The beam response subjected to a point force was obtained by hanging a weight with known magnitude at the end of the beam for a short period. Four different weights (500, 1000, 1500 and 2000 grams) were used to obtain eight instances of the beam response producing tensile and compressive strains at the instrumented surface. Both FOS and SG systems were turned off after each loading/unloading. Generated data files were processed afterwards and average strain over a 10 second window was calculated for 4 strain gauges as well as all 120 sensing points along the fiber. The window was selected in the middle of the testing period when the initial vibration response of the beam had completely dissipated. All tests were short duration (3-4 minutes) and performed at room temperature with limited temperature change.
The diameter of the sensing optical fiber is very small (0.125 mm); however, when installed on a thin beam and subjected to bending moment, the fiber will experience higher strains in comparison to the beam’s outer surface. This is because the fiber core is at a greater distance from the neutral axis than the beam’s surface. Note that based on Euler-Bernoulli beam theory, even under pure bending, the difference between fiber strain and surface strain is of importance only in applications that deal with thin structures (relative to the fiber diameter). For the present setup, to estimate the strain on the beam’s surface and make a comparison with foil strain gauges, measurements made by the FOS are multiplied by a factor of 0.96, which is calculated from the beam theory.
As shown in Figure 1, the FOS system provides high-density distributed strain values along the fiber. Obtaining a comparable strain profile of this small beam with a larger number of SG requires extra efforts with SG installation, soldering and wire management.
The strain values for four SG as well as their corresponding FOS measurements are reported in Table 1A. One can calculate the relative difference percentage as (strain_FOS – strain_SG)/strain_SG. These results are shown in Table 1B. Applying higher magnitudes of hanging weight on one end of the beam may introduce torsion-induced strain and error in bending strain measurements for both FOS and SG. Despite these uncertainties present in the test setup, the average difference between FOS and SG measurements using 32 data points is -0.1% while the STDEV is 1.5%.
Furthermore, R-squared can be calculated for the best linear fit for SG and FOS data, with the notable difference that SG data only consists of 4 strain measurements, while FOS provides 120 points along the single fiber. Since the strain values on a surface of a beam with uniform width and thickness should change linearly with distance from the point load, R-squared shows how well the measurement points represent the ideal linear regression fit. In Table 2, values for R2 are presented. Strain measurements obtained by both technologies along the length of the beam are very close to an expected straight line.
In addition, both systems were tested for repeatability of measurements under increasing and decreasing stepwise loading as shown in Figure 2. The total duration of the experiment was about 10 minutes. Both FOS and SG systems demonstrated good repeatability and return to zero. This test was performed with a different resolution of 6.443 mm for FOS resulting in 29 strain measurement points.
|Point Force Location A Location B Location C Location D|
Figure 1. Comparison of strain obtained by a single optic fiber (delivering 120 measurement points) and 4 strain gauges installed at locations A, B, C, and D. Strains produced by beam bending vary linearly with distance from the point force applied on the left end of the Aluminum cantilever beam. The test was repeated 8 times with different point loads producing tensile and compressive strains in the instrumented surface of the beam.
Table 1. (A) Strain measured by FOS and SG presented in Fig. 1 for 2 tension and 2 compression load cases. (B) Difference percentage between FOS and SG measurements. The average difference is -0.1% while the STDEV is 1.5%.
Table 2. R-squared calculated for best linear fit for Strain Vs. Distance from Point Force for each Load Case. 120 FOS measurement points along the fiber as well as 4 strain gauges are used to obtain the best linear fit and its corresponding R2.
Figure 2. Strain history at Loc A and Loc D measured by FOS and SG. The cantilever beam is subjected to stepwise loading/unloading. Results of FOS and SG show comparable repeatability and return to zero.
Figure 3. Strain vs Load at location A and D measured by Sensuron FOS. Strain measurements in loading/unloading showed high linearity and repeatability.
Figure 3 shows the repeatability and return to zero at Locations A and D for the FOS system for this typical load/unload cycle. SG measurements also showed good repeatability and return to zero as expected. We examined the linearity and repeatability of strain measurements at all 29 FOS points as well as 4 strain gauges. As reported in Table 3, the mean of R2 values for repeatability/linearity is 0.9999 for both FOS and SG systems.
Table 3. Comparison of linearity of Strain Vs. Point Force Magnitude during loading and unloading. R2 for Strain Vs. Point Force is calculated for each of 29 FOS points as well as 4 SG and statistics of those values are reported here. Mean R2 for both systems is 0.9999.
A major advantage of Sensuron’s FOS systems is the ability to provide high-density distributed strain or temperature measurements. However, each FOS system has some unique features, and it is highly valuable to quantify the accuracy of any FOS system. A direct comparison of strain measurement carried out by Sensuron’s FOS system and common Strain Gauge technology is presented. Based on multiple experiments inducing both tensile and compressive strain, the average difference between strains measured by Sensuron’s FOS and strain gauges is found to be about 0.1%. FOS strain measurements and strain gauges were found to be in close agreement with respect to repeatability and linearity during loading and unloading. Finally, the fundamental benefits of performing distributed fiber optic strain sensing with the Sensuron technology are discussed.
Sensuron’s fiber optic sensing technology provides a paradigm shift for high-density distributed strain and temperature measurement systems. Achieving this level of data fidelity is impractical using traditional strain gauges. Due to its small size, chemical inertness, and immunity to electromagnetic interference, optical fibers can be installed in environments that alternative sensing technologies cannot operate in.
In the aerospace industry, active controlling of flexible structures and wings has become a top priority in ensuring the survivability of fuel-efficient flying devices. Distributed strain sensing is critical in optimization and weight-reduction studies. Other applications include monitoring pipeline, bridges, and infrastructure of national interest.
A vast majority of applications that intrinsically require distributed strain profiles but currently employ traditional strain gauge technology would benefit from having thousands of additional measurement points. The primary reasons that strain gauges are currently deployed in limited quantities are the installation time associated with each SG, the cumbersome wire bundles, and the associated weight penalty. Sensuron’s FOS technology with its high signal to noise ratio and the resulting dynamic measurement capabilities overcomes all these issues, enabling engineers to capture information that would otherwise be impractical to obtain.