sensors Article
Sensitivity Enhancement of FBG-Based Strain Sensor Ruiya Li 1,2 1
2 3
*
ID
, Yiyang Chen 1 , Yuegang Tan 1, *, Zude Zhou 1 , Tianliang Li 3
ID
and Jian Mao 1
School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China;
[email protected] (R.L.);
[email protected] (Y.C.);
[email protected] (Z.Z.);
[email protected] (J.M.) School of Engineering, University of Birmingham, Birmingham B15 2TT, UK Department of Biomedical Engineering, National University of Singapore, Singapore 117576, Singapore;
[email protected] Correspondence:
[email protected]
Received: 16 April 2018; Accepted: 14 May 2018; Published: 17 May 2018
Abstract: A novel fiber Bragg grating (FBG)-based strain sensor with a high-sensitivity is presented in this paper. The proposed FBG-based strain sensor enhances sensitivity by pasting the FBG on a substrate with a lever structure. This typical mechanical configuration mechanically amplifies the strain of the FBG to enhance overall sensitivity. As this mechanical configuration has a high stiffness, the proposed sensor can achieve a high resonant frequency and a wide dynamic working range. The sensing principle is presented, and the corresponding theoretical model is derived and validated. Experimental results demonstrate that the developed FBG-based strain sensor achieves an enhanced strain sensitivity of 6.2 pm/µε, which is consistent with the theoretical analysis result. The strain sensitivity of the developed sensor is 5.2 times of the strain sensitivity of a bare fiber Bragg grating strain sensor. The dynamic characteristics of this sensor are investigated through the finite element method (FEM) and experimental tests. The developed sensor exhibits an excellent strain-sensitivity-enhancing property in a wide frequency range. The proposed high-sensitivity FBG-based strain sensor can be used for small-amplitude micro-strain measurement in harsh industrial environments. Keywords: fiber Bragg grating; strain; sensitivity enhancement; lever structure
1. Introduction The strain is one of the most important monitored physical parameters in the structural health monitoring (SHM) of modern mechanical equipment [1–3]. In some cases, SHM requires a high strain sensitivity to the applied strain sensors. For instance, detecting strain shifts caused by fatigue crack is often problematic because of the very low strain amplitudes, which require a strain sensor with a sub-microstrain resolution. Conventionally, strain measurements in this kind of situation rely on the use of resistive strain gauges with a resolution of about 0.5 µε, which are commercially available and standardized. In terms of frequency response, resistive strain gauges have a wide working range (max. 1 kHz~50 kHz), which can meet most requirements in SHM. However, the measured signals from traditional electrical strain sensors are easily contaminated by electromagnetic interference (EMI) in a harsh industrial environment, which deteriorates the performance of an SHM system [4]. Fiber Bragg grating (FBG)-based strain sensors exhibit advantages such as immunity to EMI, resistance to corrosion, and multiple measuring points in one optical fiber, which have attracted a great deal of attention and have been widely investigated in the SHM research field recently [5–12]. Commonly, bare FBG strain sensors are directly bound on the surfaces of monitored structures using adhesives to detect strain shifts [13–16] or are embedded in some composite material to form smart structures [17,18]. The strain sensitivity of directly-pasted or embedded bare FBG sensors is 1.21 pm/µε, Sensors 2018, 18, 1607; doi:10.3390/s18051607
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in theory [19]. As the resolution and precision of a dynamic FBG integrator are 1 pm and ±5 pm, the resolution and precision of a bare FBG strain sensor are about 0.8 µε and ±4 µε, which can meet most engineering applications. However, in some cases, the strain to be tested is at a very low level (e.g., 1~10 µε, 10~20 µε), the 1.21 pm/µε sensitivity of the bare FBG cannot be qualified for the accurate detection of this small-amplitude strain due to the noise of the FBG interrogator. Therefore, a FBG strain sensor with a higher sensitivity and accuracy is urgently needed. Some researchers bonded the two ends of a FBG with two high-stiffness tubes, respectively, and then bonded the outer ends of the two tubes to the structure surface to get a relatively higher strain sensitivity. For instance, Ren et al. [20] designed a FBG strain sensor that can achieve a sensitivity of 2.053 pm/µε through packaging the FBG using two gripper tubes. Li et al. [21] developed a FBG strain sensor with a sensitivity of 2.52 pm/µε in the same way, for the long-term structural health monitoring system of a highway bridge. The above-mentioned sensors enhance strain sensitivity by centralizing the continuous strain of a long region on the tested structure to the short FBG area. However, the distance between the two bonded points of the sensor increases the whole volume of the sensor (254 mm length; in Reference [21]). Additionally, some other researchers utilized substrates with flexure hinges to enlarge the strain at the FBG area. Zhang et al. [22] presented a diamond-frame packaged FBG strain sensor, which was temperature-insensitive and the strain sensitivity was enhanced to 1.814 pm/µε. Guo et al. [23] used a substrate with flexure hinges to improve the strain sensitivity of a FBG-based sensor. The experimental results showed that this sensor’s sensitivity could reach 3.357 pm/µε. These sensors can also achieve a higher strain sensitivity compared with directly-pasted bare FBG sensors. However, they are fragile and easy to be broken due to the thin flexure hinges. Nawrot et al. [24,25] proposed a mechanical transducer that amplifies the strain applied to FBGs. The amplification factor is larger than 30, which makes small-amplitude strains easier to be detected. The outer dimensions of this sensor are 380 × 105 mm2 . It can be applied to large engineering structures (e.g., bridges, heavy-duty gantry cranes, etc.), but it is too large to be used in industrial equipment in regular sizes. The dynamic working range is an important parameter of a strain sensor. However, References [20–23] do not provide this property as they are used for static or quasi-static strain measurements. Through the finite element method, Nawrot et al. [24,25] analyzed the resonant frequency of their sensor. When the thickness of their sensor changes as 3 mm, 5 mm, 7 mm, and 9 mm, the corresponding resonant frequencies are 148 Hz, 244 Hz, 338 Hz, and 409 Hz, respectively. The working frequency bandwidth of the sensor is not wide enough for high-frequency dynamic strain measurements in mechanical equipment. This paper presents a sensitivity-enhanced FBG strain sensor based on a substrate with a lever structure. The proposed sensor has a smaller and simpler structure and a much higher resonant frequency than the sensor in References [24,25]. Firstly, the structure and sensitization model of the sensor is introduced in Section 2. Then, in Section 3, the simulation results using the finite element method (FEM) are discussed. Finally, the experimental study of the sensing properties of the developed sensor is explained in Section 4. The strain sensitivity of the FBG strain sensor can be effectively improved by using the lever principle. Its sensitivity is over five times larger than the directly-pasted bare FBG. Adjusting the size of the lever structure can easily regulate the sensitivity and precision of the FBG strain sensor. The designed sensor has the advantages of a simple and compact structure, high strain sensitivity in a wide frequency range, convenient installation, and high consistency and reliability. The developed sensor can assist in small-amplitude micro-strain measurements in a harsh industrial environment. 2. Sensitization Model of the Sensor 2.1. The Principle of Strain Sensing of FBG FBG consists of a periodic modulation of the refraction along the fiber core. When a broadband light propagates along the optical fiber core to the fiber Bragg grating, the light (with a particular wavelength which satisfies the Bragg interference condition) is reflected back while the rest of the light
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= λB 2neff Λ
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where λB is the Bragg wavelength of the FBG, neff is the effective refractive index of the fiber core at the free space center wavelength, and Λ is the grating periodicity of the FBG. An FBG is very sensitive is transmitted with a small attenuation. The particular wavelength of the reflected light is regarded as to strain changes. The shifts in strain will cause changes of neff or Λ, and lead to the shifts of λB. Hence, the Bragg wavelength, and is expressed by the following equation: by monitoring the Bragg wavelength shift, the value of the strain can be determined. The wavelength variation response to the strain εFBG can be given by: λ B = 2ne f f Λ (1)
∆λB
= (1 − pe )εFBG (2) where λB is the Bragg wavelength of the FBG, λB neff is the effective refractive index of the fiber core at the free space center wavelength, and Λ is the grating periodicity of the FBG. An FBG is very sensitive to where pe = 0.22 is theshifts effective photo-elastic coefficient. strain changes. The in strain will cause changes of neff or Λ, and lead to the shifts of λB . Hence, by monitoring the Bragg wavelength shift, the value of the strain can be determined. The wavelength 2.2. Structure and Strain Mechanism variation response to theAmplification strain εFBG can be given by: The structure of the developed fiber∆λ Bragg grating strain sensor is shown in Figure 1. It is mainly B = (1 − pe )ε FBG (2) composed of a bare FBG sensor and an elastic λ B substrate with a lever structure. The double ends of the bare FBGs are fixed to the elastic substrate using adhesive (ND353). It is noteworthy that pre-tension where 0.22 is the effective photo-elastic coefficient. shouldpbe to the bare FBG when fixing it on the substrate to ensure the FBG can effectively e =applied detect compressive strain. The tail fiber of the bare FBG is packaged in plastic protective sleeves. The 2.2. Structure and Strain outer dimensions of thisAmplification sensor are 36Mechanism × 10.5 mm2, and the thickness of the sensor is 1 mm. The total weight ofstructure the sensor about 1.5 g. The substrate is made of stainless 304.in AsFigure its stiffness high, The of is the developed fiber Bragg grating strain sensor issteel shown 1. It isismainly it can improve the dynamic working range of the sensor. On the other hand, this sensor cannot be composed of a bare FBG sensor and an elastic substrate with a lever structure. The double ends of the used to detect straintoon structures made ofusing a low-stiffness material It (e.g., rubber) since may affect bare FBGs are fixed the elastic substrate adhesive (ND353). is noteworthy thatitpre-tension the deformation of to thethe tested coating of the FBG removed since weakens should be applied bare structure. FBG whenThe fixing it onlayer the substrate to was ensure the FBG can iteffectively the strain transfer effect. The physical parameters of the main components of the designed sensor are detect compressive strain. The tail fiber of the bare FBG is packaged in plastic protective sleeves. 2 illustrated in Table 1. The fixing method developed FBGthe strain sensor of is shown in Figure 2a. The outer dimensions of this sensor are of 36 the × 10.5 mm , and thickness the sensor is 1 mm. The double endsofofthe thesensor substrate in the FBG strain sensor were bonded to the to The total weight is about 1.5designed g. The substrate is made of stainless steel 304. Asstructure its stiffness be tested using adhesive. Reference [20] demonstrated that the double-ends adhesive fixed method is high, it can improve the dynamic working range of the sensor. On the other hand, this sensor cannot can achieve commendable strain transfer Figure 2b shows(e.g., the rubber) simplified the be used to detect strain on structures made ofeffects. a low-stiffness material sincemodel it mayofaffect designed sensor. The structure of the substrate can be simplified by the rod connections, taking the the deformation of the tested structure. The coating layer of the FBG was removed since it weakens optical fiber with aeffect. FBG into (rod CH). the strain transfer The consideration physical parameters of the main components of the designed sensor are illustrated in Table 1. The fixing method of the developed FBG strain sensor is shown in Figure 2a. Table The physical FBG parameters the sensor. The double ends of the substrate in1.the designed strain of sensor were bonded to the structure to be tested using adhesive. Reference [20] demonstrated that the double-ends adhesive Structure Material Elastic Modulus Poisson Ratiofixed method can achieve commendable strain transfer effects. Figure 2b shows the simplified model of the designed Substrate Stainless steel 304 E = 200 Gpa ν = 0.3 sensor. The structureFBG of the substrateSilica can be simplified the rod taking the optical fiber EFBG =by74.52 Gpaconnections, νFBG = 0.17 with a FBG into consideration (rod CH). Adhesive Epoxy resin Ea = 3.0 Gpa νa = 0.38
(a)
(b)
Figure 1. The designed FBG strain sensor: (a) The structure of the designed sensor; (b) real image of Figure 1. The designed FBG strain sensor: (a) The structure of the designed sensor; (b) real image of the designed sensor. the designed sensor.
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H
S4
S3, I3
B
S2, I2 K
d3
y
C
x d5 d4
S1
A
d6 D
d2 d1
(a)
(b)
Figure 2. Fixing method and simplified sensing model of the designed sensor: (a) Fixing method; Figure 2. Fixing method and simplified sensing model of the designed sensor: (a) Fixing method; (b) simplified model. (b) simplified model.
When the structure surface to be tested generated a strain ε, a relative displacement Δd is 1. The the sensor. generated between point A Table and point Hphysical (or K) inparameters the x-axisofdirection. Assuming the displacements of point H, K is zero, the displacement at point A will be Δd in the x-axis direction. Correspondingly, Structure Material Elastic Modulus Poisson Ratio we can get that ε = Δd/d1. At the same time, forces and bending moments will generate at point A, H, Stainless steel 304 200 y-axis Gpa direction and ν = 0.3 and K. Under Substrate small deformation conditions, the forcesEin= the bending moments FBG H are very small Silica 74.52 Gpa νFBG = 0.17 at point A and point and not takenEFBG into=account in the analytical study. Therefore, Adhesive Epoxy resin Ea = 3.0 Gpa νa = 0.38 the whole structure can be simplified as a secondary hyperstatic structure. Replacing the constraint conditions of point A and H with the unit forces X1 and X2, respectively (as shown in Figure 3a), based onthe thestructure law of Virtual Unit Load Method, δ11 and δ12 will generate, When surfaceWork to be and tested generated a strain displacement ε, a relative displacement ∆d is generated respectively, A when X1 and actx-axis independently. the same way, deformations δ21ofand δ22 H, between point at A point and point H (or K) inX2the direction.InAssuming the displacements point will generate, respectively,atatpoint pointAHwill when 1 and X2 act independently (as shown in Figure K is zero, the displacement be X ∆d in the x-axis direction. Correspondingly, we3b,c). can get According the deformation compatibility condition, the regular equation can be obtained: that ε = ∆d/dto 1 . At the same time, forces and bending moments will generate at point A, H, and K. Under small deformation conditions, the and bending moments at point δ11forces ∆ddirection δ12 in the X y-axis ⋅ 1 = the analytical study. Therefore, the (3) A and point H are very small and not taken intoaccount in whole δ21 δ22 X2 0 structure can be simplified as a secondary hyperstatic structure. Replacing the constraint conditions the law of Virtual Work in the of material When a3a), material obeys of pointAccording A and Hto with the unit forces X1 and X2theory , respectively (asmechanics. shown in Figure based on the Hooke’s law, and in the case of small deformations, there is a linear relationship between the virtual law of Virtual Work and Unit Load Method, displacement δ11 and δ12 will generate, respectively, displacement on the structure, which can be expressed by More’s integral as follows: at point A whenand X1 the andapplied X2 actload independently. In the same way, deformations δ21 and δ22 will generate, respectively, at point H when F X1(and X act independently (as shown in Figure 3b,c). According to the x) f N (2x) M( x)m( x) T ( x)t( x) N δ = dx + dx + dx (4) deformation compatibility condition, the regular equation can bel obtained: l l
∫
∫ EI ∫ GI p ES " # " # " # δ11 δ12 FN(x), X1M(x), and∆dT(x) are the internal force, bending where δ represents the virtual displacement, · = (3) δ21 load, δ22 respectively. X2 moment, torque caused by the actual fN(x),0m(x), and t(x) are the internal force,
bending moment, torque caused by the unit load, respectively. E and G represent the elastic modulus According to the law of structure Virtual Work in the theory of material mechanics. obeys and shear modulus of the respectively. S is the cross-sectional area. When I and Iap material are the area Hooke’s law,ofand in the casethe of small deformations, is a respectively. linear relationship between virtual moment inertia and torsional moment ofthere inertia The values ofthe virtual displacement andδthe load on the structure, which can More’s be expressed by More’s integral as follows: displacements 11, δapplied 12, δ21 and δ22 can be calculated using the integral: Z 2 Z dM⋅(dx )m( xd)3 FN ( x ) f Nd(3x ) d2 T ( x )t( x ) +dx + + 6 3 + 6 dx + δ11 = dx (4) 3 ES ES EI EI GIp l l ES 2 1 l 2 EI 3 d3 d3 d42 ⋅ d3 d43 = + + + (5) δdisplacement, where δ represents the virtual F (x), M(x), and T(x) are the internal force, bending 22 ES2 EFBGS4N 3 EI 3 EI 3 moment, torque caused by the respectively. f N (x), m(x), and t(x) are the internal force, actual load, d3 d62 ⋅ (3d5 + d6 ) d62 ⋅ d3 δ12by bending moment, torque caused the unit load, respectively. E and Grepresent the elastic modulus = = − + + δ 21 ES2 6 EI 3 EI 2 and shear modulus of the structure respectively. S is the cross-sectional area. I and Ip are the area
δ=
Z
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moment of inertia and the torsional moment of inertia respectively. The values of virtual displacements δ11 , δ12 , δ21 and δ22 can be calculated using the More’s integral: d36 d26 ·d3 d3 d2 + + + δ11 = ES EI 3EI ES 2 3 2 1 d34 d24 ·d3 Sensors 2018, 18, x FOR PEER REVIEW 5 of 11 d3 d3 δ22 = ES + + + (5) 3EI3 EI3 EFBG S4 2 2 2 ·(3d5 + d6 ) d6 ·d(5) d3 3 The values of the related 2bd6and Equation are shown in Tables 1 and 2. δ12 = δ21 =in−Figure + EI parameters 6EI3 ES2 + 2 Substituting Equation (5) into Equation (3), we can obtain that X1 = 1.5Δd and X2 = 0.2Δd. The deformation of FBG (rodrelated CH) Δd FBG can be expressed as ΔdFBG = (X2d3)/(EFBGS4) = 2.16Δd. Thus, the The values of the parameters in Figure 2b and Equation (5) are shown in Tables 1 sensitivity amplification factor q of the designed calculated and 2. Substituting Equation (5) into Equation sensor (3), wecan canbe obtain that Xas following: = 1.5∆d and X = 0.2∆d. 1
2
The deformation of FBG (rod CH) ∆dFBG asd∆dFBG εFBGcan be d3 ∆ ∆dexpressed ⋅ d1 = (X2 d3 )/(EFBG S4 ) = 2.16∆d. Thus, FBG FBG q = = = (6) the sensitivity amplification factor q of the designed sensor can be calculated as following:
ε
∆d d1
∆d ⋅ d3
ε FBG ∆dFBG · d1 ∆d FBG /d3 in=the FBG area.=Substituting the values of the parameters (6) in where εFBG is the strain of the silica q =fiber ε ∆d/d1 ∆d · d3 Table 2 into Equation (6), we can get that 5.7 is the theoretical value of sensitivity amplification factor q. According the principle fiberfiber Bragg grating the wavelength shiftof Δλthe B of the FBG can where εFBG isto the strain of theofsilica in the FBGsensing, area. Substituting the values parameters in be obtained as follows: Table 2 into Equation (6), we can get that 5.7 is the theoretical value of sensitivity amplification factor q. According to the principle of fiber Bragg grating sensing, the wavelength shift ∆λB of the FBG can be ∆λB = (1 − pe )qε obtained as follows: (7) λBB ∆λ = (1 − pe )qε (7) λB ∆λB k= =λB (1 − pe )q (8) ∆λεB k= = λ B (1 − p e ) q (8) ε sensitivity k of the developed FBG strain sensor is When λB = 1550 nm, the theoretical strain
When λB = 1550 nm, the theoretical strain sensitivity k of the developed FBG strain sensor is 6.9 pm/µε. 6.9 pm/με. H′
H
H A
X2
H′′
δ 21
A
H
δ 22
A′′ A
δ12
δ11 X1
X1
(a)
A′
X2
(b)
(c)
Figure 3. Displacement analysis of the secondary hyperstatic structure: (a) Replacing the constraint Figure 3. Displacement analysis of the secondary hyperstatic structure: (a) Replacing the constraint conditions of point A and H with unit forces; (b) virtual displacement caused by X1; (c) virtual conditions of point A and H with unit forces; (b) virtual displacement caused by X1 ; (c) virtual displacement caused by X2 displacement caused by X2 Table 2. The values of parameters in the simplified sensing model. Table 2. The values of parameters in the simplified sensing model.
Parameters Parameters d1 d1 d2 d2 d3 d3 d4 d4 d5 d5 d6 d6
Values Parameters Values Values Parameters Values 2 24 mm S1 1.5 mm 2 24mm mm 1.5 mm2 15 S2 S1 2 mm 2 mm 2 mm 2 915mm S3 S2 2 mm 9 mm S3 2 mm2 2 8.5 mm S4 0.012272 mm 8.5 mm S4 0.0122724 mm2 55mm I 2 2/3 mm mm I2 2/3 mm4 4 4 3.5 mm I 3 2/3 mmmm 3.5 mm I3 2/3
3. Simulation Analysis 3. Simulation Analysis 3.1. 3.1. Static Static Analysis Analysis Theoretical Theoretical analysis analysis by by FEM FEM was was carried carried out out using using ANSYS ANSYS software software to to verify verify the the feasibility feasibility of of the the proposed proposed method method and and structure. structure. The The physical physical properties properties of of the the material material involved involved in in the the designed designed sensor were set according to the details in Table 1. As shown in Figure 4a, one end of the substrate of the sensor was fixed, and a 10 N force was implemented on the other end of the substrate. Figure 4b exhibits that the substrate generated a deformation of Δd = 3.05 μm at this load, which reflects that the strain to be tested is ε = Δd/d1 = 127.08 με. Under the same situation, the strain εFBG of the FBG is 659 με. The finite element analysis results demonstrate that strain sensitivity amplification factor q is
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sensor were set according to the details in Table 1. As shown in Figure 4a, one end of the substrate of the sensor was fixed, and a 10 N force was implemented on the other end of the substrate. Figure 4b exhibits that the substrate generated a deformation of ∆d = 3.05 µm at this load, which reflects that the strain to be tested is ε = ∆d/d1 = 127.08 µε. Under the same situation, the strain εFBG of the FBG is 659 µε. The finite element analysis results demonstrate that strain sensitivity amplification factor q is 5.2, which is consistent with the theoretical result (5.7). The sensitivity amplification factor calculated using the FEM is a little smaller than the value obtained by the theoretical calculations of the simplified model. The main reasons involve:
• • •
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The lever structure is simplified as a rod structure in the theoretical calculation. • theoretical The lever structure is simplified as a rod the theoretical The calculation parameters are structure based onincentral sizes ofcalculation. the simplified rods. • The theoretical calculation parameters are based on central sizes of the simplified rods. while the The characteristics of the adhesive are not considered in the theoretical calculations, • The characteristics of the adhesive are not considered in the theoretical calculations, while the adhesive thickness between the substrate of the developed FBG strain sensor and the specimen Sensors 2018,thickness 18, x FOR PEER REVIEW the substrate of the developed FBG strain sensor and the6 specimen of 11 adhesive between reduces the strain transform coefficient in the FEM analysis. reduces the strain transform coefficient in the FEM analysis.
The lever structure is simplified as a rod structure in the theoretical calculation. The theoretical calculation parameters are based on central sizes of the simplified rods. Substrate of the adhesive are not considered in the theoretical ε FBGcalculations, ε FBG d while the The characteristics q = = 5.2 ɛFBG=659FBG µɛ = adhesive thickness between the substrate of the developed strain sensor and ε ∆d1 the specimen Adhesive reduces the strain transform coefficient in the FEM analysis. • • •
Force=10 N Substrate Adhesive
ε FBG ε FBG d q = = 5.2 ɛFBG=659 µɛ = ε ∆d1
FBG
Fixed
d1=24 mm
Force=10 N
(a) FBG
Δd=3.05 µm
(b)
Δd=3.05 µm Fixed Figure 4. Static structural analysis based on FEM: (a) FEM model; (b) results. d1=24 mmFEM analysis
Figure 4. Static structural analysis based on FEM: (a) FEM model; (b) FEM analysis results.
3.2. Dynamic Characteristics(a) Analysis
(b)
3.2. Dynamic Characteristics Analysis Figure 4. Static structural analysis based on FEM: (a) FEM model; (b) FEM analysis results.
Strain transducers are generally required to possess good dynamic performance to accurately
Strain transducers are generally to to possess good dynamic performance to accurately obtain3.2. the dynamic characteristics ofrequired a structure be measured. The dynamic characteristics of the Dynamic Characteristics Analysis designed sensor were analyzed via modal analysis and harmonic response analysis using ANSYS. obtain the dynamic characteristics of a structure to be measured. The dynamic characteristics of the Strain transducers are generally required to possess good dynamic performance to accurately The modal analysis results show the analysis resonant frequency of theresponse designed sensor is of 6813.5 Hz. designed sensor were analyzed via that modal harmonic analysis using obtain the dynamic characteristics of a structure to beand measured. The dynamic characteristics the ANSYS. Figure 5 showssensor the normalized strain amplitude of the FBG when the under a harmonic designed were show analyzed via the modal analysis and harmonic response analysisisusing ANSYS. The modal analysis results that resonant frequency of thesubstrate designed sensor is 6813.5 Hz. force The withmodal a 10-N amplitude and 0~10,000 Hz frequency rangeof(the interval issensor 20 Hz). The maximum analysis results show that the resonant frequency the designed is 6813.5 Hz. Figure 5 shows the normalized strain amplitude of the FBG when the substrate is under a harmonic strainFigure of the5FBG occurs when the strain frequency is near theFBG resonant designed sensor had shows the normalized amplitude of the when frequency. the substrateThe is under a harmonic force with force a 10-N amplitude and 0~10,000 Hz frequency range (the interval is 20 Hz). The maximum with awhen 10-N the amplitude and 0~10,000 Hzthan frequency range (the interval is 20 Hz). The maximum a flat response frequencies are less 6000 Hz. strain of the FBG occurs whenwhen the frequency theresonant resonant frequency. The designed sensor had strain of the FBG occurs the frequencyisisnear near the frequency. The designed sensor had a flat response when the frequencies less than6000 6000 Hz. a flat response when the frequencies areare less than Hz.
Strain modal Strain modal
6840 Hz 6840 Hz
Figure 5. The harmonic response of the ANSYS simulation.
Figure 5. The harmonicresponse response of Figure 5. The harmonic of the theANSYS ANSYSsimulation. simulation. 4. Experimental Study of the Sensing Properties
4. Experimental Study of the Sensing Properties 4.1. Static Properties
4.1. Static Properties
Figure 6 shows the schematic of the experimental setup and instruments. The designed
FBG-based strain sensor, the bare FBG and the resistance strain were bonded the Figure 6 shows the schematic of sensor, the experimental setup andgauge instruments. Theon designed FBG-based strain sensor, the bare FBG sensor, and the resistance strain gauge were bonded on the
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4. Experimental Study of the Sensing Properties 4.1. Static Properties Figure 6 shows the schematic of the experimental setup and instruments. The designed FBG-based strain sensor, the bare FBG sensor, and the resistance strain gauge were bonded on the surface of an aluminum inPEER theREVIEW same sensing direction. The aluminum specimen was installed Sensorsspecimen 2018, 18, x FOR 7 of 11 on the tensile testing machine, which accurately controlled the tensile force applied to the specimen. An FBG surface(GAUSSIAN of an aluminum specimenwith in the direction. aluminum specimen was used to interrogator OPTICS) a 1same pm sensing resolution and aThe 1 Hz sampling rate was Sensors 2018, PEER REVIEW of 11 installed on 18, thex FOR tensile testing machine, which accurately controlled the tensile force applied to7the detect the central wavelength shifts of the designed FBG-based strain sensor and the bare FBG sensor. specimen. An FBG interrogator (GAUSSIAN OPTICS) with a 1 pm resolution and a 1 Hz sampling A high-resolution resistance indicator was utilized to demodulate theand signals surface of an specimen in the(TST5912) same direction. The aluminum specimen was of the rate was used toaluminum detect thestrain central wavelength shiftssensing of the designed FBG-based strain sensor the installed on the tensile testing machine, which accurately controlled the tensile force applied to theunload resistance strain gauge. During the experiment, the tensile machine was controlled to load and bare FBG sensor. A high-resolution resistance strain indicator (TST5912) was utilized to demodulate specimen. An FBG interrogator (GAUSSIAN OPTICS) with a 1 pm resolution and a 1 Hz sampling the signals of the resistance strain gauge. During the experiment, the tensile machine was controlled in the range of 0–2000 N with an interval of 200 N. At every load/unload step, the test signals from the was to detect central wavelength of the designed strain sensor andthe the torate load andused unload in thethe range of 0–2000 N withshifts an interval of 200 As N. FBG-based At every step, FBG interrogator and resistance stain indicator were collected. the testload/unload time was relatively short, bare FBG sensor. A FBG high-resolution strain stain indicator (TST5912) utilized demodulate test signals from the interrogatorresistance and resistance indicator were was collected. Asto the test time room temperature could be considered constant. the signals of the resistance strain gauge. During the experiment, the tensile machine was controlled was relatively short, room temperature could be considered constant. to load and unload in the range of 0–2000 N with an interval of 200 N. At every load/unload step, the test signals from the FBG interrogator and resistance stain indicator were collected. As the test time was relatively short, room temperature could be considered constant.
(a)
(b)
Figure 6. Experimental setup: (a) Schematic diagram; (b) real images.
Figure 6. Experimental setup: (a) Schematic diagram; (b) real images.
1200
1000 1400 800 1200 600 1000 400 800 200 600 0 400 200
40
80
120
Stain (με)
Bare FBG Linear fit of designed FBG-based sensor Linear fit of Bare FBG
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Designed FBG-based Sensor 2nd Bare FBG 2nd Designed FBG-based Sensor 3rd Bare FBG 3rd Designed FBG-based Sensor 1st Bare FBG 1st Designed FBG-based Sensor 2nd Bare FBG 2nd Designed FBG-based Sensor 3rd Bare FBG 3rd
0
Wavelenght shift of FBG (pm) Wavelenght shift of FBG (pm)
Wavelenght shift of FBG (pm) Wavelenght shift of FBG (pm)
(a) (b) Here, we assume that the strain transform coefficients from the surface of the aluminum Figure 6. Experimental setup: (a)designed Schematicsensor diagram; (b)all real100%. images. specimen to the strain gauge, baretransform FBG, and the detected Here, we assume that the strain coefficients from were the surface ofThe thestrain aluminum specimen by the strain gauges was regarded as the real strain on the specimen surface. Figure 7a lists the to the strain Here, gauge,webare FBG, and the designed sensor were all 100%. The strain detected by the strain that the strain coefficients from the surface of the aluminum wavelength shiftsassume of the designed sensortransform and the bare FBG in the experiments to demonstrate the gaugesrepeatability was regarded as thestrain real strain on specimen surface. Figure lists wavelength specimen toofthe strain gauge, bare FBG, and the designed sensor were all 7a 100%. The strain detected the FBG sensor. Thethe repeatability error of the designed sensor isthe less than 0.5%. shifts by the7bstrain gauges was regarded as in the realexperiments strain on the to specimen surface. Figure 7a lists the of the of the designed sensor thefitting bareresults FBG demonstrate repeatability Figure shows theand linear of the repeated experimental data. The strainthe sensitivity of the wavelength shifts of designed sensor the bare FBG in the experiments demonstrate the designed sensor 6.2the pm/με anderror the linear coefficient 0.99986. The actual strain FBG strain sensor. Theis repeatability ofand thecorrelation designed sensor isisless thanto 0.5%. Figure 7b shows repeatabilityfactor of the of FBG strain sensor. The repeatability error of the designed sensor is result. less than 0.5%. amplification the designed FBG strain sensor is 5.2, which matches the FEM As the the linear fitting results of repeated experimental data. The strain sensitivity of the designed sensor is Figure 7band shows the linear fitting of repeated experimental data. The strain the resolution precision of the FBGresults integrator are 1 pm and ±5 pm respectively, thesensitivity resolution of and 6.2 pm/µε and the linear correlation coefficient is 0.99986. The actual is strain amplification factor of the designed sensor is 6.2 pm/με and the linear correlation coefficient 0.99986. The actual strain precision of the developed sensor are 0.16 με and ±0.80 με respectively. designedamplification FBG strainfactor sensor is 5.2, which matches the FEM the resolution andAs precision of of the designed FBG strain sensor is 5.2,result. which As matches the FEM result. the the FBGresolution integrator are 1 pm and ±FBG 5 pmintegrator respectively, theand resolution and precision of the developed and precision of the are 1 pm ±5 pm respectively, the resolution and 1400 1400 FBG-based Sensor 1st Designed FBG-based sensor precision ofDesigned theFBG developed sensor are 0.16 με and ±0.80 με respectively. sensor are 0.16 µε and ± Bare 1st0.80 µε respectively.
160
200
1000 1400 800 1200 600 1000 400 800 200 600 0 400 200
Designed FBG-based sensor Bare FBGy=6.2x-0.68 Linear fit of designed FBG-based sensor Linear fit of Bare FBG
y=6.2x-0.68
0
40
80
y=1.2x-0.73
120 y=1.2x-0.73 160 200
Stain (με)
0 (a) (b) 0 40 80 120 160 200 0 40 80 120 160 200 Stain (με)(b) linear fitting. Stain Figure 7. Repeatability and (με) linearity of the FBG strain sensor: (a) Repeatability experiment;
0
4.2. Dynamic Properties
(a)
(b)
Figure 7. Repeatability and linearity of the FBG strain sensor: (a) Repeatability experiment; (b) linear fitting.
to investigate the dynamic of the developed sensor,experiment; a dynamic experimental Figure In 7. order Repeatability and linearity of the capabilities FBG strain sensor: (a) Repeatability (b) linear fitting. setup was established (as shown in Figure 8). The designed sensor was fixed on the uniform strength 4.2. Dynamic Properties
In order to investigate the dynamic capabilities of the developed sensor, a dynamic experimental setup was established (as shown in Figure 8). The designed sensor was fixed on the uniform strength
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4.2. Dynamic Properties In order to investigate the dynamic capabilities of the developed sensor, a dynamic experimental 8 of 11 setup was established (as shown in Figure 8). The designed sensor was fixed on the uniform strength beam which which was was excited excited by by aa vibration vibration exciter. exciter. In In contrast, contrast, aa dynamic dynamic strain strain gauge gauge and and aa bare bare FBG FBG beam were also fixed on the same side of the uniform strength beam and in the same sensing direction. were also fixed on the same side of the uniform strength beam and in the same sensing direction. The The signals of designed the designed sensor were collected FBG interrogator with signals of the sensor andand the the barebare FBGFBG were collected by by thethe FBG interrogator with a a sampling rateofof2 2kHz. kHz.The Thesignal signalofofthe theresistance resistancestain staingauge gaugewas wasrecorded recorded by by aa dynamic dynamic strain strain sampling rate indicator (TST5912). (TST5912). The The driving driving signal signal of of the the vibration vibration exciter exciter was was controlled controlled by by the the signal signal generator generator indicator and power amplifier. and power amplifier. Sensors 2018, 18, x FOR PEER REVIEW
Figure Figure 8. 8. Schematic Schematic diagram diagram of of dynamic dynamic properties properties experiment. experiment.
The dynamic response of the FBG strain sensor was tested with the excitation frequencies varied The dynamic response of the FBG strain sensor was tested with the excitation frequencies varied in the in the range of 5 Hz to 100 Hz with an interval of 5 Hz. As the power of the vibration is too low to range of 5 Hz to 100 Hz with an interval of 5 Hz. As the power of the vibration is too low to exert a greater exert a greater force on the cantilever beam when the frequency is high, the highest excitation force on the cantilever beam when the frequency is high, the highest excitation frequency was set to 100 Hz. frequency was set to 100 Hz. The test results were compared with the bare FBG and the strain gauge. The test results were compared with the bare FBG and the strain gauge. It is worthwhile pointing out that It is worthwhile pointing out that as the designed sensor has a thickness of 1 mm. It is unfair to as the designed sensor has a thickness of 1 mm. It is unfair to compare the testing results of bare FBG and compare the testing results of bare FBG and the designed sensor directly when they are utilized to the designed sensor directly when they are utilized to test the bending strain on the uniform strength beam. test the bending strain on the uniform strength beam. The thickness of the uniform strength beam is The thickness of the uniform strength beam is 8 mm, therefore, the distance between the bare FBG and the 8 mm, therefore, the distance between the bare FBG and the neutral layer of the uniform strength neutral layer of the uniform strength beam is 4 mm while the distance between the FBG on the designed beam is 4 mm while the distance between the FBG on the designed sensor and the neutral layer of sensor and the neutral layer of the uniform strength beam is 5 mm. The detected wavelength shifts of the the uniform strength beam is 5 mm. The detected wavelength shifts of the designed sensor were designed sensor were divided by t = 5/4 = 1.25 to eliminate the sensitization effect caused by the thickness divided by t = 5/4 = 1.25 to eliminate the sensitization effect caused by the thickness of the substrate of the substrate of the designed sensor. As shown in Figure 9, the strain sensitivity and strain amplification of the designed sensor. As shown in Figure 9, the strain sensitivity and strain amplification factor of factor of the designed sensor remains consistent with the static test results at a frequency range from 5 Hz the designed sensor remains consistent with the static test results at a frequency range from 5 Hz to to 100 Hz. The mean values of the strain sensitivity and strain amplification factor are 5.9 pm/µε and 100 Hz. The mean values of the strain sensitivity and strain amplification factor are 5.9 pm/με and 5.1 respectively, considering the thickness of the designed FBG sensor. The maximum errors are 2.7% and 5.1 respectively, considering the thickness of the designed FBG sensor. The maximum errors are 2.7% 2.4%, respectively. The standard deviations of the tested strain sensitivity and strain amplification factor are and 2.4%, respectively. The standard deviations of the tested strain sensitivity and strain 0.06 pm/µε and 0.03, respectively. amplification factor are 0.06 pm/με and 0.03, respectively. Vibration tests—by knocking on the cantilever beam—were carried out to get the response of the designed FBG strain sensor at higher frequencies. The cantilever beam was hung using elastic rope to 5 Hz make sure it was in a free foundation, as shown in Figure 10. The signals of the designed FBG strain sensor and bare FBG were collected—by knocking the cantilever beam with a hammer—by the FBG Mean 5.9 pm/µɛ interrogator (sampling rate: 2 kHz). 25 Hz
Standard deviation 0.06 pm/µɛ
50 Hz Mean 5.1 Standard deviation 0.03
(a)
(b)
Figure 9. The response of FBG stain sensor, bare sensor and strain gauge under 5–100 Hz excitation frequency: (a) Dynamic displacement measurement; (b) the sensitivity and amplification factor.
of the designed sensor. As shown in Figure 9, the strain sensitivity and strain amplification factor of the designed sensor remains consistent with the static test results at a frequency range from 5 Hz to 100 Hz. The mean values of the strain sensitivity and strain amplification factor are 5.9 pm/με and 5.1 respectively, considering the thickness of the designed FBG sensor. The maximum errors are 2.7% and 2.4%, respectively. The standard deviations of the tested strain sensitivity and strain Sensors 2018, 18, 1607 9 of 12 amplification factor are 0.06 pm/με and 0.03, respectively. 5 Hz
25 Hz
Mean 5.9 pm/µɛ Standard deviation 0.06 pm/µɛ
50 Hz Mean 5.1
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Vibration tests—by knocking on the cantilever beam—were carried out to get the response of the designed FBG strain sensor at higher frequencies. The cantilever beam (a) (b) was hung using elastic rope to make sure it was in a free foundation, as shown in Figure 10. The signals of the designed FBG Figure 9. The response of FBG stain sensor, bare sensor and strain gauge under 5–100 Hz excitation Figure 9. The of were FBG stain sensor, bareknocking sensor and gauge under excitation the strain sensor andresponse bare FBG collected—by thestrain cantilever beam 5–100 with aHz hammer—by frequency: (a) Dynamic displacement measurement; (b) the sensitivity and amplification factor. frequency: (a) Dynamic displacement measurement; (b) the sensitivity and amplification factor. FBG interrogator (sampling rate: 2 kHz).
Flexible cord Designed sensor
Bare FBG Hammer
Uniform strength beam
Figure10. 10.Schematic Schematicdiagram diagramofofknocking knockingexperiment. experiment. Figure
From the time domain waveform in Figure 11, it can be seen clearly that the designed sensor is From the time domain waveform in Figure 11, it can be seen clearly that the designed sensor is more sensitive than the bare FBG in the knocking experiment. To quantitatively compare the strain more sensitive than the bare FBG in the knocking experiment. To quantitatively compare the strain sensitivity of the designed FBG sensor and the bare FBG, we obtained the frequency spectrum of the sensitivity of the designed FBG sensor and the bare FBG, we obtained the frequency spectrum of testing results via fast Fourier transform (FFT). According to the laws of the sampling, as the sampling the testing results via fast Fourier transform (FFT). According to the laws of the sampling, as the rate of the FBG interrogator is 2 kHz, the frequency spectrum from 0 to 1 kHz can be analyzed. As sampling rate of the FBG interrogator is 2 kHz, the frequency spectrum from 0 to 1 kHz can be analyzed. shown in Figure 11, the frequency spectrum obtained from the designed sensor’s testing data and the As shown in Figure 11, the frequency spectrum obtained from the designed sensor’s testing data frequency spectrum obtained from the bare FBG’s testing data show a high concordance in spectral and the frequency spectrum obtained from the bare FBG’s testing data show a high concordance in distributions. Both the designed FBG strain sensor and the bare FBG can detect the first-order eigenspectral distributions. Both the designed FBG strain sensor and the bare FBG can detect the first-order frequency 298 Hz and the second-order eigen-frequency 768 Hz of the uniform strength beam, which eigen-frequency 298 Hz and the second-order eigen-frequency 768 Hz of the uniform strength beam, is consistent with the modal analysis results of 280.1 Hz and 728.7 Hz, respectively, by FEM. For the which is consistent with the modal analysis results of 280.1 Hz and 728.7 Hz, respectively, by FEM. dynamical strain in 298 Hz and 768 Hz, the sensitivity amplification factor q of the designed FBG For the dynamical strain in 298 Hz and 768 Hz, the sensitivity amplification factor q of the designed sensor are 107/(17 × 1.25) = 5.0 and 25.8/(4.1 × 1.25) = 5.0, respectively, considering the thickness of the FBG sensor are 107/(17 × 1.25) = 5.0 and 25.8/(4.1 × 1.25) = 5.0, respectively, considering the thickness substrate of the designed sensor. Additionally, in the knocking experiment, dynamic strain signals in of the substrate of the designed sensor. Additionally, in the knocking experiment, dynamic strain some other frequencies (406 Hz, 529 Hz, and 939 Hz) have been stimulated. For dynamical strain in signals in some other frequencies (406 Hz, 529 Hz, and 939 Hz) have been stimulated. For dynamical these frequencies, the sensitivity amplification factor q of the designed FBG sensor are 7.5/(1.2 × 1.25) = 5.0, strain in these frequencies, the sensitivity amplification factor q of the designed FBG sensor are 8.5/(1.3 × 1.25) = 5.2, 9.4/(1.5 × 1.25) = 5.0, respectively. Therefore, the designed sensor keeps a constant 7.5/(1.2 × 1.25) = 5.0, 8.5/(1.3 × 1.25) = 5.2, 9.4/(1.5 × 1.25) = 5.0, respectively. Therefore, the designed sensitivity amplification factor in a wide frequency range. sensor keeps a constant sensitivity amplification factor in a wide frequency range. Comparing to existing FBG-based strain sensors in References [20–25], the particular mechanical Comparing to existing FBG-based strain sensors in References [20–25], the particular mechanical configuration in this paper brings lots of advantages to the designed sensor. Firstly, the proposed configuration in this paper brings lots of advantages to the designed sensor. Firstly, the proposed sensor sensor has a small and compact structure, which make it possible to apply it in regular-sized has a small and compact structure, which make it possible to apply it in regular-sized mechanical mechanical equipment. Secondly, the structural design of the sensor is very simple, which makes it easier to manufacture. The simple structure can enhance the reliability of the sensor in engineering applications. Thirdly, the particular mechanical configuration in the designed sensor can easily amplify the strain of FBG to enhance the overall sensitivity based on the lever principle. Through changing the sizes and materials of the mechanical configuration, the strain amplification factor of the mechanical configuration can be controlled to transfer more or less strain to the FBG.
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equipment. Secondly, the structural design of the sensor is very simple, which makes it easier to manufacture. The simple structure can enhance the reliability of the sensor in engineering applications. Thirdly, the particular mechanical configuration in the designed sensor can easily amplify the strain of FBG to enhance the overall sensitivity based on the lever principle. Through changing the sizes and materials of the mechanical configuration, the strain amplification factor of the mechanical configuration can be controlled to transfer more or less strain to the FBG. Consequently, the measurement range and sensitivity can be easily adjusted to adapt to different measurement demands. Finally, the developed sensor possesses good dynamic response characteristics and can be qualified for dynamic strain measurements in a wide frequency range with a constant high Sensors 2018, 18, x FOR PEER REVIEW 10 of 11 strain sensitivity.
Time domain waveform
529 Hz 107
406 Hz
8.5
768 Hz 25.8
7.5
939 Hz 9.4
298 Hz
Frequency spectrum 17
4.1 1.2
1.3
1.5
Figure 11.11. Time domain waveform and thethe frequency spectrum of of thethe bare FBG and thethe designed Figure Time domain waveform and frequency spectrum bare FBG and designed sensor in the knocking experiment. sensor in the knocking experiment.
5. 5. Conclusions Conclusions AA sensitivity enhancing method for FBG-based strain sensor proposed in this paper. sensitivity sensitivity enhancing method for FBG-based strainissensor is proposed in A this paper. A enhanced FBG-based strain sensor was designed and realized. This sensor mainly consists of anconsists FBG sensitivity enhanced FBG-based strain sensor was designed and realized. This sensor mainly and substrate with a lever with structure which mechanically amplifies theamplifies strain at the FBGstrain area.at of an an elastic FBG and an elastic substrate a lever structure which mechanically The strain sensing model of the designed sensor was analyzed by material mechanics theory and was FBG area. The strain sensing model of the designed sensor was analyzed by material mechanics verified FEM and experimental test.and The experimental designed sensor hasThe a strain sensitivity of 6.2 theorythrough and was verified through FEM test. designed sensor haspm/µε, a strain which is as 5.2 times of the bare FBG sensor. The designed sensor possesses a good linearity and sensitivity of 6.2 pm/με, which is as 5.2 times of the bare FBG sensor. The designed sensor possesses a low repeatability error. In addition, as the lever structure of the designed sensor has a high stiffness, a good linearity and a low repeatability error. In addition, as the lever structure of the designed sensor thehas proposed sensor can a high resonant frequency, andresonant its dynamic test range wide. Due to a high stiffness, theachieve proposed sensor can achieve a high frequency, andisits dynamic test itsrange high strain sensitivity, the designed sensor has a wide application prospects for the small-amplitude is wide. Due to its high strain sensitivity, the designed sensor has a wide application prospects micro-strain measurementsmicro-strain in harsh industrial environments. for the small-amplitude measurements in harsh industrial environments. Author Contributions: R.L. and Y.C. conceived, designed and performed the experiments; T.L. and J.M. analyzed Author Contributions: R.L. and Y.C. conceived, designed and performed the experiments; T.L. and J.M. the data; Y.T. and Z.Z. contributed materials and analysis tools; R.L. wrote the paper. analyzed the data; Y.T. and Z.Z. contributed materials and analysis tools; R.L. wrote the paper. Acknowledgments: This work is supported by the Key Project of National Nature Science Foundation of China Acknowledgments: This the work is supported by the&Key Project ofCooperation National Nature Science Foundation China under Grant No. 51475343, International Science Technology Program of China under of Grant under Grant No. 51475343, the International Science & Technology Cooperation Program of China under Grant No. 2015DFA70340, and the Fundamental Research Funds for the Central Universities of China under Grant No. 2016-YB-019.
Conflicts of Interest: The authors declare no conflict of interest.
References
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No. 2015DFA70340, and the Fundamental Research Funds for the Central Universities of China under Grant No. 2016-YB-019. Conflicts of Interest: The authors declare no conflict of interest.
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