- Email: [email protected]
Strain characteristics of the silica-based fiber Bragg gratings for 30–273 K
Accepted Manuscript Strain characteristics of the silica-based fiber Bragg gratings for 30 ∼ 273K Litong Li, Dajuan Lv, Minghong Yang, Liangming Xiong, Jie Luo, Lu Tan PII: DOI: Reference:
S0011-2275(17)30260-6 https://doi.org/10.1016/j.cryogenics.2018.03.002 JCRY 2793
To appear in:
Cryogenics
Received Date: Revised Date: Accepted Date:
29 July 2017 30 January 2018 3 March 2018
Please cite this article as: Li, L., Lv, D., Yang, M., Xiong, L., Luo, J., Tan, L., Strain characteristics of the silicabased fiber Bragg gratings for 30 ∼ 273K, Cryogenics (2018), doi: https://doi.org/10.1016/j.cryogenics.2018.03.002
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Strain characteristics of the silica-based fiber Bragg gratings for 30 ~ 273K Litong Li,a,b* Dajuan Lv, a,b Minghong Yang,b Liangming Xiong,a Jie Luoa, Lu Tana a
State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Yangtze Optical Fibre and Cable Joint Stock Limited Company, Wuhan, China, 430070 b National Engineering Laboratory for Fiber Optic Sensing Technology, Wuhan University of Technology, Wuhan, China, 430070
1
Highlights
The strain characteristic of silica-based FBG was experimented from 30 K to 273 K by a dynamic experiment.
The static tensile comparison test of silica-based FBG was doing three times in the liquid nitrogen environment.
The strain-wavelength response of silica-based FBG was linear at constant temperature in the low temperature environment.
The relationship between the strain coefficient and temperature could be described by a cubic curve at cryogenic temperatures.
The curve equation of strain coefficient can be used for silica-based FBG standardization procedures at cryogenic temperatures.
Abstract: This work studied the strain coefficient of silica-based fiber Bragg grating (FBG) at cryogenic temperatures. A dynamic temperature test with an oxygen-free copper specimen in the temperature range of 30 to 273 K was designed. The relationship between the strain coefficient and temperature could be characterized by three-order polynomial. A static tensile test was carried out in liquid nitrogen environment verified the effectiveness of the dynamic results. Good correlation was obtained from the two experiment results. Finally, the factors affecting the measurement error were discussed. Keywords: Fiber Bragg grating; Cryogenic temperatures; Strain coefficient; Three-order polynomial *
Corresponding author: [email protected]
1 Introduction Cryogenic environment sensing was critically important in various advanced technology fields, such as aerospace, life science and nuclear power. Many traditional electrical sensors, such as the resistive foil strain gauge and thermocouple, were constrained by electromagnetic interference and the size when applied in such harsh circumstance1-3. Optical fiber sensors, characterized by small profile, light weight, resistant to harsh environment, immune to electromagnetic interference, undergone a tremendous development in the field of cryogenic environment monitoring. Among these numerous sensors, fiber Bragg grating (FBG) was the most extensively researched over the past few years4-9. Tadahito et al. reported a real-time strain measurement of a composite rocket liquid hydrogen tank at 77K using fiber Bragg grating (FBG) sensors10. Li et al. designed a fiber Bragg grating sensor for cryogenic long-range displacement measurement 11. Antonella et al. developed a distributed and multi-point fiber-optic monitoring system along a superconducting power transmission line down to 30 K and over 20 m distance12. However, FBG’s cross-sensitivity between temperature and strain still existed at cryogenic temperatures. It was necessary to distinguish the external cause of wavelength change. The thermal expansion coefficient (CTE) and thermo-optical coefficient (TOC) affected the temperature sensitivity of FBG, while the elastic coefficient affected the strain sensitivity. The correlation coefficients of silica-based FBGs would no longer be constant at cryogenic temperatures, and the known sensing parameters were no longer applicable. 2
Meanwhile, calibrations of FBG sensors at cryogenic temperatures before any measurements remained an unsolved problem. Therefore, how to measure the correlation coefficients of silica-based FBGs at cryogenic temperatures was an attractive research topic. In 2012, Guo et al. reported that the strain sensitivity was stable and temperature-dependent from 123 to 273 K14. In 2016, Kang et al. investigated the CTE and the TOC of FBG sensor from ambient room temperature (293 K) to cryogenic temperature (113 K)15. In 2017, numerical and experimental investigation of FBG sensors at room temperature of 298 K and cryogenic temperatures of 77 K, 10 K and 4.2 K was demonstrated by Rangaraj et al.16. From the published papers, it could be obtained that the temperature response of FBG was non-linear and the temperature sensitivity of FBG decreased with decreasing temperature in the cryogenic environment. FBG was not suitable for cryogenic temperature measurement if it was not encapsulated in the suitable material with a higher thermal expansion coefficient. On the other hand, the strain response of FBG was linear at constant temperature, and the strain sensitivity was stable and temperature-dependent, increased with decreasing temperature in the cryogenic environment. However, little research has been done on the strain coefficient measurement of silica-based FBG at cryogenic temperatures under 77K. In this work, we proposed a test in a vacuum cryogenic vessel with an oxygen-free copper specimen to measure the strain coefficient of silica-based FBG in the temperature range of 30~273K. The basic principle of the FBG test was theoretically described and the thermal strain performance of the FBG was studied. In particular, a static tension experiment was presented in the nitrogen environment in order to verify the effectiveness of the dynamic temperature results. Furthermore, the uncertainty of the test results has been analyzed. 2 Sensing principle A FBG was periodic modulation of the refractive index within the core of an optical fiber. 3
The Bragg wavelength was given as:
B 2neff .
(1)
Where B was the center wavelength of FBG, was the period of the grating, and neff was the effective refractive index of the fiber grating core. The temperature change T and the strain
would both cause a change in the grating period and the refractive index of the
fiber core. Differentiating Eq.(1):
B 1 neff 1 1 neff 1 [ ] [ ]T , B neff T neff
(2)
K 1 Pe ,
(3)
KT 1
1 1 neff + + . T neff
(4)
Where was the thermal expansion coefficient of FBG, was the thermo-optical coefficient of FBG, Pe was the elastic coefficient of FBG. Also K was the strain coefficient of FBG, and
K T 1 was the temperature coefficient of FBG17. The Eq. (2) could be
expressed as:
B =K KT 1T (1 Pe ) ( )T . B
(5)
When the FBG was pasted on a metal specimen, since the temperature changes, the metal would produce a thermal strain along the FBG, where
m was the thermal expansion
coefficient of the metal specimen. The temperature sensitivity of the metal-pasted FBG was therefore determined by the combination of the thermal strain effect and the direct thermal effect. We can finally determine that the wavelength shift of FBG would be calculated as follows18 19:
4
B (1 Pe )( m )T ( )T =T [ + m Pe ( m )] B
(6)
Thus, the relationship between the strain coefficient K could be obtained by
1 B m B T . K 1 Pe 1 m Since the general value of than the CTE
(7)
was 5.5 × 10−7/°C at room temperatures, was much less
m of metal specimen (normal lager than 10 × 10−6), the Eq.(7) could be
simplified to
1 B m B T K 1 Pe 1 m 1 B 1 B B T B T = = m T Where
.
(8)
B and were the differential item of the wavelength change and strain T T
change, respectively. When ambient temperature remained constant, the strain coefficient was given by
K 1 Pe
3
B . B
(9)
Experiment and discussion Two FBGs were encapsulated by cryogenic adhesives (DG-4, Blue star Co Ltd., China)
onto an oxygen-free copper specimen, as shown in Fig.1 (a). FBGs were made from the fused silica HIPOSH® fiber (YOFC Ltd.,China) (with core/cladding of 9 µm/125 µm). The pre-stretch wavelength of FBG was 2 nm, and meanwhile the length and thickness of adhesives were 3 cm and 0.2 mm respectively. One end of the oxygen-free copper specimen 5
was fixed at the object stage of the cryogenic vessel to ensure the heat exchange. During the test, the wavelength shift of FBG could only be affected by the thermal strain of the specimen and the thermo-optic effect20. The thermal strain of the specimen could be measured by a cryogenic Cu-Ni strain gauge (KFL, Kyowa Inc., Japan) which was pasted near the FBGs. A Lakeshore Model 331 cryogenic thermocouple placed near the FBGs was used as a reference for the standard temperature measurement. A photo of the oxygen-free copper specimen was presented in Fig.1 (b).
Installation hole
Resistance strain gauge FBG
Cryogenic adhesive Thermocouple (a)
(b)
Fig. 1 (a) The schematic diagram of the FBG pasted in the copper specimen; (b) The photo of the copper specimen after installation
We have designed an optical fiber flange sealing export to ensure the light transmission at high vacuums and low temperatures, as shown in Fig.2. The experimental set-up of the dynamic temperature test was illustrated in Fig.3 (a). The pressure in the cryogenic vessel drops to 10−2 Torr through the use of a molecular vacuum pump (Sumitomo Heavy Industries Ltd., Japan). After the refrigerator (Sumitomo Heavy Industries Ltd., Japan) has worked for 2 h, the temperature in the surface of the oxygen free copper specimen dropped down from
6
room temperature to nearly 30 K. While the temperature would rise to 273 K slowly after 48 h if turned the refrigerator off. The Lakeshore cryogenic temperature (accuracy: 0.1 K) test system kept a real-time record of the temperature at 1 Hz. At the same time, the wavelength demodulation (Bayspec Ltd., USA) rate for FBG was set to save the data at 1 Hz. So the temperature data and the sensor data could correspond to each other. The photo of the experimental set-up was presented in Fig.3 (b). Wedge sealing piece fiber
Armored cable
Nut
flange
Fig. 2 The structure design of the optical fiber flange sealing export
7
Refrigerator
Cryogenic vessel
Oxygen-free copper attached with FBGs
(a)
Demodulation
Computer
(b)
Fig. 3 (a) Dynamic temperature experimental set-up; (b) The photo of the dynamic temperature experimental set-up
During the temperature-rise process, the long-term heat conduction would make the data more accurate. The wavelength responses of two FBGs at the temperature-rise stage were plotted in Fig.4, and from which, we could know that both of the wavelength change of two FBGs were nonlinear from 30 K to 273 K. The red line in Fig.4 was quadratic polynomial fit curve of Bragg wavelength change versus temperature. Fig.5 illustrated the strain shifts of the oxygen-free copper specimen under different temperatures.
8
Fig. 4 The wavelength change and fitting curve of the two FBGs in the cryogenic test
Fig. 5 The strain curve of the copper specimen in the cryogenic test
After quadratic curve fitting for the test data, we could get the equation. For FBG1
1 =-0.1357+0.00554t (5.343E 5)t 2 .
(10)
2 =-0.3674+0.00602t (5.134E 5)t 2 .
(11)
For FBG2
For the oxygen-free copper specimen
=0.00306 (3.06E 6)t+(2.98E -8)t 2 . 9
(12)
Where t was in Kelvin and the temperature range is from 30 K to 273 K. In our previous work, we have studied the TOC of silica-based FBG at cryogenic temperatures range from 30 K to 273 K21. It could be expressed as:
( 0.23E 3)t 2 +0.2466t 3.8593 (E-7) .
(13)
So we could calculate the strain coefficient by For FBG1
(0.23E 3)t 2 +0.4414t 33.791 K 1 = . 0.596t+30.6
(14)
(0.23E 3)t 2 +0.4134t 35.84 . 0.596t+30.6
(15)
For FBG2
K 2 =
After the average calculation of Eq. (14) and Eq. (15), the strain coefficient could be given by:
K =
(0.23E 3)t 2 +0.4274t 34.81 . 0.596t+30.6
(16)
Where t was in Kelvin and the temperature ranged from 30 K to 273 K. The relationship between the strain coefficient and temperature could be described by a cubic curve. In order to verify the accuracy of the dynamic test data, a static tensile experiment in the liquid nitrogen environment was designed. The schematic drawing of the test system was shown in Fig.6. The stretcher was made of resistant material and equipped with a liquid nitrogen tank. It could ensure that all of the tests were performed in the liquid nitrogen environment and the temperature was constant. The tensile specimen was made of aluminum alloy, a FBG was encapsulated by cryogenic adhesives (DG-4, Blue star Co Ltd, China) on an aluminum alloy tensile specimen.
10
Stretcher
Liquid nitrogen tank Tension specimen
Demodulation
Computer
Fig. 6 The set up of the tensile test equipment at cryogenic temperature
The tension load was changed from 0 kN to 15 kN at a step of 1 kN, with a duration time of nearly 30 seconds. After that, the tension load decreased slowly to 0 kN. This tensile process was repeated three times. We could acquire the strain of the tensile specimen from Eq. (17) as follow, where F was the tension force and the young's modulus ( E ) of aluminum alloy was 80 GPa at the liquid nitrogen temperature. A was the cross-section of the specimen (60 mm2 ):
F , AE
(17)
Fig.7 showed the wavelength change results and the linear fitting curves of the FBG during the three tests. It could be observed from Fig 7 that the FBG showed excellent linearity and good repetition. Table.1 showed the fitting function of the three tests. After the calculation of Eq.(9), the strain coefficient of FBG was found to be 0.916, 0.907 and 0.92 at 77 K.
11
0.0025
Test 1 Test 2 Test 3
0.0020
wavelength change(nm)
wavelength change(nm)
0.0025
0.0015 0.0010 0.0005
0.0020
Test 1 Linear Fitting y=-1.00265E-5+0.916X
0.0015
R=0.999
0.0010 0.0005 0.0000
0.0000 0
500
1000
1500
2000
2500
0
3000
500
1000
strain()
wavelength change(nm)
0.0020
wavelength change(nm)
Test 2
0.0025
Linear Fitting y=-1.01546E-5+0.907X
0.0015
1500
2000
2500
3000
2000
2500
3000
strain()
R=0.999
0.0010 0.0005 0.0000
0.0025 0.0020
Test 3 Linear Fitting y=-8.0837E-5+0.92X
0.0015
R=0.999 0.0010 0.0005 0.0000
0
500
1000
1500
2000
2500
3000
0
500
1000
1500
strain()
strain()
Fig. 7 The wavelength-strain curve of the FBG in three tests Table 1 Tensile test data table Number of test Test1
Fitting function
y= -1.00265E-5+0.916x y= -1.01546E-5+0.907x y= -8.08373-5+0.92x
Test2 Test3
The uncertainty u ( K ) of the test data could be expressed as22:
u ( K ) s ( K )
s( K )=
1 n 1
s ( K ) n
n
( K i 1
i
K ) 2
(18)
(19)
Where K was the average value of the test data, n was the test times. The dynamic temperature testing results (0.904, 0.903) at 77 K were close to the static tension results 12
(0.916, 0.907 and 0.920) in the liquid nitrogen environment. After the calculation of Eq.(18) and Eq.(19),the uncertainty of the test data at 77K was 0.003. Meanwhile the dynamic temperature test result (0.88) at 123 K also accorded well with Guo et al.’s work14, where the strain coefficient was 0.879 at 123 K. Also the dynamic temperature test deviation may come from the strain transfer factor, cryogenic chemical properties of adhesive, the test error of strain data and the non-steady state of cryogenic system. Furthermore, to ensure the accurate accuracy of the test data, the measurement should be repeated for several times and a good repeatability could be obtained. From the static tension test results, we could obtain the strain-wavelength response was linear
at
constant
temperature,
and
the
strain
sensitivity
was
stable
and
temperature-dependent. During the dynamic temperature test, the strain response of FBG sensors was non-linear and could be approximated by third-order polynomial. When the temperature changes, the free energy of the fiber material would change correspondingly, the physical properties (elastic modulus, shear modulus and poisson ratio) of optical fibers would change simultaneously. Also the decreasing of fiber core’s effective refractive index would also bring down the elastic coefficient of FBG when the temperature decreased23. The strain coefficient of FBG increased with decreasing temperature in the cryogenic environment which was agreed well with the published works14, 16. 4 Conclusion In conclusion, the strain characteristic of silica-based FBG was studied from 30 K to 273 K by a dynamic experiment. The static tensile comparison test was performed three times in the liquid nitrogen environment. Based on the analysis of the experimental data, we got the proposed formula for the strain coefficient of silica-based FBG in the temperature range of 30~273 K. The strain-wavelength response of silica-based FBG was linear at constant temperature. The results supported that the relationship between the strain coefficient and 13
temperature could be described by a cubic curve at cryogenic temperatures. The results of two test methods were consistent, and the curve equation could be used for silica-based FBG standardization procedures at cryogenic temperatures. Acknowledgments The work was supported by Hubei Provincial Natural Science Foundation of China (2015CFA054) and the Open Projects Foundation of Yangtze Optical Fibre and Cable Joint Stock Limited Company (YOFC grant No.SKLD1502). References 1.
James, Stephen W., et al. "Strain response of fibre Bragg grating sensors at cryogenic temperatures." Measurement Science and Technology 13.10 (2002): 1535.
2.
Rajini-Kumar, R., et al. "Performance evaluation of metal-coated fiber Bragg Grating sensors for sensing cryogenic temperature." Cryogenics 48.3(2008):142-147.
3.
Parne, Saidi, et al. "Polymer-coated fiber Bragg Grating Sensor for cryogenic temperature measurements." Microwave & Optical Technology Letters 53.5(2011):1154–1157.
4.
Sengupta, D., et al. "Strain-Temperature Discrimination Using a Single FBG at Cryogenic Region." Sensors & Transducers 131.8 (2011): 36.
5.
Yamada, H., et al. "Measurement and improvement of characteristics using optical fiber temperature sensors at cryogenic temperatures." Physica C: Superconductivity and its applications 471.21 (2011): 1570-1575.
6.
Shou, Ma, et al. "On-line monitoring system for downhole temperature and pressure." Optical Engineering 53.8 (2014): 087102-087102.
7.
Zaynetdinov, Madrakhim, et al. "A fiber Bragg grating temperature sensor for 2–400 K." IEEE Sensors Journal 15.3 (2015): 1908-1912.
8.
Thekkethil, S. R., et al. "Design of cryogenic flow meter using fiber Bragg grating sensors." SENSORS, 2015 IEEE. IEEE, 2015.
14
9.
Tanaka, Y., et al. "Experimental investigation of optical fiber temperature sensors at cryogenic temperature and in high magnetic fields." Physica C: Superconductivity 470.20 (2010): 1890-1894.
10. Mizutani, Tadahito, Nobuo Takeda, and Hajime Takeya. "On-board strain measurement of a cryogenic composite tank mounted on a reusable rocket using FBG sensors." Structural Health Monitoring 5.3 (2006): 205-214. 11. Li, Jicheng, H. Neumann, and R. Ramalingam. "Design, fabrication, and testing of fiber Bragg grating sensors for cryogenic long-range displacement measurement." Cryogenics 68 (2015): 36-43. 12. Chiuchiolo, Antonella, et al. "Cryogenic-temperature profiling of high-power superconducting lines using local and distributed optical-fiber sensors." Optics letters 40.19 (2015): 4424-4427. 13. Esposito, Marco, et al. "Fiber Bragg Grating sensors to measure the coefficient of thermal expansion of polymers at cryogenic temperatures." Sensors and Actuators A: Physical 189 (2013): 195-203. 14. Guo, Zhan-Sheng, Jiemin Feng, and Hui Wang. "Cryogenic temperature characteristics of the fiber Bragg grating sensors." Cryogenics 52.10 (2012): 457-460. 15. Kang, Donghoon, et al. "Thermal characteristics of FBG sensors at cryogenic temperatures for structural health monitoring." International Journal of Precision Engineering and Manufacturing 17.1 (2016): 5-9. 16. Venkatesan, V. N., and R. Ramalingam. "Numerical and experimental investigation of FBG strain response at cryogenic temperatures." IOP Conference Series: Materials Science and Engineering. Vol. 171. No. 1. IOP Publishing, 2017. 17. Xiang, Longhai, et al. "Design and experimental research on cantilever accelerometer based on fiber Bragg grating." Optical Engineering 55.6 (2016): 066113-066113. 18. Wei H, et al. "High-Sensitivity Fiber Bragg Grating Temperature Sensor with Polymer Jacket and Its Low-Temperature Characteristic". Acta Optica Sinica, 24.10 (2004):1316-1319. 19. Scalea, F. L. D. "Measurement of thermal expansion coefficient using strain gages." Experimental Mechanics, 38. 4(1998):233-241. 15
20. Jung, J, et al. "Fiber Bragg grating temperature sensor with controllable sensitivity." Applied Optics 38.13(1999):2752. 21. Li, Litong, et al. "FFPI-FBG hybrid sensor to measure the thermal expansion and thermo-optical coefficient of a silica-based fiber at cryogenic temperatures." Chinese Optics Letters 13.10 (2015): 100601. 22. Cheng, Shu Hui, et al. "Study on Uncertainty of FBG Pressure Transducer Calibration." Control & Instruments in Chemical Industry 3 (2017):233-235. 23. Zhao, L. J. "Influence of environment temperature wide-range variation on Brillouin shift in optical fiber." Acta Physica Sinica 59.9(2010):6219-6223.
16
S0011-2275(17)30260-6 https://doi.org/10.1016/j.cryogenics.2018.03.002 JCRY 2793
To appear in:
Cryogenics
Received Date: Revised Date: Accepted Date:
29 July 2017 30 January 2018 3 March 2018
Please cite this article as: Li, L., Lv, D., Yang, M., Xiong, L., Luo, J., Tan, L., Strain characteristics of the silicabased fiber Bragg gratings for 30 ∼ 273K, Cryogenics (2018), doi: https://doi.org/10.1016/j.cryogenics.2018.03.002
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Strain characteristics of the silica-based fiber Bragg gratings for 30 ~ 273K Litong Li,a,b* Dajuan Lv, a,b Minghong Yang,b Liangming Xiong,a Jie Luoa, Lu Tana a
State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Yangtze Optical Fibre and Cable Joint Stock Limited Company, Wuhan, China, 430070 b National Engineering Laboratory for Fiber Optic Sensing Technology, Wuhan University of Technology, Wuhan, China, 430070
1
Highlights
The strain characteristic of silica-based FBG was experimented from 30 K to 273 K by a dynamic experiment.
The static tensile comparison test of silica-based FBG was doing three times in the liquid nitrogen environment.
The strain-wavelength response of silica-based FBG was linear at constant temperature in the low temperature environment.
The relationship between the strain coefficient and temperature could be described by a cubic curve at cryogenic temperatures.
The curve equation of strain coefficient can be used for silica-based FBG standardization procedures at cryogenic temperatures.
Abstract: This work studied the strain coefficient of silica-based fiber Bragg grating (FBG) at cryogenic temperatures. A dynamic temperature test with an oxygen-free copper specimen in the temperature range of 30 to 273 K was designed. The relationship between the strain coefficient and temperature could be characterized by three-order polynomial. A static tensile test was carried out in liquid nitrogen environment verified the effectiveness of the dynamic results. Good correlation was obtained from the two experiment results. Finally, the factors affecting the measurement error were discussed. Keywords: Fiber Bragg grating; Cryogenic temperatures; Strain coefficient; Three-order polynomial *
Corresponding author: [email protected]
1 Introduction Cryogenic environment sensing was critically important in various advanced technology fields, such as aerospace, life science and nuclear power. Many traditional electrical sensors, such as the resistive foil strain gauge and thermocouple, were constrained by electromagnetic interference and the size when applied in such harsh circumstance1-3. Optical fiber sensors, characterized by small profile, light weight, resistant to harsh environment, immune to electromagnetic interference, undergone a tremendous development in the field of cryogenic environment monitoring. Among these numerous sensors, fiber Bragg grating (FBG) was the most extensively researched over the past few years4-9. Tadahito et al. reported a real-time strain measurement of a composite rocket liquid hydrogen tank at 77K using fiber Bragg grating (FBG) sensors10. Li et al. designed a fiber Bragg grating sensor for cryogenic long-range displacement measurement 11. Antonella et al. developed a distributed and multi-point fiber-optic monitoring system along a superconducting power transmission line down to 30 K and over 20 m distance12. However, FBG’s cross-sensitivity between temperature and strain still existed at cryogenic temperatures. It was necessary to distinguish the external cause of wavelength change. The thermal expansion coefficient (CTE) and thermo-optical coefficient (TOC) affected the temperature sensitivity of FBG, while the elastic coefficient affected the strain sensitivity. The correlation coefficients of silica-based FBGs would no longer be constant at cryogenic temperatures, and the known sensing parameters were no longer applicable. 2
Meanwhile, calibrations of FBG sensors at cryogenic temperatures before any measurements remained an unsolved problem. Therefore, how to measure the correlation coefficients of silica-based FBGs at cryogenic temperatures was an attractive research topic. In 2012, Guo et al. reported that the strain sensitivity was stable and temperature-dependent from 123 to 273 K14. In 2016, Kang et al. investigated the CTE and the TOC of FBG sensor from ambient room temperature (293 K) to cryogenic temperature (113 K)15. In 2017, numerical and experimental investigation of FBG sensors at room temperature of 298 K and cryogenic temperatures of 77 K, 10 K and 4.2 K was demonstrated by Rangaraj et al.16. From the published papers, it could be obtained that the temperature response of FBG was non-linear and the temperature sensitivity of FBG decreased with decreasing temperature in the cryogenic environment. FBG was not suitable for cryogenic temperature measurement if it was not encapsulated in the suitable material with a higher thermal expansion coefficient. On the other hand, the strain response of FBG was linear at constant temperature, and the strain sensitivity was stable and temperature-dependent, increased with decreasing temperature in the cryogenic environment. However, little research has been done on the strain coefficient measurement of silica-based FBG at cryogenic temperatures under 77K. In this work, we proposed a test in a vacuum cryogenic vessel with an oxygen-free copper specimen to measure the strain coefficient of silica-based FBG in the temperature range of 30~273K. The basic principle of the FBG test was theoretically described and the thermal strain performance of the FBG was studied. In particular, a static tension experiment was presented in the nitrogen environment in order to verify the effectiveness of the dynamic temperature results. Furthermore, the uncertainty of the test results has been analyzed. 2 Sensing principle A FBG was periodic modulation of the refractive index within the core of an optical fiber. 3
The Bragg wavelength was given as:
B 2neff .
(1)
Where B was the center wavelength of FBG, was the period of the grating, and neff was the effective refractive index of the fiber grating core. The temperature change T and the strain
would both cause a change in the grating period and the refractive index of the
fiber core. Differentiating Eq.(1):
B 1 neff 1 1 neff 1 [ ] [ ]T , B neff T neff
(2)
K 1 Pe ,
(3)
KT 1
1 1 neff + + . T neff
(4)
Where was the thermal expansion coefficient of FBG, was the thermo-optical coefficient of FBG, Pe was the elastic coefficient of FBG. Also K was the strain coefficient of FBG, and
K T 1 was the temperature coefficient of FBG17. The Eq. (2) could be
expressed as:
B =K KT 1T (1 Pe ) ( )T . B
(5)
When the FBG was pasted on a metal specimen, since the temperature changes, the metal would produce a thermal strain along the FBG, where
m was the thermal expansion
coefficient of the metal specimen. The temperature sensitivity of the metal-pasted FBG was therefore determined by the combination of the thermal strain effect and the direct thermal effect. We can finally determine that the wavelength shift of FBG would be calculated as follows18 19:
4
B (1 Pe )( m )T ( )T =T [ + m Pe ( m )] B
(6)
Thus, the relationship between the strain coefficient K could be obtained by
1 B m B T . K 1 Pe 1 m Since the general value of than the CTE
(7)
was 5.5 × 10−7/°C at room temperatures, was much less
m of metal specimen (normal lager than 10 × 10−6), the Eq.(7) could be
simplified to
1 B m B T K 1 Pe 1 m 1 B 1 B B T B T = = m T Where
.
(8)
B and were the differential item of the wavelength change and strain T T
change, respectively. When ambient temperature remained constant, the strain coefficient was given by
K 1 Pe
3
B . B
(9)
Experiment and discussion Two FBGs were encapsulated by cryogenic adhesives (DG-4, Blue star Co Ltd., China)
onto an oxygen-free copper specimen, as shown in Fig.1 (a). FBGs were made from the fused silica HIPOSH® fiber (YOFC Ltd.,China) (with core/cladding of 9 µm/125 µm). The pre-stretch wavelength of FBG was 2 nm, and meanwhile the length and thickness of adhesives were 3 cm and 0.2 mm respectively. One end of the oxygen-free copper specimen 5
was fixed at the object stage of the cryogenic vessel to ensure the heat exchange. During the test, the wavelength shift of FBG could only be affected by the thermal strain of the specimen and the thermo-optic effect20. The thermal strain of the specimen could be measured by a cryogenic Cu-Ni strain gauge (KFL, Kyowa Inc., Japan) which was pasted near the FBGs. A Lakeshore Model 331 cryogenic thermocouple placed near the FBGs was used as a reference for the standard temperature measurement. A photo of the oxygen-free copper specimen was presented in Fig.1 (b).
Installation hole
Resistance strain gauge FBG
Cryogenic adhesive Thermocouple (a)
(b)
Fig. 1 (a) The schematic diagram of the FBG pasted in the copper specimen; (b) The photo of the copper specimen after installation
We have designed an optical fiber flange sealing export to ensure the light transmission at high vacuums and low temperatures, as shown in Fig.2. The experimental set-up of the dynamic temperature test was illustrated in Fig.3 (a). The pressure in the cryogenic vessel drops to 10−2 Torr through the use of a molecular vacuum pump (Sumitomo Heavy Industries Ltd., Japan). After the refrigerator (Sumitomo Heavy Industries Ltd., Japan) has worked for 2 h, the temperature in the surface of the oxygen free copper specimen dropped down from
6
room temperature to nearly 30 K. While the temperature would rise to 273 K slowly after 48 h if turned the refrigerator off. The Lakeshore cryogenic temperature (accuracy: 0.1 K) test system kept a real-time record of the temperature at 1 Hz. At the same time, the wavelength demodulation (Bayspec Ltd., USA) rate for FBG was set to save the data at 1 Hz. So the temperature data and the sensor data could correspond to each other. The photo of the experimental set-up was presented in Fig.3 (b). Wedge sealing piece fiber
Armored cable
Nut
flange
Fig. 2 The structure design of the optical fiber flange sealing export
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Refrigerator
Cryogenic vessel
Oxygen-free copper attached with FBGs
(a)
Demodulation
Computer
(b)
Fig. 3 (a) Dynamic temperature experimental set-up; (b) The photo of the dynamic temperature experimental set-up
During the temperature-rise process, the long-term heat conduction would make the data more accurate. The wavelength responses of two FBGs at the temperature-rise stage were plotted in Fig.4, and from which, we could know that both of the wavelength change of two FBGs were nonlinear from 30 K to 273 K. The red line in Fig.4 was quadratic polynomial fit curve of Bragg wavelength change versus temperature. Fig.5 illustrated the strain shifts of the oxygen-free copper specimen under different temperatures.
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Fig. 4 The wavelength change and fitting curve of the two FBGs in the cryogenic test
Fig. 5 The strain curve of the copper specimen in the cryogenic test
After quadratic curve fitting for the test data, we could get the equation. For FBG1
1 =-0.1357+0.00554t (5.343E 5)t 2 .
(10)
2 =-0.3674+0.00602t (5.134E 5)t 2 .
(11)
For FBG2
For the oxygen-free copper specimen
=0.00306 (3.06E 6)t+(2.98E -8)t 2 . 9
(12)
Where t was in Kelvin and the temperature range is from 30 K to 273 K. In our previous work, we have studied the TOC of silica-based FBG at cryogenic temperatures range from 30 K to 273 K21. It could be expressed as:
( 0.23E 3)t 2 +0.2466t 3.8593 (E-7) .
(13)
So we could calculate the strain coefficient by For FBG1
(0.23E 3)t 2 +0.4414t 33.791 K 1 = . 0.596t+30.6
(14)
(0.23E 3)t 2 +0.4134t 35.84 . 0.596t+30.6
(15)
For FBG2
K 2 =
After the average calculation of Eq. (14) and Eq. (15), the strain coefficient could be given by:
K =
(0.23E 3)t 2 +0.4274t 34.81 . 0.596t+30.6
(16)
Where t was in Kelvin and the temperature ranged from 30 K to 273 K. The relationship between the strain coefficient and temperature could be described by a cubic curve. In order to verify the accuracy of the dynamic test data, a static tensile experiment in the liquid nitrogen environment was designed. The schematic drawing of the test system was shown in Fig.6. The stretcher was made of resistant material and equipped with a liquid nitrogen tank. It could ensure that all of the tests were performed in the liquid nitrogen environment and the temperature was constant. The tensile specimen was made of aluminum alloy, a FBG was encapsulated by cryogenic adhesives (DG-4, Blue star Co Ltd, China) on an aluminum alloy tensile specimen.
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Stretcher
Liquid nitrogen tank Tension specimen
Demodulation
Computer
Fig. 6 The set up of the tensile test equipment at cryogenic temperature
The tension load was changed from 0 kN to 15 kN at a step of 1 kN, with a duration time of nearly 30 seconds. After that, the tension load decreased slowly to 0 kN. This tensile process was repeated three times. We could acquire the strain of the tensile specimen from Eq. (17) as follow, where F was the tension force and the young's modulus ( E ) of aluminum alloy was 80 GPa at the liquid nitrogen temperature. A was the cross-section of the specimen (60 mm2 ):
F , AE
(17)
Fig.7 showed the wavelength change results and the linear fitting curves of the FBG during the three tests. It could be observed from Fig 7 that the FBG showed excellent linearity and good repetition. Table.1 showed the fitting function of the three tests. After the calculation of Eq.(9), the strain coefficient of FBG was found to be 0.916, 0.907 and 0.92 at 77 K.
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0.0025
Test 1 Test 2 Test 3
0.0020
wavelength change(nm)
wavelength change(nm)
0.0025
0.0015 0.0010 0.0005
0.0020
Test 1 Linear Fitting y=-1.00265E-5+0.916X
0.0015
R=0.999
0.0010 0.0005 0.0000
0.0000 0
500
1000
1500
2000
2500
0
3000
500
1000
strain()
wavelength change(nm)
0.0020
wavelength change(nm)
Test 2
0.0025
Linear Fitting y=-1.01546E-5+0.907X
0.0015
1500
2000
2500
3000
2000
2500
3000
strain()
R=0.999
0.0010 0.0005 0.0000
0.0025 0.0020
Test 3 Linear Fitting y=-8.0837E-5+0.92X
0.0015
R=0.999 0.0010 0.0005 0.0000
0
500
1000
1500
2000
2500
3000
0
500
1000
1500
strain()
strain()
Fig. 7 The wavelength-strain curve of the FBG in three tests Table 1 Tensile test data table Number of test Test1
Fitting function
y= -1.00265E-5+0.916x y= -1.01546E-5+0.907x y= -8.08373-5+0.92x
Test2 Test3
The uncertainty u ( K ) of the test data could be expressed as22:
u ( K ) s ( K )
s( K )=
1 n 1
s ( K ) n
n
( K i 1
i
K ) 2
(18)
(19)
Where K was the average value of the test data, n was the test times. The dynamic temperature testing results (0.904, 0.903) at 77 K were close to the static tension results 12
(0.916, 0.907 and 0.920) in the liquid nitrogen environment. After the calculation of Eq.(18) and Eq.(19),the uncertainty of the test data at 77K was 0.003. Meanwhile the dynamic temperature test result (0.88) at 123 K also accorded well with Guo et al.’s work14, where the strain coefficient was 0.879 at 123 K. Also the dynamic temperature test deviation may come from the strain transfer factor, cryogenic chemical properties of adhesive, the test error of strain data and the non-steady state of cryogenic system. Furthermore, to ensure the accurate accuracy of the test data, the measurement should be repeated for several times and a good repeatability could be obtained. From the static tension test results, we could obtain the strain-wavelength response was linear
at
constant
temperature,
and
the
strain
sensitivity
was
stable
and
temperature-dependent. During the dynamic temperature test, the strain response of FBG sensors was non-linear and could be approximated by third-order polynomial. When the temperature changes, the free energy of the fiber material would change correspondingly, the physical properties (elastic modulus, shear modulus and poisson ratio) of optical fibers would change simultaneously. Also the decreasing of fiber core’s effective refractive index would also bring down the elastic coefficient of FBG when the temperature decreased23. The strain coefficient of FBG increased with decreasing temperature in the cryogenic environment which was agreed well with the published works14, 16. 4 Conclusion In conclusion, the strain characteristic of silica-based FBG was studied from 30 K to 273 K by a dynamic experiment. The static tensile comparison test was performed three times in the liquid nitrogen environment. Based on the analysis of the experimental data, we got the proposed formula for the strain coefficient of silica-based FBG in the temperature range of 30~273 K. The strain-wavelength response of silica-based FBG was linear at constant temperature. The results supported that the relationship between the strain coefficient and 13
temperature could be described by a cubic curve at cryogenic temperatures. The results of two test methods were consistent, and the curve equation could be used for silica-based FBG standardization procedures at cryogenic temperatures. Acknowledgments The work was supported by Hubei Provincial Natural Science Foundation of China (2015CFA054) and the Open Projects Foundation of Yangtze Optical Fibre and Cable Joint Stock Limited Company (YOFC grant No.SKLD1502). References 1.
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2.
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Parne, Saidi, et al. "Polymer-coated fiber Bragg Grating Sensor for cryogenic temperature measurements." Microwave & Optical Technology Letters 53.5(2011):1154–1157.
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Yamada, H., et al. "Measurement and improvement of characteristics using optical fiber temperature sensors at cryogenic temperatures." Physica C: Superconductivity and its applications 471.21 (2011): 1570-1575.
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Shou, Ma, et al. "On-line monitoring system for downhole temperature and pressure." Optical Engineering 53.8 (2014): 087102-087102.
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Zaynetdinov, Madrakhim, et al. "A fiber Bragg grating temperature sensor for 2–400 K." IEEE Sensors Journal 15.3 (2015): 1908-1912.
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Thekkethil, S. R., et al. "Design of cryogenic flow meter using fiber Bragg grating sensors." SENSORS, 2015 IEEE. IEEE, 2015.
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9.
Tanaka, Y., et al. "Experimental investigation of optical fiber temperature sensors at cryogenic temperature and in high magnetic fields." Physica C: Superconductivity 470.20 (2010): 1890-1894.
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20. Jung, J, et al. "Fiber Bragg grating temperature sensor with controllable sensitivity." Applied Optics 38.13(1999):2752. 21. Li, Litong, et al. "FFPI-FBG hybrid sensor to measure the thermal expansion and thermo-optical coefficient of a silica-based fiber at cryogenic temperatures." Chinese Optics Letters 13.10 (2015): 100601. 22. Cheng, Shu Hui, et al. "Study on Uncertainty of FBG Pressure Transducer Calibration." Control & Instruments in Chemical Industry 3 (2017):233-235. 23. Zhao, L. J. "Influence of environment temperature wide-range variation on Brillouin shift in optical fiber." Acta Physica Sinica 59.9(2010):6219-6223.
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