1 Fiber Strain Sensitivity
The two direct measurements of all Sensuron interrogators are mechanical strain and temperature. This is due to the inherent sensitivity of the Bragg wavelength, as seen below in the well-known Bragg equation.
In the absence of thermal effects, obtaining the strain from the above equation is very straight forward.
The temperature sensitivity stems from two phenomena, changes in the core refractive index with respect to temperature and thermally induced strain when the fiber is bonded to the surface of a material with a coefficient of thermal expansion much higher than the fiber. In equation (1), the temperature dependency of the refractive index is described by the thermo-optic coefficient. is the coefficient of thermal expansion of pure silica, relating the thermally induced expansion/contraction of the Fiber Bragg Grating (FBG) to shifts in the reflected Bragg wavelength. The acquired strain data is always the apparent strain which includes effects due to mechanical strain and temperature.
A critical objective behind fiber optic strain sensing is eliminating the thermal strain component, such that the final strain is only the mechanical and load-induced strain. One approach is to remove the average strain measured before the load application and after the load removal. This type of baseline correction can be used effectively if the temperature change is small and gradual. These conditions are usually met in short duration loading within a contained space and in room temperature. Sensuron has developed more elaborate techniques for temperature compensation in environments with more complex and/or transient temperature changes. Please contact us at firstname.lastname@example.org to discuss details.
A cantilever beam setup resembling many thin-walled structures dominantly under bending deformation was selected to compare strains obtained from FOS vs SG. High strains, both in tension and compression, can be achieved with a relatively low and easily manageable force by using a beam with small thickness. Different strain levels can be achieved and measured both by changing the magnitude of the point force and by moving farther from the point force toward the base. It also structurally resembles an idealized airplane wing. A single fiber installed on the surface provides high-density distributed strain measurements covering a wide strain range while several SG can be installed adjacent to the fiber to provide multiple comparison points as shown in Figure 2.
Beam theory can present a baseline for the surface strain given the properties of the beam. However, surface strain is a function of h3 (h=beam thickness). This makes the calculated strain values highly sensitive to fluctuations and measurement errors in h. Furthermore, the exact elastic modulus of the material which is required in strain calculation may not be known a priori with adequate certainty.
The 5051 Aluminum beam used in our test has the following specifications: measured thickness=2.93 mm; measured width=25.06 mm; free length= 235 mm. Figure 2 shows the details about the beam structure and loading mechanism.
The standard process recommended by most SG manufacturers for SG installation was implemented in the installation of both SGs and optic fiber to minimize measurement inaccuracies caused by inadequate bond between SG or fiber and the beam surface. The process involved degreasing, abrading with silicon carbide paper #320, cleaning, burnishing, and finally applying conditioner/neutralizer. M-bond 200 was used as the bonding agent for both installations. The sample was not loaded for at least 1 hour after SG and fiber installation to allow the adhesive to cure properly and completely.
Figure. The cantilever beam setup: drawings, assembly, and the actual test sample with FOS and 4 strain gauges subjected to a point load creating positive tensile strain in sensors.
Strain gauges come in different shapes and resistance. They require a signal conditioner and I/O hardware to convert mechanical strain to changes in electrical voltage by a data acquisition unit.
The specifications of the four 350 ohms strain gauges are as follows: Type: SGD-5/350-LY43, Gauge Factor= 2.12.
The distance between four SGs was set to 32 times the FOS system’s resolution to facilitate correlating SG results with the correspondent strain measurement from the FOS’s distributed strain.
A National Instruments NI 9237 4-channel Strain/Bridge Input Module was mounted on an NI cDAQ-9185 Ethernet CompactDAQ Chassis. A LabView VI was developed to obtain strain data from the DAQ system and store the data. Quarter bridge configuration with 3 wires was used. Micro Measurements 326-DFV 3-conductor cable with a length of 0.4 m was used to connect each SG to an NI-9945 Quarter Bridge Completion Module. High precision soldering was performed under microscope by an experienced electrical technician. Prior to each test, a software-based calibration provided with NI-9237 was performed which included shunt scaling. While the system has a maximum sampling rate of 19 kHz, in this study the sampling frequency was set to 100 Hz.
An FBG sensing fiber with an approximate length of 194 mm and diameter of 0.125 mm was properly installed on the cantilever beam coupon. An optical patch cable with a length of 5 m was used to connect the sensing fiber to a broadband reflector (BBR). Sensuron’s Summit system was used to measure strain with an acquisition rate of 16.25 Hz and a spatial resolution of 1.61 mm. Spatial resolution is the distance between the centers of two adjacent strain measurement points and is equal to the portion of the fiber along which the strain is surveyed, averaged, and reported by the interrogator. Based on this configuration, a total of 120 sensing points were achieved along the fiber.
Unlike the SG system which separately reports strain measurements for each gauge, FOS system reports measurements along the total length of a sensing fiber. In the case of this installation, a 194 mm sensing fiber will result in 120 sensing points (194/1.61= 120) along its length.
An extensive calibration procedure is not required for ensuring the overall accuracy of a fiber optic strain sensor. When the system is turned on, it automatically sets all initial strain values to zero.