Temperature-Compensated Magnetostrictive ... - OSA Publishing

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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 35, NO. 22, NOVEMBER 15, 2017

Temperature-Compensated Magnetostrictive Current Sensor Based on the Configuration of Dual Fiber Bragg Gratings Jiahui Han, Haofeng Hu, Hui Wang, Bowen Zhang, Xiaowei Song, Zhenyang Ding, Xuezhi Zhang, and Tiegen Liu

Abstract—For the optical current sensor that combines FBG and magnetostrictive material, a key problem is that the performance of FBG and magnetostrictive material is influenced by the operating temperature. In this paper, in order to overcome this problem, we proposed a method of temperature compensation based on the dual FBG configuration, which can make the measuring result of magnetic field be essentially temperature independent. In this method, two FBGs with the same type are bonded on two giant magnetostrictive materials, respectively. The two giant magnetostrictive materials have the identical shape and come from the same bulk material, while they have the orthogonal magnetostriction directions. We perform the experiment to investigate the performance of this method at different temperatures and at different magnetic fields, in order to verify the feasibility of this method. The experiment results demonstrate that this method significantly decreases the influence of temperature, and thus it can maintain a relative good performance in the temperature range of 20 °C–70 °C. Index Terms—Fiber Bragg grating, magnetostriction, optical fiber sensor.

I. INTRODUCTION

I

N RECENT years, the optical current sensor (OCS) has attracted extensive interest due to its light weight, compact

Manuscript received August 15, 2017; revised October 2, 2017; accepted October 19, 2017. Date of publication October 23, 2017; date of current version November 16, 2017. This work was supported in part by the National Natural Science Foundation of China under Grant 61405140, in part by the National Instrumentation Program under Grant 2013YQ030915, in part by the Natural Science Foundation of Tianjin under Grant 15JCQNJC02000, and in part by the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars. (Corresponding Author: Haofeng Hu.) J. Han, H. Hu, X. Song, Z. Ding, X. Zhang, and T. Liu are with the School of Precision Instrument and Opto-Electronics Engineering, Institute of Optical Fiber Sensing, and Tianjin Optical Fiber Sensing Engineering Center, Key Laboratory of Opto-Electronics Information Technology, Tianjin University, Tianjin 300072, China (e-mail: [email protected]; haofeng_hu@ tju.edu.cn; [email protected]; [email protected]; [email protected]; [email protected]). H. Wang is with the School of Precision Instrument and Opto-Electronics Engineering, Key Laboratory of Opto-Electronics Information Technology, Tianjin University, Tianjin 300072, China, and also with the College of Physics and Information Engineering, Hebei Normal University, Shijiazhuang 050024, China (e-mail: [email protected]). B. Zhang is with the School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, NSW 2052, Australia, and also with the Photonics and Optical Communications Group, Sydney, NSW 2052, Australia (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2017.2766119

structure, high electrical isolation and so on [1], [2]. Various methods have been proposed to develop the optical current sensor, including the current sensor based on magneto-optical material [3], [4], the current sensor based on magnetic fluid [5], [6], the current sensor by using fiber coil [7], [8], etc. In particular, the sensor combining the magnetostrictive material and FBG is a main kind of optical current sensor [9]–[11]. The magnetostrictive material will deform under the magnetic field, and the magnetostrictive material will transmit the deformation to the FBG that bonded on it. The magnetic field can be thus measured by the shift of Bragg wavelength of the FBG. This kind of sensor has the advantages of small size, insensitivity to source intensity fluctuations, and ease of multiplexing [10]. However, the performance of FBG and magnetostrictive material is significantly influenced by the operating temperature. Up to now, several methods have been proposed to overcome this problem. In particular, J. Mora et al. proposed a method in which the sensor is formed by two different alloys and one of them has a giant magnetostriction [12]. However, the thermal expansion coefficients of the two different alloys have to be identical, which can not be valid in practice. M. Li et al. present a giant magnetostrictive magnetic fields sensor based on dual fiber Bragg gratings. One of the FBGs is epoxy-bonded on both ends to the surface of the giant magnetostrictive material, and the other grating is held with only one end fixed on the giant magnetostrictive material [13]. However, this method can only compensate the influence of temperature variation on the fiber Bragg gratings, but it ignores the thermal expansion effect of the giant magnetostrictive material. In this paper, we propose a temperature compensation method based on the dual-FBG configuration of optical current sensor, which can essentially decrease the temperature dependence. In this method, two FBGs with the same type are bonded on two giant magnetostrictive materials respectively. The two giant magnetostrictive materials have the identical shape and come from the same bulk material, and moreover, they have the orthogonal magnetostriction directions. In this case, when the temperature is changed, the wavelength shifts of the two sensing heads are identical, and thus the difference between the two Bragg wavelengths is independent of the temperature. We perform the experiment of the magneto sensing at varies temperatures based on the dual-FBG system, in order to verify the feasibility of the proposed method.

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HAN et al.: TEMPERATURE-COMPENSATED MAGNETOSTRICTIVE CURRENT SENSOR BASED ON THE CONFIGURATION OF DUAL FBG

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II. THEORY OF TEMPERATURE COMPENSATION BASED ON THE DUAL FBG CONFIGURATION The central wavelength of FBG will change with both the stress and temperature that the FBG senses. The shift of the wavelength can be expressed as [14]: ΔλB = (1 − Pe ) · ε + (αf + ξ) · ΔT, λB

(1)

where λB is the Bragg wavelength of FBG, ΔλB is the change of Bragg wavelength, Pe is the elastic-optic coefficient of optical fiber, αf and ξ are the thermal expansion coefficient and the thermo-optic coefficient of optical fiber respectively, ΔT and ε are the change of temperature and strain respectively. The magnetostrictive material has an elastic deformation along the magnetostriction direction under the magnetic field. The strain caused by the magnetic field (in the linear region) can be expressed as: ε = k · H,

(2)

where k is a coefficient proportional to the magnetostrictive constant of giant magnetostrictive material, H is the applied magnetic field. In addition to the magnetic field, the giant magnetostrictive material is also affected by the temperature. When the FBG is bonded on the giant magnetostrictive material, the wavelength shift of FBG as a function of magnetic field and temperature is given by [12]: ΔλB = (1 − Pe ) · k · H λB

Fig. 1.

+ [(1 − Pe ) · (αG M M − αf ) + αf + ζ] · ΔT, (3) where αG M M is the thermal expansion coefficient of giant magnetostrictive material. For the method proposed in this paper, there are two FBGs that bonded on two giant magnetostrictive materials respectively. The two giant magnetostrictive materials with the identical shape and thermal expansion coefficient come from the same bulk material, while they have the orthogonal magnetostriction directions, as shown in Fig. 1. The shift of wavelengths ΔλB 1 and ΔλB 2 for the two sensing heads can be expressed as: ⎧ Δλ B1 ⎪ λB 1 = (1 − Pe ) · k1 · H ⎪ ⎪ ⎪ ⎪ ⎨ + [(1 − Pe ) · (αG M M − αf ) + αf + ζ] · ΔT . Δ λ B2 ⎪ = (1 − P ) · k · H ⎪ e 2 ⎪ λ B2 ⎪ ⎪ ⎩ + [(1 − Pe ) · (αG M M − αf ) + αf + ζ] · ΔT (4) According to (4), one can have: ΔλB 2 ΔλB 1 − = (1 − Pe ) · (k1 − k2 ) · H. λB 1 λB 2

(5)

For the second giant magnetostrictive material, whose direction of magnetostriction is perpendicular to the magnetic field, the strain caused by magnetic field can be ignored. In this case,

The fabrication procedure of the sensing heads.

(5) can be rewritten as: ΔλB 1 ΔλB 2 − = (1 − Pe ) · k1 · H. λB 1 λB 2

(6)

It can be seen from (6) that the difference of the two Bragg wavelengths is free from temperature, and the magnetic field H can be measured according to the difference of the two Bragg wavelengths according to (6). III. EXPERIMENT RESULTS AND DISCUSSION In order to verify the feasibility of the dual-FBG configuration for temperature compensation, the corresponding experiment is performed. The schematic of experimental setup is shown in Fig. 2. A FBG demodulator based on the fiber F-P tunable filter (FFP-TF) is employed, and its wavelength resolution is 1 pm. The PZT in F-P filter is driven by a sawtooth wave, which makes the length of the F-P cavity change periodically. Thus, the transmission light of F-P filter is narrowband scanning light and the central wavelength of it varies within the wavelength range of the ASE broadband light source. The coupler divides the light into two parts, and one of the lights is divided into two channels by the beam splitter. The light goes into the FBG after travelling through the circulator. The other light travels through the F-P etalon for wavelength calibration. The output light from the etalon and the reflected light from the sensing head are

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Fig. 2.


Schematic of dual-FBG optical current sensor system.

detected by the photoelectric detection module and collected by data acquisition card. The sampling rate for each channel is 200 kHz. There are sequenced signals of light intensity on each channel. The PZT in the F-P filter is influenced by temperature, thus the repeatability of the relation between the wavelength of narrowband scanning light and driving voltage is not perfect. The F-P etalon is thus employed to calibrate the wavelength. For the F-P etalon, each peak intensity corresponds to a certain wavelength, and the relation between sampling points and wavelengths can be obtained. Therefore, the central wavelength of FBG can be obtained based on the sampling point that corresponds to the peak intensity. The central wavelengths of the two FBGs that coated with polyimide are 1545.3 nm and 1545.2 nm respectively at 25 °C. In order to avoid the creep properties of epoxy resin and thus to improve the transfer efficiency of deformation, the glassceramic solder of lower melting point is used to weld the fiber and Tb-Dy-Fe giant magnetostrictive material (25 mm × 5 mm × 3 mm). However, the cohesiveness between the glassceramic solder of lower melting point and giant magnetostrictive material is poor. In order to overcome this problem, the titanium that has the well cohesiveness with the glass-ceramic solder of lower melting point is coated on the border of the giant magnetostrictive material as the substrate of welding. The two ends of the FBG were welded on the substrate by the glass-ceramic solder of lower melting point. The manufacture of the sensing heads was completed at room temperature, and in order to keep the FBGs in a stretched state, a pre-stretching was performed to enforce a shift of 0.2 nm for the central wavelength of FBG. The solenoid coil is employed to produce a magnetic field and the sensing heads are put inside it. The solenoid coil and the sensing heads are put into the temperature chamber, in which the temperature can be adjusted, as shown in Fig. 2. Actually, the experimental setup is employed to simulate the current measurement for straight conducting wire with great current by generating the identical magnetic field of it at the position of the sensors. The magnetic field produced by straight conducting wire is related with the current I and the distance between the wire and the sensing head r. The range of the magnetic field in the center of the solenoid coil in our experiment is 0–800 Oe,

Fig. 3.

Bragg wavelength of the first sensing head at different magnetic fields.

Fig. 4.

Bragg wavelengths of the two sensing heads at different temperatures.

which is equivalent to the magnetic field that come from the straight conducting wire whose current is 0–8000 A when the distance between the wire and the sensing head is 20 mm. The variation of the central wavelength of the first sensing head with the magnetic field at the temperature of 25 °C is shown in Fig. 3. It can be seen that the central wavelength of the first sensing head is approximately proportional to the magnetic field in the range of 200 Oe-800 Oe, and the magnetic field sensitivity of the first sensing head is 0.84 pm/Oe in the range of 200 Oe-800 Oe. The central wavelengths of the two sensing heads at different temperatures are measured, and the result is shown in Fig. 4. It can be seen from Fig. 4 that the central wavelengths of the two sensing heads both increase with the increase of temperature, and the variation of central wavelength with temperature is considerable. In particular, the temperature sensitivity of the sensing head is about 22.2 pm/ °C. When the variation of the temperature is 25 °C, the wavelength shift is about 555 pm, which is equivalent to the wavelength shift caused by the magnetic field variation of 800 Oe. Therefore, the temperature dependence of the sensing head could cause a significant impact on the measurement accuracy, which has to be compensated to achieve the accurate measurement.


Fig. 5. The variation of the wavelength difference with the magnetic field at different temperatures.

Fig. 6. The variation of Bragg wavelengths of the two sensing heads and the wavelength difference with the temperature under the same magnetic field (500 Oe).

For the dual-FBG optical current sensor system investigated in this work, the central wavelengths of the two sensing heads are measured at different temperatures and different magnetic fields, and the variations of the wavelength difference of the two FBGs with the magnetic field at different temperatures are shown in Fig. 5. In addition, the variation of the wavelength difference with the temperature under the same magnetic field (500 Oe) is shown in Fig. 6. It can be seen from Fig. 5 that the variation of the wavelength difference of the two FBGs with the magnetic field at different temperatures is almost coincident. The sensitivity of magnetic field is 0.77 pm/Oe–0.85 pm/Oe in the range of 20 °C–70 °C and 200 Oe–800 Oe according to Fig. 5. The wavelength resolution of the FBG demodulator is 1 pm. Since the mean value of magnetic field sensitivity in the range of 20 °C–70 °C and 200 Oe–800 Oe is 0.81 pm/Oe, the sensing resolution of magnetic field is 1.23 Oe. Besides, the curves for different temperatures in Fig. 5 are slightly different, which means that the dependence of the measurement on the temperature is slight. As can be seen from Fig. 6, the temperature sensitivity of the wavelength difference is −0.68 pm/°C at 500 Oe, which is greatly reduced compared with

Fig. 7.

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The relative error of the measured magnetic field.

the temperature sensitivity of 21.53 pm/°C for the single sensing head. Ideally, the wavelength difference at a certain magnetic field is a constant, which does not change with the temperature. However, the result in Fig. 6 shows that the wavelength difference decreases slightly with the increase of temperature. This is because the magnetostriction coefficient of giant magnetostrictive material is actually temperature dependent [15]. Although the thermal expansion effect of giant magnetostrictive material is compensated in our method, the influence of temperature can not be totally eliminated. For the dual-FBG optical current sensor system investigated in this work, the magnetic field sensitivity is relatively large in the range of 200 Oe–800 Oe, as shown in Fig. 5. If we look carefully in Fig. 5, we can find that the relation between wavelength difference and the magnetic field is not exactly linear. Therefore, we employ the cubic-polynomial function instead of linear function to fit the relation between them, in order to achieve a lower fitting error. Besides, we ignore the dependence of magnetostriction coefficient of magnetostrictive material on the temperature, and we consider the fitting curve for 45 °C as the calibration curve, because 45 °C is the central value of the temperature range (20 to 70 °C) discussed in this work. In this case, the relative error of the measured magnetic field is shown in Fig. 7. It can be seen in Fig. 7 that the relative error of H increases gradually when the temperature deviates away from 45 °C. This is because the magnetostriction coefficient of giant magnetostrictive material decreases slightly as the temperature increases, and it results in an increase of the relative error of H when the temperature deviates from 45 °C. Besides, it can be seen in Fig. 7 that the relative error of H is below 5% in the range of 20 to 70 °C. In particular, when the temperature deviation is as high as 25 °C (at 20 °C and 70 °C), the relative error can be close to 5%, while when the temperature deviation is 5 °C (at 40 °C and 50 °C), the error is below 1.5%. Therefore, the dual-FBG optical current sensor proposed in this paper significantly decreases the influence of temperature to a low degree, and thus has a relative good performance.

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single giant magnetostrictive material system, this method can efficiently reduce the measurement error over a wide range of temperatures. It is shown by the experiment results that in the range of 200 Oe–800 Oe and 20 °C–70 °C, the relative error of measured magnetic field for the dual-FBG system is within 5%. Although the dual-FBG system proposed in this paper maintains a relative good performance in different temperatures, it ignores the temperature influence on the magnetostriction coefficient, which means that the temperature compensation is not thorough. In our future work, the temperature dependence of magnetostriction coefficient will be studied, and the more comprehensive method will be investigated to compensate the temperature thoroughly, in order to achieve an even lower error.

REFERENCES

Fig. 8. The variation of (a) magnetic field sensitivity with temperature and (b) temperature sensitivity with magnetic field.

In order to assess the influence of the cross-sensitivity effect, the variation of magnetic field sensitivity with temperature and the variation of temperature sensitivity with magnetic field are calculated according to Fig. 5, as shown in Fig. 8. It can be seen that the magnetic field sensitivity decrease as the temperature increases, and the absolute value of temperature sensitivity is increase as the magnetic field increase. In order to quantitatively analyze the cross-sensitivity effect, the cross-sensitivity coefficient, which is the first derivative of magnetic field sensitivity versus temperature [16], is calculated. The linear function was employed to fit the relation between magnetic field sensitivity and temperature, and the cross-sensitivity coefficient of the sensor, which equals to the slope of the line between the magnetic field sensitivity and the temperature, is calculated to be −1.59 × 10−6 nm/(Oe ·◦ C). In addition to the measurement of positive magnetic field discussed in the paper, the proposed method can be also applied to measure the negative magnetic field. The strain of Tb-Dy-Fe giant magnetostrictive material is an even function of magnetic field intensity. If we applied a bias magnetic field, the magnetostrictive material will be elongate at the positive magnetic field, while it will be shorten at the negative magnetic field. In this way, both the positive magnetic field and negative magnetic field can be measured, and thus the AC current can be also measured by this method in the case that the hysteresis can be ignored. IV. CONCLUSION In this paper, we proposed a dual-FBG configuration of optical current sensor for temperature compensation, and we fabricated the sensing heads to perform the experiment of magnetic field measurement at different temperatures. Compared with the

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Jiahui Han was born in Hebei, China, in 1993. She received the B.S. degree from Tianjin University, Tianjin, China, in 2015. She is currently working toward the M.S. degree in optical engineering. Her research interest includes optical current sensor.

Xiaowei Song was born in Henan, China, 1994. He received the B.S. degree from Tianjin University, Tianjin, China, in 2017. He is currently working toward the M.S. degree in optical engineering. His research interest includes optical current sensor.

Haofeng Hu received the B.S., M.S., and Ph.D. degrees from Nankai University, Tianjin, China, in 2006, 2009, and 2011, respectively. He is currently an Associate Professor in Tianjin University, Tianjin. His research interests include polarimetry and optical fiber sensing.

Zhenyang Ding received the B.Eng., M.Eng., and Ph.D. degrees from Tianjin University, Tianjin, China, in 2008, 2010, and 2013, respectively. His research interest includes fiber sensing.

Hui Wang was born in Hebei, China, in 1977. He received the B.S. degree from Hebei Normal University, Hebei, in 2000, and the M.S. degree from Harbin Institute of Technology, Harbin, China, in 2003. His research interests include polarimetry and optical fiber sensing.

Bowen Zhang was born in Liaoning, China, 1994. He received the B.Eng. degree from Tianjin University, Tianjin, China, in 2016. He is currently working toward the Ph.D. degree in optical communication technologies in the University of New South Wales, Sydney, NSW, Australia. His research interest includes active fibers.

Xuezhi Zhang received the B.S. and Ph.D. degrees from Nankai University, Tianjin, China, in 2007 and 2012, respectively. He is currently an Associate Professor in Tianjin University, Tianjin, China. His research interest includes optical fiber sensing.

Tiegen Liu received the B.Eng., M.Eng., and Ph.D. degrees from Tianjin University, Tianjin, China, in 1982, 1987, and 1999, respectively. He is currently a Professor in Tianjin University. He is also a Chief Scientist of the National Basic Research Program of China under Grant 2010CB327802. His research interests include optical fiber sensing and photoelectric detection.