Abstract

Fiber Bragg grating (FBG) accelerometers using transverse forces are very sensitive. When a transverse force is applied to a lightly stretched string fixed by its two ends, a much stronger axial force along the string will be induced. So, the transverse force is amplified and converted into the axial force. At a given pre-strain of the string, the maximum amplification and requirements to obtain it have not been clearly demonstrated. Here, we theoretically prove and experimentally verify that the maximum amplification occurs when the strain induced by the transverse force approximately equals the pre-strain. This revelation improves the understanding of FBG accelerometers using transverse forces.

© 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. T. A. Berkoff and A. D. Kersey, “Experimental demonstration of a fiber Bragg grating accelerometer,” IEEE Photonics Technol. Lett. 8(12), 1677–1679 (1996).
    [Crossref]
  2. M. D. Todd, G. A. Johnson, B. A. Althouse, and S. T. Vohra, “Flexural beam-based fiber Bragg grating accelerometers,” IEEE Photonics Technol. Lett. 10(11), 1605–1607 (1998).
    [Crossref]
  3. A. Stefani, S. Andresen, W. Yuan, N. Herholdt-Rasmussen, and O. Bang, “High Sensitivity Polymer Optical Fiber-Bragg-Grating-Based Accelerometer,” IEEE Photonics Technol. Lett. 24(9), 763–765 (2012).
    [Crossref]
  4. P. F. Costa Antunes, C. A. Marques, H. Varum, and P. S. Andre, “Biaxial optical accelerometer and high-angle inclinometer with temperature and cross-axis insensitivity,” IEEE Sens. J. 12(7), 2399–2406 (2012).
    [Crossref]
  5. Y. X. Guo, D. S. Zhang, Z. D. Zhou, L. Xiong, and X. W. Deng, “Welding-packaged accelerometer based on metal-coated FBG,” Chin. Opt. Lett. 11(7), 21–23 (2013).
  6. Y. Zhang, W. Zhang, Y. Zhang, L. Chen, T. Yan, S. Wang, L. Yu, and Y. Li, “2-d medium–high frequency fiber bragg gratings accelerometer,” IEEE Sens. J. 17(3), 614–618 (2017).
    [Crossref]
  7. N. Basumallick, P. Biswas, R. Chakraborty, S. Chakraborty, K. Dasgupta, and S. Bandyopadhyay, “Fibre bragg grating based accelerometer with extended bandwidth,” Measurement Science & Technology 27(3), 035008 (2016).
    [Crossref]
  8. K. Li, T. H. T. Chan, M. H. Yau, T. Nguyen, D. P. Thambiratnam, and H. Y. Tam, “Very sensitive fiber Bragg grating accelerometer using transverse forces with an easy over-range protection and low cross axial sensitivity,” Appl. Opt. 52(25), 6401–6410 (2013).
    [Crossref]
  9. K. Li, T. H. T. Chan, M. H. Yau, D. P. Thambiratnam, and H. Y. Tam, “Experimental verification of the modified spring-mass theory of fiber Bragg grating accelerometers using transverse forces,” Appl. Opt. 53(6), 1200–1211 (2014).
    [Crossref]
  10. K. Li, T. H. T. Chan, M. H. Yau, D. Thambiratnam, and H. Y. Tam, “Biaxial fiber Bragg grating accelerometer using axial and transverse forces,” IEEE Photonics Technol. Lett. 26(15), 1549–1552 (2014).
    [Crossref]
  11. K. Li, M. H. Yau, T. H. T. Chan, D. Thambiratnam, and H. Y. Tam, “Fiber Bragg grating strain modulation based on nonlinear string transverse-force amplifier,” Opt. Lett. 38(3), 311–313 (2013).
    [Crossref]
  12. K. Li and M. H. Yau, “Maximum amplification of string transverse-force amplifier (simulated, experimental and theoretical results),” figshare (2018), https://doi.org/10.6084/m9.figshare.7054373 .

2017 (1)

Y. Zhang, W. Zhang, Y. Zhang, L. Chen, T. Yan, S. Wang, L. Yu, and Y. Li, “2-d medium–high frequency fiber bragg gratings accelerometer,” IEEE Sens. J. 17(3), 614–618 (2017).
[Crossref]

2016 (1)

N. Basumallick, P. Biswas, R. Chakraborty, S. Chakraborty, K. Dasgupta, and S. Bandyopadhyay, “Fibre bragg grating based accelerometer with extended bandwidth,” Measurement Science & Technology 27(3), 035008 (2016).
[Crossref]

2014 (2)

K. Li, T. H. T. Chan, M. H. Yau, D. P. Thambiratnam, and H. Y. Tam, “Experimental verification of the modified spring-mass theory of fiber Bragg grating accelerometers using transverse forces,” Appl. Opt. 53(6), 1200–1211 (2014).
[Crossref]

K. Li, T. H. T. Chan, M. H. Yau, D. Thambiratnam, and H. Y. Tam, “Biaxial fiber Bragg grating accelerometer using axial and transverse forces,” IEEE Photonics Technol. Lett. 26(15), 1549–1552 (2014).
[Crossref]

2013 (3)

2012 (2)

A. Stefani, S. Andresen, W. Yuan, N. Herholdt-Rasmussen, and O. Bang, “High Sensitivity Polymer Optical Fiber-Bragg-Grating-Based Accelerometer,” IEEE Photonics Technol. Lett. 24(9), 763–765 (2012).
[Crossref]

P. F. Costa Antunes, C. A. Marques, H. Varum, and P. S. Andre, “Biaxial optical accelerometer and high-angle inclinometer with temperature and cross-axis insensitivity,” IEEE Sens. J. 12(7), 2399–2406 (2012).
[Crossref]

1998 (1)

M. D. Todd, G. A. Johnson, B. A. Althouse, and S. T. Vohra, “Flexural beam-based fiber Bragg grating accelerometers,” IEEE Photonics Technol. Lett. 10(11), 1605–1607 (1998).
[Crossref]

1996 (1)

T. A. Berkoff and A. D. Kersey, “Experimental demonstration of a fiber Bragg grating accelerometer,” IEEE Photonics Technol. Lett. 8(12), 1677–1679 (1996).
[Crossref]

Althouse, B. A.

M. D. Todd, G. A. Johnson, B. A. Althouse, and S. T. Vohra, “Flexural beam-based fiber Bragg grating accelerometers,” IEEE Photonics Technol. Lett. 10(11), 1605–1607 (1998).
[Crossref]

Andre, P. S.

P. F. Costa Antunes, C. A. Marques, H. Varum, and P. S. Andre, “Biaxial optical accelerometer and high-angle inclinometer with temperature and cross-axis insensitivity,” IEEE Sens. J. 12(7), 2399–2406 (2012).
[Crossref]

Andresen, S.

A. Stefani, S. Andresen, W. Yuan, N. Herholdt-Rasmussen, and O. Bang, “High Sensitivity Polymer Optical Fiber-Bragg-Grating-Based Accelerometer,” IEEE Photonics Technol. Lett. 24(9), 763–765 (2012).
[Crossref]

Bandyopadhyay, S.

N. Basumallick, P. Biswas, R. Chakraborty, S. Chakraborty, K. Dasgupta, and S. Bandyopadhyay, “Fibre bragg grating based accelerometer with extended bandwidth,” Measurement Science & Technology 27(3), 035008 (2016).
[Crossref]

Bang, O.

A. Stefani, S. Andresen, W. Yuan, N. Herholdt-Rasmussen, and O. Bang, “High Sensitivity Polymer Optical Fiber-Bragg-Grating-Based Accelerometer,” IEEE Photonics Technol. Lett. 24(9), 763–765 (2012).
[Crossref]

Basumallick, N.

N. Basumallick, P. Biswas, R. Chakraborty, S. Chakraborty, K. Dasgupta, and S. Bandyopadhyay, “Fibre bragg grating based accelerometer with extended bandwidth,” Measurement Science & Technology 27(3), 035008 (2016).
[Crossref]

Berkoff, T. A.

T. A. Berkoff and A. D. Kersey, “Experimental demonstration of a fiber Bragg grating accelerometer,” IEEE Photonics Technol. Lett. 8(12), 1677–1679 (1996).
[Crossref]

Biswas, P.

N. Basumallick, P. Biswas, R. Chakraborty, S. Chakraborty, K. Dasgupta, and S. Bandyopadhyay, “Fibre bragg grating based accelerometer with extended bandwidth,” Measurement Science & Technology 27(3), 035008 (2016).
[Crossref]

Chakraborty, R.

N. Basumallick, P. Biswas, R. Chakraborty, S. Chakraborty, K. Dasgupta, and S. Bandyopadhyay, “Fibre bragg grating based accelerometer with extended bandwidth,” Measurement Science & Technology 27(3), 035008 (2016).
[Crossref]

Chakraborty, S.

N. Basumallick, P. Biswas, R. Chakraborty, S. Chakraborty, K. Dasgupta, and S. Bandyopadhyay, “Fibre bragg grating based accelerometer with extended bandwidth,” Measurement Science & Technology 27(3), 035008 (2016).
[Crossref]

Chan, T. H. T.

Chen, L.

Y. Zhang, W. Zhang, Y. Zhang, L. Chen, T. Yan, S. Wang, L. Yu, and Y. Li, “2-d medium–high frequency fiber bragg gratings accelerometer,” IEEE Sens. J. 17(3), 614–618 (2017).
[Crossref]

Costa Antunes, P. F.

P. F. Costa Antunes, C. A. Marques, H. Varum, and P. S. Andre, “Biaxial optical accelerometer and high-angle inclinometer with temperature and cross-axis insensitivity,” IEEE Sens. J. 12(7), 2399–2406 (2012).
[Crossref]

Dasgupta, K.

N. Basumallick, P. Biswas, R. Chakraborty, S. Chakraborty, K. Dasgupta, and S. Bandyopadhyay, “Fibre bragg grating based accelerometer with extended bandwidth,” Measurement Science & Technology 27(3), 035008 (2016).
[Crossref]

Deng, X. W.

Y. X. Guo, D. S. Zhang, Z. D. Zhou, L. Xiong, and X. W. Deng, “Welding-packaged accelerometer based on metal-coated FBG,” Chin. Opt. Lett. 11(7), 21–23 (2013).

Guo, Y. X.

Y. X. Guo, D. S. Zhang, Z. D. Zhou, L. Xiong, and X. W. Deng, “Welding-packaged accelerometer based on metal-coated FBG,” Chin. Opt. Lett. 11(7), 21–23 (2013).

Herholdt-Rasmussen, N.

A. Stefani, S. Andresen, W. Yuan, N. Herholdt-Rasmussen, and O. Bang, “High Sensitivity Polymer Optical Fiber-Bragg-Grating-Based Accelerometer,” IEEE Photonics Technol. Lett. 24(9), 763–765 (2012).
[Crossref]

Johnson, G. A.

M. D. Todd, G. A. Johnson, B. A. Althouse, and S. T. Vohra, “Flexural beam-based fiber Bragg grating accelerometers,” IEEE Photonics Technol. Lett. 10(11), 1605–1607 (1998).
[Crossref]

Kersey, A. D.

T. A. Berkoff and A. D. Kersey, “Experimental demonstration of a fiber Bragg grating accelerometer,” IEEE Photonics Technol. Lett. 8(12), 1677–1679 (1996).
[Crossref]

Li, K.

Li, Y.

Y. Zhang, W. Zhang, Y. Zhang, L. Chen, T. Yan, S. Wang, L. Yu, and Y. Li, “2-d medium–high frequency fiber bragg gratings accelerometer,” IEEE Sens. J. 17(3), 614–618 (2017).
[Crossref]

Marques, C. A.

P. F. Costa Antunes, C. A. Marques, H. Varum, and P. S. Andre, “Biaxial optical accelerometer and high-angle inclinometer with temperature and cross-axis insensitivity,” IEEE Sens. J. 12(7), 2399–2406 (2012).
[Crossref]

Nguyen, T.

Stefani, A.

A. Stefani, S. Andresen, W. Yuan, N. Herholdt-Rasmussen, and O. Bang, “High Sensitivity Polymer Optical Fiber-Bragg-Grating-Based Accelerometer,” IEEE Photonics Technol. Lett. 24(9), 763–765 (2012).
[Crossref]

Tam, H. Y.

Thambiratnam, D.

K. Li, T. H. T. Chan, M. H. Yau, D. Thambiratnam, and H. Y. Tam, “Biaxial fiber Bragg grating accelerometer using axial and transverse forces,” IEEE Photonics Technol. Lett. 26(15), 1549–1552 (2014).
[Crossref]

K. Li, M. H. Yau, T. H. T. Chan, D. Thambiratnam, and H. Y. Tam, “Fiber Bragg grating strain modulation based on nonlinear string transverse-force amplifier,” Opt. Lett. 38(3), 311–313 (2013).
[Crossref]

Thambiratnam, D. P.

Todd, M. D.

M. D. Todd, G. A. Johnson, B. A. Althouse, and S. T. Vohra, “Flexural beam-based fiber Bragg grating accelerometers,” IEEE Photonics Technol. Lett. 10(11), 1605–1607 (1998).
[Crossref]

Varum, H.

P. F. Costa Antunes, C. A. Marques, H. Varum, and P. S. Andre, “Biaxial optical accelerometer and high-angle inclinometer with temperature and cross-axis insensitivity,” IEEE Sens. J. 12(7), 2399–2406 (2012).
[Crossref]

Vohra, S. T.

M. D. Todd, G. A. Johnson, B. A. Althouse, and S. T. Vohra, “Flexural beam-based fiber Bragg grating accelerometers,” IEEE Photonics Technol. Lett. 10(11), 1605–1607 (1998).
[Crossref]

Wang, S.

Y. Zhang, W. Zhang, Y. Zhang, L. Chen, T. Yan, S. Wang, L. Yu, and Y. Li, “2-d medium–high frequency fiber bragg gratings accelerometer,” IEEE Sens. J. 17(3), 614–618 (2017).
[Crossref]

Xiong, L.

Y. X. Guo, D. S. Zhang, Z. D. Zhou, L. Xiong, and X. W. Deng, “Welding-packaged accelerometer based on metal-coated FBG,” Chin. Opt. Lett. 11(7), 21–23 (2013).

Yan, T.

Y. Zhang, W. Zhang, Y. Zhang, L. Chen, T. Yan, S. Wang, L. Yu, and Y. Li, “2-d medium–high frequency fiber bragg gratings accelerometer,” IEEE Sens. J. 17(3), 614–618 (2017).
[Crossref]

Yau, M. H.

Yu, L.

Y. Zhang, W. Zhang, Y. Zhang, L. Chen, T. Yan, S. Wang, L. Yu, and Y. Li, “2-d medium–high frequency fiber bragg gratings accelerometer,” IEEE Sens. J. 17(3), 614–618 (2017).
[Crossref]

Yuan, W.

A. Stefani, S. Andresen, W. Yuan, N. Herholdt-Rasmussen, and O. Bang, “High Sensitivity Polymer Optical Fiber-Bragg-Grating-Based Accelerometer,” IEEE Photonics Technol. Lett. 24(9), 763–765 (2012).
[Crossref]

Zhang, D. S.

Y. X. Guo, D. S. Zhang, Z. D. Zhou, L. Xiong, and X. W. Deng, “Welding-packaged accelerometer based on metal-coated FBG,” Chin. Opt. Lett. 11(7), 21–23 (2013).

Zhang, W.

Y. Zhang, W. Zhang, Y. Zhang, L. Chen, T. Yan, S. Wang, L. Yu, and Y. Li, “2-d medium–high frequency fiber bragg gratings accelerometer,” IEEE Sens. J. 17(3), 614–618 (2017).
[Crossref]

Zhang, Y.

Y. Zhang, W. Zhang, Y. Zhang, L. Chen, T. Yan, S. Wang, L. Yu, and Y. Li, “2-d medium–high frequency fiber bragg gratings accelerometer,” IEEE Sens. J. 17(3), 614–618 (2017).
[Crossref]

Y. Zhang, W. Zhang, Y. Zhang, L. Chen, T. Yan, S. Wang, L. Yu, and Y. Li, “2-d medium–high frequency fiber bragg gratings accelerometer,” IEEE Sens. J. 17(3), 614–618 (2017).
[Crossref]

Zhou, Z. D.

Y. X. Guo, D. S. Zhang, Z. D. Zhou, L. Xiong, and X. W. Deng, “Welding-packaged accelerometer based on metal-coated FBG,” Chin. Opt. Lett. 11(7), 21–23 (2013).

Appl. Opt. (2)

Chin. Opt. Lett. (1)

Y. X. Guo, D. S. Zhang, Z. D. Zhou, L. Xiong, and X. W. Deng, “Welding-packaged accelerometer based on metal-coated FBG,” Chin. Opt. Lett. 11(7), 21–23 (2013).

IEEE Photonics Technol. Lett. (4)

K. Li, T. H. T. Chan, M. H. Yau, D. Thambiratnam, and H. Y. Tam, “Biaxial fiber Bragg grating accelerometer using axial and transverse forces,” IEEE Photonics Technol. Lett. 26(15), 1549–1552 (2014).
[Crossref]

T. A. Berkoff and A. D. Kersey, “Experimental demonstration of a fiber Bragg grating accelerometer,” IEEE Photonics Technol. Lett. 8(12), 1677–1679 (1996).
[Crossref]

M. D. Todd, G. A. Johnson, B. A. Althouse, and S. T. Vohra, “Flexural beam-based fiber Bragg grating accelerometers,” IEEE Photonics Technol. Lett. 10(11), 1605–1607 (1998).
[Crossref]

A. Stefani, S. Andresen, W. Yuan, N. Herholdt-Rasmussen, and O. Bang, “High Sensitivity Polymer Optical Fiber-Bragg-Grating-Based Accelerometer,” IEEE Photonics Technol. Lett. 24(9), 763–765 (2012).
[Crossref]

IEEE Sens. J. (2)

P. F. Costa Antunes, C. A. Marques, H. Varum, and P. S. Andre, “Biaxial optical accelerometer and high-angle inclinometer with temperature and cross-axis insensitivity,” IEEE Sens. J. 12(7), 2399–2406 (2012).
[Crossref]

Y. Zhang, W. Zhang, Y. Zhang, L. Chen, T. Yan, S. Wang, L. Yu, and Y. Li, “2-d medium–high frequency fiber bragg gratings accelerometer,” IEEE Sens. J. 17(3), 614–618 (2017).
[Crossref]

Measurement Science & Technology (1)

N. Basumallick, P. Biswas, R. Chakraborty, S. Chakraborty, K. Dasgupta, and S. Bandyopadhyay, “Fibre bragg grating based accelerometer with extended bandwidth,” Measurement Science & Technology 27(3), 035008 (2016).
[Crossref]

Opt. Lett. (1)

Other (1)

K. Li and M. H. Yau, “Maximum amplification of string transverse-force amplifier (simulated, experimental and theoretical results),” figshare (2018), https://doi.org/10.6084/m9.figshare.7054373 .

Supplementary Material (1)

NameDescription
» Dataset 1       This excel file shows the simulated, experimental and theoretical results of the paper "Maximum amplification of string transverse-force amplifier and its applications in fiber Bragg grating accelerometers". It should be used together with the paper.

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Figures (3)

Fig. 1.
Fig. 1. Diagram of the string transverse-force amplifier
Fig. 2.
Fig. 2. Simulated and experimental results at the 3 different pre-strains
Fig. 3.
Fig. 3. Experimental setups: applying a pre-strain (a) and transverse force (b)

Tables (4)

Tables Icon

Table 1. Simulated relationships at the 3 pre-strains based on Eq. (1)

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Table 2. Maximum amplifications and the required induced-strains at the 3 pre-strains

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Table 3. Experimental results at the pre-strain 0.0000431

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Table 4. Comparison between the simulated and the theoretical results

Equations (7)

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Δ F l / F t = Δ ε ( Δ ε + 1 ) 2 ( ε + Δ ε ) 2 Δ ε + Δ ε 2 ,
d ( Δ F l / F t ) d Δ ε = d ( Δ ε ( Δ ε + 1 ) 2 ( ε + Δ ε ) 2 Δ ε + Δ ε 2 ) d Δ ε = 1 2 ( 2 Δ ε + 1 ) [ ( ε + Δ ε ) 2 Δ ε + Δ ε 2 ] Δ ε ( Δ ε + 1 ) ( 2 Δ ε + Δ ε 2 ) 1 2 ( ε + ε Δ ε + 3 Δ ε + 2 Δ ε 2 ) [ ( ε + Δ ε ) 2 Δ ε + Δ ε 2 ] 2 = 0
( 2 Δ ε + 1 ) [ ( ε + Δ ε ) 2 Δ ε + Δ ε 2 ] Δ ε ( Δ ε + 1 ) ( 2 Δ ε + Δ ε 2 ) 1 2 ( ε + ε Δ ε + 3 Δ ε + 2 Δ ε 2 ) = 0 ( 2 Δ ε + 1 ) ( ε + Δ ε ) ( 2 Δ ε + Δ ε 2 ) Δ ε ( Δ ε + 1 ) ( ε + ε Δ ε + 3 Δ ε + 2 Δ ε 2 ) = 0 ( 2 Δ ε + 1 ) ( ε + Δ ε ) ( 2 + Δ ε ) ( Δ ε + 1 ) ( ε + ε Δ ε + 3 Δ ε + 2 Δ ε 2 ) = 0 ε Δ ε 2 + ( 3 ε 1 ) Δ ε + ε = 0.
Δ ε = 1 3 ε 1 6 ε + 5 ε 2 2 ε .
Δ F l / F t = Δ ε ( Δ ε + 1 ) 2 ( ε + Δ ε ) 2 Δ ε + Δ ε 2 = Δ ε + 1 2 ( ε + Δ ε ) 2 Δ ε + 1 = 1 3 ε 1 6 ε + 5 ε 2 2 ε + 1 2 ( ε + 1 3 ε 1 6 ε + 5 ε 2 2 ε ) 4 ε 1 3 ε 1 6 ε + 5 ε 2 + 1
Δ ε = 1 3 ε ( 1 + 1 2 ( 5 ε 2 6 ε ) 1 8 ( 5 ε 2 6 ε ) 2 + ( 5 ε 2 6 ε ) ) 2 ε = 1 3 ε ( 1 + 5 ε 2 2 3 ε 36 ε 2 8 + ( ε ) ) 2 ε = 1 3 ε ( 1 3 ε 2 ε 2 + ( ε ) ) 2 ε 1 3 ε ( 1 3 ε 2 ε 2 ) 2 ε = ε .
Δ F l / F t = Δ ε ( Δ ε + 1 ) 2 ( ε + Δ ε ) 2 Δ ε + Δ ε 2 ε ( ε + 1 ) 4 ε 2 ε + ε 2 = ( ε + 1 ) 4 2 ε + ε 2 1 4 2 ε = 1 8 2 ε .

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