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CH3.PDF (79.23Kb) 3. Technical approach As described above, the goal of this work is to develop a miniature instrument based on optical fiber sensors to perform DMA in situ during composite manufacturing. The approach is to attach a fiber optic strain gage to a miniature actuator, as illustrated in Figure 3-1. Candidate materials for the actuator include piezoelectric, magnetostrictive, and shape memory alloy materials. Piezoelectric actuators were chosen due to their ability to produce large forces and measurable strains, and due to their compatibility with typical composite manufacturing methods, including autoclaves, RTM, and compression molding. By immersing the sensor/actuator assembly into a curing thermoset resin and applying a steady-state sinusoidally varying excitation to the actuator, a time-varying shear stress will be transferred from the actuator into the adjacent resin. The mechanical response of the resin and the sensor/actuator assembly will be constrained by the changing mechanical impedance of the resin. Therefore, the rheological properties of the resin, which can be related to the mechanical impedance by the sensor geometry, can be determined by monitoring the strain response of the sensor assembly through the optical fiber strain gage. EFPI silicone elastomer strain gage epoxy epoxy input fiber electrical leads PZT piezoelectric actuator conductive epoxy Figure 3-1. Prototype rheometer sensor. 3.1 Fiber Optic Strain Gage An optical fiber sensor design was chosen for the strain gage element of the rheometer because the small size of the fiber presents a good potential for miniaturization. Optical fibers may be embedded in fiber reinforced composites with little or no change in the 15Russell G. May, Jr. Chapter 3. Technical Approach 15 mechanical properties of the composite if the sensor is aligned with the reinforcing fibers.27 In addition, the use of optical fiber strain gages improves immunity to electromagnetic interference, which may plague resistive strain gages in a typical manufacturing environment. Other attributes of optical fibers that commend them for this application include elimination of ground loops, excellent strain resolution, and an ability to operate at high temperatures. In principle, the embedded viscoelasticity sensor can be used as a strain gage after fabrication of the composite part, in order to monitor internal strains. The optical fiber sensor used for measuring strain in the viscoelasticity sensor is a modification of the extrinsic Fabry-Perot interferometer (EFPI) design.28 The standard EFPI sensor is a phase-modulated sensor that uses optical path length difference in an interferometric cavity to measure strain, as illustrated in Figure 3-2. A single-mode fiber, used as an input/output fiber, and a multimode fiber, used purely as a reflector, form an air gap that acts as a low-finesse Fabry-Perot cavity. The hollow core fiber, a glass capillary tube, serves to align the two fibers collinearly. As the sensor is strained, the silica tube and hence the air gap changes in length, which causes a change in the phase difference between the reference and sensing reflections R1 and R2. The intensity of the light monitored at the output of a coupler by a photodetector responds sinusoidally to a linear strain field. Two different systems for determining the strain using an EFPI sensor were used in the course of the research reported here. In the first system, a light source with a broad spectral width, such as a superluminescent light emitting diode (SLED) was used to replace the laser diode shown in Figure 3-2. Since the coherence length of the light emitted by the source is inversely proportional to the source spectral width, interference effects within the EFPI gap can be eliminated by choosing the spectral width so that the coherence length is less than the round-trip length of the reflection that transits the cavity. In that case, no interference results, and the intensity of light monitored at the photodetector depends on the optical losses in the cavity. 27 G.P. Carman and G.P. Sendeckyj, “Review of the mechanics of embedded optical fiber sensors,” Jour. of Composites Tech. & Research, 17, July 1995, pp. 183 - 193. 28 Murphy, K., Gunther, M., Vengsarkar, A., and Claus, R., "Quadrature phase-shifted, extrinsic Fabry-Perot optical fiber sensors," Optics Letters, 16, No. 4, Feb. 1991. 16Russell G. May, Jr. Chapter 3. Technical Approach 16 Laser Diode Sensor Head Coupler Data Acquisition Photodetector System Multimode (Reflector) fiber Hollow-Core Fiber Shattered R 1 R 2 Fiber End Single-Mode S (Input) Fiber d Epoxy Figure 3-2. Geometry of EFPI strain sensor. Since the light emitted by the input/output fiber into the cavity is divergent due to diffraction effects resulting from the small core diameter (9 µm) of the fiber, the amount of light returned to the photodetector will depend on the separation of the input/output fiber and the reflector fiber. As depicted in Figure 3-3, the divergent light is intercepted and reflected by the reflector fiber. Only that part of the reflected light that is captured by the core of the input/output fiber is returned to the photodetector, and the remainder is lost. If the reflector fiber is moved closer to the input/output fiber, the total spread of the light is reduced, and the percentage of light captured by the core is increased. The light loss suffered in the cavity has been characterized analytically, and may be expressed as29 1 Γ (dB) = ± 10 log 1+ 2s , s 2 (2) kgw 29 C.M. Miller, Optical Fiber Splices and Connectors:Theory and Methods, Marcel Dekker, NY, 1986, 142-150. 17Russell G. May, Jr. Chapter 3. Technical Approach 17 where Γ s is the optical loss in decibels, s is the longitudinal gap between the fiber ends, π/λ kg = 2 is the propagation constant of the light in the gap, and w is the mode field radius of the fiber for a single electromagnetic mode propagating at wavelength λ, and is defined as the radial distance from the axis of the fiber at which the intensity E2 is 1/e2 from that at the axis of the fiber. This expression neglects the loss due to Fresnel reflections, which do not change as the gap distance s varies, and accounts for the loss due to divergence of light from the input fiber. The mode field radius depends on the wavelength of light, the refractive index profile, and the core diameter, and is therefore fixed for a given fiber at a single wavelength. Therefore, a one-to-one relationship exists between the optical power detected by the photodetector and the separation between the input/output fiber and the reflector fiber. This relationship may be used to determine the fiber gap, given the optical power incident on the photodetector. For the investigation of the viscoelasticity research early in the research, this intensity-based sensor design was used to measure the displacement ∆L. If the fibers are attached to the actuator with two spots of adhesive separated by a distance Lg (the gage ∆ ∆ length), then the relative strain in the actuator is L/Lg, where L is the change in separation s. The main disadvantage of this method of interrogating EFPI strain gages is that any additional losses between the sensor and photodetector, such as bend-induced losses in the optical fiber or losses due to connector misalignment, will be interpreted as a change in the cavity gap, resulting in errors. For this reason, an alternate method of sensor interrogation, which is less sensitive to loss-induced errors, was employed in the latter half of the research. 18Russell G. May, Jr. Chapter 3. Technical Approach 18 cladding epoxy core epoxy input/output fiber reflector fiber s substrate L (gage length) Figure 3-3. Divergence of light emitted from single mode input/output fiber, leading to longitudinal separation loss in air gap cavity. The glass capillary alignment tube is omitted to clarify the illustration of light divergence. In the second approach to EFPI interrogation, called the absolute fiber sensor system, the light reflected from the cavity is measured using a spectrometer, as shown in Figure 3-4. If a broad spectrum of light, such as white light, is injected into a Fabry Perot cavity, the spectrum of the light reflected from the cavity has a modulation imposed on it that is uniquely determined by the cavity length.30 If a light source with a broad spectral output, such as white light or a light emitting diode (LED) is used as a source for the EFPI, the exact air gap separation s can be determined. Because the optical path length of the cavity changes with the wavelength, the phase difference between the two reflections R1 and R2 is a function of the wavelength. The result is a signal that varies with wavelength. Mathematically, it can be shown that if the wavelength of the light injected into the EFPI is scanned from λ1 to λ2, then the change ∆φ in measured phase of the output signal determines the length of the cavity by ∆ϕ⋅λ ⋅λ 1 2 s = , (3) 4π⋅∆λ 30 Tuan A. Tran, Digital Spectral Analysis and Adaptive Processing Technique for Phase Modulated Optical Fiber Sensors, PhD Dissertation, Virginia Polytechnic Institute and State University, 1996, pp. 42-75. 19Russell G. May, Jr. Chapter 3. Technical Approach 19 where ∆λ is the difference of the two wavelengths to be scanned. By scanning the phase difference accumulated between λ1 and λ2, one can apply Equation 3 to compute the corresponding gap length. Broadband fiber LED input fiber coupler diffraction spectrometer EFPI grating sensor CCD array mux Lab Computer serial multiplexer LabView LabView A/D Virtual Driver Instrument Figure 3-4.
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