k 1i 4 k 2i C z 2 k 3i C α 2 k 4i C β ) .
D M 02 = I 0out I 2out I 0in I 2in = 4 k 2o z 0 +(2 k 4o 4 k 2o )β+2 k 3o α+(2 k 1o 4 k 2o C z 2 k 3o C α 2 k 4o C β ) 4 k 2i z 0 +(2 k 4i 4 k 2i )β+2 k 3i α+(2 k 1i 4 k 2i C z 2 k 3i C α 2 k 4i C β ) .
D M 21 = I 2out I 1out I 2in I 1in = 4 k 2o z 0 +(2 k 3o 4 k 2o )α+(2 k 4o 4 k 2o )β+(2 k 1o 4 k 2o C z 2 k 3o C α 2 k 4o C β ) 4 k 2i z 0 +(2 k 3i 4 k 2i )α+(2 k 4i 4 k 2i )β+(2 k 1i 4 k 2i C z 2 k 3i C α 2 k 4i C β ) .
D in =2 k 1i 4 k 2i C z 2 k 3i C α 2 k 4i C β .
D out =2 k 1o 4 k 2o C z 2 k 3o C α 2 k 4o C β .
z 0 =(4 k 2i D out 4 k 2o D in )[(4 k 2i 2 k 3i )(D M 21 D M 02 )(4 k 2o 4 k 2i D M 01 )2 k 4i (D M 21 D M 01 ) (4 k 2o 4 k 2i D M 02 )(4 k 2o 4 k 2i D M 02 )(4 k 2o 4 k 2i D M 21 )]/{4 k 2i [(4 k 2o 4 k 2i D M 01 ) (D M 21 D M 02 )(4 k 2o 2 k 3i 2 k 3o 4 k 2i )+(4 k 2o 4 k 2i D M 01 )(4 k 2o 4 k 2i D M 02 ) (4 k 2o 4 k 2i D M 21 )+(4 k 2o 4 k 2i D M 02 )(D M 21 D M 01 )(4 k 2o 2 k 4i 2 k 4o 4 k 2i )]} D in /4 k 2i .
α=(4 k 2i D out 4 k 2o D in )(D M 21 D M 02 )(4 k 2o 4 k 2i D M 01 )/[(4 k 2o 4 k 2i D M 01 ) (D M 21 D M 02 )(4 k 2o 2 k 3i 2 k 3o 4 k 2i )+(4 k 2o 4 k 2i D M 01 )(4 k 2o 4 k 2i D M 02 ) (4 k 2o 4 k 2i D M 21 )+(4 k 2o 4 k 2i D M 02 )(D M 21 D M 01 )(4 k 2o 2 k 4i 2 k 4o 4 k 2i )].
β=(4 k 2i D out 4 k 2o D in )(D M 21 D M 01 )(4 k 2o 4 k 2i D M 02 )/[(4 k 2o 4 k 2i D M 01 ) (D M 21 D M 02 )(4 k 2o 2 k 3i 2 k 3o 4 k 2i )+(4 k 2o 4 k 2i D M 01 )(4 k 2o 4 k 2i D M 02 ) (4 k 2o 4 k 2i D M 21 )+(4 k 2o 4 k 2i D M 02 )(D M 21 D M 01 )(4 k 2o 2 k 4i 2 k 4o 4 k 2i )].
{ 4 x e 4α z e +4α( z 0 α)4=0. 4 y e 4β z e +4β( z 0 β)4=0 αx+βy+z z 0 =0. .
z e = ω r 0 z 0 +ω r 1 z 1 +ω r 2 z 2 ω r 0 +ω r 1 +ω r 2 .
{ I 0out I 1out = k p ( V 0out V 1out )=α[4 k 2o z 0 +(2 k 3o 4 k 2o )α+2 k 4o β+(2 k 1o 4 k 2o C z 2 k 3o C α 2 k 4o C β )]. I 0in I 1in = k p ( V 0in V 1in )=α[4 k 2i z 0 +(2 k 3i 4 k 2i )α+2 k 4i β+(2 k 1i 4 k 2i C z 2 k 3i C α 2 k 4i C β )]. I 0out I 2out = k p ( V 0out V 2out )=β[4 k 2o z 0 +(2 k 4o 4 k 2o )β+2 k 3o α+(2 k 1o 4 k 2o C z 2 k 3o C α 2 k 4o C β )]. I 0in I 2in = k p ( V 0in V 2in )=β[4 k 2i z 0 +(2 k 4i 4 k 2i )β+2 k 3i α+(2 k 1i 4 k 2i C z 2 k 3i C α 2 k 4i C β )].
{ k p ( V 0out V 1out )| ( C z +z, C α , C β ) = C α (4 k 2o z+2 k 1o 4 k 2o C α ). k p ( V 0out V 1out )| ( C z +z, C α 0.1°, C β ) =( C α 0.1°)[4 k 2o z+2 k 1o 4 k 2o ( C α 0.1°)2 k 3o 0.1°]. k p ( V 0out V 2out )| ( C z +z, C α 0.1°, C β ) = C β [4 k 2o z+2 k 1o 4 k 2o ( C α 0.1°)2 k 3o 0.1°]. k p ( V 0out V 2out )| ( C z +z, C α , C β 0.1°) =( C β 0.1°)[4 k 2o z+2 k 1o 4 k 2o ( C β 0.1°)2 k 4o 0.1°].

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