- Email: [email protected]
FBG pressure sensor based on the double shell cylinder with temperature compensation
Measurement 42 (2009) 408–411
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
FBG pressure sensor based on the double shell cylinder with temperature compensation Wentao Zhang *, Fang Li, Yuliang Liu State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 14 March 2007 Received in revised form 25 June 2008 Accepted 17 August 2008 Available online 29 August 2008
Keywords: Fiber Bragg grating Temperature compensation Pressure sensor
a b s t r a c t A novel fiber Bragg grating (FBG) pressure sensor based on the double shell cylinder with temperature compensation is presented. In the sensing scheme, a sensing FBG is affixed in the tangential direction on the outer surface of the inner cylinder, and another FBG is affixed in the axial direction to compensate the temperature fluctuation. Based on the theory of elasticity, the theoretical analysis of the strain distribution of the sensing shell is presented. Experiments are carried out to test the performance of the sensor. A pressure sensitivity of 0.0937 nm/MPa has been achieved. The experimental results also demonstrate that the two FBGs have the same temperature sensitivity, which can be utilized to compensate the temperature induced wavelength shift during the pressure measurement. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Fiber Bragg grating (FBG) sensor has been developed rapidly during the past several years due to its small size, high sensitivity and feasibility in multiplexing. By monitoring the shift of the Bragg wavelength many kinds of the measurands can be calibrated such as temperature, strain, displacement and pressure. The early research on pressure sensors shows that many structures and materials have been developed to enhance the sensitivity such as the glass bubble [1], the polymer [2], the cantilever [3] and the flat diaphragm [4]. However, the FBG and the encapsulating materials are sensitive to both temperature and pressure. How to discriminate the temperature induced wavelength shift in the FBG sensors is of great importance for practical use. Hsu [5] has reported a temperature compensation structure for the FBG pressure sensor. The structure was made of three kinds of materials with different thermal expansion coefficients, which can induce the negative strain in the FBG to counteract the thermally induced red shift of the Bragg wavelength. However, this structure is * Corresponding author. Tel./fax: +86 10 82304016. E-mail address: [email protected] (W. Zhang). 0263-2241/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2008.08.007
rather complicated and it is difficult to control the initial stress in the FBG which is crucial to the capability of the temperature compensation. In this paper, a novel FBG pressure sensor based on the double shell cylinder is developed. The theoretical analysis of the strain distribution in the cylinder is presented in the first part of the paper, which demonstrates that the tangential strain in the cylinder is dominate while the axial strain can be ignored. Based on this principle, the sensor is fabricated and the experiment is performed. The experimental setup and the result are given in the next part of the paper. Finally, the conclusion of the investigation is presented.
2. Principle of measurement The proposed FBG pressure sensor is configured as a hydraulic pressure sensor or air pressure sensor shown in Fig. 1. The sensor includes two stainless steel shells. The outer shell is to protect the inner structures and the sensing shell is a thin-wall cylinder which acts as the sensing element. The bottom of the sensing shell contacts the bottom of the outer shell tightly. The two shells are made of same steel materials but the outer one is much thicker
W. Zhang et al. / Measurement 42 (2009) 408–411
w¼
pR2 1 1 l ebx ðcos bx þ sin bxÞ 1 2 Et
409
ð2Þ
Then the tangential stain is
es ¼
Fig. 1. The FBG pressure sensor scheme.
than the inner. Thus the sensing shell will not be elongated due to the pressure because the outer shell is much more rigid. Two FBGs are affixed at the middle area of the outer surface of the sensing shell in perpendicular directions, the axial direction for temperature compensation FBG and the tangential direction for sensing FBG. When the hydraulic pressure acts on the inner surface of the sensing cylinder, the tangential strain induces the red wavelength shift in the sensing FBG. Fig. 2 shows the deformation of the sensing shell (dashed). Based on the theory of elasticity, the problems of symmetrical deformation of circular cylindrical shells reduce to the integration of the equation [6] 4
d w p lN x þ 4b4 w ¼ z þ dx4 D DR
ð1Þ
in which the following notations are used:
D¼
Et 3 ; 12ð1 l2 Þ
b4 ¼
Et 4DR
2
where w is the radical deformation of the shell, pz, the radical pressure, E, the Young’s modulus of the shell, t, thickness of the shell, l, Poisson’s ratio of the shell, R, the inner diameter of the sensing shell and Nx, axial force pz = p, Nx = pR/2, which is independent of x, and the boundary conditions are
wjx¼0 ¼ 0;
dw ¼ 0; dx x¼0
so we then obtain
pR 1 1 l ebx ðcos bx þ sin bxÞ 1 Et 2
ð3Þ
It can be found from Eq. (3) that the tangential strain in the x direction is not uniform. According to the principle of Saint-Venant [7], the local bending at the both ends (A and B in Fig. 1) dies out rapidly as the distance from the loaded end increases. Then the second term in the square brackets of the right-hand side of the Eq. (3) is dominating. In practical application, the influence of local bending can be omitted when its stress is less than 5% of the principle stress. So when the first term decreases to the 5% of the second term, we obtain
pffiffiffiffiffi 3 Rt ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x0 ¼ p 4 3ð 1 l 2 Þ
ð4Þ
From Fig. 2, it can be found that the location of the FBG should be optimized in order to achieve the best sensitivity pffiffiffiffiffi of the sensor. For steel l = 0.3, we obtain x0 2:34 Rt . The axial strain of the shell, or the strain in the temperature compensation FBG, can be given as
pR2 E 2Rt þ 2R0 t0 þ t20
ec ¼
ð5Þ
where R0 is the inner diameter of the outer shell and t0 is the thickness of the outer shell. Substitute the values in the Eqs. (3) and (5), and we can find that the strain in the temperature compensation FBG is about 3.57% of the strain in the sensing FBG, which can be omitted. The wavelength shift of the sensor due to the pressure and temperature is
DkBSþT ¼ ð1 pe Þes þ ½f þ ð1 pe Þðas aÞDT kB
ð6Þ
where a and as, are the thermal expansion coefficients of the fiber and the steel, respectively. n is the thermo-optic coefficient of the fiber. The two FBGs are affixed on the same shell and thus have the same temperature sensitivity, which can be written as [8]
DkTB ¼ ½f þ ð1 pe Þðas aÞDT kB
ð7Þ
So the pressure sensitivity of the sensor can be obtained by subtracting Eq. (7) from Eq. (6):
DkSB pR 1 ¼ ð1 pe Þ 1 l Et 2 kB
ð8Þ
3. Experiment and results
Fig. 2. The deformation of the sensing shell.
The experiment is carried out to evaluate the performance of the sensor fabricated. The values of the parameters in our sensor configuration are shown in Table 1. x0 is calculated to be 9.1 mm, so the FBG is affixed in the area
410
W. Zhang et al. / Measurement 42 (2009) 408–411
Table 1 Parameters used in the sensor design R t R0 t0 E
15 mm 1 mm 25 mm 8 mm 160 GPa 0.3 6.67 106/°C 0.55 106/°C 11.8 106/°C 0.22 About 1527 nm 80 mm
l n
a as pe kB L
Fig. 4. Bragg wavelength versus pressure (sensing FBG).
from x = 10 to 70 mm. The experimental setup is shown in Fig. 3. The sensor was installed within a high pressure vessel which was fed by a hydraulic pump. The pressure induced Bragg wavelength shift was monitored by a high accuracy FBG interrogator (PI Optics, PI03B). The accuracy of the FBG interrogator is 1 pm, and the accuracy of the pressure measurement in the pressure vessel is 0.01 MPa. The pressure load increases or decreases by a step of 1 MPa. The test repeated for five times and the result is shown in Fig. 4. It can be found that the sensor has good linearity and stability. When the measured pressure is from 0.1 to 4 MPa, the maximum deviation of the results is less than 1% of the full scale. The experimental sensitivity is calculated to be 0.0937 nm/MPa, which is in the same order of magnitude as the theoretical value which is 0.0949 nm/MPa. Thus the accuracy of the FBG pressure sensor is about 11 kPa. The discrepancy between the experimental result and the estimated is due to the dimension error in fabricating the sensing shell. On the other hand, the wavelength of the temperature compensation FBG has a shift of only 1 pm from 0 to 4 MPa, which implies that it is insensitive to pressure (Fig. 5). The next step of our experiment is to evaluate the performance of the temperature compensation. Only when the two FBGs have the same temperature sensitivity, can we discriminate the temperature induced wavelength shift
Fig. 3. The experimental setup.
Fig. 5. Bragg wavelength versus pressure (temperature compensation FBG).
by subtracting the wavelength shift of the temperature FBG from the shift of the sensing FBG. So the sensor is put into a temperature controllable chamber. The result of the test is shown in Figs. 6 and 7, from which we can find the two FBGs have nearly the same temperature sensitivity. The sensitivities of the two FBGs given by the test result are 0.0203 and 0.0202 nm/°C, respectively, which is in close agreement with the theoretical sensitivity of 0.0244 nm/°C calculated from Eq. (7). Thus, the temperature effect can be compensated by subtracting the two shifts of the FBGs during the pressure measurement.
Fig. 6. Bragg wavelength versus temperature (sensing FBG).
W. Zhang et al. / Measurement 42 (2009) 408–411
411
experiment. And the two FBGs show the same temperature sensitivity of 0.020 nm/°C. Acknowledgements This work was supported by the Key Projects Program of Chinese Academy of Sciences under Grant No. CXJJ177. The authors also thank Y.H. Liu for the help in the experiment. References Fig. 7. Bragg wavelength versus temperature (temperature compensation FBG).
4. Conclusions In this paper, a novel scheme of FBG pressure sensor based on the double shell cylinder with temperature compensation is presented. The strain distribution of the cylinder is given by the theoretical analysis, which shows that the uniform tangential strain can be found in the middle area of the sensing shell. The theoretical analysis also shows that the two FBGs have the same temperature sensitivity, which can be utilized to compensate the temperature induced wavelength shift during the measurement of pressure. The pressure sensitivity of 0.0937 nm/MPa has been achieved in the
[1] M.G. Xu, H. Geiger, et al, Fiber grating pressure sensor with enhanced sensitivity using a glass bubble housing, Electron. Lett. 32 (1996) 128–129. [2] Zhang Ying, Feng De Jun, Liu Zhi Guo, High sensitivity pressure sensor using a shielded polymer-coated fiber Bragg grating, IEEE Photon. Technol. Lett. 13 (6) (2001) 618–619. [3] Jun Shao, Jun-hua Liu, Xue-guang Qiao, A FBG pressure sensor based on bourdon and cantilever beam of uniform strength, J. Optoelectron. Laser 17 (2006) 807–809. [4] Hai-wei Fu, Jun-mei Fu, Xue-guang Qiao, Fiber Bragg grating pressure sensor based on corrugated diaphragm, Semiconduct. Photon. Technol. 10 (2004) 278–281. [5] Y.S. Hsu, Likarn Wang, Wen-Fung Liu, et al, Temperature compensation of optical fiber Bragg grating pressure sensor, IEEE Photon. Technol. Lett. 18 (7) (2006) 874–876. [6] S. Timoshenko, Theory of Plates and Shells, McGraw-Hill, New York, 1959. pp. 467–471. [7] S.P. Timoshenko, J.N. Goodier, Theory of Elasticity, third ed., McgrawHill, New York, 1970. p. 39. [8] Y.Q. Liu, Z.Y. Guo, Y. Zhang, Simultaneous pressure and temperature measurement with polymer-coated fiber Bragg grating, Electron. Lett. 36 (6) (2000) 564–566.
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
FBG pressure sensor based on the double shell cylinder with temperature compensation Wentao Zhang *, Fang Li, Yuliang Liu State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 14 March 2007 Received in revised form 25 June 2008 Accepted 17 August 2008 Available online 29 August 2008
Keywords: Fiber Bragg grating Temperature compensation Pressure sensor
a b s t r a c t A novel fiber Bragg grating (FBG) pressure sensor based on the double shell cylinder with temperature compensation is presented. In the sensing scheme, a sensing FBG is affixed in the tangential direction on the outer surface of the inner cylinder, and another FBG is affixed in the axial direction to compensate the temperature fluctuation. Based on the theory of elasticity, the theoretical analysis of the strain distribution of the sensing shell is presented. Experiments are carried out to test the performance of the sensor. A pressure sensitivity of 0.0937 nm/MPa has been achieved. The experimental results also demonstrate that the two FBGs have the same temperature sensitivity, which can be utilized to compensate the temperature induced wavelength shift during the pressure measurement. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Fiber Bragg grating (FBG) sensor has been developed rapidly during the past several years due to its small size, high sensitivity and feasibility in multiplexing. By monitoring the shift of the Bragg wavelength many kinds of the measurands can be calibrated such as temperature, strain, displacement and pressure. The early research on pressure sensors shows that many structures and materials have been developed to enhance the sensitivity such as the glass bubble [1], the polymer [2], the cantilever [3] and the flat diaphragm [4]. However, the FBG and the encapsulating materials are sensitive to both temperature and pressure. How to discriminate the temperature induced wavelength shift in the FBG sensors is of great importance for practical use. Hsu [5] has reported a temperature compensation structure for the FBG pressure sensor. The structure was made of three kinds of materials with different thermal expansion coefficients, which can induce the negative strain in the FBG to counteract the thermally induced red shift of the Bragg wavelength. However, this structure is * Corresponding author. Tel./fax: +86 10 82304016. E-mail address: [email protected] (W. Zhang). 0263-2241/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2008.08.007
rather complicated and it is difficult to control the initial stress in the FBG which is crucial to the capability of the temperature compensation. In this paper, a novel FBG pressure sensor based on the double shell cylinder is developed. The theoretical analysis of the strain distribution in the cylinder is presented in the first part of the paper, which demonstrates that the tangential strain in the cylinder is dominate while the axial strain can be ignored. Based on this principle, the sensor is fabricated and the experiment is performed. The experimental setup and the result are given in the next part of the paper. Finally, the conclusion of the investigation is presented.
2. Principle of measurement The proposed FBG pressure sensor is configured as a hydraulic pressure sensor or air pressure sensor shown in Fig. 1. The sensor includes two stainless steel shells. The outer shell is to protect the inner structures and the sensing shell is a thin-wall cylinder which acts as the sensing element. The bottom of the sensing shell contacts the bottom of the outer shell tightly. The two shells are made of same steel materials but the outer one is much thicker
W. Zhang et al. / Measurement 42 (2009) 408–411
w¼
pR2 1 1 l ebx ðcos bx þ sin bxÞ 1 2 Et
409
ð2Þ
Then the tangential stain is
es ¼
Fig. 1. The FBG pressure sensor scheme.
than the inner. Thus the sensing shell will not be elongated due to the pressure because the outer shell is much more rigid. Two FBGs are affixed at the middle area of the outer surface of the sensing shell in perpendicular directions, the axial direction for temperature compensation FBG and the tangential direction for sensing FBG. When the hydraulic pressure acts on the inner surface of the sensing cylinder, the tangential strain induces the red wavelength shift in the sensing FBG. Fig. 2 shows the deformation of the sensing shell (dashed). Based on the theory of elasticity, the problems of symmetrical deformation of circular cylindrical shells reduce to the integration of the equation [6] 4
d w p lN x þ 4b4 w ¼ z þ dx4 D DR
ð1Þ
in which the following notations are used:
D¼
Et 3 ; 12ð1 l2 Þ
b4 ¼
Et 4DR
2
where w is the radical deformation of the shell, pz, the radical pressure, E, the Young’s modulus of the shell, t, thickness of the shell, l, Poisson’s ratio of the shell, R, the inner diameter of the sensing shell and Nx, axial force pz = p, Nx = pR/2, which is independent of x, and the boundary conditions are
wjx¼0 ¼ 0;
dw ¼ 0; dx x¼0
so we then obtain
pR 1 1 l ebx ðcos bx þ sin bxÞ 1 Et 2
ð3Þ
It can be found from Eq. (3) that the tangential strain in the x direction is not uniform. According to the principle of Saint-Venant [7], the local bending at the both ends (A and B in Fig. 1) dies out rapidly as the distance from the loaded end increases. Then the second term in the square brackets of the right-hand side of the Eq. (3) is dominating. In practical application, the influence of local bending can be omitted when its stress is less than 5% of the principle stress. So when the first term decreases to the 5% of the second term, we obtain
pffiffiffiffiffi 3 Rt ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x0 ¼ p 4 3ð 1 l 2 Þ
ð4Þ
From Fig. 2, it can be found that the location of the FBG should be optimized in order to achieve the best sensitivity pffiffiffiffiffi of the sensor. For steel l = 0.3, we obtain x0 2:34 Rt . The axial strain of the shell, or the strain in the temperature compensation FBG, can be given as
pR2 E 2Rt þ 2R0 t0 þ t20
ec ¼
ð5Þ
where R0 is the inner diameter of the outer shell and t0 is the thickness of the outer shell. Substitute the values in the Eqs. (3) and (5), and we can find that the strain in the temperature compensation FBG is about 3.57% of the strain in the sensing FBG, which can be omitted. The wavelength shift of the sensor due to the pressure and temperature is
DkBSþT ¼ ð1 pe Þes þ ½f þ ð1 pe Þðas aÞDT kB
ð6Þ
where a and as, are the thermal expansion coefficients of the fiber and the steel, respectively. n is the thermo-optic coefficient of the fiber. The two FBGs are affixed on the same shell and thus have the same temperature sensitivity, which can be written as [8]
DkTB ¼ ½f þ ð1 pe Þðas aÞDT kB
ð7Þ
So the pressure sensitivity of the sensor can be obtained by subtracting Eq. (7) from Eq. (6):
DkSB pR 1 ¼ ð1 pe Þ 1 l Et 2 kB
ð8Þ
3. Experiment and results
Fig. 2. The deformation of the sensing shell.
The experiment is carried out to evaluate the performance of the sensor fabricated. The values of the parameters in our sensor configuration are shown in Table 1. x0 is calculated to be 9.1 mm, so the FBG is affixed in the area
410
W. Zhang et al. / Measurement 42 (2009) 408–411
Table 1 Parameters used in the sensor design R t R0 t0 E
15 mm 1 mm 25 mm 8 mm 160 GPa 0.3 6.67 106/°C 0.55 106/°C 11.8 106/°C 0.22 About 1527 nm 80 mm
l n
a as pe kB L
Fig. 4. Bragg wavelength versus pressure (sensing FBG).
from x = 10 to 70 mm. The experimental setup is shown in Fig. 3. The sensor was installed within a high pressure vessel which was fed by a hydraulic pump. The pressure induced Bragg wavelength shift was monitored by a high accuracy FBG interrogator (PI Optics, PI03B). The accuracy of the FBG interrogator is 1 pm, and the accuracy of the pressure measurement in the pressure vessel is 0.01 MPa. The pressure load increases or decreases by a step of 1 MPa. The test repeated for five times and the result is shown in Fig. 4. It can be found that the sensor has good linearity and stability. When the measured pressure is from 0.1 to 4 MPa, the maximum deviation of the results is less than 1% of the full scale. The experimental sensitivity is calculated to be 0.0937 nm/MPa, which is in the same order of magnitude as the theoretical value which is 0.0949 nm/MPa. Thus the accuracy of the FBG pressure sensor is about 11 kPa. The discrepancy between the experimental result and the estimated is due to the dimension error in fabricating the sensing shell. On the other hand, the wavelength of the temperature compensation FBG has a shift of only 1 pm from 0 to 4 MPa, which implies that it is insensitive to pressure (Fig. 5). The next step of our experiment is to evaluate the performance of the temperature compensation. Only when the two FBGs have the same temperature sensitivity, can we discriminate the temperature induced wavelength shift
Fig. 3. The experimental setup.
Fig. 5. Bragg wavelength versus pressure (temperature compensation FBG).
by subtracting the wavelength shift of the temperature FBG from the shift of the sensing FBG. So the sensor is put into a temperature controllable chamber. The result of the test is shown in Figs. 6 and 7, from which we can find the two FBGs have nearly the same temperature sensitivity. The sensitivities of the two FBGs given by the test result are 0.0203 and 0.0202 nm/°C, respectively, which is in close agreement with the theoretical sensitivity of 0.0244 nm/°C calculated from Eq. (7). Thus, the temperature effect can be compensated by subtracting the two shifts of the FBGs during the pressure measurement.
Fig. 6. Bragg wavelength versus temperature (sensing FBG).
W. Zhang et al. / Measurement 42 (2009) 408–411
411
experiment. And the two FBGs show the same temperature sensitivity of 0.020 nm/°C. Acknowledgements This work was supported by the Key Projects Program of Chinese Academy of Sciences under Grant No. CXJJ177. The authors also thank Y.H. Liu for the help in the experiment. References Fig. 7. Bragg wavelength versus temperature (temperature compensation FBG).
4. Conclusions In this paper, a novel scheme of FBG pressure sensor based on the double shell cylinder with temperature compensation is presented. The strain distribution of the cylinder is given by the theoretical analysis, which shows that the uniform tangential strain can be found in the middle area of the sensing shell. The theoretical analysis also shows that the two FBGs have the same temperature sensitivity, which can be utilized to compensate the temperature induced wavelength shift during the measurement of pressure. The pressure sensitivity of 0.0937 nm/MPa has been achieved in the
[1] M.G. Xu, H. Geiger, et al, Fiber grating pressure sensor with enhanced sensitivity using a glass bubble housing, Electron. Lett. 32 (1996) 128–129. [2] Zhang Ying, Feng De Jun, Liu Zhi Guo, High sensitivity pressure sensor using a shielded polymer-coated fiber Bragg grating, IEEE Photon. Technol. Lett. 13 (6) (2001) 618–619. [3] Jun Shao, Jun-hua Liu, Xue-guang Qiao, A FBG pressure sensor based on bourdon and cantilever beam of uniform strength, J. Optoelectron. Laser 17 (2006) 807–809. [4] Hai-wei Fu, Jun-mei Fu, Xue-guang Qiao, Fiber Bragg grating pressure sensor based on corrugated diaphragm, Semiconduct. Photon. Technol. 10 (2004) 278–281. [5] Y.S. Hsu, Likarn Wang, Wen-Fung Liu, et al, Temperature compensation of optical fiber Bragg grating pressure sensor, IEEE Photon. Technol. Lett. 18 (7) (2006) 874–876. [6] S. Timoshenko, Theory of Plates and Shells, McGraw-Hill, New York, 1959. pp. 467–471. [7] S.P. Timoshenko, J.N. Goodier, Theory of Elasticity, third ed., McgrawHill, New York, 1970. p. 39. [8] Y.Q. Liu, Z.Y. Guo, Y. Zhang, Simultaneous pressure and temperature measurement with polymer-coated fiber Bragg grating, Electron. Lett. 36 (6) (2000) 564–566.