sensors Article

Model Study of the Influence of Ambient Temperature and Installation Types on Surface Temperature Measurement by Using a Fiber Bragg Grating Sensor Yi Liu 1,2, * and Jun Zhang 1 1 2

*

School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China; [email protected] Digital Manufacture Key Lab of Hubei Province, Wuhan University of Technology, Wuhan 430070, China Correspondence: [email protected]; Tel.: +86-27-8765-1793

Academic Editors: Manuel Lopez-Amo, Jose Miguel Lopez-Higuera and Jose Luis Santos Received: 2 April 2016; Accepted: 21 June 2016; Published: 1 July 2016

Abstract: Surface temperature is an important parameter in clinical diagnosis, equipment state control, and environmental monitoring fields. The Fiber Bragg Grating (FBG) temperature sensor possesses numerous significant advantages over conventional electrical sensors, thus it is an ideal choice to achieve high-accuracy surface temperature measurements. However, the effects of the ambient temperature and installation types on the measurement of surface temperature are often overlooked. A theoretical analysis is implemented and a thermal transfer model of a surface FBG sensor is established. The theoretical and simulated analysis shows that both substrate strain and the temperature difference between the fiber core and hot surface are the most important factors which affect measurement accuracy. A surface-type temperature standard setup is proposed to study the measurement error of the FBG temperature sensor. Experimental results show that there are two effects influencing measurement results. One is the “gradient effect”. This results in a positive linear error with increasing surface temperature. Another is the “substrate effect”. This results in a negative non-linear error with increasing surface temperature. The measurement error of the FBG sensor with single-ended fixation are determined by the gradient effect and is a linear error. It is not influenced by substrate expansion. Thus, it can be compensated easily. The measurement errors of the FBG sensor with double-ended fixation are determined by the two effects and the substrate effect is dominant. The measurement error change trend of the FBG sensor with fully-adhered fixation is similar to that with double-ended fixation. The adhesive layer can reduce the two effects and measurement error. The fully-adhered fixation has lower error, however, it is easily affected by substrate strain. Due to its linear error and strain-resistant characteristics, the single-ended fixation will play an important role in the FBG sensor encapsulation design field in the near future. Keywords: Fiber Bragg Gratings; fiber optics sensors; surface temperature measurement; error

1. Introduction Surface temperature is an important parameter in clinical diagnosis, equipment state control, and environmental and safety monitoring fields. It can reveal the hot and cold level of the measurement object, evaluate the physiological health situation [1] and running state of equipment [2], and diagnose diseases and device faults. High-accuracy surface temperature measurement technology is a key point to implement exact evaluation and diagnosis. The Fiber Bragg Grating (FBG) temperature sensor is a new temperature sensor and is utilized widely [3–5]. Compared to thermocouple or thermal resistor sensors, it possesses a fused silica wire as a signal route, which can effectively reduce thermal Sensors 2016, 16, 975; doi:10.3390/s16070975

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transmission of signal wires and improve the measurement accuracy [6]. In addition, the FBG sensor, characterized by high security, strong non-interference, small size, light weight, easy installation, and low costs, satisfies the harsh manufacturing environment [7]. It is an ideal choice to achieve high accurate measurement for equipment surface temperature. For traditional temperature sensors, many methods of placing temperature sensors on the surface of the measurement object, such as adhesive bonding, mounts installing, tape fixing, etc., are standard methods to obtain the surface temperature [8]. However, these methods still cannot avoid measurement error. Hennecke et al. [9] discussed the measurement error induced by a local heat sink on the surface. It is a measurement error induced by the high thermal conductivity of a thermocouple. Zvizdic [10] established a model of surface temperature measurement errors of thermocouples in vertical natural convection cooled channels. Kuznetsov et al. [11] discussed the influence of special glues and pastes on errors of temperature measurements by thermocouples. For the FBG temperature sensor, a new temperature sensor, the effect of the ambient temperature and installation types of sensors on precision of surface temperature measurement are often overlooked. Generally speaking, the cross-sensitivity of the FBG temperature sensor is only considered when it is fixed. Soumen et al. mounted a single FBG near a tool tip by using a tape to eradicate the cross-sensitivity issue [12]. The influence of conducting heat on the surface and installation on the measurement has not been discussed. In order to fully reveal the relationship between surface temperature measurement errors and the installation types of FBG temperature sensors, we established a thermal transfer model of surface temperature measurement with the FBG sensor and propose a calibration system of surface temperature measurement error. The measurement errors which are induced by three installation types are theoretically analyzed and experimentally tested. According to the results of the theoretical and experimental analysis, two effects which determine measurement error are found. 2. Surface Temperature Measurement Principle of FBG Sensor 2.1. Principle of FBG Sensor The FBG consists of a periodic modulation of the refraction along the fiber core, as shown in Figure 1. When a broadband light signal is injected into the optical fiber, most of the wavelength of light will reflect weakly on each of subsequent plate. At a particular wavelength which satisfies the Bragg interference condition, an intense reflected signal is generated. The particular wavelength is called the Bragg wavelength, λB , which is determined by Equation (1). λ B “ 2ne f f ¨ Λ

(1)

where λB , the Bragg grating wavelength, is the free space center wavelength of the input light that will be back-reflected from the Bragg grating; Λ is the grating periodicity of the FBG; and neff is the effective refractive index of the fiber core at the free space center wavelength. These two factors will be affected by changes in strain and temperature. For isotropic and homogeneous strain, the change of wavelength ∆λ B is ∆λ B “ λ B p1 ´ Pe qε z ` λ B pαΛ ´ αn q∆T

(2)

where ε z and ∆T are the change of strain and temperature in the FBG, and Pe is an effective strain-optic constant. It is defined as: Pe “

n2e f f 2

rp12 ´ vpp11 ´ p12 qs

(3)

The parameters p11 and p12 are components of the strain-optic tensor, and v is Poisson’s ratio. For Ge-doped silica-core fiber p11 “ 0.113, p12 “ 0.252, v “ 0.16, and ne f f “ 1.482, Pe “ 0.3012. In Equation (2), the parameter αΛ “ Λ1 ¨ BBΛ T is the thermal expansion coefficient for the fiber (approximately 0.55 ˆ 10´6 for silica). The parameter αn “

1 ne f f

Bn

¨ BeTf f is the thermal-optic coefficient,

For Ge-doped silica-core fiber p11  0.113 , p12  0.252 , v  0.16 , and neff  1.482 , Pe  0.3012 . In Equation (2), the parameter   

1    T

is the thermal expansion coefficient for the fiber

(approximately 0.55 × 10−6 for silica). The parameter  n 

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1 neff 3 of 12  is the thermal-optic coefficient, neff T

−6 whichisisapproximately approximatelyequal equal to to 8.6 8.6 ˆ × 10 Ge-doped silica-core fiber. Using these parameters and 6 for which 10´for Ge-doped silica-core fiber. Using these parameters the Expression (2), the shift in the Bragg grating center wavelength due to strain and temperature and the Expression (2), the shift in the Bragg grating center wavelength due to strain and temperature changesisisgiven givenby byEquation Equation(4): (4): changes

B  1.048 pm /    z  13.7 pm/ C  T ∆λ B “ 1.048 pm{µε ¨ ε z ` 13.7 pm{˝ C ¨ ∆T

(4) (4)

Foraafree freeFBG FBG(floating (floatingon onthe thespecimen), specimen),only onlytemperature temperaturecan canaffect affectthe thecenter centerwavelength. wavelength. For Hence,this thisfree freeFBG FBGcan canbebeused usedtotomeasure measuretemperature. temperature.The Thewavelength wavelengthshift shiftofofFBG FBGtemperature temperature Hence, sensor is given by Equation (5): sensor is given by Equation (5):  13.7 pm/C  T B 13.7 pm{˝ C ¨ ∆T ∆λB“

(5) (5)

ForaaFBG FBGbonded bondedon onthe thespecimen, specimen,ititcan cansense senseboth boththe thechanges changesofofsurrounding surroundingtemperature temperature For and strain transferred from the specimen. The wavelength shift of the bonding sensor givenby by and strain transferred from the specimen. The wavelength shift of the bonding sensor isisgiven Equation (4). Equation (4).

Figure 1. A1.schematic representation of a Bragg grating with incident, reflected, and transmitted light beams. Figure A schematic representation of a Bragg grating with incident, reflected, and transmitted light beams.

2.2. Temperature Field Model of FBG 2.2. Temperature Field Model of FBG When a FBG is fixed on a hot surface, it is in contact with the surface in a narrow line and the remainder cylindrical air.contact Heat energy transfers hot surface the When aofFBG is fixed surface on a hotcontacts surface,with it is in with the surfacefrom in a the narrow line andtothe optical fiber and dissipates intocontacts the surrounding air by heat transfers convection. Inthe order simplify the remainder of cylindrical surface with air. Heat energy from hot to surface to the model,fiber we and suppose the optical is a thinair and with an cross-section. The optical dissipates into thefiber surrounding bylong heat wire convection. In octagonal order to simplify the model, diameter of the its inscribed circle to the diameter D ofan theoctagonal optical fiber 250 micrometer we suppose optical fiber is is a equal thin and long wire with cross-section. The (including diameter cladding,circle and coating). The the optical fibermicrometer is 20 mm. The heat transfer ofcore, its inscribed is equal to theinstallation diameter Dlength of theofoptical fiber 250 (including core, model ofand the coating). FBG mounted on the surface is shown in Figure 2a.isThe bottom 3, is model in contact cladding, The installation length of the optical fiber 20 mm. Theface, heatFace transfer of with themounted heat source andsurface its temperature kept constant at Tbottom 0. The two end faces 1 andwith 2) ofthe the the FBG on the is shown in Figure 2a. The face, Face 3, is(Faces in contact optical fiber sotemperature small that kept we consider with the surroundings. The heat source andisits constant them at T0 . as Theheat twoinsulation end faces (Faces 1 and 2) of the optical remaining sidethat faceswe (Faces 4–10)them are in with thewith air. The convection heat-transfer coefficient fiber is so small consider as contact heat insulation the surroundings. The remaining side is h and the 4–10) surrounding temperature is Tair. . According to symmetry, each cross-section of the optical faces (Faces are in contact with the The convection heat-transfer coefficient is h and the  surrounding is T8 . According to symmetry, each the optical fiber has a fiber has a temperature uniform temperature distribution along the axiscross-section of the fiber.ofThe three-dimensional uniform temperature distribution along the axis of the fiber. The three-dimensional temperature field temperature field can be simplified into a two-dimensional temperature field as shown in Figure 2b. can be simplified into a two-dimensional temperature field as shown in Figure 2b. The temperature field of the optical fiber is determined by the steady-state thermal conductivity Equation (6) without heat generation. B2 T B2 T ` 2 “0 Bx2 By

(6)

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The temperature Sensors 2016, 16, 975

field of the optical fiber is determined by the steady-state thermal conductivity 4 of 12 Equation (6) without heat generation.

(a)

(b)

Figure 2. 2. Temperature field model model of of FBG FBG sensor. sensor. (a) model of of FBG FBG sensor sensor and and (b) (b) 2D 2D heat heat Figure Temperature field (a) 3D 3D model conductivity model on the cross-section. conductivity model on the cross-section.

On Face 3, the temperature is a constant T20T; therefore, the Dirichlet boundary condition is applied  2T  0 (6) 2 2 as follows: x y 0q “ T0 the Dirichlet boundary condition is applied (7) On Face 3, the temperature is a constantTpx, T0; therefore, as follows: On Face i (i = 4, 5, . . . , 10), the Robin boundary condition [13] is given, as follows:

T(ˇx,0)  T0 BT ˇˇ ` q “ hpT ´ T8 q Bx boundary By ˇΣ“Face_i On Face i (i = 4, 5, …, 10), the Robin condition [13] is given, as follows: Ñ BT Kn i ¨ p

(7) (8)

Ñ T TK is the conductivity of material. where ni is the normal unit vector ofKFace ni ·( i and  )  h(T  T ) (8) x y to A finite element method (FEM) is employed Equation (6) with boundary condition Faceresolve _i Equations (7) and (8). The material thermal properties and structure size for FBG sensor used in the where ni simulation is the normal vector of Face numerical are unit listed in Table 1. i and K is the conductivity of material.

A finite element method (FEM) is employed to resolve Equation (6) with boundary condition Table 1. thermal Parameters in the numerical simulation. Equations (7) and (8). The material properties and structure size for FBG sensor used in the numerical simulation are listed in Table 1. Parameters

Values

W/(m¨ ˝ C)

Conductivity of Fiber Core Kf , in the numerical simulation. 1.4 (SiO2 ) Table 1. Parameters Conductivity of coating layer Kc , W/(m¨ ˝ C) 2 (Polyimide) 1 (laboratory condition) Parameters Values Convection coefficient of Coating h, W/(m2 ¨ ˝ C) Radii of coating 125(SiO2) Conductivity of Fiber CorerpK(µm) f, W/(m·°C) 1.4 Surrounding Temperature T8 , ˝ C 23 Conductivity of coating layer Kc, W/(m· °C) 2 (Polyimide) Temperature on hot surface T0 , ˝ C 90 Convection coefficient of Coating W/(m2·°C) 1 (laboratory Radii of optical fiber rf , h, µm 62.5 condition)

Radii of coating rp (μm) 125 Surrounding Temperature T , °C 23 The simulation result of heat flux and temperature field on optical fiber cross-section is shown in Temperature on hot surface T0 , °C 90 Figure 3. fiber f, μm When the FBG isRadii used of to optical measure the rtemperature of the hot surface,62.5 only one side of the fiber contacts with the hot surface; therefore, the heat energy flows from this edge to the other side and The simulation result of heat and temperature field optical cross-section is shown dissipates into the surrounding air,flux as in Figure 3a. Along theon heat flowfiber direction, the temperature in Figure 3. reduces. The rate of reduction (gradient of temperature) is determined by the thermal conductivity the FBG and is used to measure the temperature of the hot surface,ofonly fiber of theWhen FBG material convection condition. The thermal conductivity the one fiberside coreofisthe greater contacts hot surface; therefore, the heat energy flows from this edge to the and than that with of thethe coating layer. Thus, the temperature field on the cross-section of the fiberother core side which is dissipates into the surrounding air, as in Figure 3a. Along the heat flow direction, the temperature used to detect temperature is even, but it is lower than the real temperature of the surface measured reduces. rate of3b. reduction (gradient of temperature) determined of bythe thefiber thermal as shownThe in Figure The difference between the averageistemperature core conductivity and real hot of the FBG material is and condition. surface temperature theconvection measurement error. The thermal conductivity of the fiber core is greater

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than that Sensors 2016,of 16,the 975 coating layer.

Thus, the temperature field on the cross-section of the fiber core which 5 of 12 is used to detect temperature is even, but it is lower than the real temperature of the surface measured Sensorsthan 2016, 16, 975 that ofinthe coating layer. Thus, thebetween temperature field ontemperature the cross-section the core fiberand corereal which as shown Figure 3b. The difference the average of theoffiber hot5 of 12 is the measurement issurface used totemperature detect temperature is even, but iterror. is lower than the real temperature of the surface measured as shown in Figure 3b. The difference between the average temperature of the fiber core and real hot surface temperature is the measurement error.

(a)

(b)

Figure 3. (a) Heat flux and (b) temperature field on optical fiber cross-section.

Figure 3. (a) (a)Heat flux and (b) temperature field on optical fiber (b) cross-section.

2.3. Numerical Analysises Measurement Error of FBG Sensors Figure 3. (a)ofHeat flux and (b) temperature field on optical fiber cross-section.

2.3. Numerical Analysises of Measurement Error of FBG Sensors

In the industrial environment, the thermal convection between the sensor and surroundings can

2.3.the Numerical Analysises of Measurement Error ofconvection FBG Sensorsbetween the sensor and surroundings In industrial environment, the thermal influence measurement error. A variety of convection coefficients, h = 1, 5, 10, 20, 40 W/(m2·°C), are can 2 ˝ influence measurement error. A variety of convection coefficients, = 1, error 5, 10, proposed study theenvironment, influence of the conditionbetween on measurement of20, the 40 FBGW/(m sensor. In theto industrial the convection thermal convection thehsensor and surroundings can ¨ C), 2·°C), are proposed to studyare thelisted influence of the convection condition measurement error of the Other parameters inA Table 1. of The simulation results of hon temperature are shown in FBG influence measurement error. variety convection coefficients, = 1, 5, 10, 20,error 40 W/(m are proposed to the influence of convection condition onresults measurement error of the FBG sensor. Figure 4a.parameters Asstudy the convection coefficient increase, temperature error rapidly. Theare reading sensor. Other are listed inthe Table 1. The the simulation ofincreases temperature error shown in Other parameters are than listed in real Table 1. The simulation results oferror temperature error areby shown in of4a. theAs sensor is lower the temperature on the hot surface, which is determined the heat Figure the convection coefficient increase, the temperature increases rapidly. The reading Figure 4a. As the convection coefficient increase, the temperature error increases rapidly. The reading flow direction. The convection coefficient values in Figure 4a represent several typical measurement of the sensor is lower than the real temperature on the hot surface, which is determined by the heat the sensor is(such temperature thelaboratory, hot surface, determined theinheat environments asthan h = 1the forreal a closed system in h =which 5 for aissmall open system the flow of direction. The lower convection coefficient values on inthe Figure 4a represent several typicalbymeasurement laboratory, h = The 10 for an open system outdoors, h =Figure 20 for 4a fanrepresent convection in a workshop, and h = 30 flow direction. convection coefficient values in several typical measurement environments (such as h = 1 for a closed system in the laboratory, h = 5 for a small open system in the for air-cooling(such in equipment). environments, FBG sensors show distinctly environments as h = 1 for aUnder closed different system inwork the laboratory, h = 5 for a small open system in the laboratory, h = 10 for an open system outdoors, h = 20 for fan convection in a workshop, and h = 30 for laboratory, h = 10 for an open system outdoors, h = 20 for fan convection in a workshop, and h = 30 different error levels. air-cooling in equipment). Under different work environments, FBG sensors showshow distinctly different for air-cooling in equipment). Under different work environments, FBG sensors distinctly error different levels. error levels.

(a)

(b)

Figure 4. Measurement error numerical analysis of FBG Sensor. (a) The influence of convection on (a) (b) temperature error; (b) The influence of temperature difference between surrounding and hot surface on temperature error. error numerical analysis of FBG Sensor. (a) The influence of convection on Figure 4. Measurement

Figure 4. Measurement error numerical analysis of FBG Sensor. (a) The influence of convection on temperature error; (b) The influence of temperature difference between surrounding and hot surface temperature error; (b)convection The influence of temperature differenceerror between surrounding andtemperature hot surface Under the same conditions, the measurement is still affected by the on temperature error. on temperature error. of hot surface measured. The temperature of the hot surface measured, T = 40, 50, 60, 70, 80, 90 °C, 0

Under the same convection conditions, the measurement is still affected is changed to study the dependent relationship between theerror measurement errorby ofthe thetemperature FBG sensor Under the same convection conditions, of the measurement error is still by70, the80, temperature T0 affected of hot surface measured. The temperature the hot surface measured, = 40, 50, 60, 90 °C,

of hotissurface temperature of the between hot surface measured, T0error = 40, 70,sensor 80, 90 ˝ C, changedmeasured. to study theThe dependent relationship the measurement of50, the60, FBG is changed to study the dependent relationship between the measurement error of the FBG sensor and the real temperature of hot surface. In order to simulate the open system in the laboratory, a convection coefficient equal to 10 W/(m2 ¨ ˝ C) is employed. Other parameters are listed in Table 1. The simulation results are shown in Figure 4b. As the measured temperature increases, the temperature error increases linearly. When 90 ˝ C surface temperature is measured by the FBG sensor, the error induced by thermal transfer is 11.9 ˝ C.

and the 2016, real 16, temperature of hot surface. In order to simulate the open system in the laboratory, Sensors 975 6 of 12 a convection coefficient equal to 10 W/(m2·°C) is employed. Other parameters are listed in Table 1. The and the real temperature of in hotFigure surface. to simulatetemperature the open system in thethe laboratory, a simulation results are shown 4b.InAsorder the measured increases, temperature 2 convection coefficient 10 °C W/(m ·°C) istemperature employed. Other parameters are listed in Tablethe 1. The error increases linearly.equal Whento90 surface is measured by the FBG sensor, error Sensors 2016, 16, 975 6 of 12 simulation results transfer are shown Figure induced by thermal is in 11.9 °C. 4b. As the measured temperature increases, the temperature error increases linearly. When 90 °C surface temperature is measured by the FBG sensor, the error induced by thermal transfer is 11.9 Sensor °C. 3. 3. Measurement MeasurementErrors Errorsof ofthe theFBG FBG Sensorin inDifferent DifferentInstallation InstallationTypes Types 3. Measurement Errors of the FBG Sensor in Different Installation Types 3.1. 3.1. Experimental Experimental Principle Principle and and Method Method

errorsof ofand surface-mounted FBGtemperature temperature sensor difference between 3.1.Measurement Experimental Principle Method Measurement errors aasurface-mounted FBG sensor areare thethe difference between the the result of the measurement and the true value of what is being measured. Generally speaking, the result ofMeasurement the measurement and the true value of what is being measured. Generally speaking, the true errors of a surface-mounted FBG temperature sensor are the difference between true value is difficult to obtain. To study measurement the measurement error of FBG the FBG temperature sensor on value is difficult obtain. To study of the temperature sensor on the result of theto measurement and thethe true value of whaterror is being measured. Generally speaking, thethe the surface, a surface-typed temperature standard must be fabricated. It is a reference whose surface, a surface-typed temperature standard must be fabricated. It the is a FBG reference whose temperature true value is difficult to obtain. To study the measurement error of temperature sensor on temperature is known. A calibrated FBG temperature sensor is fixed on it with different installation is known. A calibrated FBG temperature sensor is fixed on it with different installation types, as in the surface, a surface-typed temperature standard must be fabricated. It is a reference whose types, as in Figure 5. The measurement errors are obtained by comparing the difference between Figure 5. The measurement errors areFBG obtained by comparing difference readingthe of temperature is known. A calibrated temperature sensor is the fixed on it withbetween differentthe installation reading of the FBG sensor and the temperature of the surface-typed temperature standard. thetypes, FBG sensor and the temperature of the surface-typed temperature standard. as in Figure 5. The measurement errors are obtained by comparing the difference between the reading of the FBG sensor and the temperature of the surface-typed temperature standard. FBG Interrogator FBG

FBG

Interrogator

Computer

FBG Temperature

Fiber

Computer

Standard Temperature Standard

Fiber Figure 5. 5. Surface Surface error error measurement measurement principle principle schematic. schematic. Figure Figure 5. Surface error measurement principle schematic.

3.2. Surface-Typed Surface-Typed Temperature 3.2. Temperature Standard Standard Setup Setup 3.2. Surface-Typed Temperature Standard Setup As shown in Figure for the consists of of the As shown in Figure 6, 6, the the experimental experimental set-up set-up for the temperature temperature standard standard consists the As shown in Figure 6, the experimental set-up for the temperature standard consists of the following devices: a Dewar flask, a cork, a piece of red copper which is fixed under the bottom following devices: a Dewar flask, a cork, a piece of red copper which is fixed under the bottom of the devices: a Dewar flask, The a cork, a piece of red copper which is fixed under bottom of the of following theand cork, and a thermometer. Dewar flask is filled hot water. Thethe thermometer is a cork, a thermometer. The Dewar flask is filled with hotwith water. The thermometer is a standard cork, and a thermometer. The Dewar flask is filled with hot water. The thermometer is a standard standard mercury-in-glass type (Grade II) and verified in accordance with the verification regulation mercury-in-glass type (Grade II) and verified in accordance with the verification regulation of type (Grade(II). II) and thickness verified in accordance with theis verification regulation of of mercury-in-glass standard mercury-in-glass the copper 1 mm it is inundated standard mercury-in-glass (II). The The thickness of theofcopper sheet issheet 1 mm and it isand inundated with hot standard mercury-in-glass (II). The thickness of the copper sheet is 1 mm and it is inundated with hot with hot water. The temperature difference of the two sides of thesheet copper very sheetsmall is very small0.2 (about water. The temperature of the the copper (about °C). water. The temperaturedifference differenceof ofthe the two two sides sides of copper sheet isisvery small (about 0.2 °C). ˝ C). The 0.2 upside temperature of the copper sheet is approximately equal to that of the hot water. The upside temperature of the copper sheet is approximately equal to that of the hot water. The The upside temperature of the copper sheet is approximately equal to that of the hot water. The The change ofwater the water temperature is very slow (about 0.3 ˝because C/h) because of the big specific heat of change of of the temperature 0.3 °C/h) °C/h) thebig bigspecific specific heat water change the water temperatureisisvery veryslow slow (about (about 0.3 because ofofthe heat of of water water and the heat preservation property of the vacuum in the Dewar flask. Thus, the copper sheet and thethe heat preservation in the the Dewar Dewarflask. flask.Thus, Thus,the thecopper copper sheet is an and heat preservationproperty propertyof of the the vacuum vacuum in sheet is an is an ideal quasi-static-state surface-typed temperature standard. Its temperature is in accordance ideal quasi-static-state standard. Its Its temperature temperatureisisininaccordance accordance with ideal quasi-static-statesurface-typed surface-typed temperature temperature standard. with with that of the hot water in Dewar flask. The thermometer is dipped into the water and used to that of the hot ininthe Dewar flask. The thermometer dipped into the water and used that of the hotwater water thethe Dewar flask. The thermometer isis dipped into the water and used to to measure the temperature accurately. Its reading is regarded as the temperature of the surface-typed measure thethe temperature asthe thetemperature temperatureofofthe the surface-typed measure temperatureaccurately. accurately.Its Itsreading reading is regarded regarded as surface-typed temperature standard. temperature standard. temperature standard. thermometer thermometer

fiber fiber cork cork

copper redred copper Dewar flask Dewar flask

FBG FBG vacuum vacuum hot hot water water

Figure 6. 6. Principle setup of of aasurface-typed surface-typedtemperature temperature standard. Figure Principleschematic schematicand andexperimental experimental setup standard. Figure 6. Principle schematic and experimental setup of a surface-typed temperature standard.

3.3. Experimental Sensor and Installation Types A FBG temperature sensor (its center wavelength is 1297 nm) is dipped into the hot water in the temperature standard setup. The temperature of hot water is changed six times from 46–92 ˝ C and measured by the standard mercury-in-glass thermometers (Grade II). The reflected wavelength of the FBG is recorded by the FBG interrogator (MOI MS130). The calibrated curve is shown in Figure 7.

Sensors 2016, 16, 975 Sensors 2016, 16, 975 3.3. Experimental

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Sensor and Installation Types

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A FBG temperature sensor (its center wavelength is 1297 nm) is dipped into the hot water in the 3.3. Experimental Sensor and Installation Types

Sensorstemperature 2016, 16, 975 standard setup. The temperature of hot water is changed six times from 46–92 °C and7 of 12

A FBG temperature sensor (its center wavelength is 1297 nm) is dipped into the hot water in the measured by the standard mercury-in-glass thermometers (Grade II). The reflected wavelength of temperature standard setup. The temperature of hot water is changed six times from 46–92 °C and the FBG is recorded by the FBG interrogator (MOI MS130). The calibrated curve is shown in Figure 7. measured bybetween the standard mercury-in-glass thermometers (Grade II).λ The reflected wavelength of The relationship the temperature T and center wavelength of the FBG temperature sensor The relationship between the temperature T and center wavelength λ of the FBG temperature sensor thefitted FBG is recorded by the FBG interrogator (MOI MS130). The calibrated curve is shown in Figure 7. can be as follows: can be fitted as follows: The relationship between the temperature T and center wavelength λ of the FBG temperature sensor  0.010T` 1296.633 (9) (9) λ“ 0.010T 1296.633 can be fitted as follows: The temperature sensitivity FBG sensor about 10  sensor 0.010 T isis 1296.633 The temperature sensitivity of of thethe FBG about 10 pm/°C. pm/˝ C.

(9)

The temperature sensitivity of the FBG sensor is about 10 pm/°C.

Figure 7. Temperature sensitivity FBGused usedininthe the experiment. Figure 7. Temperature sensitivitycurve curvefor for the FBG experiment. Figure 7. Temperature sensitivity curve for the FBG used in the experiment.

General speaking, thereare are three three installation types are employed in practice measurement. They General speaking, there installation types are employed in practice measurement. are single-ended fixation, double-ended fixation, and full fixation. Three calibrated FBG temperature They are General single-ended fixation, and full fixation. Three calibrated speaking, there aredouble-ended three installationfixation, types are employed in practice measurement. They FBG sensors are installed on the surface of the red copper sheet of the temperature standard setup with temperature sensorsfixation, are installed on the surface thefull red copperThree sheet of the temperature standard are single-ended double-ended fixation,of and fixation. calibrated FBG temperature three different installation types. In Figure 8, the installation type I is the single-ended fixed model. setupsensors with three differentoninstallation In Figure the installation type I is the single-ended are installed the surfacetypes. of the red copper8,sheet of the temperature standard setup with fixed The red copper sheet is the surface-typed temperature standard which simulates the surface of three installation types. In Figure 8, thetemperature installation type I is the single-ended fixed model. Thedifferent redobject. copper sheet the surface-typed standard simulates themodel. surface measured The FBGissensor is fixed on the red copper sheet by twowhich magnets. One magnet is on of The red copper sheet is the surface-typed temperature standard which simulates the surface of measured object. The FBG sensor is fixed on the red copper sheet by two magnets. One magnet the upper surface of the copper sheet and presses the fiber. Another magnet is under the copper sheetis on measured object. The FBG sensor is fixed on the red copper sheet by two magnets. One magnet is on the upper surface of thebycopper sheet and presses theisfiber. magnet under the copper and can be pulled the upper one. Since the FBG only Another fixed at one end, itiscan freely stretch andsheet the upper surface of the copper sheet and presses the fiber. Another magnet is under the copper sheet cling the redby copper sheet. one. In installation FBGfixed sensor fixed onitthe red copper sheet and and can betopulled the upper Since thetype FBGII,isthe only at is one end, can freely stretch and can be pulled by the upper one. Since the FBG is only fixed at one end, it can freely stretch and bythe fourred magnets at sheet. two ends the FBG. Installation type III sensor is the adhesive model. The FBG cling to copper In of installation type II, the FBG is fixedbonding on the red copper sheet by cling to the red copper sheet. In installation type II, the FBG sensor is fixed on the red copper sheet is pasted at ontwo the red copper surface by the acrylate adhesive andadhesive is fixed fully. four magnets ends of the FBG. Installation type III is the bonding model. The FBG is by four magnets at two ends of the FBG. Installation type III is the adhesive bonding model. The FBG pasted on the on redthe copper surface by the acrylate adhesive is pasted red copper surface by the acrylate adhesiveand andisisfixed fixed fully. fully.

Figure 8. Schematic diagram and photograph of three common installation types of sensor. Figure 8. Schematic diagram and photograph of three common installation types of sensor.

Figure 8. Schematic diagram and photograph of three common installation types of sensor.

4. Results and Discussions Fixation modes of sensors greatly influence surface temperature measurement results. Three fixation modes are discussed in this paper, which are the single-ended fixation with magnets, the double-ended fixation with magnets, and the full fixation with adhesive. Suppose the mercury thermometer reading is T1 , the FBG sensor reading is T2 , and the surface temperature measurement

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4. Results and Discussions Sensors 2016,Fixation 16, 975 modes of sensors greatly influence surface temperature measurement results. Three8 of 12

fixation modes are discussed in this paper, which are the single-ended fixation with magnets, the double-ended fixation with magnets, and the full fixation with adhesive. Suppose the mercury T1T , the FBGsurface sensor reading is T2, and the surface temperature measurement error thermometer is ∆T. Thus, reading ∆T = T1is´ temperature measurement errors are tested under three 2 . The errorconditions. is ΔT. Thus, ΔT = T1 − T2. The surface temperature measurement errors are tested under three different different conditions.

4.1. Measurement Errors of Sensor under Three Different Types of Installation 4.1. Measurement Errors of Sensor under Three Different Types of Installation

Ambient temperature is 23 ˝ C in the experiments. The surface measurement errors, ∆T, of the Ambient temperature is 23 °C in the experiments. The surface measurement errors, ΔT, of the FBG sensor under three different types of installation are shown in Figure 9. Three curves show the FBG sensor under three different types of installation are shown in Figure 9. Three curves show the different change trends. TheThe measurement sensorwith withthe the single-ended fixation increase, different change trends. measurementerrors errorsof of the the sensor single-ended fixation increase, thosethose withwith double-ended fixation decrease, and those with fully-adhered fixation fluctuate as the double-ended fixation decrease, and those with fully-adhered fixation fluctuate as the surface temperature rises. How areare sosoprominent generated? surface temperature rises. How prominent differences differences generated?

Figure 9. Surface temperature measurement errors of sensor under three different types of installation.

Figure 9. Surface temperature measurement errors of sensor under three different types of installation.

4.2. Influence of Installation Type of FBG on Measurement Error

4.2. Influence of Installation Type of FBG on Measurement Error For the single-ended fixation, Figure 10 shows the measurement error increases as the surface

For the single-ended fixation, Figurebetween 10 shows the and measurement error increases as the surface temperature increases. The relationship errors surface temperatures is approximately temperature increases. The relationship between errors and surface temperatures is approximately linearly dependent. The error is about 8 °C (percentage error is about 8/92 = 8.7%) when the surface linearly dependent. is about 8 ˝between C (percentage is about 8/92 = 8.7%) when temperature is 92The °C. error The relationship the errorerror ΔT and the surface temperature T1 the can surface be ˝ fitted as follows: temperature is 92 C. The relationship between the error ∆T and the surface temperature T1 can be fitted as follows: T  0.17119T  7.62874 (10) 1

“ 0.17119T 1 ´ 7.62874 The difference between the real∆T surface temperature and reading of FBG sensor is caused by the (10) gradient of temperature on the surface. Each FBG sensor has a sensing point which is used to sense The difference between the real surface temperature and reading of FBG sensor is caused by the temperature. The sensing point detects the temperature around itself, rather than the temperature the gradient of temperature on the surface. Each FBG sensor has a sensing point which is used of the object or surface. There is a serious temperature gradient between a hot surface and the cool to sense the temperature. The sensing point the detects thepoint temperature around than the ambience. Thus, the weak deviation between sensing and hot surface willitself, inducerather significant temperature of theerror. object or surface. Therethe is asurface serious between a hot surface measurement Moreover, the hotter is, temperature the greater thegradient temperature gradient is and and the Thus, the weak the sensing and hot surface the cool moreambience. the measurement error will deviation be. We callbetween this phenomenon thepoint “gradient effect”. The will experimental are in accord simulation Figure 4b. Only slopes the of two lines induce significantresults measurement error.with Moreover, theresults hotterinthe surface is, thethe greater temperature are slightly different. It is measurement caused by the different convection coefficients between thethe experiment and gradient is and the more the error will be. We call this phenomenon “gradient effect”. the simulation. Since the can freely on theresults surface in of Figure the measured object, is impossible The experimental results are FBG in accord withstretch simulation 4b. Only the itslopes of two lines to be affected by the of by the the measured object. It is a highly robust installation method in the and are slightly different. It isstrain caused different convection coefficients between the experiment the simulation. Since the FBG can freely stretch on the surface of the measured object, it is impossible to be affected by the strain of the measured object. It is a highly robust installation method in the surface temperature measurement where there is an intense stress effect on the substrate. The remainder of the trouble is the large error when the installation method is used in the high-accuracy surface temperature measurement. Considering the stable linear error relationship, the compensation technology could resolve this problem satisfactorily. Therefore, the installation method, single-ended fixation, properly becomes a new research focus in the FBG sensor encapsulation design field.

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Sensors 2016, 16, 975 of 12 surface temperature measurement where there is an intense stress effect on the substrate.9 The remainder of the trouble is the large error when the installation method is used in the high-accuracy surface temperature temperaturemeasurement. measurementConsidering where there an intense stressrelationship, effect on the The surface theisstable linear error the substrate. compensation remainder the trouble is the large error when the Therefore, installationthe method is usedmethod, in the high-accuracy Sensorstechnology 2016, 16, 975of could resolve this problem satisfactorily. installation single-ended9 of 12 surface temperature measurement. Considering stable linear error relationship,design the compensation fixation, properly becomes a new research focus the in the FBG sensor encapsulation field. technology could resolve this problem satisfactorily. Therefore, the installation method, single-ended fixation, properly becomes a new research focus in the FBG sensor encapsulation design field.

Figure 10. Surface temperaturemeasurement measurement errors errors of with thethe single-ended fixation. Figure 10. Surface temperature ofthe thesensor sensor with single-ended fixation. Figure 10. Surface temperature errors of the sensor with the single-ended fixation. For the double-ended fixation,measurement the measurement errors of the sensor change slowly, and then

For the double-ended fixation, the measurement errors of the sensor change slowly, and then decrease rapidly as the surface temperature increases in Figure 11. The relationship between errors decrease rapidly as the surface temperature increases in 11.sensor The relationship For the temperatures double-ended the measurement errors of the change and then and surface isfixation, non-linearly dependent. TheFigure error at about 65 °C is slowly, zero.between When theerrors ˝ and surface temperatures issurface non-linearly Theinerror at 11. about 65 C is zero. When the surface decrease rapidly as the temperature increases Figure Theindicates relationship between errors surface temperature exceeds 66 °C, the dependent. error ΔT becomes negative. This that the readings of ˝ C, theiserror and surface temperatures non-linearly dependent. The error at about 65 °C is zero. When the temperature exceeds 66 ∆T becomes negative. This indicates that the readings of the the FBG temperature sensor are higher than those of the surface. The largest error is about −11.1 °C FBG ˝ Cbetween surface temperature exceeds 66 °C, the error becomes negative. indicates that the readings of temperature sensor are than those ofthe theΔT surface. The largest error isThe about ´11.1 (percentage (percentage error is higher about −12.2%) when surface temperature isThis 91 °C. relationship ˝ the FBG temperature sensor are higher than those of the surface. The largest error is about −11.1 °C error ΔT and surface can be fitted as errorthe is about ´12.2%) whentemperature the surfaceT1temperature is follows: 91 C. The relationship between the error ∆T (percentage error is about −12.2%) when the surface temperature is 91 °C. The relationship between and surface temperature T1 can befitted as follows: 2 T  0.00498T  0.36903T  2.27916 1 the error ΔT and surface temperature T1 can be1fitted as follows:

∆T

“ ´0.00498T122` 0.36903T1 ´ 2.27916 T  0.00498T  0.36903T  2.27916 1

1

(11)

(11)

(11)

Figure 11. Surface temperature measurement errors of sensor with the double-ended fixation. Figure 11. Surface temperature measurement errors of sensor with the double-ended fixation. Figure 11. Surface temperature measurement errors of sensor with the double-ended fixation.

This abnormal phenomenon may be due to two effects. One is the previous “gradient effect”. The bare FBG is also influenced by the gradient of temperature on the surface in the double-ended fixation. Another effect is caused by the substrate expansion. The FBG sensor is fixed at two ends of the Bragg grating. It cannot freely stretch. The coefficient of linear thermal expansion of the substrate (red copper) is much greater than that of fiber (SiO2 ). When the temperature rises, the FBG expands together with the expansion of substrate. The remarkable substrate-induced expansion of the FBG

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This abnormal phenomenon may be due to two effects. One is the previous “gradient effect”. The bare FBG is also influenced by the gradient of temperature on the surface in the double-ended fixation. Another effect is caused by the substrate expansion. The FBG sensor is fixed at two ends of Sensors 2016, 16, 975 10 of 12 the Bragg grating. It cannot freely stretch. The coefficient of linear thermal expansion of the substrate (red copper) is much greater than that of fiber (SiO2). When the temperature rises, the FBG expands together with the expansion of substrate. substrate-induced of induced the FBG causes the increase of FBG sensor readingsThe T2 remarkable and counteracts the decline of expansion the readings causes the increase of FBG sensor readings andphenomena counteractsas thethe decline of the effect” readings induced by by the temperature gradient effect. We callT2the “substrate which is also the temperature gradient effect. We call the phenomena as the “substrate effect” which is also determined by Equation (4). Thus, the thermal strain effect of the substrate will change the temperature determined byand Equation Thus, the results thermalforstrain effect of thefixation. substrate will change gradient effect disturb(4). measurement the double-ended It is harmful to the temperature gradient and disturb measurement results strain for theindouble-ended fixation. It is measurement of surfaceeffect temperature. In addition, the mechanical the substrate also influences harmful to the measurement of surface temperature. In addition, the mechanical strain in the measurement results. substrate also influences measurement results. For the fully-adhered fixation, the measurement error of the sensor increases, and then decreases For the fully-adhered fixation, the measurement error of the sensor increases, and thenerror decreases as the surface temperature increases in Figure 12. The fluctuation of the measurement is no ˝ ˝ as thethan surface increases in Figure fluctuation of the measurement error is no more 2 Ctemperature (percentage error is about 3%) in 12. the The temperature range of 35~95 C. The relationship more than 2 °C (percentage error is about 3%) in the of 35~95 °C. The relationship between the error ∆T and the surface temperature T1temperature can be fittedrange as follows: between the error ΔT and the surface temperature T1 can be fitted as follows: ∆T “ ´0.0024T122 ` 0.3011T1 ´ 7.54728 (12) T  0.0024T1  0.3011T1  7.54728 (12)

Figure 12. Surface measurement errors errors of of sensor sensor with with the the full full fixation. fixation. Figure 12. Surface temperature temperature measurement

The measurement errors of the sensor with the full fixation are similar in the change trends to The measurement errors of the sensor with the full fixation are similar in the change trends to that that with double-ended fixation. However, the measurement error of the sensor with the fullywith double-ended fixation. However, the measurement error of the sensor with the fully-adhered adhered fixation is smaller than that with double-ended fixation. This may be due to the adhesive fixation is smaller than that with double-ended fixation. This may be due to the adhesive effect. effect. The adhesive layer has two functions. Firstly, the adhesive layer increases the thickness of the The adhesive layer has two functions. Firstly, the adhesive layer increases the thickness of the conducting heat layer between the fiber core and the environment and thermal resistance, thus conducting heat layer between the fiber core and the environment and thermal resistance, thus reducing reducing the gradient of the temperature between the fiber core and the surface of the substrate. It the gradient of the temperature between the fiber core and the surface of the substrate. It works as works as a jacket on the fiber to prevent the thermal dissipation. The gradient effect is restrained and a jacket on the fiber to prevent the thermal dissipation. The gradient effect is restrained and the the measurement error reduces. Secondly, the thickness of the adhesive layer is about 2~3 mm and measurement error reduces. Secondly, the thickness of the adhesive layer is about 2~3 mm and thicker thicker than the substrate (1 mm red copper). The rigidity of the adhesive layer is close to that of the than the substrate (1 mm red copper). The rigidity of the adhesive layer is close to that of the substrate. substrate. The thermal expansion of the substrate will be restrained by the adhesive layer on it. The thermal expansion of the substrate will be restrained by the adhesive layer on it. Therefore, the Therefore, the substrate effect is restrained and the measurement error is also reduced. Both of the substrate effect is restrained and the measurement error is also reduced. Both of the effects bring about effects bring about a great decline in the measurement error. Finally, it shows about 2 °C error in the a great decline in the measurement error. Finally, it shows about 2 ˝ C error in the range of 35–95 ˝ C. range of 35–95 °C. The sensor with the fully-adhered fixation shows little error in this experiment, The sensor with the fully-adhered fixation shows little error in this experiment, however, one must pay however, one must pay attention to the measurement condition in practice. The measurement error attention to the measurement condition in practice. The measurement error will change as the material will change as the material and the dimension of substrate, and the stress in the substrate, change. and the dimension of substrate, and the stress in the substrate, change. Particularly, the stress-induced Particularly, the stress-induced change of the Bragg wavelength is much larger than that induced by change of the Bragg wavelength is much larger than that induced by temperature in some machine parts. Therefore, the installation method, fully-adhered fixation, is only available in the measuring object whose temperature is close to the surroundings temperature and in which there is no stress.

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5. Conclusions The ambient temperature and installation types of FBG sensors are an easily overlooked issue. However, they greatly influence equipment surface temperature measurement results. High-accuracy surface temperature measurement is a challenging task. In order to reveal error sources, a theoretical analysis, a thermal transfer model of the FBG, and a calibration system of the surface temperature measurement error system are proposed. The measurement errors of the FBG temperature sensor with three different fixation types are tested. Experimental results show that two effects influence measurement results. The gradient effect results in an increasing linear error and the substrate effect results in a decreasing non-linear error with increasing surface temperature. The measurement error of the FBG sensor with single-ended fixation is determined by the gradient effect and is a linear error which is not affected by the substrate strain and is good for the compensation process. The measurement error of the FBG sensor with double-ended fixation is determined by the two effects and the substrate effect is dominant. Thus, the measured reading is higher than the real surface temperature. The measurement error of the FBG sensor with fully-adhered fixation is similar to that with double-ended fixation. However the adhesive layer can reduce the two effects and the measurement error in 35–95 ˝ C is smallest, thus, it is used widely in surface temperature measurement. However, it is not available in the measurement whose measured object is affected by substrate strain. Sometimes the strain effect will exceed the change of the Bragg wavelength induced by temperature. Therefore, the single-ended fixation, which has the strain-resistant ability and the stable linear error, will play an important role in the FBG sensor encapsulation design field in the near future. Acknowledgments: This work is 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), the Natural Science Foundation of Hubei Province, China (Grant No.2014CFB830) and the International Postdoctoral Exchange Fellowship Program from China Postdoctoral Council. Author Contributions: Yi Liu finished theoretical analysis, designed the experiments and wrote the manuscript. Jun Zhang performed the experiments and interpreted the data. All authors have read and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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