sensors Article

A Fiber Bragg Grating Sensing-Based Micro-Vibration Sensor and Its Application Tianliang Li *, Yuegang Tan and Zude Zhou School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430000, Hubei, China; [email protected] (Y.T.); [email protected] (Z.Z.) * Correspondence: [email protected]; Tel.: +86-133-4988-6661 Academic Editor: Vittorio M. N. Passaro Received: 14 February 2016; Accepted: 12 April 2016; Published: 15 April 2016

Abstract: This paper proposes a fiber Bragg grating sensing-based micro-vibration sensor. The optical fiber has been directly treated as an elastomer to design the micro-vibration sensor, which possesses two FBGs. The mass is fixed on the middle of the fiber, and the vertical vibration of the mass has been converted into the axial tension/compression of the fiber. The principle of the sensor has been introduced, and the experiment conclusions show that the sensor sensitivity is 2362 pm/g within the range of 200–1200 mm/s2 , which is consistent with theoretical analysis sensitivity of 2532.6 pm/g, and it shows an excellent linearity of 1.376%, while the resonant frequency of the sensor is 34 Hz, and the flat frequency range resides in the 0–22 Hz range. When used to measure micro-vibrations, its measured frequency relative error is less than 1.69% compared with the values acquired with a MEMS accelerometer, and the amplitude values of its measured vibration signal are consistent with the MEMS accelerometer under different excitation conditions too, so it can effectively realize the micro-vibration measurements. Keywords: micro-vibration; fiber Bragg grating; vibration sensor

1. Introduction Compared with traditional electronic vibration sensors, fiber Bragg grating (FBG) sensing offers many advantages, for instance, immunity from electromagnetic interference and high temperatures, small size, corrosion resistance and ability to multiplex, so accelerometer design methods based on FBG are particularly attractive. Many scholars have done an in-depth research on them. Berkoff et al. proposed a new accelerometer, where the mass rested on a compliant material supported by a rigid base plate, and FBG embedded in the compliant material, using the mass’s movement conversion of the axial strain of the FBG by the compliant material [1]. Au et al. presented a tapered plate FBG accelerometer, where the FBGs have been pasted on the surface of the tapered plate; the experiment shows that its sensitivity is 18.93 µε/g, and the maximum input signal frequency is up to 150 Hz [2]. A flexural beam utilized as primary transduction mechanism for demonstrating a FBG accelerometer has been described in [3]; it has good acceleration sensitivity of 212.5 µε/g, and the resonant frequency is on the order of 1 kHz. Basumallick et al. proposed a method to improve the sensitivity of cantilever-mass-based FBG accelerometers by altering the distance between the axis of the FBG sensor to the neutral axis of the cantilever [4], and it’s demonstrated that its sensitivity is about 1062 pm/g. All of the above FBG vibration sensors’ principles are based on pasted FBGs, so these sensors’ sensing properties are limited by the pasting process and the elastomer structure. Antunes et al. described the implementation and testing of an optical fiber-based accelerometer with cross axis insensitivity; its principle is based on an improved cantilever beam, and vertical vibration is converted into tension and compression movement along the FBGs’ axial direction by dangly arranged FBGs [5]. A L-shaped modified cantilever beam FBG-based accelerometer with Sensors 2016, 16, 547; doi:10.3390/s16040547

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self-temperature compensation has been studied in [6]; its sensitivity is 46 pm/g for frequencies below 50 Hz and 306 pm/g for frequencies above 150 Hz. da Costa Antunes et al. designed an accelerometer, where the inertial mass, supported by a L-shaped aluminum cantilever beam, was connected to the structure base by a steel leaf spring; when exposed to an external acceleration, the inertial mass’s movement along the vertical direction was converted into a contraction/expansion of the optical fiber through the L-shaped beam; it can be used to monitor structures with frequencies up to 45 Hz [7]. Reference [8] described the implementation and testing of an optical fiber biaxial accelerometer based on four FBGs placed in opposite positions; this is a simple solution to measure acceleration in two orthogonal directions, and its sensitivities were 87.848 and 92.351 pm/g, for each sensitive direction with resonant frequencies of 846.01 and 845.33 Hz, respectively. A fiber Bragg grating single-axis acceleration sensor based on a double-membrane has been proposed in [9]; its cross coupling of non-directional accelerations is minimized by introducing a unique double-membrane fixture of the sensor's mass of inertia leading to an almost diagonal form of the sensors stiffness-matrix; according to FEM simulation of the sensor, its resonance frequency is 6.0 kHz with a sensitivity of 1 pm/g. The references [10,11] proposed a non-contact vibration sensor based on fiber Bragg gratings, mainly used to measure displacement vibrations; the diaphragm is used as the elastomer, and its principle is similar to that described in [9]. Zhang et al. presented a novel FBG accelerometer, where the elastomer is the fiber itself, and the mass is fixed on the middle of the two FBGs to sense the vibration; it has good flat response from 10–130 Hz with a sensitivity of 231.8 pm/g [12]. A metal bellows-based FBG accelerometer is proposed and experimentally demonstrated in [13], the mass is also directly fixed on the fiber, the principle of the it is similar to the sensor in reference [12]; its sensitivity is 548.7 pm/g within a wide frequency response range 5–110 Hz. Guo et al. presented a fiber Bragg grating-based accelerometer with a fully metalized package, the elastic coefficient of fiber is greatly improved by this processing, the experiments shows that its resonant frequency is 3.6 kHz, and the sensitivity is 1.7 pm/g within the range of 0–8 g [14]. Based on the above investigation, the sensitivity of previous FBG accelerometers is commonly relatively lower. And all of these aren’t suited to measure micro-vibrations. Li et al. used the transverse property of optical fiber to design a triaxial vibration sensor; its sensitivity in the y direction is 971.8 pm/g, which is larger than the above designed FBG vibration sensors [15], but in [15], only experiments were used to verify the triaxial vibration measurement theoretical model, and it lacks a rigorous sensitivity theoretical model, so this paper mainly proposes a FBG-based vibration sensor to monitor micro-vibrations and builds an effective model for the sensitivity, which meets the micro-vibration requirements. In this paper, a micro-vibration sensor based on FBG sensing has been proposed. The optical fiber has been directly treated as an elastomer, which possesses two FBGs, and the vertical vibration of the mass has been converted into the axial tension/compression of FBG to achieve the micro-vibration measurement. The principle of the sensor and experimental analyses are introduced. 2. Model and Principle of Micro-Vibration Sensor Commonly designed FBG vibration sensors mainly use the mechanical structure as elastomer, such as the cantilevers in [6,7]. This paper directly uses the optical fiber as elastomer to design the vibration sensor (Figure 1), the z direction freedom of mass is limited by the dam-board. Its structure is very small and simple; also it’s easily to achieve quasi-distributed vibration measurements. According to the mechanics of the material, the horizontal direction stiffness Kx of sensor can be expressed as: Kx “

2E f A f l

(1)

where Ef is the Young’s Modulus of optical fiber, and Af means the cross-sectional area of the optic fiber. According to the material mechanics, the lateral bending stiffness of the fiber can be described as KL = Ef If = πEf D4 /64. Young’s Modulus Ef and diameter of optical fiber D are 72 GPa and 125 µm, respectively.

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as KL = EfIf = πEfD4/64. Young’s Modulus Ef and diameter of optical fiber D are 72GPa and 125 μm, 3 of 14 respectively.

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(a)

(b) Figure1.1.Vibration Vibration model a bare optical fiberFBG withand FBG and lumped (a) Horizontal Figure model of aofbare optical fiber with lumped mass. (a)mass. Horizontal vibration vibration model of a bare optical fiber with FBG and lumped mass; (b) Vertical vibration model of a model of a bare optical fiber with FBG and lumped mass; (b) Vertical vibration model of a bare optical bare optical fiber with FBG and lumped mass. fiber with FBG and lumped mass.

The lateral bending stiffness of fiber KL is equal to 8.63 × 10−5 N/m, which is close to 0, so the The lateral bending stiffness of fiber KL is equal to 8.63 ˆ 10´5 N/m, which is close to 0, so the optical fiber can be considered as a string. Its lateral vibration model can be simplified as shown in optical fiber can be considered as a string. Its lateral vibration model can be simplified as shown in Figure 1b. Combining with geometrical deformation method, the strain increment of the fiber are Figure 1b. Combining with geometrical deformation method, the strain increment of the fiber are separately Δε0 and Δεy under mass in the equilibrium position or vibrating position, which can be separately ∆ε0 and ∆εy under mass in the equilibrium position or vibrating position, which can be expressed by: expressed by: b 0  ∆ε0“

2  yy0202 ´  ll ll2 `

ll

(2) (2)

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l 22 ` y22 ´ l ∆εy “  l  y  l (3) (3) y ll where y0 represents the distance between the equilibrium position of the mass and a horizontal line, where y0 represents the distance between the equilibrium position of the mass and a horizontal line, y is the vertical direction movement of inertial mass, L(L = 2l) is the initial length of the optical fiber y is the vertical direction movement of inertial mass, L(L = 2l) is the initial length of the optical fiber between both fixed ends, ay is the acceleration along the y direction. between both fixed ends, ay is the acceleration along the y direction. Pre-stress is exerted on the optical fiber during the sensor packaging process; the corresponding Pre-stress is exerted on the optical fiber during the sensor packaging process; the corresponding pre-strain of the fiber is ε0 . Combining the equation of static theory with Equation (1), when the mass pre-strain of the fiber is ε0. Combining the equation of static theory with Equation (1), when the mass is in the equilibrium position, the gravity of mass mg can be represented by: is in the equilibrium position, the gravity of mass mg can be represented by: 2E 2 Ef fAAffpε(00` ∆ε 00q) y mg mg“ p∆ε y00 ` 1ql ( 00  1)l

(4) (4)

where under the the inertial inertial mass massgravity, gravity,ggrepresents representsacceleration accelerationofofgravity. gravity. is the the strain strain increment increment under where ∆ε Δε00 is Combining optical fiber KyKalong the vibration direction can be Combiningwith withEquation Equation(4), (4),the thestiffness stiffnessofof optical fiber y along the vibration direction can written as: be written as: 2E f A f pε 0 ` ∆ε 0 q mg Ky “ “ (5) ymg 1ql 2Ep∆ε (` 0 f Af 0 0   0 ) Ky   (5) x/y  0 is1)the l stiffness ratio between the horizontal Combining Equation (1) with Equationy0(5), the(R and vibration direction stiffness, and it can be described by: Combining Equation (1) with Equation (5), the Rx/y is the stiffness ratio between the horizontal and vibration direction stiffness, and it can be by:1 ∆εdescribed 0`1 R x {y “ « (6) ε 0 ` ∆ε 0 ε 0 ` ∆ε 0

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 0  1 1  Rx / y  (6)  0   0  0   0 From Equation (6), the stiffness ratio versus ∆ε0 + ε0 is shown in Figure 2. From Figure 2, the From Equation (6), the stiffness ratio versus Δε0 + ε0 is shown in Figure 2. From Figure 2, the Rx/y Rx/y is far more than 1, which means the Kx >> Ky . The sensitivity of the vibration sensor is inversely is far more than 1, which means the Kx >> Ky. The sensitivity of the vibration sensor is inversely proportional to the TheThe FBGFBG vibration sensor waswas designed using thethe axial feature of of optical proportional to stiffness. the stiffness. vibration sensor designed using axial feature fiber optical in [13],fiber andinthe mass is 17.9 g, while the sensor’s sensitivity is only 231.48 pm/g. When [13], and the mass is 17.9 g, while the sensor’s sensitivity is only 231.48 pm/g. When the vertical direction of optical fiber is considered as the vibration direction, improve the the vertical direction of optical fiber is considered as the vibration direction,ititwill will greatly greatly improve sensitivity of the FBG vibration sensorsensor to usetothe same mass mass as reference [13].[13]. Therefore, thethe vertical the sensitivity of the FBG vibration use the same as reference Therefore, vertical vibration property can used to a micro-vibration vibration property can be used tobe design a design micro-vibration sensor.sensor. 4

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Combining Equation (4) with the definition of resonant frequency, the resonant frequency wv of Combining Equation (4) with the definition of resonant frequency, the resonant frequency wv of vibration direction can be written as:

vibration direction can be written as:

K d2 E A (   0 ) wv c Kyy  2Ef f Af f pε0 0 ` ∆ε ( 0  1)lm 0 q m “ wv “ m

(7)

(7)

p∆ε 0 ` 1qlm

When the excited vibration frequency w 90%) are separately 1298.226 and 1310.027 nm. During the processing of the sensor, at first, we use the optical fiber to connect with the mass, and then exert an appropriate pre-stress on the fiber. The FBGs’ center wavelengths shift is about 1.45 nm compared with the initial center wavelength. Initial length of the optical fiber L is 30 mm. Combining Equation (7) with Equation (15), the natural frequency and sensitivity of sensor can be calculated, which are separately 21.9 Hz and 2532.5 pm/g.

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Equation (15), the natural frequency and sensitivity of sensor can be calculated, which are Equation (15), theand natural and sensitivity of sensor can be calculated, which are separately 21.9 Hz 2532.5frequency pm/g. Sensors 2016, 16, 547 7 of 14 separately 21.9 Hz and 2532.5 pm/g.

Figure 5. Schematic diagram and physical map of the experiments to determine the sensors’ sensing Figure Schematic diagram physical the experiments to determine the sensors’ Figure 5. Schematic diagram andand physical mapmap of theofexperiments to determine the sensors’ sensing properties. sensing properties. properties.

3.1. Sensitivity Experiments 3.1. Sensitivity Experiments During the experiment, the acceleration amplitude changes from 200 mm/s2 to 1200 mm/s2 22 to During the experiment, experiment, the8acceleration acceleration amplitude changes from 200mm/s mm/s to 1200mm/s mm/sis22 from 200 1200 under a constant frequency the of Hz throughamplitude adjustingchanges the signal generator. The experiment constant frequency Hz through adjusting thefirst signal generator. The is under aaconstant frequency 8ofHz8 through adjusting thebeing signal generator. Theand experiment is repeated repeated six times with theofamplitude of acceleration increased thenexperiment decreased to repeated six times with the amplitude of acceleration beingAccording first increased and then to six times with therepeatability amplitude ofand acceleration being first increased and then decreased to decreased demonstrate demonstrate the hysteresis of the sensor. to Equation (14), the plot of demonstrate the repeatability and ofAccording the sensor. to Equation (14), theaddition plot of repeatability and of hysteresis the sensor. Equation the6.plot of Figure the the addition value Δλhysteresis 2 + Δλ1 versus applied acceleration aytoisAccording shown in(14), Figure From 6, the the addition value Δλ2applied + Δλ 1 versus applied ay is shown in Figure 6. the From Figure 6, the value ∆λ2 + ∆λ acceleration ayacceleration isand shown in Figure 6. From 6, micro-vibration micro-vibration sensor’s repeatability error hysteresis error can be obtained separately as 1 versus micro-vibration sensor’s repeatability error and hysteresis error can be obtained separately as sensor’sand repeatability hysteresis can be obtained separately we as 3.247% 3.247% 3.589%. In error orderand to further studyerror the sensor’s sensing properties, averageand the 3.589%. six sets 3.247% and 3.589%. In and order to further study the sensor’s sensing weofwhich average sixdata, sets In order to further study thethen sensor’s sensing properties, average sets experimental of experimental data, obtained a linear fittedwe curve ofproperties, the six sensor, is the shown in of experimental data, and then obtained linear which fitted ofinfitted the sensor, which is expressed shown in and then a linear fitted of the iscurve shown Figure 7. From Figure 7, we can Figure 7. obtained From Figure 7, we cancurve get that theasensor, linearity is 1.376%; the equation can be 2 Figure 7. From Figure 7, we can get that the linearity is 1.376%; the fitted equation can be expressed getΔλ that the fitted can be expressed as ∆λ2 +sensitivity ∆λ1 = 0.2362 ˆ ay +pm/g 0.8489 as 2 +the Δλlinearity 1 = 0.2362is×1.376%; ay + 0.8489 (unit equation of ay is mm/s ). The experimental of 2362 is 2). The experimental sensitivity of 2362 pm/g is as Δλof 2 +aΔλ 1 = 0.2362 ×The ay + experimental 0.8489analysis (unit ofsensitivity ay is mm/sof (unit mm/s pm/g is consistent with theof theoretical consistent with the2 ).theoretical sensitivity of2362 2532.6 pm/g, so the validity sensor’s y is consistent with theof theoretical analysis sensitivity of 2532.6 pm/g, so the compared validity sensor’s analysis sensitivity 2532.6 so the validity of sensor’s theoretical sensitivity modeofiswith verified. theoretical sensitivity modepm/g, is verified. Its sensitivity is greatly increased the theoretical sensitivity mode is verified. Its sensitivity is greatly increased compared with the Its sensitivity is greatly compared with the sensitivity of the devices described in [13–15]. sensitivity of the devicesincreased described in [13–15]. sensitivity of the devices described in [13–15]. 300

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Figure 6. The value ∆λ Δλ2 + + Δλ Figure 6. The addition addition value ∆λ11 versus versus applied applied acceleration acceleration aayy—the —the inset inset shows shows the the center center 2 22 2 and 2center Figure 6. The addition value Δλ 2 + Δλ 1 versus applied acceleration a y—the inset shows the y of 400 mm/s , 800 mm/s 1200 mm/s . 2. wavelength shift response in the time domain with a 2 wavelength shift response in the time domain with ay of 400 mm/s , 800 mm/s and 1200 mm/s wavelength shift response in the time domain with ay of 400 mm/s2, 800 mm/s2 and 1200 mm/s2.

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Experimental data Experimental Fitted line data Fitted line

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Figure 7. The linear fitting curve of addition value Δλ2 + Δλ1 versus applied acceleration ay. Figure 7. The The linear linear fitting fitting curve curve of of addition addition value value ∆λ Δλ2 + + Δλ Figure 7. ∆λ11 versus versus applied applied acceleration acceleration aayy. . 2

A/A/ pmpm

3.2. Amplitude-Frequency Property Experiments 3.2. Amplitude-Frequency Property Experiments 3.2. Amplitude-Frequency Property Experiments In order to demonstrate the sensor’s amplitude-frequency properties, the acceleration 2the In order to at demonstrate amplitude-frequency the acceleration amplitude is set 400 mm/s , thesensor’s frequency increases from 2 properties, to the 40 acceleration Hz. Figure 8 shows In order to demonstrate the sensor’s amplitude-frequency properties, amplitude 2, the frequency increases from 2 to 40 Hz. Figure 8 shows amplitude is set at 400 mm/s amplitude-frequency curve of theincreases FBG micro-vibration sensor. 8 amplitude-frequency shows that sensor’s is set at 400 mm/s2 , the frequency from 2 to 40 Hz. FigureFigure 8 shows amplitude-frequency curve of the FBG micro-vibration sensor. Figure 8 Hz. shows sensor’s resonance frequency is about 34 Hz, and it has a flat response within 2 to 22 The that experimental curve of the FBG micro-vibration sensor. Figure 8 shows that sensor’s resonance frequency is about resonance frequency is about 34 Hz,the and it has a flat responsevalue within 221.9 to 22 Hz. The experimental resonance frequency is larger than theoretical computed of Hz. Because the effect of 34 Hz, and it has a flat response within 2 to 22 Hz. The experimental resonance frequency is larger resonance frequency is larger than the theoretical computed value of 21.9 Hz. Because the effect of mass’s neglectedvalue in theoftheoretical model,the andeffect the equivalent stiffness ofisthe sensor in is than thedimension theoreticaliscomputed 21.9 Hz. Because of mass’s dimension neglected mass’s dimension issituation. neglected in the theoretical model, and the equivalent stiffness of the sensor is less than in the real the theoretical model, and the equivalent stiffness of the sensor is less than in the real situation. less than in the real situation. In study the sensitivity of we tried tried the the xx direction direction of of the the sensor sensor as the In order order to to study the cross cross sensitivity of the the sensor, sensor, we as the In order to study the crossrepeated sensitivitythe of theabove sensor,experiment. we tried the xCombining direction of the sensor8,as the excitation direction, and Figure the excitation direction, and repeated the above experiment. Combining Figure 8, the amplitude-frequency excitation direction, curves and ofrepeated the above experiment. Combining Figure 8, the amplitude-frequency the FBG micro-vibration sensor in the x and y-direction are shown curves of the FBG micro-vibration sensor in the x and y-direction are shown in Figure 9. From Figurein 9, amplitude-frequency curves of the FBG micro-vibration sensor in theparallel x and y-direction are shownthe in Figure 9. From Figure 9, we can find that the pink curve is almost to the x axis without we can find that the pink curve is almost parallel to the x axis without the frequency of 34 Hz, which Figure 9. From Figure 9, werepresents can find that the pink curve is almost parallel to the x the axis without the frequency Hz, interference which the of cross response of the the pink sensor; of represents of the34cross response the interference sensor; the amplitude of curve isamplitude about 6 pm, frequency of 34 is Hz, which represents the crossby interference response of The the sensor; the amplitude of the pink curve about 6 pm, mainly caused the FBG interrogator. cross interference of the mainly caused by the FBG interrogator. The cross interference of the sensor can be decreased by the the pink curve is about 6by pm, caused byFBGs the FBG interrogator. The cross interference of the sensor can decreased themainly addition addition ofbe two FBGs by about 0.51% = (6ofˆtwo 2/2362). by about 0.51% = (6 × 2/2362). sensor can be decreased by the addition of two FBGs by about 0.51% = (6 × 2/2362). 450 450 400 400 350 350 300 300 250 250 200 200 150 150 100 100 50 50 0 0 0 0

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3.3. Experiments ofofDampling Dampling Characteristics 3.3. Experiments DamplingCharacteristics Characteristics 3.3. Experiments of The damping ratio isisone one of the most important indicators indicatorsto toevaluate evaluatethe the performance of the the The dampingratio ratiois oneof ofthe themost most important important performance of of the The damping indicators to evaluate the performance sensor, because be to the sensors’ sensors’ structure. According theory sensor, because itcan can be used used to optimize optimize the structure. According to tothethe theory of of sensor, because it it can be used to optimize the sensors’ structure. According to the theory of vibration, vibration, the damping ratio of sensor can obtained through the logarithmic damping coefficient vibration, the damping ratio of sensor be obtained through the logarithmic damping coefficient the damping ratio of sensor can be obtained through the logarithmic damping coefficient method in method thehammer hammerexperiment. experiment. The logarithmic logarithmic damping can bebe expressed as:as: method ininthe The dampingcoefficient coefficient can expressed the hammer experiment. The logarithmic damping coefficient can be expressed as: wwtv t 2 11 ln xx11 1 ln( ´eeξw t ) ))ww == 2 2πξ v nT  vT dd (16)(16) ww ((t t 1 e 1 ==xn1ln vT 2 2 v  nTd ) x n e  a n e δ “ ln n x“nn11 lnp q “ ξwv Td 1“ (16) 1  ´ ξw p t ` nT q 2 v d n x n `1 n e 1´ξ where the1st 1streference referencepeak peak value value in in the peak value in the where x1xis1 isthe the time time domain, domain,xxn+1n+1isisthe thenth nthreference reference peak value in the where xdomain, reference peak value in time domain, xn+1 is the nth reference peak value in 1 is the 1st time ξ means damping ratio, T d the is period of vibration. According to Equation (16), thethe time domain, ξ means damping ratio, Td is period of vibration. According to Equation (16), thedamping time domain, ξ means damping ratio, Td is period of vibration. According to Equation (16), the ratio can be written as: damping ratio can be written as: damping ratio can be written as: δ  (17)(17) ξ “= = ?4 22   22 (17) 4π ` δ 4   v

v

d

The FBG micro-vibrationsensor sensorisisfixed fixed on on the the table, and thethe table The FBG micro-vibration and using usingthe thehammer hammerwe weknock knock table The FBG micro-vibration sensor is fixed on the table, and using the hammer we knock the table along vertical direction. Thetime timedomain domainand andspectrum spectrumofofthe themicro-vibration micro-vibration sensor sensor is is shown shown in along thethe vertical direction. The along the vertical direction.Equations The time (16) domain spectrum of the micro-vibration sensor is shown in Figure 10. Combining and and (17),damping the damping the micro-vibration FBG micro-vibration Figure 10. Combining Equations (16) and (17), the ratio ratio of theofFBG sensor in sensor Figureis 10. Combining Equations (16) and (17), the damping ratio of the FBG about 0.08955. The damping ratio the vibration sensor is very small becausemicro-vibration itsdamping damping is is about 0.08955. The damping ratio of theofvibration sensor is very small because its sensor is about 0.08955. dampingstructural ratio of the vibration sensor isthe very small because itsget damping is mainly composed ofThe optical damping. Figure weget can that mainly composed of optical fiber fiber structural damping. Also Also from from the Figure 10, we10,can that sensors’ is sensors’ mainly composed of optical fiber structural damping. Also from the Figure 10, we can get that resonance frequency is about 34 Hz, which is consistent with the result from Figure 8. resonance frequency is about 34 Hz, which is consistent with the result from Figure 8. sensors’ resonance frequency is about 34 Hz, which is consistent with the result from Figure 8. 500

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Figure 10. Time domain and spectrum of the micro-vibration sensor.

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4. Micro-Vibration Measurement Experiments and Discussion Sensors 2016, 16, 547 10 of 14 4. Micro-Vibration Measurement Experiments and Discussion In order to further evaluate the performance of the FBG micro-vibration sensor, several 4. Micro-Vibration Measurement Experiments and Discussion comparative are carried out based on the micro-vibration system.sensor, The principle In ordertests to further evaluate the performance of the FBGexperiment micro-vibration several In the order toare further evaluate the performance of the FBG micro-vibration sensor,The several diagram of micro-vibration experiment is shown in Figure 11. Thissystem. experimental system comparative tests carried out based onsystem the micro-vibration experiment principle comparative tests are carried outcantilever based on the micro-vibration experiment system. The principlerange consists micro-stroke actuator, structure and lever structure, etc. The movement diagramofofathe micro-vibration experiment system is shown in Figure 11. This experimental system diagram of the micro-vibration experiment system is shown in Figure 11. This experimental system of the micro-stroke actuator is from 100 nmstructure to 100 μm. is mainly range used to consists of a micro-stroke actuator, cantilever andThe levercantilever structure,structure etc. The movement of consists of a micro-stroke actuator, cantilever structure and lever structure, etc. The movement range amplify the micro-stroke actuator’s displacement, and convert horizontal micro-displacements into the micro-stroke actuator is from 100 nm to 100 µm. The cantilever structure is mainly used to amplify of the micro-stroke actuator is from 100 nm to 100 μm. The cantilever structure is mainly used to vertical vibrations of the actuator’s cantileverdisplacement, structure. Both a MEMS vibration sensor (range: ±10 g; the micro-stroke actuator’s displacement, and convert horizontal micro-displacements intointo vertical amplify the micro-stroke and convert horizontal micro-displacements revolution:1.9 μg)cantilever and of FBG micro-vibration sensorBoth are afixed on the cantilever structure (Figure vibrations the structure. Both a MEMS vibration sensor (range:sensor ˘10 g;(range: revolution:1.9 µg) verticalofvibrations the cantilever structure. MEMS vibration ±10 g; 11), The vibration sensor is taken as reference. In order to avoid any interference between the two and MEMS FBG micro-vibration sensor are fixed on the cantilever structure (Figure 11), The MEMS vibration revolution:1.9 μg) and FBG micro-vibration sensor are fixed on the cantilever structure (Figure 11), sensors, a reference. small sensor distance between them. The MEMS vibration taken reference. In order to avoid any interference between the is two sensor isthere takenisas In is order toasavoid any interference between the two sensors, there a small sensors, there isthem. a small distance between them. distance between

Figure The principlediagram diagram of of the the micro-vibration simulation experiment system. Figure 11. 11. The principle micro-vibration simulation experiment system. Figure 11. The principle diagram of the micro-vibration simulation experiment system.

4.1. Experiments of Hammering Excitation

4.1. Experiments Experiments of of Hammering Hammering Excitation Excitation 4.1.

Using the hammer to hit the root of the cantilever, the hammering excitation signal is Using the the hammer hammer to by hitthe theMEMS root and of the the hammering excitation signal is Using to hit the root of the cantilever, the hammering is simultaneously acquired FBGcantilever, micro-vibration sensors. Due excitation to the fact signal the simultaneously acquired by the MEMS and FBG micro-vibration sensors. Due to the fact the simultaneously acquired can by bethe MEMS as and FBGsignal, micro-vibration to obtained the fact the hammering excitation simplified a pulse the resonant sensors. frequencyDue can be hammering excitation can be be simplified asofaasensor. pulse Figure signal,12the the resonant frequency can be obtained obtained from theexcitation response signals of simplified the two kinds shows the response signals of the two hammering can as pulse signal, resonant frequency can be of sensorssignals under the hammering excitation. Figure 12 reveals that the for domain signals, fromkinds the response response signals of the the two kinds kinds of sensor. sensor. Figure 12 shows shows thetime response signals ofthe the two two from the of two of Figure 12 response signals of the tendency of the MEMS and FBG micro-vibration sensor is almost the same. The resonant frequency kinds of sensors under the hammering excitation. Figure 12 reveals that for time domain signals, the kinds of sensors under the hammering excitation. Figure 12 reveals that for time domain signals, the of the micro-vibration experiment system can be estimated from the signals obtained from the two tendency of the frequency of tendency the MEMS MEMS and and FBG FBGmicro-vibration micro-vibrationsensor sensorisisalmost almostthe thesame. same.The Theresonant resonant frequency kinds of sensors;experiment both experimental results are same, from whichthe is about 18.86 Hz (Table 1). two Thiskinds thethe micro-vibration system can be estimated obtained from from the of micro-vibration experiment system can be estimated fromsignals the signals obtained the two hammering excitation test also confirms the performance of FBG micro-vibration sensor is good.

of sensors; both experimental results are same, which is about Hz (Table hammering kinds of sensors; both experimental results are same, which18.86 is about 18.86 1). HzThis (Table 1). This excitation test also confirms theconfirms performance of FBG micro-vibration sensor is good. hammering excitation test also of FBG micro-vibration sensor is good. MEMS accelerator vibration signal in the 1st hammering test FBG vibration signal in the 1st hammering test the performance x 10 -3

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(b) (b) Figure the two kinds of of sensors’ signals signals for the the hammeringexcitation excitation Figure12. 12.The Theresponsivity responsivity of of Figure 12. The responsivity of the the two two kinds kinds of sensors’ sensors’ signalsfor for thehammering hammering excitation experiment. (a) The time domain and spectrum of the two kinds of sensors for the 1st hammering experiment. (a) (a) The The time time domain domain and experiment. and spectrum spectrum ofthe thetwo twokinds kindsofofsensors sensorsfor forthe the1st1sthammering hammering excitation experiment; (b) The time domain and spectrum of the two kinds of sensors for the 2nd excitation experiment; (b) The time domain spectrum of the two kinds of sensors for the 2nd excitation experiment; (b) The time domain and spectrum of the two kinds of sensors for the 2nd hammering excitation experiment. hammering excitation experiment. hammering excitation experiment. Table1. Theresonance resonancefrequency frequency of of micro-vibration micro-vibration structure and FBG Table 1.1.The structure obtained by the MEMS and FBG The resonance frequency of micro-vibration structureobtained obtainedby bythe theMEMS MEMS and FBG Table micro-vibrationsensor. sensor. micro-vibration micro-vibration sensor. TestNumber Number FBG FBGMicro-Vibration Micro-Vibration Sensor Test Sensor Test Number FBG Micro-Vibration Sensor 1 18.92 Hz 1 18.92 Hz 1 18.92 Hz 18.86 Hz Hz 22 2 18.86 18.86 Hz

MEMS MEMSSTM300 STM300 MEMS STM300 18.86 18.86Hz Hz 18.86 Hz 18.86 Hz 18.86 Hz 18.86 Hz

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4.2. ScanningFrequency Frequency Experiments 4.2. 4.2. Scanning Scanning Frequency Experiments Experiments In order to study in depth the performance of the FBG micro-vibration sensor, scanning In ordertotostudy study in depth the performance of themicro-vibration FBG micro-vibration sensor, frequency scanning In order in depth performance of the FBG sensor,isscanning frequency experiments have the been done in this part. The current amplitude a constant, the frequency experiments have been done in this part. The current amplitude is a constant, the experiments have been done part. current is aThe constant, the frequency increases frequency increases from 1 in to this 8 Hz, andThe interval is amplitude set at 1 Hz. time interval between each frequency from 1 tois8set Hz, and is set at 1 Hz. The time interval between each from 1 to 8increases Hz, and Hz.interval The time interval between each frequency wasdriven kept at frequency was kept interval at about 3~4 s at by1manual operation. The micro-stroke actuator has been frequency was kept at about 3~4 s by manual operation. The micro-stroke actuator has been driven about 3~4 s by manual operation. The micro-stroke actuator has been driven by the above electrical by the above electrical signals. The time domain and spectrum maps of the MEMS and FBG by the above electrical signals. The time domain and spectrum maps of the MEMS andforFBG signals. The time domainfor and maps of the MEMS and FBG1–8 micro-vibration micro-vibration sensors thespectrum scanning frequency experiment within Hz are shown sensors in Figure 13.the micro-vibration sensors for the scanning frequency experiment within 1–8 Hz are shown inexcitation Figure scanning experiment Hz arethe shown Figure 13. For the hammering time domain map of 13. the For the frequency time domain map of within the two1–8 sensors, sameinconclusion of the For the time domain map of the two sensors, the same conclusion of the hammering excitation two sensors, the conclusion of the excitation experiment be reached. experiment cansame be reached. When thehammering excitation frequency is changed, can it generates at When impactthe experiment caninbeFigure reached. When the determine excitation frequency changed, it impact phenomenon 13, so wegenerates can the changed is time the frequency the excitation frequency is changed, it at impact phenomenon inof Figure 13,generates so we through can at determine phenomenon in Figure 13, so we can determine the changed time of the frequency through the impact phenomenon in frequency Figure 13. through the impact phenomenon in Figure 13. the changed time of the impact phenomenon in Figure 13.

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Figure13. 13.Time Timedomain domainand and spectrum spectrum map map of sensors forfor thethe Figure of the the MEMS MEMSand andFBG FBGmicro-vibration micro-vibration sensors scanning frequency experiments within 1–8 Hz. scanning experiments within map 1–8 Hz. Figure 13.frequency Time domain and spectrum of the MEMS and FBG micro-vibration sensors for the

scanning frequency experiments within 1–8 Hz.

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12 of 14 The frequency components of the MEMS and FBG micro-vibration sensors can be obtained from the spectrum maps in Figure 13, which are shown in Table 2. From Table 2, we can get that: the collected frequencycomponents components FBG and micro-vibration sensor are consistent the MEMS The frequency of of thethe MEMS FBG micro-vibration sensors can bewith obtained from vibration sensor; for the 1× components, it’s consistent with the MEMS vibration sensor. The FBG the spectrum maps in Figure 13, which are shown in Table 2. From Table 2, we can get that: the micro-vibration sensor is more sensitive to high-frequency components; it can get more frequency collected frequency components of the FBG micro-vibration sensor are consistent with the MEMS multiplication. may1ˆ becomponents, caused by the itself orthe theMEMS measured body, sensor. but on the vibration sensor;This for the it’sstructure consistent with vibration Thewhole FBG the FBG micro-vibration sensor can effectively measure the vibration, as well as display good micro-vibration sensor is more sensitive to high-frequency components; it can get more frequency performance. This may be caused by the structure itself or the measured body, but on the whole the multiplication.

FBG micro-vibration sensor can effectively measure the vibration, as well as display good performance. Table 2. Signals’ frequency components of the MEMS and FBG micro-vibration sensors for the scanning frequency experiments. Table 2. Signals’ frequency components of the MEMS and FBG micro-vibration sensors for the scanning frequency experiments. 1× (Fundamental

MEMS

FBG Micro-Vibration Sensor

0.9003/2.045/3.006/4.044/5.02/ MEMS

frequency)/Hz

1ˆ (Fundamental frequency)/Hz

Frequency

FBG Micro-Vibration Sensor

0.9155/2.09/3.006/4.004/5.02/5.996/6.973/7.996

0.9003/2.045/3.006/4.044/5.02/ 5.996/6.973/7.996

0.9155/2.09/3.006/4.004/5.02/5.996/6.973/7.996

5.996/6.973/7.996

9.995/12.04/14.05/15.01/15.99/18.07/18.62/ 9.995/11.99/14.05/15.01/15.99/18.07/18.63/20.13/21.03/ 9.995/12.04/14.05/15.01/15.99/18.07/18.62/ 9.995/11.99/14.05/15.01/15.99/18.07/18.63/20.13/

Frequency multiplication/Hz

multiplication/Hz

20.11/21.04/23.96/25.01/28.03/29.98/32.09

20.11/21.04/23.96/25.01/28.03/29.98/32.09

21.03/23.97/24.98/27.98/30/32.06/34.97/36.13/40.07

23.97/24.98/27.98/30/32.06/34.97/36.13/40.07

4.3. 4.3.Accuracy AccuracyComparison ComparisonExperiments Experiments To Tostudy studythe themeasurement measurementaccuracy accuracyofofthe theFBG FBGvibration vibrationsensor, sensor,we weadjust adjustthe themicro-stroke micro-stroke actuator incentive stroke work to different frequencies or current amplitudes. Figure 14 actuator incentive stroke work to different frequencies or current amplitudes. Figure 14shows showsthe the time timedomain domainand andspectrum spectrummap map of ofthe thetwo two sensors sensors at at aa frequency frequency of of 10 10 Hz Hz and and current current of of 0.8 0.8 A. A. From Figure 14, we see that the time domain signals of the two sensors are almost the same. There From Figure 14, we see that the time domain signals of the two sensors are almost the same. There exists existsaamass massofofglitches glitchesininthe theMEMS MEMSvibration vibrationsignal’s signal’stime timedomain domainmap, map,but butthe thesignal signalofofthe theFBG FBG micro-vibration micro-vibrationsensor sensorisisvery verysmooth. smooth.Also Alsothe thefrequency frequencymultiplication multiplicationcharacteristics characteristicsof ofthe theFBG FBG micro-vibration micro-vibrationsensor sensorare areeven evenmore moreobvious obviouscompared comparedwith withthe theMEMS MEMSvibration vibrationsensor. sensor. Time domain of MEMS vibration sensor

Time domain of FBG vibration sensor 0.02

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Figure14. 14.Time Time domain spectrum oftwo the sensors two sensors s frequency 10 current Hz and Figure domain andand spectrum mapmap of the with swith frequency of 10 Hzofand A. (a) Time domain and spectrum of the MEMS vibration (b) domain Time domain ofcurrent 0.8 A. of (a)0.8 Time domain and spectrum map of map the MEMS vibration senor; senor; (b) Time and and spectrum map of the FBG micro-vibration senor. spectrum map of the FBG micro-vibration senor.

In order to further verify the measurement properties of the FBG micro-vibration sensor, the In order to further verify the measurement properties of the FBG micro-vibration sensor, the amplitude of the fundamental frequency has been chosen in Figure 15. It shows the measured amplitude of the fundamental frequency has been chosen in Figure 15. It shows the measured acceleration of the two kinds of sensors under different current amplitudes with a frequency of 1 Hz, acceleration of the two kinds of sensors under different current amplitudes with a frequency of 1 Hz, 2 Hz, 5 Hz and 10 Hz. From Figure 15, we can find that the measured acceleration amplitude of the 2 Hz, 5 Hz and 10 Hz. From Figure 15, we can find that the measured acceleration amplitude of the FBG micro-vibration sensor is consistent with the MEMS vibration sensor. Also two other FBG micro-vibration sensor is consistent with the MEMS vibration sensor. Also two other conclusions conclusions can be obtained: (1) There is no difference between the measured acceleration can be obtained: (1) There is no difference between the measured acceleration amplitudes of the two amplitudes of the two sensors at 1 Hz and 2 Hz; (2) When the excited frequencies are set at 5 and 10 sensors at 1 Hz and 2 Hz; (2) When the excited frequencies are set at 5 and 10 Hz, the acquired signal Hz, the acquired signal amplitude of the FBG micro-vibration sensor is slightly larger than that of amplitude of the FBG micro-vibration sensor is slightly larger than that of the MEMS vibration sensor. the MEMS vibration sensor. There are two main reasons that could responsible for this There are two main reasons that could responsible for this phenomenon: (i) the FBG micro-vibration

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sensor is fixed in nearer to the end of the cantilever structure the MEMS vibration phenomenon: (i)place the FBG micro-vibration sensor is fixed in placecompared nearer towith the end of the cantilever sensor, so the relative error between the two sensors will be increased as the vibration amplitude structure compared with the MEMS vibration sensor, so the relative error between the two sensors increases; (ii) the fitted line is obtained under an excitation 8 Hz, althoughunder the FBG will be increased as the vibration amplitude increases; (ii)frequency the fitted ofline is obtained an vibration sensor has a flat response between 2 to 22 Hz, there exists a small non-linearity 6 excitation frequency of 8 Hz, although the FBG vibration sensor has a flat response between 2 tofrom 22 Hz, to 22 Hz, and it’s not absolutely parallel to the x axis in the Figure 8. This causes the sensitivity to there exists a small non-linearity from 6 to 22 Hz, and it’s not absolutely parallel to the x axis in the increase thethe excitation frequency growth. analysis, the tendency the two Figure 8.along This with causes sensitivity to increase alongFrom withthe theabove excitation frequency growth.ofFrom the sensors’ signals are the same, which demonstrates that the FBG micro-vibration sensor can be applied above analysis, the tendency of the two sensors’ signals are the same, which demonstrates that the to measure micro-vibrations, reliabilitymicro-vibrations, of the FBG micro-vibration sensor need FBG micro-vibration sensor but canthe beaccuracy applied and to measure but the accuracy and to be further improved. reliability of the FBG micro-vibration sensor need to be further improved.

(a)

(b)

Figure15. 15.Comparison Comparison measured acceleration graphs twoofkinds of under sensors under Figure of of thethe measured acceleration graphs of the of twothe kinds sensors different different amplitude of current with frequencies of (a) 1 Hz and 2 Hz; (b) 5 Hz and 10 Hz. amplitude of current with frequencies of (a) 1 Hz and 2 Hz; (b) 5 Hz and 10 Hz.

5. Conclusions 5. Conclusions This paper has proposed a fiber Bragg grating sensing-based micro-vibration sensor. The This paper has proposed a fiber Bragg grating sensing-based micro-vibration sensor. The optical optical fiber has been directly treated as an elastomer, and the mass is fixed on the middle of the fiber has been directly treated as an elastomer, and the mass is fixed on the middle of the fiber. fiber. The vertical vibration of the mass has been converted into the axial tension/compression of The vertical vibration of the mass has been converted into the axial tension/compression of the fiber, the fiber, and finally this deformation induces the same variations of the two FBGs’ wavelength. and finally this deformation induces the same variations of the two FBGs’ wavelength. Adding the two Adding the two FBGs’ center wavelength shift, the sensitivity has increased two-fold compared with FBGs’ center wavelength shift, the sensitivity has increased two-fold compared with the FBG signal and the FBG signal and eliminated the interference from the x-direction. The principle of the sensor has eliminated the interference from the x-direction. The principle of the sensor has been studied in this been studied in this paper, and the experimental conclusions show that: (i) the sensitivity of the FBG paper, and the experimental conclusions show that: (i) the sensitivity of the FBG micro-vibration sensor micro-vibration sensor is 2362 pm/g within the range of 200–1200 mm/s2, which is consistent with is 2362 pm/g within the range of 200–1200 mm/s2 , which is consistent with the theoretical sensitivity the theoretical sensitivity of 2532.6 pm/g, illustrating that the theoretical sensitivity model of the of 2532.6 pm/g, illustrating that the theoretical sensitivity model of the sensor is correct; (ii) it shows sensor is correct; (ii) it shows an excellent linearity which is 1.376%; (iii) the resonant frequency of an excellent linearity which is 1.376%; (iii) the resonant frequency of the sensor is 34 Hz, and the flat the sensor is 34 Hz, and the flat frequency range lies within 0–22 Hz. When used to measure frequency range lies within 0–22 Hz. When used to measure micro-vibrations, the relative error of the micro-vibrations, the relative error of the measured frequency is less than 1.69% compared with a measured frequency is less than 1.69% compared with a MEMS vibration sensor; and the amplitude MEMS vibration sensor; and the amplitude values of its measured vibration signal are consistent values of its measured vibration signal are consistent with the MEMS accelerometer under different with the MEMS accelerometer under different excitation conditions, too. This method has excitation conditions, too. This method has effectively improved the sensitivity compared with the effectively improved the sensitivity compared with the traditional FBG vibration sensor, and it can traditional FBG vibration sensor, and it can be used to measure micro-vibrations with high precision. be used to measure micro-vibrations with high precision. Acknowledgments: Project supported by the International S&T Cooperation Program of China (Grant Acknowledgments:and Project supported International S&T Cooperation (Grant No.2015DFA70340) the Key Programbyof the Natural Science Foundation of HubeiProgram Province of of China (Grant No. 2014CFA100). and the Key Program of Natural Science Foundation of Hubei Province of China (Grant No. No.2015DFA70340) 2014CFA100). Author Contributions: Tianliang Li analyzed and interpreted the data and wrote the main manuscript text. Yuegang Tan discussed extensively the results and the interpretations and reviewed the manuscript. After the Author Contributions: Li reviewed analyzed the andmanuscript. interpreted the data and wrote the main manuscript text. manuscript was finished,Tianliang Zude Zhou Yuegang Tan discussed extensively the results and the interpretations and reviewed the manuscript. After the Conflicts of Interest: The authors declare no conflict of interest. manuscript was finished, Zude Zhou reviewed the manuscript.

Conflicts of Interest: The authors declare no conflict of interest.

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