fiber bragg grating based shear-force sensor: modeling and testing

1728 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 22, NO. 7, JULY 2004

Fiber Bragg Grating Based Shear-Force Sensor:Modeling and Testing

S. C. Tjin, Member, IEEE, R. Suresh, and N. Q. Ngo

Abstract—This paper presents the design and fabrication ofa novel shear-force sensor using fiber Bragg grating (FBG) asthe sensing element. The basic design consists of layers of carboncomposite material (CCM) with an embedded FBG. A deformablelayer of silicon rubber between the layers of CCM allows theapplied shear force to change the grating periodicity and, hence,the reflected Bragg wavelength. The shift in the reflected Braggwavelength shows a linear variation with the applied shear force.A theoretical model is established to study the shear sensingability. In addition, numerical modeling is also carried out by thefinite-element method (FEM). The experimental results are foundto be in good agreement with the theoretical predictions as wellas the FEM results. In this paper, the basic concept of shear-forcemeasurement using FBG and related theoretical model andFEM simulation results are discussed together with experimentalverification.

Index Terms—Fiber Bragg grating (FBG), fiber-optic sensor,shear-force sensor.

I. INTRODUCTION

THE FORMATION of fiber Bragg grating (FBG) was firstdiscussed by Hill et al. in 1978 for application in lightwave

communication [1]. Later, Meltz et al. considered the possibilityof using the FBG for sensing the strain and the temperature [2].Since then, FBG has been utilized for sensing different measur-ands, such as pressure, temperature, and strain [3], [4]. The mostcommonly used FBG is the uniform FBG, which is sensitive toany stimulus that changes its grating periodicity, such as tem-perature, pressure, and axial strain [5], [6].

This paper presents the application of a uniform FBG fordevelopment of a shear-force sensor. Shear-force sensorshave potential applications as a slip sensor in robotic armsand normal/shear strain mapping at the foot sole of diabeticpatients. Another emerging area where the shear-force sensorcould be of importance is structural health monitoring (SHM).In SHM, a shear-force sensor can be used for frictional forcemeasurement between different structural components orthermal shear stresses developed between different structuralcomponents due to ambient temperature fluctuations.

Although shear force is an important measurement param-eter, there are very few such sensors available commercially.Shear-force sensors based on the magneto-resistive element, thecapacitive element, the silicon semiconductor, and microelec-

Manuscript received August 25, 2003; revised December 20, 2003.The authors are with the Photonics Research Center, School of Electrical and

Electronic Engineering, Nanyang Technological University, Singapore 639798,Singapore (e-mail: [email protected]).

Digital Object Identifier 10.1109/JLT.2004.831171

tromechanical systems (MEMS) have been reported [7]–[15]. Inthe following, a brief discussion of these sensors is presented.

In 1991, Akasofu et al. reported a shear-force transducerbased on capacitive element with a measurement range of 1–4N and sensitivity of 0.665 V/N [7]. Another sensor based onthe capacitive element was reported by Zhu and Spronck in1992 with a measurement range of 0–10 N, a resolution of0.05 N, and nonlinearity of 5% [8]. The magneto-resistive-ele-ment-based sensor was reported by Chen et al. in 1993 with ameasurement range of 0–10 lbf/in [9]. Troy et al. also reporteda capacitive-element-based sensor for articulated grippers in1995 [10]. A sensor based on light intensity modulation for aplantar shear testing was reported by Lebar et al. in 1996 with aforce range of 0–22.3 N [11]. The sensor reported by Zielinskain 1996 was based on reflection of a light blob and the forcerange was 10 N with a resolution of 0.1 N [12]. In 1997, Zee etal. reported a sensor using conductive-silicon-based rubber, andthe typical measurement range was 20 N [13]. Lin and Davidalso reported a silicon-based sensor with a measurement rangeof 0–3 N and sensitivity up to 0.04 V/N in 2000 [14]. Recentlyin 2003, Shikida et al. reported a MEMS-based sensor for themeasurement of the hardness of an object and the contact force[15].

Using FBG for shear-force measurement offers the advan-tages over all these sensors. The advantages include immunityto electromagnetic interference and multiplexing capability; i.e.,a single string of fiber can support a number of sensors, and,hence, shear force at different points along the fiber can be mea-sured simultaneously.

This paper discusses the theoretical and numerical modelingof a uniform FBG- based shear-force sensor. First, a brief reviewof the technique for converting shear force to axial strain is pre-sented, followed by the theoretical and numerical modeling ofthe sensor. Experimental verification of the theoretical and nu-merical model is also discussed.

II. PRINCIPLE OF SHEAR-FORCE MEASUREMENT BY FBGs

FBGs are narrow-band reflection filters permanently writteninto the core of the single-mode optical fiber. Once the gratingsare imprinted in the core of the fiber, input light is partially re-flected at each grating. Maximum reflection occurs when eachpartial reflection is in phase with its neighbors. This occurs atthe Bragg wavelength, given by [3]

(1)

where is the reflected Bragg wavelength, is the effectiverefractive index of the fiber core, and is the period of the

0733-8724/04$20.00 © 2004 IEEE

TJIN et al.: FBG BASED SHEAR FORCE SENSOR: MODELING AND TESTING 1729

Fig. 1. Basic sensor structure and sensing concept (a) without applied shear force and (b) with applied shear force.

grating. Any external perturbation that can change the gratingperiodicity or effective refractive index changes the Braggwavelength. This shift in the Bragg wavelength will be ameasure of the applied perturbation. When the fiber is strained,the Bragg wavelength varies due to the change in the gratingperiodicity and the change in the refractive index because ofthe induced photoelastic effect. A sensitivity of 1.06 pmhas been reported [16]. A change in the temperature of the fiberalso produces a shift in the Bragg wavelength due to thermalexpansion, which changes the grating spacing, and a changein the index of refraction with temperature. Temperaturesensitivity of the order of 25 pm C has been reported [16].The shift in the Bragg wavelength with strain and temperaturecan be expressed as [3]

(2)

where is the axial strain in the fiber, is the Poisson’s ratio ofthe fiber material, are the strain–optic coefficients, is thethermooptic coefficient, and is the temperature change. Asgiven in (2), the reflected Bragg wavelength changes with thevariation of either the strain and/or the temperature.

This property of FBGs is used in the development of manytypes of sensors. When the FBG is exposed to any perturbationthat changes its length, the reflected Bragg wavelength shiftsaccordingly. In the technique of shear-force measurement, theFBG is embedded at a small angle between an upper layerand a lower layer of carbon composite material (CCM) witha deformable layer of silicon rubber. When the shear forceis applied on the upper surface of the sensor, the upper layermoves with respect to the lower layer in the direction of theapplied shear force. This relative movement between the upperand lower layers of the CCM deforms the silicon rubber matrix,thus stretching the fiber embedded in between. In turn, thisstretching changes the length of the fiber and thus shifts thereflected Bragg wavelength. Fig. 1 shows the sensor withoutand with the application of the shear force. Fig. 1(a) showsthe sensor with no applied shear force. Fig. 1(b) shows thesensor under applied shear force, where the solid line showsthe unstrained fiber and the dashed line shows the stretched

fiber under the applied shear force. This technique ensures away of transferring the applied shear force to the axial strainin the fiber. The following sections discuss the analytical andnumerical modeling of the sensor.

III. THEORETICAL MODEL AND ANALYSIS

A theoretical model is developed to establish an explicit rela-tionship between the applied shear force and the shift in the re-flected Bragg wavelength. The main parameters for this modelare the applied shear force, the induced strain in the fiber, and thereflected Bragg wavelength. For ease of analysis, it is assumedthat the fiber is along the diagonal of the deformable layer ma-trix, although in an actual sensor, the embedded fiber is not trulyalong the diagonal (see Fig. 1). The CCM layer is ignored, andonly the silicon rubber matrix of the deformable layer is consid-ered in this model. This assumption is realistic, taking into con-sideration the very high stiffness of CCM as compared with thatof the deformable layer matrix. Only the part of the sensor withfiber embedded in the silicon rubber matrix is taken into consid-eration [Fig. 2(a)]. Thus, the dimension of the sensor is reducedaccordingly. The reduced dimensions of the sensor are termedas the effective dimensions. The idealized model of the sensor isshown in the Fig. 2(b). It should be noted that the length is muchgreater than the thickness of the sensor; however, for the sake ofclarity, thickness is exaggerated in the figures. In addition, thedependence of the reflected Bragg wavelength on temperature isneglected in this model as the experiment was performed undera temperature-controlled laboratory condition. Let the total ap-plied shear force be , the force carried by the matrix be ,and the force carried by the fiber be . In this analysis, thefiber and the deformable layer matrix are considered individu-ally, and the individual effects are superimposed. Let and

be the horizontal elongations in the deformable layer ma-trix and the fiber, respectively. The effective sensor dimensionsare length , width , and height . By definition, shear stress isgiven by

ForceArea

(3)


Fig. 2. Theoretical model. (a) Part of the sensor taken into consideration. (b) Extended view.

For the deformable layer matrix, the shear strain is

(4)

where is the shear modulus of the matrix.It is known that

(5)

Thus, equating (4) and (5) yield

(6)

We know that the shear modulus can be written as

(7)

where and are the Young’s modulus and Poisson’s ratio,respectively, of the deformable layer matrix.

Solving (6) and (7), we obtain the horizontal elongation ofthe matrix as

(8)

where

(9)

If the elongation of the fiber along the diagonal is , then theelongation of the fiber [see Fig. 2(b)] can be written in terms ofthe horizontal elongation of the fiber ( ) as

(10)

The horizontal force on the fiber is . This force componentcan be written in terms of the diagonal force ( ) as

(11)

Although the angle changes with the applied force, however,we can take it as constant because the change in the value ofcosine of the angle is very small. Thus, the cosine value is keptconstant here, i.e., it is assumed that [Fig. 2(b)], which istrue only when . Thus, the thickness should be very smallas compared with the length. Elongation along the diagonal canbe written as

(12)

where shows the stiffness of the fiber, which can be writtenas

(13)

where and are the Young’s modulus and cross-sectionalarea of the fiber, respectively. Solving (11)–(13), the horizontalelongation of the fiber can be written as

(14)

As we know from the compatibility condition, the horizontalelongation of the fiber and the deformable layer matrix shouldbe the same (i.e., ), and thus

(15)

The total applied force is the sum of the forces carried by thefiber and the force carried by the matrix . That is

(16)

Solving (13)–(15), we obtain the horizontal elongation of thefiber as

(17)

Thus, the elongation of the fiber along the diagonal is given by

(18)

Now, the strain in the fiber elongation original length isgiven as

(19)

Hence

(20)

From (9), (13), and (20), we obtain

(21)

Variation of the Bragg wavelength is given by

(22)


Combining (21) and (22), we have

(23)

where

(24)

It should be noted from (23) that the unit of is 1/N. Theparameter values used in this model are given in Table I [17].

IV. NUMERICAL SIMULATION

Numerical analysis has been carried out to understand themechanical behavior of the sensor using the finite-elementmethod (FEM). Commercially available software ANSYS5.6 was used to perform the analysis [18]. It is assumed that,similar to the analytical model, the fiber is attached to thematrix along the diagonal. The CCM layer is ignored andonly the embedded fiber portion in the silicon rubber matrix isconsidered. Presently, two-dimensional (2-D) modeling is con-ducted. In FEM, the physical domain (which is the deformablelayer of the silicon rubber) is discretized into elementary areascalled elements. In the present model,the element dimension istaken as 0.25 mm. The lower edge was fixed and used as theboundary condition. The physical domain was meshed using2-D-quadratic (solid four-node) element having 2 degrees offreedom at each node. Embedded fiber was meshed using the2-D spar (link) element. The effective dimension of the de-formable layer was taken as length 4 cm, width 2 cm,and thickness 1 mm. A portion of this model is shown inFig. 3.

The Galerkin finite-element discretization of the 2-D domainleads to [19]

(25)

where is the load vector, is the stiffness matrix, andis the displacement vector. This set of equations describes thebehavior of each node and results in a series of algebraic equa-tions, which can be solved to obtain the unknown displacement.The simplest way of determining the strain in the fiber is byapplying the shear force at the surface of the deformable layer,performing static analysis, and obtaining the displacement ofthe fiber as is done in the analytical model. This displacement,in turn, leads to the strain, and, hence, the wavelength shift canbe determined. Material parameters used in this model are listedin Table I.

V. SENSOR CONFIGURATION AND FABRICATION

The sensor consists of the layers of CCM (Fiberdux913C-XAS) with the embedded FBG. A layer of deformablesilicon rubber separates the upper and lower layers of the CCM.After embedding to the CCM, the whole structure was curedat 120 C for about 4 h. The FBG is 1 cm long, and its overalldiameter is 125 m. The use of the CCM as an embeddingmaterial and silicon rubber as a deformable layer offers theadvantage of being easily available and minimizes the need

TABLE IVALUES OF VARIOUS PARAMETERS USED FOR THEORETICAL AND

NUMERICAL MODELING

for extra adhesive at the silicon rubber/CCM interface as thesematerials have good adhesion.

VI. EXPERIMENTAL VERIFICATION

A. Analytical Model

Using the parameter values given in Table I and the effectivedimensions of the sensor as length 4.44 cm, width2 cm, and thickness 1.44 mm (sensor 1), we obtain

(26)

Thus, the wavelength shift is obtained as

(27)

The reference Bragg wavelength is 1554.74 nm. The fiberwas fabricated by the phase mask (QPS Technology, Inc.)technique. The experimental setup consists of an ANDOtunable laser source (with a center wavelength of 1554 nm anda span of 10 nm), an ANDO 6317 optical spectrum analyzer(with a resolution of 0.05 nm), a circulator, and the shear-forcedevice. This device is made of aluminum and is fabricated dueto the lack of a standard device to apply the shear force and toensure that the sensor measures only the shear force appliedhorizontally. A schematic of the experimental setup is given inFig. 4, where the dashed line shows the shear-force device and

is the applied shear force.Analytical and experimental results of this sensor are shown

in Fig. 5, where good agreement between the experimental andtheoretical models can be observed.

B. Numerical Model

For verification of the FEM simulation result, the experimentwas carried out for the sensor (sensor 2) with the following ef-fective dimensions: length of 4.15 cm; width of 2.162 cm; andheight of 1 mm. The experimental, theoretical, and simula-tion results for this sensor are given in Fig. 6. A good agreementamong the experimental, theoretical, and numerical models isobtained.


Fig. 3. FEM model of the shear-force sensor.

Fig. 4. Schematic of the experimental setup used for testing the sensor.

Fig. 5. Comparison of analytical and experimental results of sensor (sensor 1).

VII. RESULTS AND DISCUSSION

As described previously, theoretical and numerical modelshave been established for FBG-based shear-force sensors. Therelationship between the Bragg wavelength shift and the appliedshear force has been derived. The analysis shows that the Braggwavelength shift depends on the sensor dimensions as well ason the material properties of both the fiber and the deformablelayer matrix. Experimental verification of this analytical modelhas been carried out, and a good agreement between the exper-

Fig. 6. Comparison of analytical, experimental, and FEM results (sensor 2).

imental and analytical results has been observed. The analyt-ical model shows a sensitivity of 70 pm/N for sensor 1, whereasthe experimental result shows a sensitivity of 73 pm/N. Usingthe experimental result as a reference, the error between the ex-perimental and theoretical results is found to be 4.1%, whichshows a fairly good agreement. This error may be attributed tothe experimental errors as well as the assumptions made in thetheoretical model. The theoretical result shows an almost 100%linearity (with a regression coefficient of ), but the exper-


imental result shows some nonlinearity ( ), whichcan be attributed to the friction of the shear-force device as wellas the slight nonlinear nature of the deformable layer matrix.In this experiment, elastomeric silicon rubber was used as thedeformable layer matrix, which shows some nonlinearity. Themajor limitation of this analytical model is that it fits well onlyin the linear region and does not explain the failure point of thesensor.

FEM-based numerical analysis was also conducted. Forsensor 2, the simulation result shows a sensitivity of 63 pm/N( ), while the experimental result shows a sensitivity of67 pm/N ( ), and the error is approximately 5%,which can be attributed to the assumptions made in modelingthe sensor. FEM itself is an approximate method; thus, someerror could be due to the inherent approximate nature of FEM.Theoretical analysis of sensor 2 shows a sensitivity of 58 pm/N( ). The error is approximately 13%, which could bedue to the assumptions made in the analytical modeling, thefriction of the shear-force device, as well as the measurementerror of the sensor dimensions. The results of the FEM matchthe experimental results much more closely compared with theanalytical results. This is because the analytical model assumesa connection between the fiber and the matrix only at theend. The FEM model, on the other hand, assumes continuousbonding and, hence, models the complicated behavior in amuch more accurate fashion.

It is found that in the analytical model the sensitivity dependson the effective sensor dimensions. The two sensors tested inthis study show different sensitivities, which are due to the dif-ferent effective sensor dimensions. Although the sensors werenot tested up to the failure point, based on previous experimentalresults, the force sensing range of these sensors are estimatedapproximately as 70 N and 85 N, for sensor 1 and sensor 2, re-spectively, which is higher than other sensors reported so far[7]–[15].

VIII. CONCLUSION

A new concept of shear-force measurement using FBGs hasbeen introduced. In order to establish an explicit relationshipbetween the applied shear force and the shift in the reflectedBragg wavelength, theoretical and numerical models have beendeveloped. Experimental verification of both the analytical andnumerical models has been conducted, and a good agreementamong the analytical, numerical, and experimental results hasbeen observed.

REFERENCES

[1] K. O. Hill, F. Fuji, D. C. Johnson, and B. S. Kawasaki, “Photosensitivityin optical fiber waveguides: Application to reflection filter fabrication,”Appl. Phys. Lett., vol. 32, pp. 647–649, 1978.

[2] G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratingin optical fibers by a transverse holographic method,” Opt. Lett., vol. 14,pp. 823–825, 1989.

[3] A. D. Kersey, M. A. David, H. J. Patrick, M. LeBlanc, K. P. Koo, C.G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J.Lightwave Technol., vol. 15, pp. 1442–1463, Aug. 1997.

[4] X. Wan and H. F. Taylor, “Fiber Bragg grating pair interferometersensor with improved multiplexing capacity and high resolution,” IEEEPhoton. Technol. Lett., vol. 15, pp. 742–744, May 2003.

[5] S. C. Tjin, J. Hao, Y. Z. Lam, Y. C. Ho, and B. K. Ng, “A pressure sensorusing fiber Bragg grating,” Fiber Integr. Opt., vol. 20, no. 1, pp. 59–69,2001.

[6] H. B. Liu, H. Y. Liu, G. D. Peng, and P. L. Chu, “Strain and temperaturesensor using a combination of polymer and silica fiber Bragg gratings,”Opt. Commun., vol. 219, pp. 139–142, 2003.

[7] K. I. Akasofu and M. R. Neuman, “A thin film variable capacitance shearforce sensor for medical and robotics applications,” in Proc. Annu. Int.Conf. IEEE Engineering Medicine Biology Society, vol. 13, 1991, pp.1601–1602.

[8] F. Zhu and J. W. Spronck, “A capacitive tactile sensor for shear andnormal force measurement,” Sens. Actuators A, Phys., vol. 31, pp.115–120, 1992.

[9] L. H. Chen, S. Jin, and T. H. Tiefel, “Tactile shear sensing usinganisotropically conductive polymer,” Appl. Phys. Lett, vol. 62, no. 19,pp. 2440–2442, 1993.

[10] A. C. Troy and C. L. Ren, “A thin film capacitive tactile normal/shearforce array sensor,” in Proc. IEEE-IECON, 21st Int. Conf. IndustrialElectronics, Control Instrumentation, vol. 2, 1995, pp. 1196–1201.

[11] A. M. Lebar, G. F. Harris, H. Zhu, J. J. Wertsch, and H. Zhu, “A optoelec-tric plantar shear sensing transducer : Design, validation and preliminarysubject tests,” IEEE Trans. Rehab. Eng., vol. 4, pp. 310–319, Dec. 1996.

[12] T. Zielinska, “Shear force sensor for robots,” in Proc. IEEE Int. Symp.Industrial Electronics, vol. 1, June 1996, pp. 49–52.

[13] F. Zee, E. G. M. Holweg, W. Jongkind, and G. Honderd, “Shear forcemeasurement using a rubber based tactile matrix sensor,” in Proc. IEEE10th Int. Conf. Advanced Robotics, July 1997, pp. 733–738.

[14] W. Lin and J. B. David, “A silicon-based shear force sensor: Develop-ment and characterization,” Sens. Actuators A, vol. 84, pp. 33–44, 2000.

[15] M. Shikida, T. Shimizu, K. Sato, and K. Itoigawa, “Active tactile sensorfor detecting contact force and hardness of an object,” Sens. ActuatorsA, Phys., vol. 103, pp. 213–218, 2003.

[16] S. C. Tjin, Y. Wang, X. Sun, P. Moyo, and J. M. W. Brownjohn, “Ap-plication of quasidistributed fiber Bragg gratings sensors in reinforcedconcrete structures,” Meas. Sci. Technol., vol. 13, pp. 583–589, 2002.

[17] C. Seo and T. Kim, “Temperature sensing with different coated metalson fiber Bragg grating sensors,” Microwave Opt. Tech. Lett., vol. 21, pp.162–165, 1999.

[18] ANSYS User’s Guide for Revision 5.5, ANSYS, Inc., Canonsburg, PA,1998.

[19] K. J. Bathe, Finite Element Procedures. Englewood Cliffs, NJ: Pren-tice- Hall, 1996.

S. C. Tjin (M’93), photograph and biography not available at the time of pub-lication.

R. Suresh, photograph and biography not available at the time of publication.

N. Q. Ngo, photograph and biography not available at the time of publication.

fiber bragg grating based shear-force sensor: modeling and testing

Documents