Sensors and Actuators A 117 (2005) 103–109

Athermal fibre Bragg grating strain gauge with metal coating inmeasurement of thermal expansion coefficient

Yu-Lung Loa,∗, Yong-Chang Lina, Yung-Mien Chenb

a Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwanb Sr. Mechanical System Architect, Philips Optical Storage, Taipei, Taiwan

Received 10 June 2004; accepted 14 June 2004Available online 13 August 2004

Abstract

This study presents an athermal strain gauge based on fibre Bragg grating (FBG) in measuring thermal expansion coefficient of a lowexpansion nickel alloy block for demonstration. In order to design an athermal fibre Bragg grating strain gauge, the metal coating is electrolessplated onto an optical fibre to function as a thermal compensator. Therefore, the Bragg wavelength will not shift with the ambient temperaturec sion nickela s a result, thea©

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hange, and only shift regarding to the mechanical strain onto FBG. In measuring the thermal expansion coefficient of a low expanlloy block, data are in good agreement between the tests by using the athermal FBG and resistance strain gauge techniques. Athermal strain gauge based on FBG is demonstrated and feasible for the future applications.2004 Elsevier B.V. All rights reserved.

eywords:Fibre Bragg grating; Temperature compensations; Athermal strain gauge

. Introduction

Developing in optical fibre sensors, many researchers rec-gnized the non-unique functionality (phase or wavelengths a function of strain and temperature) as a shortcoming

n optical fibre sensors, and have striven towards develop-ng sensors and sensor configurations capable of measuring

ultiple parameters. Recent approach in multiple parame-er measurement was toward simultaneous measurement ofxial strain and temperature[1,2]. Xu et al.[3] used two dif-

erent pitches of Bragg grating written on the same place toimultaneously measure axial strain and temperature. Singhnd Sirkis[4] and Jin et al.[5] used a multiplexing method

o measure strain and temperature simultaneously on surfaceounted or embedded cases. Bhatia et al.[6] demonstrated

imultaneous axial strain and temperature measurements us-ng long-period gratings in different resonance bands. Lee etl. [7] proposed a simple optical fibre sensor for the mea-

∗ Corresponding author. Tel.: +886 2757575x62123; fax: +886 235293.E-mail address:loyl@mail.ncku.edu.tw (Y.-L. Lo).

surement of vibration. The sensor consists of two fibre Bgratings (FBG) that have partially overlapped reflection stra and are mounted on the opposite sides of a flexible bWith this setting, the light intensity reflected by the gratiis modulated in accord with the vibration of the beamadverse thermal effects can be largely eliminated.

Recently, Lo[8] proposed a simple optical fibre configration to measure strain and temperature simultaneousing one in-fibre Bragg grating that is partially glued tospecimen and partially free attached to the surface. Athe application in the simultaneous strain and tempermeasuring capability of one in-fibre Bragg grating to msure the thermal expansion coefficient was presented band Chuang[9]. The Bragg wavelength reflected fromsensor section not glued to the specimen is used tosure temperature variations; and the Bragg wavelengtflected from the sensor section glued to the specimeaffected by thermal strain variations. The thermal exsion coefficient, therefore, can be determined by calculathe difference of the spectral separation between two Bwavelengths.

924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2004.06.017

104 Y.-L. Lo et al. / Sensors and Actuators A 117 (2005) 103–109

The special design on FBG only for temperature measure-ment is quite popular because FBG could be easily isolatedfrom the external loading; however, none of FBGs are de-signed for the real athermal strain gauge due to the isolationfrom the thermal effect is extremely hard. If an athermal straingauge is developed, several special applications of measure-ments could be broadened.

In this study, we deposit the metal coating upon an opticalfibre as a thermal compensator, and then glue the athermalFBG strain gauge onto a low expansion nickel alloy blockfor demonstration. It is based on the concept proposed by Loand Kuo[10] in designing the athermal package of FBGs foroptical fibre communications; and is a novel application ofthis package to fibre strain gauge design.

1.1. Basic theory of the temperature compensationtechnology

Our study aims to resolve the thermal problems by pro-viding a new compensating device to correct the tempera-ture deviation of the FBG. This device includes the means ofcompressing the fibre Bragg grating as the optical fibre expe-riences an increment in temperature. The proposed athermalFBG strain gauge is illustrated inFig. 1. The metal coatingplated on the fibre functions as a thermal compensator whilet struc-t eedst cture.I com-p metac .

ator,t raggw dingt n bef nc-t

w icalfi no tot

F untedo

strain-optic coefficient of an optical fibre. The notation,neandνF, in Pe are the effective refractive index and Poissonratio of an optical fibre, andP1 andP12 represent the com-ponents of the strain-optic tensor. Notice that the axial strainεaxis is defined positive when the fibre increases its length(i.e. for a tension force).Eq. (1)shows that Bragg wavelengthshifting effects of the two terms are contradictory. Therefore,the Bragg wavelength will not shift regarding to the temper-ature change.

2. Analysis of metal coating on FBG

This section describes the analysis of the fibre/coating sys-tem for a thermal compensator. From the cross section of athermal compensator used for an athermal FBG strain gaugeis found the optical fibre and metal coating. Therefore, in the-ory, the two-phase constant model[10,12] is applied for de-signing the metal coating thickness associated with the effec-tive thermal expansion coefficient and the effective Young’smodulus in the composite thermal compensator.

In Fig. 2a, to simplify the thermal analysis, the assumptionthat the optical fibre is on the fixed ends is reasonable for thesuccessful function of the thermal compensator. While thetemperature is increasing, the axial force,Fthermo, inducedb ressf thea FBGc

ε

wt f

F gramo

he athermal FBG strain gauge is surface adhered to theure in points A and B. The athermal FBG strain gauge no be preloaded before it is surface adhered onto the struf the ambient temperature increases, then the thermalensator expands to compress the FBG. Therefore, theoating can compensate for the thermal effect into FBG

To understand the function of an athermal compenshe study characterizes the performance of the FBG in Bavelength associated with the external factors inclu

emperature and strain. The details of derivations caound in [11]. To achieve the intended compensating fuion, the required condition can be expressed as[10](

∆λBλB

)thermo

+(

∆λBλB

)axial−strain

= 0

(ξ + αF)∆T + (1 − Pe)εaxis = 0(1)

hereαF is the thermal expansion coefficient of an optbre,ξ = (1/ne)(∂ne/∂T) is the thermo-optic coefficient of aptical fibre,εaxis is the axial mechanical strain applied

he FBG,Pe = n2e/2[P12 − νF(P11 + P12)] is the effective

ig. 1. The embodiment of the FBG athermal strain gauge surface mon structure.

l

y thermal effect that applied to FBG is negative (comporce) while�T is positive, and vice-versa. Therefore,xial mechanical compression strain that induced intoan be further shown as

axis = Fthermo

EFAF= − [LFαF + αCLC]∆T

LF + EFAFLC/ECAC(2)

hereLC andLF are the lengths as illustrated inFig. 2a,�T ishe temperature deviation,EF andEC are Young’s modulus o

ig. 2. (a) Configuration of a thermal compensator; (b) free-body-diaf the configuration with temperature increasing.

Y.-L. Lo et al. / Sensors and Actuators A 117 (2005) 103–109 105

the FBG and thermal compensator,αF andαC are the thermalexpansion coefficient of the FBG and thermal compensator,and the other parameter such asAF andAC are the cross sec-tional area of the FBG and thermal compensator depicted inFig. 2(b). To meet the required condition for thermal com-pensation inEq. (1), the ratio ofLC to LF can be expressedas

LC

LF= ξ + PeαF

(1 − Pe)αC − (ξ + αF)EFAF/ECAC(3)

From above, ifαC andEC of the thermal compensatorare all designed, the lengths ofLC andLF can be determinedby Eq. (3) for an athermal FBG strain gauge. The next twosubsections, the calculations ofαC andEC is introduced.

2.1. Analysis of effective thermal expansion coefficientin a thermal compensator

To investigate the effective thermal expansion coefficientin a thermal compensator, this section applies the two-phaseconstant model[10,12]to analyze the related thermal effectsbetween an optical fibre and metal coating. Since the lengthof the metal coating is longer than the cross sectional area ofthe thermal compensator, a generalized plane strain can be as-sumed.Fig. 3shows the coordinate of the two-phase constantm lvedf ands con-s formt y. Thea g arei thea canb

ε

w tstt thec e

obtained and it can be determined in detail by[10]. There-fore, the so-called effective thermal expansion coefficient ofa thermal compensator under the selective copper coatingthickness can be defined as

αC = εaxis(1)|thermo

∆T= C(1)

∆T(5)

Table 1illustrates various parameters in analysis, and thecopper is chosen as the metal coating in this study.Fig. 4shows that the axial strain of a thermal compensator in thefibre core for different copper thickness are associated withvarious temperature variations. It is found that the axial straincaused by thermal effect in the fibre core varies linearly withtemperature variations; thus, the slope can be defined as theso-called effective thermal expansion coefficient. As shownin Fig. 4, when the metal coating is deposited more thanaround 300�m thickness, the estimated thermal expansioncoefficient of a thermal compensator is approximated to 16.5× 10−6/◦C which is almost same as that in the bulk copper,as illustrated inTable 1. It proves that this analytical modelis feasible for the further analysis.

2.2. Analysis of effective Young’s modulus in a thermalcompensator

fibrea ulusi brea rdeda df+a tinga hip,t so

E

thee bothof

TP

P

r

YSLPT

odel. These governing differential equations can be soor each load scenario to find the displacement, strainstresses in each constituent in terms of some unknowntants. The deformation fields in this system under uniemperature change are modeled as the axis-symmetrxial strains at the fibre and inner surfaces of the coatin

dentical to maintain continuity at the interface. Thereby,xial strain produced by thermal factor in an optical fibree expressed as[10,12]

(1)axis|thermo= ∂uz

∂Z= C(1) (4)

hereuz is the deformation in thez-axis, and (1) represenhe 1st domain that represents the optical fibre. FromEq. (4),o calculate the axial strain caused by thermal effect inenter region of an optical fibre, the constantC(1) needs to b

Fig. 3. Two-phase constant model.

Since the thermal compensator consists of an opticalnd metal coating; therefore, the effective Young’s mod

n this composite will be a combination of the optical find metal coating. Here, the fibre/coating section is regas an equivalent compensator. InFig. 5, the thermal induce

orce,Fthermo, that distributes all across the area,AC = AmetalAF, must be equal to the combination of the forces,FmetalndFF, that are both confined in the area of the metal coand optical fibre. According to the stress-strain relations

herefore, as shown inFig. 5, the effective Young’s moduluf the thermal compensator can be derived as[13]

C = EmetalAmetal+ EFAF

Ameatl+ AF(6)

Since the effective thermal expansion coefficient andffective Young’s modulus of a thermal compensator arebtained byEqs. (5) and (6), the ratio ofLC to LF could be

ound byEq. (3).

able 1arameters in analysis

arameters Materials

Optical fibre Coppe

oung’s modulus (GPa) 72 110hear modulus (GPa) 30 40.7ame’s constant (GPa) 20 95.1oission ratio 0.2 0.35hermal expansion coefficient (×10−6/ ◦C) 0.55 16.5

106 Y.-L. Lo et al. / Sensors and Actuators A 117 (2005) 103–109

Fig. 4. Relationship between axial strain caused by thermal effect and temperature variation in term of various thickness of metal coating.

Fig. 5. Effective Young’s modulus of the fibre/coating system under the thermal loading.

3. Basic theory of the athermal FBG strain gauge

SinceLF, LC, αC andEC in an athermal FBG strain gaugehas been obtained fromSection 3, the athermal FBG straingauge could be characterized. In order to analyze the mech-anism inFig. 1, the free-body diagram of external loadingfrom the structure to the athermal strain gauge is illustratedin Fig. 6. In Fig. 6(a), while the external loading, F, is appliedto the fibre ends, according to the equilibrium in force anddeformation, the relationships can be respectively expressedas

EFεFAF = ECεCAC

LFεF + LCεC = (LF + LC)εexternal(7)

whereEi, εi,Ai andLi are Young’s modulus, axial strain, thecross section area and the length, respectively regarding toi =F (fibre) and C (thermal compensator), andεexternalrepresentsthe strain from the structure. If the athermal FBG strain gaugeis designed, we find thatεF = �λB/λB andεexternal = α�Tas the case illustrated inFig. 1 for measuring the thermalexpansion coefficient of the structure. Thus, we can calculatethe thermal expansion coefficient of the structure by using

the formula as

α∆T = ∆λB

λB

(LF + LC(EFAF/ECAC))

(LF + LC)(8)

Fig. 6. (a) Configuration of the thermal compensator; (b) free-body-diagramof the configuration with temperature increasing.

Y.-L. Lo et al. / Sensors and Actuators A 117 (2005) 103–109 107

whereα is the thermal expansion coefficient of the structure,and it should be noticed that the wavelength shift�λB fromFBG is insensitive to the thermal effect.

4. Experiment and results

We use an athermal FBG strain gauge to measure the ther-mal expansion coefficient of a low expansion nickel alloyblock for demonstration. In order to resolve the fibre Bragggrating sensitivity with ambient temperature, we plate thecopper on the fibre as a compensator in this study. Because

face mo

the fibre itself is a nonconductor, the copper could not be elec-troplated onto the fibre directly. For this reason, the copperfilm is plated onto the fibre by the electroless plating method.It is well known that electroless plating produces an internalstress in the coating, so the thickness of the coating is lim-ited by using electroless plating[10]. Based on the electrolessplating method, for this experiment, the copper coating thick-ness is around 5�m. In this design of a thermal compensator,the effective thermal expansion coefficient,αC, is estimatedas 4.37× 10−6/◦C as illustrated inFig. 4. The related materialproperties of an optical fibre and the metal coating are listedin Table 1, ξ = 6.52× 10−6 (1/◦C), and (1−Pe) = 0.78. The

Fig. 7. Athermal FBG strain gauge sur

Fig. 8. Thermal expansion coefficient measure

Fig. 9. Thermal expansion coefficient measu

unted on a low expansion nickel alloy block.

ment by using the athermal FBG strain gauge.

rement by using the resistance strain gauge.

108 Y.-L. Lo et al. / Sensors and Actuators A 117 (2005) 103–109

length of a thermal compensator,LC, 25 mm, is designed andmanufactured in the experiment; and according toEq. (3),it is found that the length ofLF is designed as 15 mm. Thepreloading mechanism also is implemented in the manufac-turing process for surface adhering the athermal FBG straingauge onto a low expansion nickel alloy block. As a result,Fig. 7illustrates the athermal FBG strain gauge that has beenglued on a low expansion nickel alloy block.

The light source used in this system is amplified sponta-neous emission (ASE) from an erbium doped fibre amplifier(EDFA) as a low coherent and high power broadband source.The resolution of the optical spectrum analyzer (HP-OSA) isset at 0.1 nm. To demonstrate the athermal FBG strain gauge,the experiments are conducted in an oven to control temper-ature from 30◦C to 80◦C. The Bragg wavelength from anathermal FBG strain gauge regarding to temperature is illus-trated inFig. 8. After linear tendency analysis, the thermalexpansion coefficient of a low expansion nickel alloy blockis calculated by usingEq. (8), and the average of three data is5.001× 10−6/◦C. In addition, by using the resistance straingauge and a half-bridge strain indicator to measure the ther-mal expansion coefficient of a low expansion nickel alloyblock is for comparison, and the strain regarding to tempera-ture from 30◦C to 80◦C is illustrated inFig. 9. The thermalexpansion coefficient in average is 5.7381× 10−6/◦C. Asa tal se-t traing posedh

thea ex-a ticalm rolessp

5

tudyc is de-s to afi ther l bi-m ionsa sign.T pen-s andp cor-r raggg ous.

A

a-t ni-

versities under the grant number A-91-E-FA08-1-4, Taiwan,ROC.

References

[1] A. Vengsarkar, W. Michie, L. Jankovic, B. Culshaw, R. Claus, Fibreoptic sensor for simultaneous measurement of temperature and strain,SPIE 1367 (1990) 249–260.

[2] W. Michie, B. Culshaw, R. Roberts, R. Davidson, Fibre optic tech-nique for simultaneous measurement of strain and temperature vari-ations in composite materials, SPIE, 1991, pp. 342–355.

[3] M.G. Xu, J.L. Archambault, L. Reekie, J.P. Dakin, Discriminationbetween strain and temperature using dual wavelength fibre gratingsensors, Electron. Lett. 30 (1994) 1085–1087.

[4] H. Singh, J.S. Sirkis, Simultaneously measuring temperature andstrain using optical fibre microcavities, J. Lightwave Technol. 15(1997) 647–653.

[5] X.D. Jin, J.S. Sirkis, J.K. Chung, V.S. Venkat, Embedded in-line fibreetalon/Bragg grating hybrid sensor to measure strain and temperaturein a composite beam, J. Intell. Mater. Syst. Struct. 9 (1998) 171–181.

[6] V. Bhatia, K.A. Murphy, R.O. Claus, Simultaneous measurementsystems employing long-period grating sensors, in: Optical FibreSensors Conference (OFS), 1996, pp. 702–705.

[7] K.O. Lee, K.S. Chiang, Z.H. Chen, Temperature-insentive fibre-Bragg-grating-based vibration sensor, Opt. Eng. 40 (2001) 2582–2585.

[8] Y.L. Lo, Using in-fibre Bragg-grating sensors for measuring axialSPIE

effi-ience

[ oat-003)

[ .G.E, J.

[ singtruct.

[ lish-

B

Y rsityi fromt sity ofM dua-t theO marts Engi-n . Hisr in tele-c ents,e nicalp er ofS

Y han-i

consequence, the difference between two experimenups is around 14.75%, therefore the new athermal FBG sauge is proved, and the compensation scheme we proere works well.

The error could be attributed to the experiment andnalytical model. The biggest error could come from, formple, the properties of the bulk copper used in the analyodel because the grain size of the copper by the electlating method is bigger than that of the bulk copper.

. Conclusions

The athermal FBG strain gauge introduced in this sonsists the advantages of simple constructions, and thign is directly to deposit the thermal compensator onbre for compensation unlike the conventional ones byeference technique for elimination. Meanwhile, the usuaetal package used for FBG in optical fibre communicatre seldom applied for the athermal FBG strain gauge deaking advantage of the metal coating as a thermal comator, the real athermal FBG strain gauge is designedroved in this study. However, the scheme will lead to inect results if there is a temperature gradient across the Brating or if the material to be measured is inhomogene

cknowledgement

The work is partially supported by Ministry of Educion Program for Promoting Academic Excellence of U

strain and temperature simultaneously on surface of structures,Opt. Eng. 37 (1998) 2272–2276.

[9] Y.L. Lo, H.S. Chuang, Measurements in thermal expansion cocient using an in-fibre Bragg-grating sensor, measurement scand technology, Inst. Phys. UK 9 (1998) 1543–1547.

10] Y.L. Lo, C.P. Kuo, Packaging a fibre bragg grating with metal cing for an athermal design, IEEE, J. Lightwave Technol. 21 (21377–1383.

11] A.D. Kersey, M.A. Davis, H.J. Patrick, M. LeBlanc, K.P. Koo, CAskins, M.A. Putnam, E.J. Friebele, Fibre grating sensors, IEELightwave Technol. 15 (1997) 1442–1463.

12] Y.L. Lo, F.Y. Xiao, Measurements of corrosion and temperature ua single-pitch Bragg grating fibre sensor, J. Intell. Mater. Syst. S9 (1998) 800–807.

13] S.W. Tsai, Introduction to Composite Materials, Technomic Pubing Co., Inc., 1980, in press.

iographies

u-Lung Loreceived the BS degree from National Cheng Kung Univen 1985, and the MS and PhD degrees in mechanical engineeringhe Smart Materials and Structures Research Center at the Univeraryland, College Park, in 1992 and 1995, respectively. After gra

ion, he joined the Industrial Technology Research Institute (ITRI) inpto-Electronics & Systems Laboratories, working on fibre optic s

tructures. He has been a member of the faculty of the Mechanicaleering Department at National Cheng Kung University since 1996esearch interests are in the areas of optical passive componentsom, fibre-optic sensors, optical techniques in precision measuremlectronic packaging, and MEMS. He has authored over 50 techublications and filed several patent disclosures. Dr. Lo is a membPIE and SEM.

ong-Chang Linreceived the BS degree from the Department of Meccal engineering, National Cheng Kung University in 2003.

Y.-L. Lo et al. / Sensors and Actuators A 117 (2005) 103–109 109

Yung-Mien Chenreceived his BS at ME, National Taiwan University in1984. In 1989 and 1993, he received his MS and PhD from Photome-chanics Laboratory, Mechanical Engineering Department, University ofMaryland at College Park. After graduation, he joined TECO as a seniorengineer doing dynamic structural analysis for electrical motors, com-pressors and air conditioners. Later on he joined Philips Key Modules

for designing compact disc drive. Then he worked for load cell industryfor 5 years and was the manager of R&D and Engineering in Asia forVishay Transducers. Currently, he is with Philips Optical Storage, Taiwanas a senior mechanical system architect. Dr. Chen is a member in Societyfor Experimental Mechanics. His research interest is in general focusingon strain measurements and optomechaincal system.