Measurement error of surface-mounted fiber Bragg grating temperature sensor Liu Yi, Zhou Zude, Zhang Erlong, Zhang Jun, Tan Yuegang, and Liu Mingyao Citation: Review of Scientific Instruments 85, 064905 (2014); doi: 10.1063/1.4885463 View online: http://dx.doi.org/10.1063/1.4885463 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Real time and simultaneous measurement of displacement and temperature using fiber loop with polymer coating and fiber Bragg grating Rev. Sci. Instrum. 85, 075002 (2014); 10.1063/1.4889885 A multiplexed fiber Bragg grating sensor for simultaneous salinity and temperature measurement J. Appl. Phys. 103, 053107 (2008); 10.1063/1.2890156 Cryogenic Fiber Optic Temperature Sensors Based on Fiber Bragg Gratings AIP Conf. Proc. 823, 267 (2006); 10.1063/1.2202425 Fiber Bragg grating vacuum sensors Appl. Phys. Lett. 87, 234101 (2005); 10.1063/1.2140082 Fiber optic sensor for dual measurement of temperature and strain using a combined fluorescence lifetime decay and fiber Bragg grating technique Rev. Sci. Instrum. 72, 3186 (2001); 10.1063/1.1372171
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 064905 (2014)
Measurement error of surface-mounted fiber Bragg grating temperature sensor Liu Yi,a) Zhou Zude, Zhang Erlong, Zhang Jun, Tan Yuegang, and Liu Mingyao School of Mechanical and Electronic Engineering, Wuhan University of Technology, 122 Luoshi Road, Wuhan, Hubei, People’s Republic of China
(Received 20 March 2014; accepted 15 June 2014; published online 30 June 2014) Fiber Bragg grating (FBG) sensors are extensively used to measure surface temperatures. However, the temperature gradient effect of a surface-mounted FBG sensor is often overlooked. A surfacetype temperature standard setup was prepared in this study to investigate the measurement errors of FBG temperature sensors. Experimental results show that the measurement error of a bare fiber sensor has an obvious linear relationship with surface temperature, with the largest error achieved at 8.1 ◦ C. Sensors packaged with heat conduction grease generate smaller measurement errors than do bare FBG sensors and commercial thermal resistors. Thus, high-quality packaged methods and proper modes of fixation can effectively improve the accuracy of FBG sensors in measuring surface temperatures. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4885463] I. INTRODUCTION
Measuring surface temperature is an important method of obtaining the surface temperature of solids and is widely used to determine the amount of heat, device temperature perception, sensor error compensation, and so on. Methods for surface temperature measurement are classified into two categories: non-contact measurement methods (such as infrared radiation thermometer) and contact measurement methods (such as thermocouple and thermal resistor). Infrared radiation thermometers are used to measure high temperatures but are beset by problems related to accuracy and cost. Contact measurement methods are therefore more widely utilized in modern industries than non-contact measurement methods. The thermocouple or thermal resistors is effective and convenient to measure the surface temperature through sticking on the surface of the object.1 However, high-accuracy measurements of this type are extremely difficult to obtain. The heat conducted from the surface to the ambience through the metal wires of the thermocouple or thermal resistor changes the surface temperature field. Using the finite element method (FEM), Tszeng et al. analyzed the “fin effects” of measuring temperature using surface-mounted thermocouples and pointed out that the actual effects are dependent on the diameter of the wire.2 Tszeng et al. also proposed a dualscale computational method to correct the measurement errors of thermocouples.3 Park et al. considered the error introduced by the leads of a thermocouple during rapid transient cooling. One important conclusion of this study is that the surface temperature measured by such an intrinsic thermocouple is erroneous by 40 ◦ C because of the heat loss of lead.4 Attia et al. systematically studied the distortion in the thermal field around inserted thermocouples and discussed its influence on the temperature measurement.5–7 As a new type of temperature sensor, fiber Bragg grating (FBG) temperature sensors feature a fused silica wire that serves as a signal route. This structure can effectively reduce a) [email protected]
0034-6748/2014/85(6)/064905/5/$30.00
the thermal transmission of signal wires and thereby improve measurement accuracy. This sensor is an ideal instrument that obtains highly accurate surface temperature. However, despite the widespread use of FBG sensors, no study has been conducted thus far on their errors in surface temperature measurement. To fully understand the measurement errors of surfacemounted FBG sensors, we analyze the temperature gradient between the surface of solid and the ambience and evaluate the measurement error induced by the structure of FBG sensors. We also propose a calibration system of the surface temperature measurement error and discuss the influence of a structure packaged with heat conduction grease on measurement errors.
II. ANALYSIS OF THE MEASUREMENT ERRORS OF FBG TEMPERATURE SENSORS
Regardless of its type, each temperature sensor has a sensing point that senses the temperature. The sensing point detects the temperature around itself instead of the temperature of the whole object or surface. The reading of the sensor represents a balance between the heat transferred to the sensing element, the heat stored by the element, and the amount of heat lost to the surrounding environment. Exact temperature measurements can only be obtained if the object, its surroundings, and the instrument all have an identical temperature. Any deviation from these conditions causes a flow of heat, which in turn generates a temperature gradient and results in measurement errors. A finite element analysis (FEA) of the temperature field of a high-temperature surface is conducted to obtain the approximate temperature distribution of the measurement space. The schematic of the model, through which these analyses and the later experimental tests are performed, is shown in Fig. 1. The model consists of the interior of the object, the heat conduction surface, and an air layer. To compare with the later experimental results, the measured object is
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Rev. Sci. Instrum. 85, 064905 (2014)
FIG. 1. FEA model of the temperature distribution in surface temperature measurement.
specified as water, and the heat conduction layer is specified as red copper. The thickness of the red copper is 1 mm. The heights of the water and air columns are 10 and 100 mm, respectively. To gauge the temperature distribution in the model, the heat boundary conditions and initial conditions are carefully considered. In Fig. 1, a free air convection coefficient (10 W/m2 K) is applied to simulate the cooling effect between the red copper and the air layer. The heat insulation condition is set between the water and the environment. The temperatures of the water and air columns are 23 ◦ C and 91.8 ◦ C, respectively. The FEA is conducted in ANSYS v14. The model is meshed into 5790 elements. The element type is SOLID90. This level of meshing leads to a good trade-off between the simulation accuracy and solution time. The results of the FEA indicate that the temperature distribution in the water, the heat conduction surface, and the air layer decreases along the vertical direction (Fig. 1). The interface between the water and copper sheet is supposed to be the origin of the temperature distribution, and the vertically upward direction is defined as the positive direction. Fig. 2(a) shows the curve of the temperature distribution, and Fig. 2(b) shows the temperature distribution within a range of 0–1.1 mm from Fig. 2(a). Fig. 2(b) shows that the difference between the temperatures of both sides of the copper sheet is as low as 0.89 ◦ C. The figure also shows that the temperature in the air layer from the red copper surface decreases at a high speed along the vertical direction. The temperature changes from a high temperature (90.2 ◦ C) to a low temperature (37.9 ◦ C) within the 4 mm range. The mean temperature gradient is (37.8 ◦ C − 91.8 ◦ C)/4 mm = −13.5 ◦ C/mm. Given that the temperature sensor is fixed on the surface and that the diameter of the bare fiber with acrylate coating is 200 μm, the temperature gradient in this area can be represented as the initial slope of the curve, which is −46.4 ◦ C/mm as shown in Fig. 2(a). This finding indicates that any deviation in the sensing point from
FIG. 2. (a) Temperature distribution of the surface region where FBG sensors are installed and (b) temperature distribution within 1.1 mm from Fig. 2(a) on an expanded time scale.
the measured surface certainly causes serious measurement errors. III. ACQUIREMENT OF MEASUREMENT ERRORS OF FBG SENSOR A. Experimental principle and method
A surface-type temperature standard is fabricated to evaluate the surface measurement errors of FBG temperature sensors. This standard is a reference whose temperature is known. A calibrated FBG temperature sensor is fixed on it, as shown in Fig. 3. The measurement errors are obtained by comparing the difference between the reading of the FBG sensor and the temperature of the surface-type temperature standard. B. Surface-type temperature standard setup
Fig. 4 shows the experimental setup for the temperature standard, which consists of the following devices: a Dewar flask, a cork, a piece of red copper fixed at the bottom of the
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Rev. Sci. Instrum. 85, 064905 (2014)
FIG. 3. Schematic of the surface error measurement principle.
cork, and a thermometer. Hot water is poured into the Dewar flask. The thermometer is a standard mercury-in-glass thermometer (Grade II) that was verified in accordance with the regulations for standard mercury-in-glass (Grade I). The copper sheet has a thickness of 1 mm and is inundated with hot water. The temperature of the copper sheet is approximately equal to that of the hot water. The change in the water temperature is very slow (about 0.3 ◦ C/h) because of the great specific heat of water and the heat preservation property of the vacuum in the Dewar flask. The copper sheet is thus an ideal surface-type temperature standard, given that its temperature is in accordance with that of the hot water in the Dewar flask. The thermometer is dipped into the water to measure the temperature accurately. Its reading is regarded as the temperature of the surface-type temperature standard.
C. Calibrated FBG temperature sensor
An FBG temperature sensor with a center wavelength of 1297 nm is dipped into the hot water in the temperature standard setup. The temperature of the hot water is changed six times from 46 ◦ C to 92 ◦ C and is measured by the standard mercury-in-glass thermometer (Grade II). The reflected wavelength of the FBG is recorded by an FBG interrogator (MOI MS130). The calibrated curve is shown in Fig. 5. The relationship between the temperature T and center wavelength λ of the FBG temperature sensor can be expressed as λ = 0.010T + 1296.633.
(1)
The temperature sensitivity of the FBG sensor is about 10 pm/◦ C.
FIG. 4. Temperature standard setup.
FIG. 5. Calibrated curve of the sensor.
IV. EXPERIMENTS AND RESULTS
The mode of fixation of a sensor greatly influences its measurement of surface temperature. This study discusses two fixation modes: single-ended magnetism fixation and single-ended heat conduction grease fixation. The first fixation mode is selected because it is commonly adopted in conventional measurements. The second fixation mode is tested for comparison with traditional temperature sensors. Supposing that the mercury thermometer reading is T1, that of the FBG sensor is T2, and the surface temperature measurement error is represented by T, that is, T = T1 − T2. The surface temperature measurement errors are tested under two different conditions. A. Measurement error of bare FBG sensors with coating
The measurement mode of bare FBG temperature sensors with acrylate coating is shown in Fig. 6. The red copper sheet is a thermostatic surface of the surface-type temperature standard that is used to simulate the surface of the measured object. The FBG sensor is fixed on the red copper sheet by two magnets. The FBG can freely stretch and cling to the red copper sheet because only one fixed point is at the end of the FBG. The temperature of the hot water is changed, and the readings of the mercury thermometer and FBG sensor are recorded simultaneously in Table I. The ambient temperature
FIG. 6. Single-ended fixed FBG temperature sensor.
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TABLE I. Measurement error of the single-ended fixed sensor.
Mercury thermometer reading T1 (◦ C) 91.8 72.9 64.1 57.2 51.7 45.4
FBG sensor reading T2 (◦ C)
Surface temperature measurement error T (◦ C)
83.7 67.8 61 55.2 50.5 45.2
8.1 5.1 3.1 2 1.2 0.2
FIG. 8. FBG temperature sensor structure with heat conduction grease.
To reduce the temperature gradient of the surface and to improve the accuracy of the surface measurement of the
FBG temperature sensor, a heat conduction grease-packaged structure is proposed in Fig. 8. The FBG sensor is fixed by two magnets, and the grating section is coated with heat conduction grease. Its brand is TS-KS101, and its thermal resistance is 2 w/m k. To determine the effect of the heat conduction grease-packaged structure on the measurement, a thermal resistor sensor is installed beside the packaged FBG sensor, whose readings are recorded simultaneously. The surface measurement errors of the two sensors are shown in Fig. 9. The relationship between the errors and surface temperature is approximately linear. At a low temperature, the two errors are very close; at a high temperature, the error of the packaged FBG sensor is smaller than that of the thermal resistor. This finding indicates that the accuracy of the FBG sensor packaged by heat conduction grease is higher than that of the commercial thermal resistor. Moreover, the error of the packaged FBG sensor is smaller than that of the bare FBG sensor with protective acrylate coating in Fig. 7. For example, at about 90 ◦ C, the measurement error of the packaged FBG sensor is 3 ◦ C, whereas that of the bare FBG sensor with protective acrylate coating is nearly 8.1 ◦ C. This difference indicates that the packaged structure can effectively reduce the temperature gradient and improve the accuracy of the surface measurement.
FIG. 7. Measurement error of a single-ended fixed sensor versus surface temperature.
FIG. 9. Measurement error of the heat conduction grease-packaged FBG sensor and thermal resistor versus surface temperature.
◦
is 23 C. The errors of the surface measurement T of the FBG sensor for different surface temperatures are shown in Fig. 7. The error of the surface measurement increases as the surface temperature increases. The relationship between errors and surface temperature is approximately linear. The error is about 8.1 ◦ C when the surface temperature is 91.8 ◦ C. The diameter of the FBG sensor is 0.3 mm (including core, cladding, and protective acrylate coating); therefore, the sensing point of the FBG sensor is located 0.15 mm from the copper surface along the horizontal direction. According to the FEA results, if an FBG sensor is fixed on the surface of the copper sheet to measure the temperature, then the temperature at the sensing point is 91.8 ◦ C − 0.15 mm × 46.4 ◦ C/mm − 0.89 ◦ C = 83.95 ◦ C. The measurement error calculated by the FEA is 91.8 ◦ C − 83.95 ◦ C = 7.85 ◦ C, which is close to that obtained in the experiments (8.1 ◦ C). B. Measurement error of the heat conduction grease-packaged FBG sensor and thermal resistor sensor
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V. CONCLUSION
ACKNOWLEDGMENTS
The surface temperature gradient and the measurement errors induced by it are easily overlooked. These issues greatly influence surface temperature measurement results. Thus, a high-accuracy surface temperature measurement is a challenging task. To reveal the influence of temperature gradient on measurement accuracy, a surface-type temperature standard setup is prepared, and the measurement errors of surface-mounted FBG temperature sensors with two different packaging conditions are obtained. The experimental results show that the bare FBG sensor with acrylate coating generates a linear error, which is good for the compensation process. The error of the FBG sensor packaged with heat conduction grease is smaller than those of the bare FBG sensor and the commercial thermal resistor. Thus, high-quality packaging can effectively improve the accuracy of FBG sensors in measuring surface temperatures.
This work was financially supported by the National Natural Science Foundation of China (Grant No. 61301064), the National Science and Technology Mayor project (Grant No. 2012ZX04001-012-05), and the China Postdoctoral Science Foundation (Grant No. 2013M542075).
1 M.
F. Cross, J. C. Bennett, and R. W. Bass, in 19th ASM-HTS Conference Proceedings (American Society for Metals (ASM), 2000), pp. 335–342. 2 T. C. Tszeng and V. Saraf, J. Heat Transfer 125, 926–935 (2003). 3 T. C. Tszeng and G. F. Zhou, J. Heat Transfer 126, 535–539 (2004). 4 E. Park, K. W. Childs, and G. M. Ludtka, National Heat Treat Conference (AIChE, Minneapolis, MN, USA, 1991), pp. 309–318. 5 M. H. Attia and L. Kops, J. Eng. Ind. 115, 444–449 (1993). 6 M. H. Attia and L. Kops, J. Eng. Ind. 108, 241–246 (1986). 7 M. H. Attia and L. Kops, J. Eng. Ind. 110, 7–14 (1988).
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 064905 (2014)
Measurement error of surface-mounted fiber Bragg grating temperature sensor Liu Yi,a) Zhou Zude, Zhang Erlong, Zhang Jun, Tan Yuegang, and Liu Mingyao School of Mechanical and Electronic Engineering, Wuhan University of Technology, 122 Luoshi Road, Wuhan, Hubei, People’s Republic of China
(Received 20 March 2014; accepted 15 June 2014; published online 30 June 2014) Fiber Bragg grating (FBG) sensors are extensively used to measure surface temperatures. However, the temperature gradient effect of a surface-mounted FBG sensor is often overlooked. A surfacetype temperature standard setup was prepared in this study to investigate the measurement errors of FBG temperature sensors. Experimental results show that the measurement error of a bare fiber sensor has an obvious linear relationship with surface temperature, with the largest error achieved at 8.1 ◦ C. Sensors packaged with heat conduction grease generate smaller measurement errors than do bare FBG sensors and commercial thermal resistors. Thus, high-quality packaged methods and proper modes of fixation can effectively improve the accuracy of FBG sensors in measuring surface temperatures. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4885463] I. INTRODUCTION
Measuring surface temperature is an important method of obtaining the surface temperature of solids and is widely used to determine the amount of heat, device temperature perception, sensor error compensation, and so on. Methods for surface temperature measurement are classified into two categories: non-contact measurement methods (such as infrared radiation thermometer) and contact measurement methods (such as thermocouple and thermal resistor). Infrared radiation thermometers are used to measure high temperatures but are beset by problems related to accuracy and cost. Contact measurement methods are therefore more widely utilized in modern industries than non-contact measurement methods. The thermocouple or thermal resistors is effective and convenient to measure the surface temperature through sticking on the surface of the object.1 However, high-accuracy measurements of this type are extremely difficult to obtain. The heat conducted from the surface to the ambience through the metal wires of the thermocouple or thermal resistor changes the surface temperature field. Using the finite element method (FEM), Tszeng et al. analyzed the “fin effects” of measuring temperature using surface-mounted thermocouples and pointed out that the actual effects are dependent on the diameter of the wire.2 Tszeng et al. also proposed a dualscale computational method to correct the measurement errors of thermocouples.3 Park et al. considered the error introduced by the leads of a thermocouple during rapid transient cooling. One important conclusion of this study is that the surface temperature measured by such an intrinsic thermocouple is erroneous by 40 ◦ C because of the heat loss of lead.4 Attia et al. systematically studied the distortion in the thermal field around inserted thermocouples and discussed its influence on the temperature measurement.5–7 As a new type of temperature sensor, fiber Bragg grating (FBG) temperature sensors feature a fused silica wire that serves as a signal route. This structure can effectively reduce a) [email protected]
0034-6748/2014/85(6)/064905/5/$30.00
the thermal transmission of signal wires and thereby improve measurement accuracy. This sensor is an ideal instrument that obtains highly accurate surface temperature. However, despite the widespread use of FBG sensors, no study has been conducted thus far on their errors in surface temperature measurement. To fully understand the measurement errors of surfacemounted FBG sensors, we analyze the temperature gradient between the surface of solid and the ambience and evaluate the measurement error induced by the structure of FBG sensors. We also propose a calibration system of the surface temperature measurement error and discuss the influence of a structure packaged with heat conduction grease on measurement errors.
II. ANALYSIS OF THE MEASUREMENT ERRORS OF FBG TEMPERATURE SENSORS
Regardless of its type, each temperature sensor has a sensing point that senses the temperature. The sensing point detects the temperature around itself instead of the temperature of the whole object or surface. The reading of the sensor represents a balance between the heat transferred to the sensing element, the heat stored by the element, and the amount of heat lost to the surrounding environment. Exact temperature measurements can only be obtained if the object, its surroundings, and the instrument all have an identical temperature. Any deviation from these conditions causes a flow of heat, which in turn generates a temperature gradient and results in measurement errors. A finite element analysis (FEA) of the temperature field of a high-temperature surface is conducted to obtain the approximate temperature distribution of the measurement space. The schematic of the model, through which these analyses and the later experimental tests are performed, is shown in Fig. 1. The model consists of the interior of the object, the heat conduction surface, and an air layer. To compare with the later experimental results, the measured object is
85, 064905-1
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064905-2
Liu et al.
Rev. Sci. Instrum. 85, 064905 (2014)
FIG. 1. FEA model of the temperature distribution in surface temperature measurement.
specified as water, and the heat conduction layer is specified as red copper. The thickness of the red copper is 1 mm. The heights of the water and air columns are 10 and 100 mm, respectively. To gauge the temperature distribution in the model, the heat boundary conditions and initial conditions are carefully considered. In Fig. 1, a free air convection coefficient (10 W/m2 K) is applied to simulate the cooling effect between the red copper and the air layer. The heat insulation condition is set between the water and the environment. The temperatures of the water and air columns are 23 ◦ C and 91.8 ◦ C, respectively. The FEA is conducted in ANSYS v14. The model is meshed into 5790 elements. The element type is SOLID90. This level of meshing leads to a good trade-off between the simulation accuracy and solution time. The results of the FEA indicate that the temperature distribution in the water, the heat conduction surface, and the air layer decreases along the vertical direction (Fig. 1). The interface between the water and copper sheet is supposed to be the origin of the temperature distribution, and the vertically upward direction is defined as the positive direction. Fig. 2(a) shows the curve of the temperature distribution, and Fig. 2(b) shows the temperature distribution within a range of 0–1.1 mm from Fig. 2(a). Fig. 2(b) shows that the difference between the temperatures of both sides of the copper sheet is as low as 0.89 ◦ C. The figure also shows that the temperature in the air layer from the red copper surface decreases at a high speed along the vertical direction. The temperature changes from a high temperature (90.2 ◦ C) to a low temperature (37.9 ◦ C) within the 4 mm range. The mean temperature gradient is (37.8 ◦ C − 91.8 ◦ C)/4 mm = −13.5 ◦ C/mm. Given that the temperature sensor is fixed on the surface and that the diameter of the bare fiber with acrylate coating is 200 μm, the temperature gradient in this area can be represented as the initial slope of the curve, which is −46.4 ◦ C/mm as shown in Fig. 2(a). This finding indicates that any deviation in the sensing point from
FIG. 2. (a) Temperature distribution of the surface region where FBG sensors are installed and (b) temperature distribution within 1.1 mm from Fig. 2(a) on an expanded time scale.
the measured surface certainly causes serious measurement errors. III. ACQUIREMENT OF MEASUREMENT ERRORS OF FBG SENSOR A. Experimental principle and method
A surface-type temperature standard is fabricated to evaluate the surface measurement errors of FBG temperature sensors. This standard is a reference whose temperature is known. A calibrated FBG temperature sensor is fixed on it, as shown in Fig. 3. The measurement errors are obtained by comparing the difference between the reading of the FBG sensor and the temperature of the surface-type temperature standard. B. Surface-type temperature standard setup
Fig. 4 shows the experimental setup for the temperature standard, which consists of the following devices: a Dewar flask, a cork, a piece of red copper fixed at the bottom of the
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Rev. Sci. Instrum. 85, 064905 (2014)
FIG. 3. Schematic of the surface error measurement principle.
cork, and a thermometer. Hot water is poured into the Dewar flask. The thermometer is a standard mercury-in-glass thermometer (Grade II) that was verified in accordance with the regulations for standard mercury-in-glass (Grade I). The copper sheet has a thickness of 1 mm and is inundated with hot water. The temperature of the copper sheet is approximately equal to that of the hot water. The change in the water temperature is very slow (about 0.3 ◦ C/h) because of the great specific heat of water and the heat preservation property of the vacuum in the Dewar flask. The copper sheet is thus an ideal surface-type temperature standard, given that its temperature is in accordance with that of the hot water in the Dewar flask. The thermometer is dipped into the water to measure the temperature accurately. Its reading is regarded as the temperature of the surface-type temperature standard.
C. Calibrated FBG temperature sensor
An FBG temperature sensor with a center wavelength of 1297 nm is dipped into the hot water in the temperature standard setup. The temperature of the hot water is changed six times from 46 ◦ C to 92 ◦ C and is measured by the standard mercury-in-glass thermometer (Grade II). The reflected wavelength of the FBG is recorded by an FBG interrogator (MOI MS130). The calibrated curve is shown in Fig. 5. The relationship between the temperature T and center wavelength λ of the FBG temperature sensor can be expressed as λ = 0.010T + 1296.633.
(1)
The temperature sensitivity of the FBG sensor is about 10 pm/◦ C.
FIG. 4. Temperature standard setup.
FIG. 5. Calibrated curve of the sensor.
IV. EXPERIMENTS AND RESULTS
The mode of fixation of a sensor greatly influences its measurement of surface temperature. This study discusses two fixation modes: single-ended magnetism fixation and single-ended heat conduction grease fixation. The first fixation mode is selected because it is commonly adopted in conventional measurements. The second fixation mode is tested for comparison with traditional temperature sensors. Supposing that the mercury thermometer reading is T1, that of the FBG sensor is T2, and the surface temperature measurement error is represented by T, that is, T = T1 − T2. The surface temperature measurement errors are tested under two different conditions. A. Measurement error of bare FBG sensors with coating
The measurement mode of bare FBG temperature sensors with acrylate coating is shown in Fig. 6. The red copper sheet is a thermostatic surface of the surface-type temperature standard that is used to simulate the surface of the measured object. The FBG sensor is fixed on the red copper sheet by two magnets. The FBG can freely stretch and cling to the red copper sheet because only one fixed point is at the end of the FBG. The temperature of the hot water is changed, and the readings of the mercury thermometer and FBG sensor are recorded simultaneously in Table I. The ambient temperature
FIG. 6. Single-ended fixed FBG temperature sensor.
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Rev. Sci. Instrum. 85, 064905 (2014)
TABLE I. Measurement error of the single-ended fixed sensor.
Mercury thermometer reading T1 (◦ C) 91.8 72.9 64.1 57.2 51.7 45.4
FBG sensor reading T2 (◦ C)
Surface temperature measurement error T (◦ C)
83.7 67.8 61 55.2 50.5 45.2
8.1 5.1 3.1 2 1.2 0.2
FIG. 8. FBG temperature sensor structure with heat conduction grease.
To reduce the temperature gradient of the surface and to improve the accuracy of the surface measurement of the
FBG temperature sensor, a heat conduction grease-packaged structure is proposed in Fig. 8. The FBG sensor is fixed by two magnets, and the grating section is coated with heat conduction grease. Its brand is TS-KS101, and its thermal resistance is 2 w/m k. To determine the effect of the heat conduction grease-packaged structure on the measurement, a thermal resistor sensor is installed beside the packaged FBG sensor, whose readings are recorded simultaneously. The surface measurement errors of the two sensors are shown in Fig. 9. The relationship between the errors and surface temperature is approximately linear. At a low temperature, the two errors are very close; at a high temperature, the error of the packaged FBG sensor is smaller than that of the thermal resistor. This finding indicates that the accuracy of the FBG sensor packaged by heat conduction grease is higher than that of the commercial thermal resistor. Moreover, the error of the packaged FBG sensor is smaller than that of the bare FBG sensor with protective acrylate coating in Fig. 7. For example, at about 90 ◦ C, the measurement error of the packaged FBG sensor is 3 ◦ C, whereas that of the bare FBG sensor with protective acrylate coating is nearly 8.1 ◦ C. This difference indicates that the packaged structure can effectively reduce the temperature gradient and improve the accuracy of the surface measurement.
FIG. 7. Measurement error of a single-ended fixed sensor versus surface temperature.
FIG. 9. Measurement error of the heat conduction grease-packaged FBG sensor and thermal resistor versus surface temperature.
◦
is 23 C. The errors of the surface measurement T of the FBG sensor for different surface temperatures are shown in Fig. 7. The error of the surface measurement increases as the surface temperature increases. The relationship between errors and surface temperature is approximately linear. The error is about 8.1 ◦ C when the surface temperature is 91.8 ◦ C. The diameter of the FBG sensor is 0.3 mm (including core, cladding, and protective acrylate coating); therefore, the sensing point of the FBG sensor is located 0.15 mm from the copper surface along the horizontal direction. According to the FEA results, if an FBG sensor is fixed on the surface of the copper sheet to measure the temperature, then the temperature at the sensing point is 91.8 ◦ C − 0.15 mm × 46.4 ◦ C/mm − 0.89 ◦ C = 83.95 ◦ C. The measurement error calculated by the FEA is 91.8 ◦ C − 83.95 ◦ C = 7.85 ◦ C, which is close to that obtained in the experiments (8.1 ◦ C). B. Measurement error of the heat conduction grease-packaged FBG sensor and thermal resistor sensor
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Liu et al.
Rev. Sci. Instrum. 85, 064905 (2014)
V. CONCLUSION
ACKNOWLEDGMENTS
The surface temperature gradient and the measurement errors induced by it are easily overlooked. These issues greatly influence surface temperature measurement results. Thus, a high-accuracy surface temperature measurement is a challenging task. To reveal the influence of temperature gradient on measurement accuracy, a surface-type temperature standard setup is prepared, and the measurement errors of surface-mounted FBG temperature sensors with two different packaging conditions are obtained. The experimental results show that the bare FBG sensor with acrylate coating generates a linear error, which is good for the compensation process. The error of the FBG sensor packaged with heat conduction grease is smaller than those of the bare FBG sensor and the commercial thermal resistor. Thus, high-quality packaging can effectively improve the accuracy of FBG sensors in measuring surface temperatures.
This work was financially supported by the National Natural Science Foundation of China (Grant No. 61301064), the National Science and Technology Mayor project (Grant No. 2012ZX04001-012-05), and the China Postdoctoral Science Foundation (Grant No. 2013M542075).
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