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Development of a chirped/differential optical fiber Bragg grating pressure sensor
View the table of contents for this issue, or go to the journal homepage for more 2008 Meas. Sci. Technol. 19 045304
(http://iopscience.iop.org/0957-0233/19/4/045304)
Meas. Sci. Technol. 19 (2008) 045304 (6pp) doi:10.1088/0957-0233/19/4/045304
Development of a chirped/differential
optical fiber Bragg grating pressure
sensor
Yen-Te Ho, An-Bin Huang and Jui-ting Lee
Department of Civil Engineering, National Chiao-Tung University, Hsinchu, Taiwan E-mail:[email protected],[email protected],[email protected] Received 22 June 2007, in final form 7 January 2008
Published 13 February 2008
Online atstacks.iop.org/MST/19/045304
Abstract
With its unique capabilities, the optical fiber Bragg grating has been used as a key component in the development of many sensors. Incorporating the theory of thin plates, the authors have developed an FBG-based pressure sensor by strategically attaching FBGs on the surface of a thin circular plate. The flexural strain in the circular plate induced by pressure applied to the circular plate is sensed by either a single FBG placed radially crossing a neutral point, or two FBGs placed respectively in zones where the strains are of opposite signs. When one FBG is used (i.e., the chirped FBG design), the applied pressure relates to the change in the chirped bandwidth of the FBG reflected waveform. When two FBGs are used (i.e., the differential FBG design), the pressure experienced by the circular plate is correlated to the difference in central wavelength from the two FBGs. In either case the sensing mechanism is immune to temperature fluctuation. The same configuration can potentially be applied for other purposes such as a load cell or displacement transducer. This paper describes the design principles of the FBG pressure sensor and demonstrates its capabilities through laboratory calibrations over a wide range of temperatures.
Keywords: optical fiber Bragg grating, pressure sensor
Introduction
Taking advantage of its unique capabilities, several types of fiber optic sensored pressure transducers have been developed recently (Kashyap1999, Kojima et al2003, Liu et al 2000, Xu et al1993, Yang et al2005, Zhao et al2004). The fiber Bragg grating (FBG) is one of the commonly used means to measure the change of pressure. The currently available FBG-based pressure sensors can generally be divided into two groups according to their modulation schemes. The first group may be referred to as the uniform strain FBG (UFBG) design where the distribution of strain across the FBG remains uniform. In the UFBG design, the change of pressure causes mainly shifting of the central wavelength of the FBG reflected waveform (Heo et al2005, Kashyap1999, Kojima et al2003, Liu et al2000b, Rao et al1994, Xu et al1996, Zhang et al
2001). The second group may be called the chirped fiber Bragg grating (CFBG) design (Dong et al2002), where the change of pressure causes a variation in the bandwidth of the FBG
reflected waveform. The variation in bandwidth or chirping of the FBG waveform is a result of non-uniform strain distribution across the FBG. The CFBG design has the advantage over the central wavelength scheme in that the bandwidth of the FBG reflected waveform is practically immune to temperature fluctuation (Xu et al1995). When a CFBG is subjected to a non-uniform strain distribution, there is possibly a change to the reflection profile as well as the bandwidth. The currently available CFBG design however, involves a more complicated mechanical design that may render the transducer less sensitive or limit its use only for the high-pressure range (Zhao
et al2004). The authors developed a pressure sensor based on the CFBG scheme. In the new design, referred to as the chirped/differential FBG design or C/D-FBG, a single or a pair of FBGs were attached to the surface of a circular diaphragm. The application of pressure induces a non-uniform strain distribution on the diaphragm. With proper positioning of either a single FBG or two FBGs, the non-uniformity of the strain distribution can be measured according to variations in
Meas. Sci. Technol. 19 (2008) 045304 Y-T Ho et al grating sensor (λj) λ wavelength shift decoding outputs λ1 broadband source input spectrum λ coupler λ returns λ wavelength encoded λ2 λ3 measurand field
Figure 1. A conceptual description of FBG multiplexing (after Kersey1992).
the bandwidth of the reflected waveform from a single FBG or difference of the central wavelengths from the two FBGs. The magnitude of pressure is then determined according to the characteristics of the FBG waveforms. The new design has many important advantages over the currently available FBG-based pressure sensors. The paper provides a brief description of the basic principles of central wavelength and chirped FBG design first and then presents details of the C/D-FBG scheme. In addition to pressure sensing, the advantages of the C/D-FBG and potential applications are also discussed.
The principles of available UFBG and CFBG design
Detailed principles of FBG and its manufacturing can be found in Dyer et al (2005), Hill et al (1978), Meltz et al (1989), Othonos and Kalli (1999) and Rao (1998). The lengths of FBGs are generally within the range of 1 to 20 mm. When the wideband light source illumines an FBG, a fraction of the light is reflected back upon interference by the FBG. When the strain within the FBG is uniform, the reflected waveform has a well-defined peak. This peak wavelength is referred to as the Bragg wavelength λB. The longitudinal strain within the Bragg grating, εB, induced by variations in temperature or stress causes a change in λB or λB (in nm or 10−9m). The approximate relationship among λB, λBand εBcan be written as follows (Rao1998):
λB
λB
= 0.74εB (1)
and
λB= 8.9 × 10−6λB◦C (2) where ◦C is the change of temperature in degree Celsius. The signal returned from an FBG carries a unique domain of wavelength λB + λB, making it possible to have multiple FBGs on the same fiber. The multiplexing among various sensors on a single fiber and conceptual description is described in figure1. The power intensity of the light source becomes weaker when it passes an FBG and a connector, and in normal conditions the maximum number of FBG sensors placed within the same fiber does not exceed 10. A resolution in λB of 1 pm to 0.1 pm may be resolved with
Clamp neutral axis ASE OSA Optical circulator h θ bn FBG force Coupler PD
Figure 2. The sketch of a temperature-independent displacement/
pressure sensor (after Yang et al2005).
the currently available FBG integration systems. The UFBG design generally involves a mechanism that causes a uniform straining (εB) of the FBG as a result of pressure changes. For an FBG with a given λB, the change in pressure is thus modulated through λB according to equation (1). A disadvantage in the UFBG design is that λBis also affected by fluctuations in temperature as indicated in equation (2). The UFBG design generally incorporates a means to either nullify or account for the temperature effects.
A grating that has a non-uniform and progressively changing period distribution along its length is known as chirped. Detailed principles and structures of CFBG can be found in Kashyap (1999). When the FBG is strained from its original period of o, the chirped bandwidth relates to the chirped period as (Kashyap1999)
λchirp= 2neff(long− short)= 2neffchirp (3)
where λchirp is the change of the chirped bandwidth, neffis
the effective mode index, longis the longest period of CFBG,
shortis the shortest period of CFBG and chirpis the period
change in the fiber.
According to equation (3) λchirp can be made strain
dependent if a strain gradient is introduced along the FBG. Yang et al (2005) reported a displacement/pressure sensor based on the CFBG design. An FBG is attached to the side of a triangle cantilever beam at an inclined angle as shown in figure 2 to measure the non-uniform strain distribution. The center of the FBG is located at the neutral axis of the cantilever as shown in figure2. The sensor is designed so that the applied displacement or pressure causes bending of the triangular beam. An important advantage of this CFBG design is that λchirp is practically immune to temperature
fluctuation. In order to configure the FBG-sensored beam into a pressure transducer, an additional diaphragm is required to provide the sealing (Yang et al2005). A linkage was used so that the beam and its FBG deform with the diaphragm as a result of pressure application. The sensitivity is thus reduced due to the addition of linkage and separation of the beam and diaphragm.
0 0.2 0.4 0.6 0.8 1 r/a -0.1 -0.05 0 0.05 ε rr Eh 2/p a 2 neutral point
Figure 3. Variation of strain in the radial direction.
Design principles of the C/D-FBG pressure sensor
According to Timoshenko and Woinowsky-Krieger (1959), for a circular thin plate with clamped edges, the amount of deflection (w) perpendicular to the plate surface relates to the uniformly applied pressure (p) and radial distance from the center (r) as,
w=3p(1− ν
2)
16Eh3 (a
2− r2)2 (4)
where a is the radius of the plate, E is Young’s modulus of the plate material, ν is Poisson’s ratio and h is the thickness of the circular plate.
No rotation of the plate (i.e.,dwdr = 0) is allowed because of clamping at the edge (r= a) and symmetry at the center (r= 0) of the plate, thus resulting in a distribution of moment as, Mr= p 16[(1 + ν)a 2− (3 + ν)r2] (5) and Mθ = p 16[(1 + ν)a 2− (1 + 3ν)r2] (6)
where Mris the moment in the radial direction per unit length and Mθ is the moment in the circumferential direction per unit length.
The maximum bending stress in radial (σrr) and circumferential (σθ θ) directions occur on the surface of the circular plate, where
σrr= 6Mr
h2 and σθ θ=
6Mθ
h2 . (7)
According to Hooke’s law, strain in the radial direction (εrr) relates to stresses as,
εrr= 1 E(σrr− νσθ θ) . (8) (a) FBG1 thin plate frame pressure (b) Fiber FBG2 thin plate frame pressure a (c) Fiber FBG3
Figure 4. (a) Photograph of the pressure sensor. (b) Sectional view of the chirped FBG pressure sensor. (c) Sectional view of the differential FBG pressure sensor.
(This figure is in colour only in the electronic version) Combining equations (5)–(8) results in
εrr=
3p(1− v2)
8Eh2 (a
2− 3r2). (9)
Figure 3 shows a plot of εrrEhpa22 against
r
a, assuming that ν equals 0.3. As indicated in figure 3 and equation (9), εrr becomes zero and changes its sign when r = a/√3. The
εrr transforms from compression to tension as r crosses the neutral point at a value of a/√3.
If a single FBG is attached to the surface of a circular thin plate in the radial direction, chirp within the FBG
Meas. Sci. Technol. 19 (2008) 045304 Y-T Ho et al 1543.8 1544.3 1544.8 Wavelength, nm -35 -30 -25 -20 -15 -10 Reflecti vity, dB 0 50 100 150 200 250 Pressure, kPa 0 30 60 90 120 ∆ λchi rp , p m 126pm 235pm Y=0.449*X-2.177 R2=0.994 (a) (b)
Figure 5. Results of the chirped FBG pressure sensor calibration: (a) waveforms at 0 kPa and 250 kPa and (b) change of the FBG waveform bandwidth against pressure.
should follow εrrdistribution on the surface of the thin plate. According to the above thin plate theory and equation (3), the FBG should reflect a broadened waveform when the plate is pressurized, because of the non-uniform εrr distribution. Unless the center of the FBG is aligned at r = a/√3, the broadened waveform should also show shifting of the central wavelength.
The new C/D-FBG pressure sensor is constructed by attaching either a single FBG or two FBGs in the radial direction on the surface of a thin circular plate. When a single FBG is used in a chirped FBG design, the center of the FBG is positioned at the neutral point, where r = a/√3. According to the above described thin plate theory, the FBG so positioned should generate a broadened waveform with little shifting of its central wavelength when a pressure is applied to the circular plate.
When two FBGs are utilized in a differential FBG design, one of them is attached towards the center of the plate (r is close to 0) and the other close to the clamped edge (r approaches a). The application of pressure should result in central wavelength shifts (i.e., λB1and λB2) in opposite directions because the
two FBGs are located at opposite sides of the neutral point. The applied pressure is modulated by the difference between
λB1and λB2or λB1− λB2. Thus, the strength of the
signal is enhanced by the subtraction. Due to non-uniformity in strains, the waveforms from both FBGs are also expected to be chirped during pressure application.
The change in temperature induces uniform straining throughout the circular plate. In a chirped FBG design, the temperature fluctuation causes the central wavelength to shift but has no effect on λchirp. In differential FBG design,
the temperature fluctuation should cause λB1and λB2to
change by equal amounts and in the same direction. Thus,
λB1− λB2 should cancel out the effects of temperature
fluctuation.
Fabrication and calibration of the C/D-FBG pressure sensor
Following the chirped FBG design, the authors attached a 3 mm long FBG on the face of a 30 mm diameter (a= 15 mm) and 0.3 mm thick (h= 0.3 mm) 316 stainless steel plate in the radial direction. A steel needle was used to scrape a line on the stainless-steel plate where the FBG was to be attached. A pre-tension of 3000 µε was applied when bonding the FBG to the surface of the stainless-steel plate using a heat cured epoxy. The center of the FBG was fixed at r = 15/√3 or 8.66 mm. Figure4shows a photograph and schematic diagram of the pressure sensor. The FBG, attached to the surface of the circular plate, directly senses strains caused by the pressure applied to the opposite side of the plate. The sensor was calibrated in a thermal chamber under 25◦C, by regulated air pressure from 0 to 250 kPa. Results shown in figure5indicate a resolution of 2.22 kPa for 1 pm of λchirp, the minimum
wavelength shift identifiable by the interrogator. The relatively low sensitivity or change in λchirpin response to pressure is
mainly due to the limited length of the FBG.
The pressure sensor of a differential FBG design had the same physical dimensions as shown in figure4. The material used for the metal plate and the procedure of attaching the FBG were the same as the chirped FBG design. The major difference is that there were two FBGs attached to the surface of the circular plate, one toward the center and the other close to the edge of the plate. The pressure sensor was calibrated in a thermal chamber under three different temperatures ranging from 25 to 50 ◦C. The results depicted in figure 6 had a resolution of 0.16 kPa per 1 pm of λB1− λB2, for the
range of 0 to 250 kPa. The resolution in a differential mode is significantly better than that of the chirped FBG design. The results also showed a strong linearity between λB1− λB2
and pressure, with coefficients of correlations generally higher than 0.99. For a given pressure, λB1− λB2 deviates no 4
0 50 100 150 200 250 Pressure, kPa 0 400 800 1200 1600 ∆λB1 -∆λ B2 T = 250C, R = 0.9997 T = 400C, R = 0.9994 T = 500C, R = 0.9987
Figure 6. Results of the differential FBG pressure sensor calibrations.
more than 5% from the average value among tests in three different temperatures, indicating that the sensor was largely immune to thermal effects for the range of temperature fluctuation.
According to equations (3), (4) and (9), there should be a linear relationship between λB1 − λB2 and the
applied pressure (p) in a differential FBG design. This linear relationship remains if the FBG is properly bonded to the metal thin plate and the pressure induced straining or deformation of the metal plate is not excessive so that E and r remain constant. Results demonstrated in figure6 showed that for the pressure range applied, there was a reasonable linearity between λB1–λB2 and p. Equation (3) assumes that the
grating period within the FBG changed from short to long
or vice versa in a linear and monotonic fashion. This implies that εrrdistribution of the thin metal plate where the FBG is attached should be linear in the chirped FBG design. For the pressure sensor described in this paper, the FBG had a length of 3 mm and the radius of the metal plate (a) was 15 mm. The corresponding r/a spanned from 0.477 to 0.677 when the center of the FBG was attached to the neutral point (r/a= 1/√3= 0.577) as indicated in figure3. The distribution of
εrrwas close but not exactly linear as shown in figure3. This may be part of the reason for the less linear performance in the chirped FBG design as described in figure5.
Conclusions
The authors have developed an FBG-based pressure sensor by strategically attaching either one or two FBGs on the surface of a thin circular plate. When one FBG is used (i.e., the chirped FBG design), the applied pressure relates to the change in the chirped bandwidth of the FBG reflected waveform. When two
FBGs are used (i.e., the differential FBG design), the pressure experienced by the circular plate is correlated to the difference in central wavelength variations from the two FBGs. Because of the limited length of FBG used in the design reported herein, the differential design had a better sensitivity to the change of pressure. In either case the sensing mechanism is immune to temperature fluctuation. The FBG signals reflect the difference in pressure between the two sides of the circular plate. Thus, it can be used as a differential or gauge pressure transducer (in reference to the atmospheric pressure).
An important advantage of the design presented herein is that the pressure is applied directly to the circular plate where the FBGs are attached without any intermediate linkage, thus enhancing its sensitivity. Analytical solutions for thin plates with different boundary conditions are readily available. Adopting these solutions, the same design can be modified to sense force as a load cell or a displacement transducer. In the case of a load cell, a concentrated force is applied to the center point of the circular plate. By attaching a displacement rod to a spring to convert displacement to a spring load, the same load cell configuration can be used to modulate displacement.
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