sensors Article
Strain-Independent Temperature Measurements with Surface-Glued Polarization-Maintaining Fiber Bragg Grating Sensor Elements Barbara Hopf 1, * , Bennet Fischer 1,† , Thomas Bosselmann 2 , Alexander W. Koch 3 and Johannes Roths 1 1 2 3
* †
Munich University of Applied Sciences, Photonics Laboratory, D-80335 Munich, Germany;
[email protected] (B.F.);
[email protected] (J.R.) Siemens AG, Corporate Technology, CT RDA SII SSI-DE, D-91058 Erlangen, Germany;
[email protected] Technical University of Munich, Institute for Measurement Systems and Sensor Technology, D-80290 Munich, Germany;
[email protected] Correspondence:
[email protected]; Tel.: +49-89-1265-3654 Currently with: INRS-EMT, Nonlinear Photonics Group, Varennes, QC J3X 1S2, Canada.
Received: 19 November 2018; Accepted: 27 December 2018; Published: 3 January 2019
Abstract: A novel technique for strain and temperature decoupling with surface-glued fiber Bragg gratings (FBGs) is presented and applied for strain-independent temperature measurements in a temperature range between −30 ◦ C and 110 ◦ C with uncertainties below 4 ◦ C over the entire measurement range. The influence of temperature-dependent glue-induced transversal forces on the fiber sensor could be eliminated with a sensor element consisting of two FBGs in identical polarization-maintaining fibers that were spliced perpendicular to each other. After aligning and gluing the sensor element with its optical axes parallel and perpendicular to the specimen, the averaged Bragg wavelength shifts of both FBGs were proven to be independent of the glue’s influence and therefore independent of any change in the material characteristics of the glue, such as aging or creeping behavior. For the first time, this methodology enables temperature measurements with surface-attached bare FBGs independently of arbitrary longitudinal and glue-induced strains. This is of great value for all applications that rely on a fully glued sensor design, e.g., in applications with high electromagnetic fields, on rotating parts, or in vacuum for space applications. Keywords: fiber optic temperature sensing; surface-attached Fiber Bragg gratings; glue-induced stress; multi-parameter measurements
1. Introduction Fiber optical temperature sensing with fiber Bragg gratings (FBGs) have gained growing importance in many industrial applications, such as temperature monitoring and temperature control of critical components [1]. Due to their advantages, such as insensitivity to high electromagnetic fields, gamma radiation, and most chemicals, a small size, and multiplexing capability, they are highly valued to replace common electrical sensors, such as thermocouples, or to enable temperature measurements in applications with harsh environmental conditions as they occur, e.g., in energy production or distribution facilities [2–7] or in space applications [8,9]. For measuring temperatures, FBGs are commonly used within a loose-tube packaging, where the FBGs are shielded from mechanical stress by a protecting capillary. Some applications, however, rely on surface-attached FBG sensing elements, which have to be glued over their entire length, especially if an air gap between the fiber and the surrounding capillary would cause severe problems. This includes all applications within high Sensors 2019, 19, 144; doi:10.3390/s19010144
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electromagnetic fields, where any gap would lead to spark discharges (e.g., hot spot detection and temperature control on the surface of the stator windings of high power generators [2]), for measuring component temperatures in vacuum, where the heat transfer from the specimen to the fiber is not sufficient (e.g., satellites in space applications [9]), or on quickly rotating components with high centrifugal forces or vibrations (e.g., monitoring of temperature distributions on turbine plates of gas turbines in power plants). The challenges in temperature sensing with surface-glued or embedded FBG elements result from the fact that FBGs are not only sensitive to temperature but also to axial and transversal strains. If the sensor element is attached to the surface of a specimen, the FBG will therefore respond to any strain on the specimen that is caused by temperature changes or by additional external mechanical loads. Without knowledge of the exact strength of these strains, the corresponding temperature will be estimated wrongly. Therefore, FBG-based multi-parameter measurement systems, which are capable of determining temperature and strain simultaneously, are essential in these applications. Several embodiments have already been presented by different researchers [10,11], relying on the evaluation of the signals of two FBGs with different sensitivities to strain and temperature, which were located near to each other. Commonly, the fiber has been fixed at two points near the FBG-sensor elements to ensure strain transfer from the specimen to the fiber, while the sensor element itself is spared from glue. The relationship between the sensor signals (usually the Bragg wavelengths of both FBGs) and the two measurands (temperature and strain) was given by a linear system of equations expressed by a sensitivity matrix [10]. Gluing the FBG over its entire sensor length adds several challenges to the task, as the glue induces significant temperature-dependent transversal forces to the fiber, mostly because of a mismatch in the coefficients of thermal expansions (CTE) of the fiber, glue, and specimen [12,13]. These glue-induced forces alter the FBG’s sensor response, especially during temperature changes, and have to be considered in temperature measurements with surface-attached FBG elements [13,14]. This is aggravated by the fact that the used glue has to assure full strain transfer in a wide thermal range, e.g., between −40 ◦ C and 150 ◦ C, which requires the use of a glue with a high glass transition temperature. Thermally cured epoxy resins have been shown to fulfill this requirement, but tend to induce high values of glue-induced birefringence, especially at low temperatures [13]. Additionally, temperature-dependent creeping behavior and stress-relaxation have been observed in thermally cured epoxy resin [15,16]. Due to the relaxation characteristics of the adhesive, the amount of glue-induced stress and its influence on the FBG sensor signal varies not only with temperature but also with time, leading to a hysteresis behavior of surface-glued FBGs during temperature cycles [13]. Moreover, epoxy resins are prone to absorb humidity up to 6% of their mass, causing a swelling of the glue depending on their chemical composition, the exposure time, and the concentration [17,18]. This volume change would also lead to glue-induced stress in the fiber core, adding to the thermal-induced stress, again leading to time-dependent glue-induced wavelength shifts and therefore uncertainties in the measurement. The solution to overcome this problem would be using a multi-parameter measurement system consisting of four FBG sensor signals with different sensitivities to temperature and the longitudinal and two transversal normal strains in the fiber. In this case, the corresponding sensitivity matrix would consist of 16 independent matrix elements [19]. Azimuthally aligned FBGs in polarization-maintaining fibers (PM-FBGs) have been proposed for measuring transversal line forces along the optical fiber axis [20]. To determine three-axial normal strains plus temperature, PM-FBGs have been combined with another technique for temperature and axial strain decoupling, such as the dual wavelength method [19,21]. Two superimposed PM-FBGs with different grating periods [19,21], for example, led to a set of four spectral peaks with slightly different sensitivities. Since their sensitivities are nearly similar, the corresponding matrix is not well-conditioned, and all work presented so far reduced the evaluated set of parameters to three in order to reduce uncertainties in the measurement, e.g., to three normal strains at isothermal temperatures [19]. The work of Abe [21] excluded one of the two transversal
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loads and measured longitudinal strain and transversal strain in direction of the fibers’ fast axis for measurement at two temperatures, 15 ◦ C and 45 ◦ C, which still is a very limited temperature range. The uncertainties in the temperature measurement were 10 ◦ C. Therefore, until now, a satisfying temperature measurement technique with surface-glued fibers has not been available. Here, we present a new approach using surface-attached PM-FBG elements for temperature measurements in the presence of arbitrary longitudinal external strains, which is additionally capable of compensating for glue-induced transversal forces independently of their strengths. The concept is based on decoupling temperature and strain by using the signals of the slow and the fast axes of two PM-FBGs. A second PM-FBG in the same type of fiber, which is spliced with its slow axis aligned to the fast axis of the first fiber, is used for transversal strain compensation. Orientating the optical axes (slow and fast axis) of the fiber parallel and perpendicular to the surface of the specimen ensures that the mechanical normal strains act only in the directions of the optical fiber axes. This investigation shows that for the slow and fast fiber axes, respectively, the averaged Bragg wavelengths of both FBGs were almost independent of the glue’s influence. The multi-parameter problem can therefore be reduced to two influencing variables—temperature and longitudinal strain—and the sensitivity matrix to four independent matrix elements. Nonlinearities in the temperature characteristics of FBGs are commonly known, and have also to be integrated in the evaluation process by introducing temperature-dependent matrix elements in the sensitivity matrix. The determination of strain and temperature is performed iteratively with the method presented in [22]. For the first time, to our knowledge, the here-presented technique enables temperature measurements with surface-glued FBGs independently of external Sensors 2018, 18,strains. x FOR PEER REVIEW 4 of 14 longitudinal glue 2. Theory: Surface-Attached FBGs for Temperature orientation given by j ∈{0°, 90 be expressedSensing as a sum of the glue-induced changes Δλi , j °} ), may th
PM-FBG sensor element (FBG consistscaused of two FBGs with differentΔBragg wavelengths λi, j and due The to transversal forces adding totandem) the changes by temperature external located at each side of a mech splice joint between standard Panda fibers (PM1550-XP, Nufern, East Granby, Δλi ,ofj one . In a simplified approach, the glue-induced transversal forces be longitudinal CT, USA). Thestrain slow axis fiber was aligned perpendicular to the slow axis of the other. Thiscan “FBG describedisasglued external line forces along the optical fiber axis, summarized tandem” withtemperature-dependent the optical fiber axes parallel and perpendicular to the surface, as depicted in Figure 1. The slow axis 1 isdue aligned to behavior the surface in the absorption direction ofofx1adhesives, , referred to as fglue (Δ T , tof ) , FBG a parameter which, to theparallel creeping or water also ◦ the 0◦ -orientation (j = 0 ), while the slow axis of FBG 2 is aligned in the direction of x2 , referred to depend on time. Therefore, their strength varies constantly leading to unknown wavelength changes ◦ ◦ as the glue90 -orientation (j = 90 ). This assures that all glue-induced normal strains in the fiber core act Δλi, jin direction that cannot be predicted in a real-world application and that, therefore, have to be only of the slow and fast axis. Shear strains in the fiber core and therefore mode coupling compensated for polarizations in the sensor evaluation in order avoid considerations. uncertainties in the measurement. between the two may be neglected into further
Figure fiber Bragg Figure 1. 1. A A surface-attached surface-attached polarization-maintaining polarization-maintaining fiber Bragg grating grating (PM-FBG) (PM-FBG) tandem tandem sensor sensor element for strain-decoupled temperature measurements: The sensor tandem consists element for strain-decoupled temperature measurements: The sensor tandem consists of of aa splice splice of of aa Panda fiber with its slow axis aligned perpendicular to the slow axis of the second fiber. Two FBGs Panda fiber with its slow axis aligned perpendicular to the slow axis of the second fiber. Two FBGs were were inscribed inscribed at at either either side side of of the the splicing splicing joint. joint. The The sensor sensor tandem tandem is is azimuthally azimuthally aligned aligned with with the the slow and fast axis parallel and perpendicular to the surface and glued along the whole length slow and fast axis parallel and perpendicular to the surface and glued along the whole length of of the the sensor sensor element element to to the the specimen. specimen.
In general, the spectrum of a PM-FBG is characterized by two Bragg peaks, for light polarized in Assuming linear dependency, the total change of Bragg wavelength is given in the form the direction of the fast and the slow fiber axis, respectively. The corresponding Bragg wavelengths are given by λi = 2neff,i f }, (indicating values originating from the fast and slow axis of ΔλΛi , j(with = K figlue∈,i{, js,f glue ΔT , t ) + Kthe T ,i , j + α sub K ε 3 ,i , j ΔT + K ε 3 ,i , j ε 3 , (2)
(
)
KTgl, i , j
where KT ,i, j and Kε3 ,i , j are the temperature and strain sensitivities of the unglued PM-FBGs, respectively, and
α sub is the CTE of the substrate material. Assuming full strain transfer from the
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the FBG). Here, neff,i is the effective refractive index and Λ is the grating period, both depending on temperature and strain. This leads to changes of the Bragg wavelengths, as given by [23] n ε + ε + ε , p ε + p ∆λs = λ0 (ξ + α)∆T − eff,s,0 s 3 3 11 12 f 2 neff, f ,0 ∆λ f = λ0 (ξ + α)∆T − 2 p11 ε f + p12 (ε 3 + ε s ) + ε 3 ,
(1)
where ξ describes the thermal optical coefficient, p11 and p12 the Pockel’s coefficients, and α the coefficient of thermal expansion (CTE) of the fiber; ε i (with i ∈ { f , s, 3}) are the normal strains in the fiber’s core in the directions of the fast, slow, and longitudinal fiber axes; and neff,i,0 (with i ∈ { f , s}) are the effective refractive indices in the slow and the fast axis without strains. glue mech The shift of Bragg wavelengths of the surface-glued sensor, ∆λi,j = ∆λi,j + ∆λth i,j + ∆λi,j ◦ (with i ∈ { f , s}, indicating the values from the fast and slow axis of the FBG in the 0 - and ◦ ◦ 90◦ -orientation given by j ∈ 0 , 90 ), may be expressed as a sum of the glue-induced changes glue
∆λi,j
due to transversal forces adding to the changes caused by temperature ∆λth i,j and external
longitudinal strain ∆λmech . In a simplified approach, the glue-induced transversal forces can be i,j described as external temperature-dependent line forces along the optical fiber axis, summarized in a parameter f glue (∆T, t), which, due to the creeping behavior or water absorption of adhesives, also depend on time. Therefore, their strength varies constantly leading to unknown wavelength glue changes ∆λi,j that cannot be predicted in a real-world application and that, therefore, have to be compensated for in the sensor evaluation in order to avoid uncertainties in the measurement. Assuming linear dependency, the total change of Bragg wavelength is given in the form ∆λi,j = K fglue ,i,j f glue (∆T, t) + KT,i,j + αsub Kε 3 ,i,j ∆T + Kε 3 ,i,j ε 3 , | {z }
(2)
gl
KT,i,j
where KT,i,j and Kε 3 ,i,j are the temperature and strain sensitivities of the unglued PM-FBGs, respectively, and αsub is the CTE of the substrate material. Assuming full strain transfer from the substrate to the gl fiber, the temperature sensitivity of the glued fiber is given by KT,i,j = KT,i,j + αsub Kε 3 ,i,j . Additionally, K fglue ,i,j expresses the influence of the glue-induced line forces to the FBG during temperature changes. Finding sensor signals, which are independent of glue-induced transversal stresses, is a main precondition for utilizing surface-attached PM-FBGs in strain and temperature decoupling. Earlier experimental evaluation with surface-attached PM-FBGs [24] indicated that the glue-induced changes glue ∆λi,j are much stronger in the slow axis compared to the fast axis, but run counter in both FBG-orientations with K fglue ,i,0◦ ≈ −K fglue ,i,90◦ (with i ∈ { f , s}). Therefore, the mean value of the Bragg wavelength changes in the slow and fast axis of both sensors ∆λi = 0.5 ∆λi,0◦ + ∆λi,90◦ with i ∈ { f , s} are supposed to be nearly independent of the glue’s influence, as was confirmed by the three-dimensional finite element method (3D-FEM) simulations shown in Section 2. The changes of the mean wavelength of both FBG ∆λi to strain and temperature are almost independent of the glue and given by gl (3) ∆λi ∼ = K ∆T + K ε ,i ε 3 . T,i
3
The equation system for strain and temperature decoupling may therefore be expressed by means of the sensitivity matrix in the form ∆λ f ∆λs
gl
!
=
K T, f gl
K T,s
Kε3 , f K ε 3 ,s
!
∆T ε3
! .
(4)
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gl ε ,i gl gl Here, K T,i = 0.5 KT,i,0◦ + KT,i,90◦ and K 3 = 0.5 Kε 3 ,i,0◦ + Kε 3 ,i,90◦ are the mean temperature and strain sensitivity constants of the two FBGs in the surface-attached FBG tandem. Temperature and strain values are evaluated by using the inverted matrix in the form !
∆T ε3 gl
1 = D
K ε 3 ,s
−K ε 3 , f
−K T,s
K T, f
gl
!
gl
∆λ f ∆λs
! (5)
gl
with D = K ε 3 , f K T,s − K T, f K ε 3 ,s indicating the determinant of the sensitivity matrix. Assuming a linear change in the Bragg wavelength with temperature is only valid in a small temperature range. In the extended temperature range between −40 ◦ C and 150 ◦ C, the change in Bragg wavelength is commonly expressed with a 3rd order polynomial function [22,25]. Using this approach, the mean wavelength can be written as ∆λi
3 =a T,i ∆T + a T2 ,i ∆T 2 + a T3 ,i ∆T = a T,i + a T2 ,i ∆T + a T3 ,i ∆T 2 ∆T. | {z }
(6)
gl
K T,i (∆T )
This would lead to systematic errors in temperature sensing if this nonlinearity was neglected in a large temperature range. The nonlinear sensor characteristic may be taken into account by replacing the constant matrix elements in the sensitivity matrix with temperature-dependent sensitivity constants gl
K T,i (∆T ) and using the iterative calculation method introduced in [22]. Starting with the sensitivity values for a reference temperature T0 , the temperature values of the previous iteration step ∆T k−1 and gl
the corresponding sensitivity values K T,i (∆T )k−1 are used to calculate new temperature values ∆T k according to ∆T k εk3
!
=
1 D (∆T )k−1
K ε 3 ,s
gl
−K T,s (∆T )k−1
−K ε 3 , f
gl
K T, f (∆T )k−1
!
∆λ f ∆λs
! (7)
with the temperature-dependent determinant of the sensitivity matrix given by D (∆T )k−1 = gl
gl
K ε 3 , f ·K T,s (∆T )k−1 − K ε 3 ,s ·K T, f (∆T ). The iteration process is continued until the difference of the actual temperature and that of the previous iteration step drops below a certain predefined threshold value, e.g., of 0.1 ◦ C, which is normally the case after about five iteration steps. 3. Simulation: Determination of Glue-Independent FBG Signals As discussed in the previous section, finding appropriate glue-independent sensor outputs for temperature and strain decoupling was a primary task. Therefore, the glue’s influence on the sensor signal was evaluated in detail with a three-dimensional mechanical finite element method (FEM) model capable of determining the full stress tensor at every node in the model of a glued PM fiber for different temperatures. In the model, the PM fiber with core, cladding, and stress-applying parts (SAPs), the gluing joints, and the aluminum specimen on which the fiber was glued were taken into account (see Figure 2a,b). The simulated thermally induced local stress values were used to analytically calculate the resulting changes of the refractive index caused by the elasto-optical effect. These local changes in the refractive index were added to the former values of the refractive index at the reference temperature [24].
sim sim sim Δneff ,i , j (ΔT , ε 3 ) = neff ,i , j (ΔT , ε 3 ) − neff ,0 (with i ∈{s, f } and j ∈{90°, 0°} )
is the simulated
change in the effective refractive index, given as the difference of the effective refractive index after sim
temperatureSensors changes 2019, 19,and 144 the initial refractive index neff ,0 of the stress-free model.
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Figure 2. The used mesh and gluing joints for the mechanical three-dimensional finite element method Figure 2. The used mesh and gluing joints for the mechanical three-dimensional finite element (3D-FEM) simulation: (a) An overview of the aluminum specimen, glue, and PM fiber; (b) A detailed method (3D-FEM) simulation: (a) gluing An overview of theshow aluminum specimen, glue,ofand PM fiber; (b) A view of the geometry of the joints. The insets the metallurgic cross-sections the glued PM-FBG after curing at 150 C forgluing one hour.joints. The insets show the metallurgic cross-sections of detailed view of the geometry of ◦the the glued PM-FBG after curing at 150 °C for one hour. The transfer to the effective refractive index of the fiber ∆nsim (∆T, ε ), a quantity that is directly 3
eff,i,j
connected to the Bragg wavelength of the FBG, was achieved by using a two-dimensional mode solver on the fiber’sdescribes cross-section thefiber middle of the on fiber.an The resulting simulated change in thein Bragg The FEM model a in PM glued aluminum specimen 5 mm height, 10 mm sim was determined analytically by using the dependency [24] wavelength ∆λ width, and 20 mm ini,jlength, with a symmetry plane at one end and a free surface at the other as
in pictured in Figure 2a. The geometry of the gluing∆njoints pictured in!Figure 2b was taken according to sim ( ∆T, ε3) eff,i,j sim sim + ξ ∆T . (8) ∆λi,j = λ0 cross-sections ε3 + the geometries observed in metallurgic neff,0 (see Figure 2b inset) after gluing with an isothermal curing process at 150 °C. A spline plot through three characteristic points (red dots in Here,glue’s εsim =surface εmech + was εth thedefine simulated in the x3 -direction theFEM centermodel. The 3 describes 3 3 Figure 2b) on the used to thestrain glue’s geometry in atthe of the fiber’s cross section, to which both the thermal strain εth and the external strain εmech 3 3 ◦ − material properties of the glue (EP353, Epoxy Technology Inc., Billerica, MA, USA), 1 − 6 sim contribute. ξ = 6.36·10 C is the thermo-optical coefficient of the fiber [22] and ∆neff,i,j (∆T, ε 3 ) = which are ◦ ◦ sim ratio, and CTE, were taken Young’s modulus, Poisson’s from manufacturer data sheets [26,27]. The nsim eff,i,j ( ∆T, ε 3 ) − neff,0 (with i ∈ { s, f } and j ∈ 90 , 0 ) is the simulated change in the effective refractive index, parameters given as the difference the effective index cladding after temperature geometry and material of theof fiber core,refractive SAP, and werechanges takenand according to the initial refractive index nsim of the stress-free model. eff,0 previous works [24]. All used material properties are summarized in Table 1. The simulation was The FEM model describes a PM fiber glued on an aluminum specimen 5 mm in height, 10 mm performed for six steps 110 with °C and −40 °Cplane withataone step 30surface °C. at the other as in width, and 20between mm in length, a symmetry endsize and aof free pictured in Figure 2a. The geometry of the gluing joints pictured in Figure 2b was taken according to the geometries metallurgic cross-sections (see Figureand 2b inset) after gluing with an Table 1. Theobserved MaterialinParameters used for mechanical optical simulation. ◦ isothermal curing process at 150 C. A spline plot through three characteristic points (red dots in Figure 2b) on the glue’s surface was used to define the glue’s geometryCTE in the FEM model. The material ) Young’s Modulus ( Poisson’s Ratio Sectionproperties Refractive Index GPa − 6 which of the glue (EP353, Epoxy Technology Inc., Billerica, MA, USA), ( ⋅10 °C −1 ) are Young’s modulus, Poisson’s ratio, and CTE, were taken from manufacturer data sheets [26,27]. The geometry and material Glue 3 0.33 54 parameters of the fiber core, SAP, and cladding were taken according to previous works [24]. All used Fiber cladding 0.16 0.54 material properties are72 summarized in Table 1. The simulation was performed for six 1.444023 steps between ◦ ◦ ◦ Fiber core 71a step size of 30 C. 0.16 0.95 1.449423 110 C and −40 C with
SAP
42
0.20
2.38
Table 1. The Material Parameters used for mechanical and optical simulation.
1.444023
SAP, stress-applying part; CTE, coefficient of thermal expansion. Section
Young’s Modulus (GPa)
Poisson’s Ratio
CTE (·10−6 ◦ C−1 )
Refractive Index
Lit.
Glue Fiber cladding Fiber core SAP
3 72 71 42
0.33 0.16 0.16 0.20
54 0.54 0.95 2.38
1.444023 1.449423 1.444023
[26,27] [24] [24] [24]
SAP, stress-applying part; CTE, coefficient of thermal expansion.
Additionally, it was assumed that significant glue-induced forces occur only below 110 ◦ C, which is the beginning of the glue’s glass transition range [13,28]. Therefore, all Bragg wavelength
Lit. [26,27] [24] [24] [24]
shifts Δλi
for the fast and slow axis of an FBG, which is not exposed to any transversal glue-
induced stress while the (thermal) strain is fully transferred from the aluminum specimen to the fiber during temperature changes. A similar fiber model but without glue and the aluminum specimen was appliedSensors for2019, this purpose, in which the front cross-section of the fiber was deflected to strain 19, 144 7 of 14 values of ε 3 = α Alu ΔT at every simulated temperature. This displacement is equivalent to the thermal strain induced by the aluminum changes were calculated with respect tospecimen. the reference temperature of 110 ◦ C, at which the model was glue = Δλisim − Δλitheor is given by the difference , j A second simulation was used to estimate the expected temperature-dependent wavelength shifts sim transversal glue-induced ∆λtheor for the fast and slow axis of an FBG, which is not exposed to i between the change in Bragg wavelength of the glued fiber Δλi , janyto the simulated values without stress while the (thermal) strain is fully transferred from the aluminum specimen to the fiber during theor A similar fiber model but without glue and the aluminum specimen was temperature changes. , and is plotted in Figure 3 for both fiber orientations ( j ∈{0°, 90°} ) and glue-induced stress Δλi applied for this purpose, in which the front cross-section of the fiber was deflected to strain values of i ∈ { s , f } ). Triangles mark the This values of the fast axis, while both fiber axes ( ε 3 = αAlu ∆T at every simulated temperature. displacement is equivalent to the circles thermal mark strain the values by the aluminum specimen. of the slowinduced axis. The values of the FBG in the 0°-orientation aretheor plotted in blue, the values of the glue The glue-induced Bragg wavelength shift ∆λi,j = ∆λsim − ∆λ is given by the difference i,j i considered to be stress-free. The glue-induced Bragg wavelength shift Δλi , j
sensor in the 90°-orientation in green. The glue-induced wavelength shifts increase with decreasing between the change in Bragg wavelength of the glued fiber ∆λsim i,j to the simulated values without ◦ ◦ temperatureglue-induced due to increasing glue-induced stress on the fiber. This effect is significantly higher in stress ∆λtheor , and is plotted in Figure 3 for both fiber orientations (j ∈ 0 , 90 ) and i the slow axis compared axis mark in both fiber oforientations. Forcircles the fast for the both fiber axes (i to ∈ {the s, f }).fast Triangles the values the fast axis, while markand the values of slow axes, ◦ -orientation are plotted in blue, the values of the sensor in the slow axis. The values of the FBG in the 0 these deviations are nearly of the same value for both orientations but with the opposite sign. Figure the 90◦ -orientation in green. The glue-induced wavelength shifts increase temperature glue sim with decreasing theor
λi effect=isΔsignificantly λi − Δλhigher 4 shows thedue glue-induced Bragg wavelength shift for averaged values to increasing glue-induced stress on the fiber. Δ This in thethe slow axis i compared to thefor fastthe axis fast in both fiber orientations. Forslow the fast and for the slow these deviations of both FBGs (triangles and circles for the axis), which is axes, supposed to be almost zero. are nearly of the same value for both orientations but with the opposite sign. Figure 4 shows the For the fast axis, the maximal value of glue the glue-induced Bragg wavelength shift at −30 °C is sim theor glue-induced Bragg wavelength shift ∆λi glue
= ∆λi
− ∆λi for the averaged values of both FBGs glue
for thefrom fast andΔ circles almost For theaxis fast and from Δλsis supposed = 9 pmto befor λ90°,sfor=the 54slow pmaxis), significantly(triangles reduced to which thezero.slow
axis, the maximal value of the glue-induced Bragg wavelength shift at −30 ◦ C is significantly reduced glue glue to◦ =Δ54 thethefast Therefore, mean of the Bragg = 13from pm∆λglue λ fglue 2 glue pm= 9for pm to=∆λ pm for slowaxis. axis and from ∆λ90◦ , f the = 13 pm to ∆λvalues = 2 pm s f 90 ,s the fast axis. Therefore, the mean values of the Bragg wavelength changes of both changes can be wavelengthforchanges of both changes can be regarded as nearly independent of the glue-induced regarded as nearly independent of the glue-induced stress for both the signals of the fast and the slow stress for both signals of the fast and the slow axis, respectively. axis,the respectively. glue Δλ90 °, f
Figure 3. Simulated temperature-dependent deviation of the Bragg wavelength changes of the glued
Figure 3. Simulated temperature-dependent deviation of the Bragg wavelength◦ changes of the glued fiber and the theoretical transversal load-free FBG: Green are the values of the FBG in the 90 -orientation, fiber and the transversal load-free areofthe values bluetheoretical of the FBG in the 0◦ -orientation, triangles ofFBG: the fastGreen and circles the slow axis. of the FBG in the 90°orientation, blue of the FBG in the 0°-orientation, triangles of the fast and circles of the slow axis.
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Figure 4. Glue-induced deviations of the mean values of the Bragg wavelength changes to the theoretical
Figure 4. Glue-induced deviations of thevalues meanofvalues ofaxis theand Bragg wavelength changes to Figure 4. Glue-induced deviations of the mean values of fast the Bragg wavelength changes tothe the theoretical transversal stress-free FBG: Triangles mark the circles of the slow axis. theoretical transversal stress-free FBG: Triangles mark values of the fast axis and circles of the slow axis. transversal stress-free FBG: Triangles mark values of the fast axis and circles of the slow axis.
4. Experimental: Experimental: Surface-Attached Surface-Attached Sensor Sensor Tandem Tandem 4.
The capability of of the the above-described above-described method in in discriminating discriminating strain strain and and temperature temperature was was 4. Experimental: Surface-Attached Sensor Tandem The capability method
investigated experimentally experimentally with with an an uncoated uncoated surface-glued surface-glued PM PM tandem, tandem, which which was was attached attached to to the the investigated 0 με and surface of of aaof spring steel bending beam. beam. This setup to between The capability thesteel above-described method indesigned discriminating strain and0 temperature was surface spring bending This setup was was designed to apply apply strain strain between µε and 760 με to the fiber and could be used at different temperatures in a climatic chamber. µε to the fiber and with could be at different temperatures in PM a climatic chamber. investigated760experimentally anused uncoated surface-glued tandem, which was attached to the Figure 5 shows schematically. The FBG tandem consists of two FBGsFBGs near Figure shows the theused usedsensor sensordesign design schematically. The FBG tandem consists of two 0 με and surface of a spring steel bending beam. This setup was designed to apply strain between a splice in commercial Panda fibers (PM1550-XP, Nufern, EastEast Granby, CT, CT, USA). At the splice, the near a splice in commercial Panda fibers (PM1550-XP, Nufern, Granby, USA). At the splice, 760 με to the fiber and could be used at different temperatures inofofathe climatic chamber. slow axisaxis of the one fiber was aligned perpendicular totothe other splicing the slow of the one fiber was aligned perpendicular theslow slowaxis axis the other fiber. The splicing processwas was performed performed with with aa filament filament splicing unit (LFS4100, Thorlabs Vytran Europe, Exeter, Exeter, GBR) process Figure 5 shows the used sensor design schematically. The FBG tandem consists of two FBGs near which is is capable capable of of visually visually aligning aligning the the fibers fibers before before splicing, splicing, by by capturing capturing the the cleaved cleaved fiber fiber ends ends which a splice in commercial fibersremoval (PM1550-XP, Nufern, Granby, At the splice, the with aa camera. camera.Panda necessary the coating coating for the theEast splicing processCT, lead USA). to an an uncoated uncoated with The necessary of the for splicing process lead to sensor element ofabout about cm in in length. length. An FBG FBG was was inscribed inscribed in mmaxis distance on each each sidefiber. (gratingThe splicing element of cm An 55 mm distance on side (grating slow axis ofsensor the one fiber was44aligned perpendicular to thein slow of the other lengths 3 mm) of the splice, using our in-house inscription setup with a UV-laser and phase mask lengths 3 mm) of the splice, using our in-house inscription setup with a UV-laser and phase mask process was performed with a filament splicing unit (LFS4100, Thorlabs Vytran Europe, Exeter, GBR) technique. To To assure assure FBG FBGwavelength wavelength multiplexing, multiplexing, phase phase masks masks with with grating grating periods periods of of 1074.8 1074.8 nm nm technique. which is capable ofnm visually aligning the fibers before splicing, by capturing the cleaved and 1068 1068 nm were used used for the the inscription inscription of FBG FBG and FBG 2, 2, respectively. respectively. The sensor sensor element, fiber ends and were for of 11 and FBG The element, with a camera. necessary removal of thethe coating theof process lead with to an uncoated whichThe was previously previously aligned by analyzing analyzing the intensityfor pattern ofsplicing the SAP SAP with with microscope with which was aligned by intensity pattern the aa microscope lateral illumination, had been pre-fixed on steel platelets (marked with 1 in Figure 5) and was then lateralofillumination, had pre-fixed steelwas platelets (markedin with 1 in Figure 5) and thenside (grating sensor element about 4 cm inbeen length. An on FBG inscribed 5 mm distance onwas each attachedtotothe thesurface surfaceofof bending beam (marked in Figure 5) small with small of UVattached thethe bending beam (marked withwith 2 in 2Figure 5) with drops drops of UV-curing lengths 3 mm) ofepoxy theThe splice, using our in-house inscription setup with acm UV-laser and phase mask curingresin. resin. Theelement sensor element then glued over the whole length4of about with a epoxy sensor was thenwas glued over the whole length of about with 4a cm thermally technique. To assure FBGepoxy wavelength multiplexing, phase with grating periods of 1074.8 nm thermally cured resin (EP353, Epoxy Inc.: Technology Inc.: Billerica, MA,isothermal USA) under isothermal cured epoxy resin (EP353, Epoxy Technology Billerica, MA,masks USA) under conditions at ◦ conditions at 150 °C twoinscription hours 150 C for two hours (marked with (marked 3 in Figure 5). 3 in 1Figure and 1068 nm were used forfor the ofwith FBG and5).FBG 2, respectively. The sensor element,
which was previously aligned by analyzing the intensity pattern of the SAP with a microscope with lateral illumination, had been pre-fixed on steel platelets (marked with 1 in Figure 5) and was then attached to the surface of the bending beam (marked with 2 in Figure 5) with small drops of UVcuring epoxy resin. The sensor element was then glued over the whole length of about 4 cm with a thermally cured epoxy resin (EP353, Epoxy Technology Inc.: Billerica, MA, USA) under isothermal conditions at 150 °C for two hours (marked with 3 in Figure 5). Figure 5. Sensor design with a surface-attached PM tandem: The fiber was azimuthally aligned with Figure 5. Sensor design with a surface-attached PM tandem: The fiber was azimuthally aligned with the slow axis of FBG1 and the fast axis of FBG2 parallel to the specimen’s surface and pre-fixed on the the slow axis of FBG1 and the fast axis of FBG2 parallel to the specimen’s surface and pre-fixed on the specimen with UV-cured epoxy resin at two points next to the FBGs (marked in blue). Afterwards, specimen with UV-cured epoxy resin at two points next to the FBGs (marked in blue). Afterwards, the entire sensing element was glued over a length of about 4 cm with thermal cured epoxy resin. the entire sensing element was glued over a length of about 4 cm with thermal cured epoxy resin.
The measurement of the Bragg wavelengths was performed with a high-resolution scanning laser interrogator (I4, FAZ Technology Ldt., Dublin, IRE) with a repeatability of 100 fm in the wavelength detection and a scanning frequency of 1 kHz [29]. The polarization state of the laser was
maintained in the entire measurement setup, including the fibers and the FBGs. The used maintained in the entire measurement setup, including the fibers and the FBGs. The used measurement setup is shown in Figure 6. The corresponding spectra of the glued FBG, taken directly measurement setup is shown in Figure 6. The corresponding spectra of the glued FBG, taken directly after the curing process at −30 °C, the temperature where high glue-induced stress was expected, are after the curing process at −30 °C, the temperature where high glue-induced stress was expected, are pictured in Figure 7 for both polarizations. The peaks of both polarizations are well-separated from pictured in Figure 7 for both polarizations. The peaks of both polarizations are well-separated from each other while no sign of strong mode coupling, indicating the absence of strong glueSensors 2019, 19, 144 showing of 14 each other while showing no sign of strong mode coupling, indicating the absence of strong9glueinduced shear stresses. induced shear stresses. The sensor element was attached on the top surface of a bending beam as depicted in Figure 6. The sensor element wasBragg attached on the topwas surface of a bending beam as depicted in Figure 6. The of the performed with a high-resolution External measurement mechanical strain may bewavelengths applied to the fiber by bending the beam with scanning a wedgelaser that External mechanical strain may be applied to the fiber by bending the beam with a wedge that interrogator (I4, FAZ Technology Ldt., Dublin, IRE) with a repeatability of 100 fm inmech the wavelength mech provides five heights, leading to compressive strains between ε 3mech = 0 µε and ε 3mech = 760 µε in ε = 0 µε ε = 760 µε in provides five heights, leading to compressive strains between and detection and a scanning frequency of 1 kHz [29]. The polarization state of the laser switched 3 3 was the FBGs. Strain cycles with increasing values up to −760 µε and back to 0 µε were performed at between a horizontal andwith a vertical linearvalues polarization and polarization wasperformed maintained −760each µε scan and back to 0 µε were at the FBGs. Strain cycles increasing up to after different temperatures, starting at 100 °C and going down toFBGs. −30 °C in used stepsmeasurement of 20 °C in a setup climatic in the entire measurement setup, including the fibers and the The is different temperatures, starting at 100 °C and going down to −30 °C in steps of 20 °C in a climatic chamber. Before6.starting a strain cycle, theoftemperature was keptdirectly constant h toprocess assure shown in Figure The corresponding spectra the glued FBG, taken afterfor the1.5 curing chamber. Before starting a strain cycle, the temperature was kept constant for 1.5 h to assure isothermal conditions in the entire setup. At every strain step, the Bragg wavelengths were measured ◦ at −30 C, the temperature glue-induced stress wasthe expected, are picturedwere in Figure 7 for isothermal conditions in thewhere entirehigh setup. At every strain step, Bragg wavelengths measured every second for five minutes and were averaged to eliminate fluctuations of the temperature control both polarizations. Theminutes peaks of both polarizations are well-separated from of each while showing every second for five and were averaged to eliminate fluctuations theother temperature control of the climatic chamber. no sign of strong mode coupling, indicating the absence of strong glue-induced shear stresses. of the climatic chamber.
Figure 6. Measurement setup for temperature strain decoupling with surface-glued PM tandem Figure setup forfor temperature strain decoupling with surface-glued PM tandem sensor Figure6.6.Measurement Measurement setup temperature strain decoupling with surface-glued PM tandem sensor elements. PC, personal computer. elements. PC, personal computer. sensor elements. PC, personal computer.
Figure7.7.Spectra Spectraof ofthe theFBGs FBGsin inthe thesensor sensortandem tandemafter afterthe thecuring curingprocess processatat−−30 Figure 30 ◦°C. C. Figure 7. Spectra of the FBGs in the sensor tandem after the curing process at −30 °C.
The attached on the top surface of aused bending beam as depicted in Figure 6. All sensor values element withoutwas external mechanical strain were for temperature calibration. The All values without external mechanical strain were used for temperature calibration. The External mechanical strain may be applied to the fiber by bending the beam with a wedge that corresponding Bragg wavelengths λi , j (with i ∈{ f , s} and j ∈{0°, 90°} ) for the slow and the i ∈{ f between , s} and εmech j ∈{0=°, 090µε °} )and λi , j (withstrains corresponding Bragg leading wavelengths for εmech the slow and provides five heights, to compressive = 760 µε the in 3 3 fast axes of both FBG orientations (0°-orientation in blue, 90°-orientation in green) are shown in fastFBGs. axes of bothcycles FBG orientations (0°-orientation in−blue, 90°-orientation are shown at in the Strain with increasing values up to 760 µε and back to 0inµεgreen) were performed Figure 8. temperatures, The mean values taken from both which the actual λi = 0at.5100 λi ,0◦°C+and λi ,90going ◦orientations, ◦ Care ° different starting down to − 30 C in steps of 20 in a climatic Figure 8. The mean values λi = 0.5 λi ,0° + λi ,90° taken from both orientations, which are the actual mesurands for temperature strain decoupling, are depicted in grey. Polynomial the form chamber. Before starting a strain cycle, the temperature was kept constant for 1.5 hfunctions to assure of isothermal mesurands for temperature strain decoupling, are depicted in grey. Polynomial functions of the form conditions in the entire setup. At every strain step, 2the Bragg wavelengths were measured every 3 λ0,i , j + aand (T − Taveraged ) + aT 2 ,ito (eliminate T − T0 ) 2 +fluctuations aT 3 ,i , j (T − Tof0 )the λ0,i , j + KT ,i , control 3 =temperature 0 i, j = T , i , j j ( ΔT ) of (9) , j second forλλfive minutes were the (9) i , j = λ0,i , j + aT ,i , j (T − T0 ) + aT 2 ,i , j (T − T0 ) + aT 3 ,i , j (T − T0 ) = λ0,i , j + KT ,i , j ( ΔT ) climatic chamber. with i ∈{ f , s} and j ∈{0°, 90°, mean} were fitted to all data and were also plotted in Figure 8. without mechanical strain were for temperature calibration. i ∈values { f , s} and j ∈{0external °, 90°, mean} withAll were fitted to all dataused and were also plotted in Figure 8. ◦ residuals, ◦ The corresponding fitting parameters arewavelengths summarizedλ in(with Tablei 2. The corresponding given as the The Bragg ∈ f , s and j ∈ 0 , 90 ) for the slow { } The fitting parameters are summarized i,jin Table 2. The corresponding residuals, given asand the ◦ -orientation in blue, 90◦ -orientation in green) are shown in the fast axes of both FBG orientations (0
((
))
Figure 8. The mean values λi = 0.5 λi,0◦ + λi,90◦ taken from both orientations, which are the actual mesurands for temperature strain decoupling, are depicted in grey. Polynomial functions of the form λi,j = λ0,i,j + a T,i,j ( T − T0 ) + a T2 ,i,j ( T − T0 )2 + a T3 ,i,j ( T − T0 )3 = λ0,i,j + KT,i,j (∆T )·( T − T0 )
(9)
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with i ∈ { f , s} and j ∈
◦
10 of 14 ◦
0 , 90 , mean were fitted to all data and were also plotted in Figure 8.
difference of the measured wavelengthinand the plotted in residuals, Figure 9,given withasvalues originating The fitting parameters are summarized Table 2. fit, Theare corresponding the difference fromofthe FBG in the 0°-orientation depicted in blue, from the FBG in the 90°-orientation in green, the measured wavelength and the fit, are plotted in Figure 9, with values originating from the FBG and ◦ ◦ themean 0 -orientation in blue,infrom theThe FBGresiduals in the 90 -orientation green, and from theamean frominthe values depicted of both FBGs grey. of the fast in axis scatter within range of values of both FBGs in grey. The residuals of the fast axis scatter within a range of ± 1 pm. In the slow ±1 pm . In the slow axis, the residuals are significantly higher and in the range of ±5 pm . The residuals axis, the residuals are significantly higher and in the range of ±5 pm. The residuals of the mean values of the mean values of both sensors reduce the uncertainties for both the signals of the fast and the of both sensors reduce the uncertainties for both the signals of the fast and the slow axis to values slow axis to values smaller than 1 pm for the whole temperature◦ range between −30 °C and 110 °C. ◦ smaller than 1 pm for the whole temperature range between −30 C and 110 C. This indicates that
This the indicates that the systematic uncertainties caused by glue-induced stress affect mainly sensor systematic caused by glue-induced stress affect mainly the sensor signals of thethe slow Sensors 2018, 18, x FORuncertainties PEER REVIEW 10 of 14 signals slow axis both and be reduced by averaging the signals of both FBGs. axisofinthe both FBGs andinmay beFBGs reduced bymay averaging the signals of both FBGs. difference of the measured wavelength and the fit, are plotted in Figure 9, with values originating from the FBG in the 0°-orientation depicted in blue, from the FBG in the 90°-orientation in green, and from the mean values of both FBGs in grey. The residuals of the fast axis scatter within a range of ±1 pm . In the slow axis, the residuals are significantly higher and in the range of ±5 pm . The residuals of the mean values of both sensors reduce the uncertainties for both the signals of the fast and the slow axis to values smaller than 1 pm for the whole temperature range between −30 °C and 110 °C. This indicates that the systematic uncertainties caused by glue-induced stress affect mainly the sensor signals of the slow axis in both FBGs and may be reduced by averaging the signals of both FBGs.
Figure 8. Temperature calibrationofofthe the surface-attached surface-attached PM FBG in the 0◦ -orientation in in Figure 8. Temperature calibration PMtandem: tandem: FBG in the 0°-orientation ◦ green, in the 90 -orientationininblue, blue,and and mean mean values green, FBGFBG in the 90°-orientation valuesiningrey. grey. Table 2. Fitting parameters of the temperature calibration of the PM tandem. Orientation j
Axis i
λ0,i,j nm
aT,i,j pm/◦ C
aT2 ,i,j ·10−2 pm/◦ C2
aT3 ,i,j ·10−6 pm/◦ C3
90◦
s 1551.3540 26.54 1.59 −2.84 f 1550.9939 25.36 1.04 −2.67 0◦ s 1556.0518 24.39 1.00 −3.32 f 1555.6985 25.64 1.08 −2.33 Figure 8. Temperature calibration of the surface-attached PM tandem: FBG in the 0°-orientation in mean s 1553.7029 25.46 1.30 −2.84 f 1553.3462 25.50 1.04 − 2.67 green, FBG in the 90°-orientation in blue, and mean values in grey.
Figure 9. Residuals of the temperature calibration: FBG in the 0°-orientation in green, FBG in the 90°orientation in blue, and mean values in grey. Table 2. Fitting parameters of the temperature calibration of the PM tandem. Orientation j
Axis i
λ0,i, j
aT ,i, j
aT 2 ,i , j
aT 3 ,i , j
nm
pm/°C
⋅10−2 pm/ °C2
⋅10−6 pm/°C3
90°
s 1551.3540 26.54 1.59 −2.84 f 1550.9939 25.36 1.04 −2.67 Figure 9. Residuals of the temperature calibration:FBG FBG the0°-orientation 0◦ -orientationin ingreen, green, FBG FBG in the Figure 9. Residuals of the temperature calibration: ininthe 0° s 1556.0518 24.39 1.00 −3.32 in the 90°90◦ -orientation in blue, and mean values in grey. orientation in blue, and mean grey. f values in1555.6985 25.64 1.08 −2.33 mean s 1553.7029 25.46 1.30 −2.84 Table 2. Fitting parameters of the temperature of the PM tandem. f 1553.3462 25.50calibration 1.04 −2.67
a
a
atemperature λ0,reference Orientationwas performed Axis Tof,i110 , j °C, since T full ,i , j strain transfer T ,i , j i, j Strain calibration at the − 2 2 − 6 j i pm/°C glue-induced from the specimen to the fiber is assured,nm while significant in the ⋅10 pm/ °C stress ⋅10 pm/ °C3 fiber can be excluded. The Bragg for both fiber orientations and the of both FBGs are 90° wavelengths s 1551.3540 26.54 1.59mean values −2.84 2
3
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Strain calibration was performed at the reference temperature of 110 ◦ C, since full strain transfer from the specimen to the fiber is assured, while significant glue-induced stress in the fiber can be excluded. The Bragg wavelengths for both fiber orientations and the mean values of both FBGs Sensors 2018, 18,inx FOR PEER10 REVIEW of 14 are plotted Figure (0◦ -orientation in blue, 90◦ -orientation in green, mean values in11grey). The wavelength data of the single FBG and the mean values were fitted with a linear function, given by λi , j = λ0,i, j + aε3 ,i , j ε 3 λi,j = λ0,i,j + aε 3 ,i,j ε 3 with i ∈{ f , s} and j∈{◦ 0°, 90 . The corresponding fits are also depicted in Figure 10, and ◦ °, mean} with i ∈ { f , s} and j ∈ 0 , 90 , mean . The corresponding fits are also depicted in Figure 10, and the the fit parameters are summarized in Table 3. The residuals are shown in Figure 11, with values fit parameters are summarized in Table 3. The residuals are shown in Figure 11, with values originating originating from the FBG in the 0°-orientation in blue, from the FBG in the 90°-orientation in green from the FBG in the 0◦ -orientation in blue, from the FBG in the 90◦ -orientation in green and from the and from the mean values of both orientations in grey. In this case, the residuals show the same mean values of both orientations in grey. In this case, the residuals show the same behavior for the fast behavior for the fast and slow axis and in both orientations and the averaged values of both and slow axisxand in both orientations and the averaged values of both orientations. This indicates Sensors 2018, 18, This FORindicates PEER REVIEW 11 of in 14 orientations. that these deviations are probably caused by systematic uncertainties that these deviations are probably caused by systematic uncertainties in the height of the wedge, the height of the wedge, which was used to introduce the strain by bending the cantilever. This limits which was used to introduce the strain by bending the cantilever. This limits the accuracy of the the accuracy of the strain measurement.λ = λ i, j 0,i , j + aε 3 ,i , j ε 3 strain measurement.
with i ∈{ f , s} and j ∈{0°, 90°, mean} . The corresponding fits are also depicted in Figure 10, and the fit parameters are summarized in Table 3. The residuals are shown in Figure 11, with values originating from the FBG in the 0°-orientation in blue, from the FBG in the 90°-orientation in green and from the mean values of both orientations in grey. In this case, the residuals show the same behavior for the fast and slow axis and in both orientations and the averaged values of both orientations. This indicates that these deviations are probably caused by systematic uncertainties in the height of the wedge, which was used to introduce the strain by bending the cantilever. This limits the accuracy of the strain measurement.
◦ -orientation in green, Figure 10. 10. Strain Strain calibration calibration of of the the surface-attached surface-attached PM tandem: tandem: FBG in the 00°-orientation Figure ◦ FBG in -orientation in blue, and mean values in the the 90 90°-orientation values in in grey. grey.
Table 3. Fitting parameters of the strain calibration of the PM tandem. Orientation j
Axis i
λ0,i,j nm
aε3 ,i,j pm/µε
90◦
s 1551.3522 1.22 f 1550.9924 1.21 0◦ s 1556.0523 1.22 f 1555.6981 1.21 s 1553.7023 Figure 10. Strain calibrationmean of the surface-attached PM tandem: FBG1.22 in the 0°-orientation in green, 1.21 FBG in the 90°-orientation in blue, and mean fvalues in1553.3452 grey.
Figure 11. Residuals of the strain calibration: FBG in the 0°-orientation in green, FBG in the 90°orientation in blue, and mean values in grey. Table 3. Fitting parameters of the strain calibration of the PM tandem.
Orientation j
Axis i
λ0,i, j
aε3 ,i, j
nm
pm/με
90°
s 1551.3522 1.22 f 1550.9924 1.21 0°calibration: s FBG 1556.0523 1.22 in green, Figure 11. Residuals Residualsofofthe thestrain strain calibration: FBG in the 0◦ -orientation in green, in 90°the in the 0°-orientation FBGFBG in the ◦ -orientation in blue, and mean values in grey. f 1555.6981 1.21 90 orientation in blue, and mean values in grey. mean s 1553.7023 1.22 f strain 1553.3452 1.21 Table 3. Fitting parameters of the calibration of the PM tandem. Orientation j
Axis i
λ0,i, j
aε3 ,i, j
nm
pm/με
5. Results Discussion: Strain-Independent Temperature Measurement Δλi (with i ∈{ f , s} for the fast and Using theand averaged changes in the Bragg wavelengths
slow axes) of both FBGs of the PM tandem enables the measurement in the ∈{ f , s} for the Δλi (withof itemperature Using the averaged changes in the Bragg wavelengths fastpresence and of external mechanical longitudinal strains with surface-glued FBG tandems. The results of the slow axes) of both FBGs of the PM tandem enables the measurement of temperature in the presence Sensors 2019, 19, 144 12 of 14 temperature determination after five iteration steps with the matrix approach Equation of external mechanical longitudinal strains with surface-glued FBG tandems. Theofresults of the1.7 is shown in Figure determination 12 marked with black temperature after five dots. iteration steps with the matrix approach of Equation 1.7 is gl black dots. shown in Figure 12 marked Strain-Independent 5. Results and elements Discussion: Temperature The matrix Kwith( Δ T) = K ( ΔT ) = a Measurement +a T , igl
T ,i ,mean
T ,i ,mean
T 2 ,i ,mean
ΔT + aT 3 ,i ,mean ΔT 2 for
The matrix elements for K ( ΔinT the ) = KBragg ( ΔT ) = aT ,i ,mean aT 2 ,i ,mean T 2 and 3 Using the averaged changes ∆λi+(with i ∈Δ{Tf ,+s}aTfor theΔfast T ,i ,meanwavelengths ,i ,mean T ,i K ε3 ,i of = athe the temperature for the strainthe sensitivity wereoftaken from the fits presence to the mean slow axes) of and both FBGs enables measurement temperature in the ,meantandem ε 3 ,iPM K = a the temperature and for the strain sensitivity were taken from the fits to the mean ,i ε 3 , i ,mean ε of external with surface-glued FBG tandems. The results thePt100 values, as givenmechanical in Tables 2longitudinal and 33 (meanstrains values). The reference temperature, measured withofthe values, as given in Tables 2 after and 3five (mean values). The reference temperature, with Pt100 temperature determination iteration steps with the matrix approachmeasured of Equation (7) the is shown sensor, is depicted in red and the corresponding strain values are shown in the lower graph in Figure 12. sensor, is depicted in red the dots. corresponding strain values are shown in the lower graph in Figure 12. in Figure 12 marked withand black
Figure Strain-independent temperature temperature measurement measurement with with surface-glued surface-glued FBGs: FBGs: upper upper graph: graph: Figure 12. 12. Strain-independent evaluated temperature (black dots) in comparison to the reference temperature of the Pt100 sensor Figure 12. Strain-independent measurement with surface-glued upper graph: evaluated temperature (black temperature dots) in comparison to the reference temperature ofFBGs: the Pt100 sensor (red), graph: (red), lower lower graph: applied applied strain. evaluated temperature (blackstrain. dots) in comparison to the reference temperature of the Pt100 sensor gl (red), lower graph: applied strain. The matrix elements K T,i (∆Twith ) = Kthe ∆T ) = amatched a T2 ,i,mean ∆T + a T3 ,i,mean ∆T 2 for the T,i,mean T,i,mean +the The temperatures evaluated FBG(tandem reference values independently temperature and K ε 3 ,iover = aεthe fortemperature the strain sensitivity were taken from the110 fits°C. to Figure the mean 3 ,i,mean of thetemperatures applied strain entire range between −30 °C and 13 values, shows The evaluated with the FBG tandem matched the reference values independently as in Tables 2 and 3 (meantemperatures values). The from reference temperature, measured of with Pt100 sensor, thegiven deviation of the evaluated the reference temperatures thethe Pt100 sensor in of the applied overthe thecorresponding entire temperature rangeare between −30 andgraph 110 °C. Figure12. 13 shows is depicted strain inofred and strain values shown at in the°C lower in Figure dependence temperature. With exception of the measurement −30 °C, all deviations stay within the deviation of the evaluated temperatures from the reference temperatures of the Pt100 sensor in Theoftemperatures evaluated with the FBG tandem matched the reference independently ±4 °C around the reference temperature. Larger deviations (up to values 7 °C) have only been a range ◦ ◦ dependence of temperature. With exception of the measurement at −30 °C,110 all deviations within of the applied strain over the entire temperature range between −30 C and C. Figure 13stay shows observed at the lowest temperature and could probably be attributed to the high glue-induced the deviation the evaluated temperatures from the reference temperatures the reference temperature. Larger deviations (up toof7 the °C)Pt100 have sensor only been a range of ±4 °C ofaround wavelength changes of about 150 pm at this temperature. Due to the small differences in the in dependence of temperature. Withand exception of the measurement at −30to◦ C,the all high deviations stay observed at the lowest temperature could probably be attributed glue-induced sensitivity constants, the suppression of these deviations by using the mean values have to be within a range of ±4 ◦ C around the reference temperature. Larger deviations (up to 7 ◦ C) have only pm Given wavelength ofpicometer about 150 at this to thebysmall achieved changes within the range. thattemperature. the glue was Due suspended hand,differences resulting in in a the been observed at the lowest temperature and could probably be attributed to the high glue-induced variableconstants, thickness ofthe thesuppression applied glue along the fiber, these areby good results that prove the capability sensitivity deviations mean values have to be wavelength changes of about 150 pm at of thisthese temperature. Due to theusing small the differences in the sensitivity of thiswithin method. achieved the picometer range. Given that the glue was suspended by hand, resulting constants, the suppression of these deviations by using the mean values have to be achieved within in a variable thicknessrange. of theGiven applied along the fiber, these are good results prove the capability the picometer thatglue the glue was suspended by hand, resulting in athat variable thickness of of this themethod. applied glue along the fiber, these are good results that prove the capability of this method.
Figure 13. Deviations of FBG temperature to reference temperature.
Figure DeviationsofofFBG FBGtemperature temperature to temperature. Figure 13.13. Deviations toreference reference temperature.
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6. Conclusions Strain-compensated temperature measurements have been successfully realized within a wide temperature range between −30 ◦ C and 110 ◦ C with surface-glued PM-FBG sensor elements for the first time, using azimuthally aligned FBG tandems consisting of two FBGs in PM fibers that were spliced with their optical axes perpendicular to each other. The main advantage of this novel methodology lies in the fact that glue-induced transversal forces could be compensated for during the evaluation process by averaging the Bragg wavelengths of the fast and of the slow axes of both PM-FBGs in the surface-glued FBG tandem. The capability to compensate for glue-induced transversal forces of varying strength have been shown for temperature-dependent glue-induced transversal stress introduced during temperature changes as a result of the high CTE of the epoxy resin. This measurement technique enabled temperature and strain decoupling with an uncertainty of several degrees in the entire measurement range. We expect a similar compensation capability for all glue-induced transversal forces that are based on volume changes of the used glue, e.g., water absorption, which will be addressed in further research. This technique for strain and temperature decoupling with surface-attached FBG tandems is therefore of great importance for all applications in which fully glued fibers are essential. Additionally, the utilization of the FBG tandem approach to embedded fiber optic multi-parameter sensing will be addressed in upcoming research, which further extends the application range of such tandem elements. 7. Patents The functional working principle and the corresponding sensor design are registered at the German Patent and Trademark Office (Deutsches Patent-und Markenamt, DPMA): DE 10 2017 201 523.3 (Faseroptische Erfassungseinrichtung sowie Verfahren zum Betreiben einer solchen faseroptischen Erfassungseinrichtung), 31.01.2017. Author Contributions: Conceptualization, B.H., T.B., and J.R.; Formal analysis, B.H. and B.F.; Funding acquisition, T.B. and J.R.; Investigation, B.H.; Methodology, B.H. and B.F.; Project administration, J.R.; Supervision, A.W.K. and J.R.; Visualization, B.H.; Writing (original draft), B.H.; Writing (review & editing), A.W.K. and J.R. Funding: This research was funded by the Federal Ministry of Education and Research (BMBF), grant number 03FH055PX3, and by the Bayerische Forschungsstiftung (BFS), grant number AZ-1146-14. The Deutsche Forschungsgemeinschaft (German Research Foundation, DFG), grant number 393121356, and the Munich University of Applied Sciences (MUAS) funded the publication through the “Open Access Publishing” program. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
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