Introduction
Chapter 3 Stable and Effective Temperature Insensitive Fiber Bragg
3.2 Experimental
3.2.1 Sensor Design and Construction
T
wo rectangular plates (6.0×1.2×1.0 cm3) are rigidly joined by two identical vertical brass rods of diameter 0.6 cm and length 9 cm as shown in Figure 3.1 (a). A circular disc (1 cm inner and 2.83cm outer diameter, thickness 1 cm) is fixed at the upper surface of the top rectangular plate; whereas, a circular plate (2.83cm diameter, thickness 1 cm) is fixed at theChapter 3: Stable and Effective Temperature Insensitive Fiber Bragg Grating Based Tilt Sensor Employing Non-pendulum Type Design Strategy
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proper care is taken in order to maintain their centres on the vertical axis of this structure. A small circular plate (1 cm diameter) is inserted into the central part of the circular disc. A hole of diameter 0.5 mm is drilled along the vertical axis of this structure; i.e., through the centre of small circular plate, top rectangular plate as well of the bottom rectangular plate. A hole of identical diameter is also drilled separately along the diameter of a steel bob (dia 2.83
Figure 3.1: (a) Schematic diagram of the proposed FBG based tilt sensor and (b) photograph of the sensor.
cm, mass ~90g). A copper wire of diameter 0.45mm is inserted into the hole and is rigidly fixed to the bob first. The two open ends of the copper wires are then fixed to the small circular plate at the top and the rectangular plate at the bottom. In this arrangement, copper wire coincides with the vertical axis of the structure; whereas bob remains at the vertical centre of the structure. Also, small circular plate inside the circular disc rests on the top
X Y
Z STU
Small circular plate
Circular disc
Circular plate Copper wire
STU
(a)
(b)
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rectangular plate in the sensor design. In order to tune strain in the copper wire, two holes with M2 threading are drilled into the small circular plate and M2 screws are fixed in it.
Turning the M2 screws moves small circular plate along the upward direction w.r.t. the top rectangular plate and thus allows strain tuning in the copper wire.
Two pairs of vertical grooves (~0.5 mm depth each) are made along the diagonally opposite points on the side cylindrical surface of the circular plate (fixed at the lower surface of the bottom rectangular plate). The two diagonals carrying the pair of vertical grooves are orthogonal to each other (see Fig. 3.1(a)). On the other hand, two pairs of vertical channels (2 mm width each) are made along the diagonally opposite points on the side cylindrical surface of the circular disc (fixed to the rectangular plate at the top). The two diagonals carrying the pair of vertical channels are orthogonal to each other (see Fig. 3.1(a)) and parallel to the diagonals used in circular plate at the bottom of the design. Four -shaped metallic strain tuning units (STUs) are designed. Length and width of the vertical legs of -shaped STUs are 10 mm and 2 mm respectively. Separation between the two vertical legs is 6 mm. Total breadth of STUs is 5 mm. These STUs are fixed onto the circular disc such that one vertical leg rests inside the channel whereas the other inside a hole drilled on the circular disc (hole diameter and depth were 2 mm and 5 mm, respectively) (Fig. 3.1(a)). Each STUs carries a vertical groove (~0.5 mm depth) on the outer surface of that leg which rests inside the channel. Each STUs also carries holes with M2 threading having M2 screws fixed in it. In the sensor design, four grooves on the STUs attached to the circular disc (on the top) and the four grooves on the cylindrical surface of the circular plate (at the bottom) are collinear.
Four FBGs are written onto a single fiber such that the distance between FBG1 and FBG2 as well as between FBG3 and FBG4 are kept identical. Starting from one groove (say, 1) on the
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lower circular plate, this fiber is then glued at the tangential point of the bob (say, T1), to the groove on the STU at the upper circular disc (say, 1), to the diagonally opposite groove on the STU at the upper circular disc (say, 3), at the tangential point of the bob (say, T3), to the groove (say, 3) on the lower circular plate, to the adjacent groove (say, 2) on the lower circular plate, at the tangential point of the bob (say, T2), to the groove on the STU at the upper circular disc (say, 2), to the diagonally opposite groove on the STU at the upper circular disc (say, 4), at the tangential point of the bob (say, T4) and finally to the groove (say, 4) on the lower circular plate. In this arrangement, all the four FBGs are in the middle of the length between the tangential points on the bob and the STUs. Further, FBG1 and FBG2 are in the same vertical plane (say, y-z plane) whereas FBG3 and FBG4 are in another vertical plane (x-z plane) which is normal to the plane carrying FBG1 and FBG2. As STUs rest on the circular disc, turning the M2 screw fixed in it results in an upward movement of these units w.r.t. the circular disc. This facilitates strain tuning in each fiber arms.
Photograph of the developed sensor is shown in Fig. 3.1(b).
3.2.2 Sensing Principle
A
s the sensor is tilted in one vertical plane, theoretically the two FBGs in that plane are loaded unequally; and the other two FBGs in the plane, perpendicular to the tilt plane, are loaded equally. A detailed theoretical analysis of the sensor response shows that, when the sensor is inclined by an angle , say in the y-z plane keeping inclination in x-z plane zero, strain in the gratings gets redistributed; and the corresponding wavelength difference in y-z and x-z plane is given by(3.1)
(4 – 3) = 0 (3.2)
1
sin2 1
1
2 Pe
AE mg
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Identically, when the sensor is inclined by an angle in the x-z plane keeping inclination in y-z plane zero, the strain in the gratings gets redistributed; and the corresponding wavelength difference in x-z and y-z plane is given by
(3.3)
(2-1) = 0 (3.4)
Here m is the mass of the bob used in the sensor design, g is the acceleration due to gravity, Pe is the photoelastic constant of the fiber, A is the area of cross-section of the fiber and E is the Young’s modulus of the material of the fiber. Referring to Eq. (3.1) and (3.3), following features of the proposed sensor are worth mentioning: (a) for small tilt angle variations, wavelength separations, (2 – 1) and (4 – 3), are linearly proportional to ; (b) sensitivity of the sensor, which is fractional change in the wavelength difference for an applied tilt, is linearly proportional to m/2; (c) sensitivity can be tuned to the desired value by suitably changing the mass of the bob (m); and (d) temperature-change during the experiment shifts each FBG’s wavelength in the same direction. As the wavelength difference of the pair of FBGs would be measured against the suitably applied tilt, temperature cross-talk in the final measurement would automatically be eliminated; making the sensor’s response temperature independent.
3.2.3 Sensor characterization
F
our FBGs were written onto a single fiber using phase-mask technique. Hydrogen-loaded single-mode optical fiber with characteristic parameters given by 7.27×1010 N/m2 as Young’s modulus of the host material (E); 1.2266×10-8 m2 as the cross section area of the fiber (A) and 0.22 as the photoelastic coefficient of the optical fiber (Pe) was used for FBG writing. FBGs
1
sin2 3
3
4 Pe
AE
mg
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FBG3 and FBG4 were kept identical. The peak reflection wavelengths of the FBGs were 1540.01 nm (FBG1, 1), 1543.75 nm (FBG2, 2), 1554.871 nm (FBG3, 3) and 1559.21 nm (FBG4, 4). Fiber carrying four FBGs was glued at two sets of diametrically opposite STUs on the top circular disc and at the corresponding two sets of diametrically opposite STUs on the bottom circular plate via tangential points of the bob as explained in the previous section.
All the four FBGs remained equidistant from the top circular disc in the corresponding fiber arms. These gratings were then equally pre-strained by a pre-determined value (1750 µε) through the four STUs. The one end of the fiber carrying four FBGs was connected to FBG interrogator (Micron Optics, SM130-700, resolution 0.05 pm). Sensor was then mounted on the available tilt stage (goniometer), which had a provision to turn the sensor within ±10o range only. This was the laboratory constraints. It is important to mention that, though the experiment was performed within the maximum tilt limit of the available goniometer, i.e., within the tilt range of ±10o, sensor is actually designed for a ±45o applied tilt. To carry out the experiment, the sensor was first tilted in the plane of FBG3 and FBG4 (x-z plane), keeping the tilt in the plane of FBG1 and FBG2 (y-z plane) zero. The tilt angle was varied from -10o to 10o (forward) and then back to -10o (reverse) in a suitable minimum steps allowed by the goniometer. During the experiment, reflection spectra of four FBGs against the applied tilt angle () were monitored using the interrogator.