Author Affiliations
1School of Civil and Architectural Engineering, Guilin University of Technology, Guilin, Guangxi 541004, China2Collaborative Innovation Center for Exploration of Hidden Nonferrous Metal Deposits and Development of New Materials in Guangxi, Guilin University of Technology, Guilin, Guangxi 541004, China3Guangxi Key Laboratory of Geomechanics and Geotechnical Engineering, Guilin, Guangxi 541004, Chinashow less
Fig. 1. Structural diagram of fiber Bragg grating tilt sensor
Fig. 2. Force analysis diagram of fiber Bragg grating tilt sensor. (a) Force state of sensor when it is horizontal; (b) force state of sensor when tilt angle is θ
Fig. 3. Sensor calibration experiment. (a) Physical image of fiber Bragg grating tilt sensor; (b) experimental installations
Fig. 4. Theoretical analysis and experimental comparison of fiber Bragg grating tilt sensor
Fig. 5. Performance test of sensor with tilt angle of 7°
Fig. 6. Fitting curve of positive stroke repeatability test of fiber Bragg grating tilt sensor
Fig. 7. Fitting curve of reverse stroke repeatability test of fiber Bragg grating tilt sensor
Fig. 8. Measurement error analysis of fiber Bragg grating tilt sensor
Fig. 9. Temperature test results. (a) Central wavelengths of FBG1 and FBG2 varying with temperature in horizontal condition; (b) central wavelengths of FBG1 and FBG2 varying with temperature at tilt angle of 1°
Fig. 10. Sensor performance test with out-of-plane tilt
L /mm | m /kg | S1 /[pm·(°)-1] | ε/10-4 |
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| 0.252 | 377.32 | 7.796 | 65.0 | 0.286 | 427.41 | 8.831 | | 0.320 | 477.30 | 9.862 | | 0.354 | 527.00 | 10.888 | | 0.212 | 330.24 | 6.823 | 67.5 | 0.240 | 373.23 | 7.711 | | 0.269 | 417.62 | 8.629 | | 0.297 | 460.33 | 9.511 | | 0.172 | 278.40 | 5.752 | 70.0 | 0.195 | 315.19 | 6.512 | | 0.218 | 351.87 | 7.270 | | 0.240 | 386.86 | 7.993 |
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Table 1. Sensitivity of sensor under different size parameters and strain value at full scale (l=10 mm, a=16 mm)
Dimension parameter | Value |
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L /mm | 65 | l /mm | 10 | a /mm | 16.3 | m /kg | 0.263 | E /GPa | 72 | S /mm2 | 0.0123 |
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Table 2. Dimensional parameters of sensor
Test experiment No. | Sensitivity of positive stroke /[pm·(°)-1] | Sensitivity of reverse stroke /[pm·(°)-1] |
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1 | 357.84 | 357.34 | 2 | 360.86 | 359.65 | 3 | 360.15 | 358.40 |
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Table 3. Sensitivity of fiber Bragg grating tilt sensor
Angle /(°) | Arithmetic mean value /nm | Fitted value /nm | Absolute deviation /nm |
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-5.0 | -1.8104 | -1.7940 | 0.0163 | -4.5 | -1.6439 | -1.6145 | 0.0294 | -4.0 | -1.4543 | -1.4350 | 0.0193 | -3.5 | -1.2757 | -1.2555 | 0.0202 | -3.0 | -1.0943 | -1.0760 | 0.0183 | -2.5 | -0.9058 | -0.8965 | 0.0093 | -2.0 | -0.7269 | -0.7170 | 0.0099 | -1.5 | -0.5374 | -0.5375 | 0.0002 | -1.0 | -0.3512 | -0.3580 | 0.0068 | -0.5 | -0.1575 | -0.1785 | 0.0211 | 0 | -0.0060 | 0.0010 | 0.0070 | 0.5 | 0.1615 | 0.1805 | 0.0190 | 1.0 | 0.3420 | 0.3600 | 0.0180 | 1.5 | 0.5157 | 0.5395 | 0.0238 | 2.0 | 0.7004 | 0.7190 | 0.0186 | 2.5 | 0.8980 | 0.8985 | 0.0005 | 3.0 | 1.0844 | 1.0780 | 0.0065 | 3.5 | 1.2514 | 1.2575 | 0.0061 | 4.0 | 1.4200 | 1.4370 | 0.0170 | 4.5 | 1.5838 | 1.6165 | 0.0327 | 5.0 | 1.7728 | 1.7960 | 0.0232 |
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Table 4. Linearity error calculation of fiber Bragg grating tilt sensor
Angle /(°) | |ΔHmax| in first set of experiments /nm | |ΔHmax| in second set of experiments /nm | |ΔHmax| in third set of experiments /nm |
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-5.0 | 0.0073 | 0.0145 | 0.0198 | -4.5 | 0.0159 | 0.0114 | 0.0008 | -4.0 | 0.0015 | 0.0054 | 0.0135 | -3.5 | 0.0001 | 0.0049 | 0.0150 | -3.0 | 0.0238 | 0.0356 | 0.0087 | -2.5 | 0.0237 | 0.0433 | 0.0449 | -2.0 | 0.0306 | 0.0313 | 0.0451 | -1.5 | 0.0324 | 0.0435 | 0.0247 | -1.0 | 0.0473 | 0.0414 | 0.0216 | -0.5 | 0.0458 | 0.0134 | 0.0269 | 0 | 0.0087 | 0.0378 | 0.0024 | 0.5 | 0.0301 | 0.0488 | 0.0372 | 1.0 | 0.0458 | 0.0237 | 0.0192 | 1.5 | 0.0421 | 0.0460 | 0.0108 | 2.0 | 0.0426 | 0.0455 | 0.0210 | 2.5 | 0.0466 | 0.0465 | 0.0442 | 3.0 | 0.0386 | 0.0449 | 0.0468 | 3.5 | 0.0300 | 0.0292 | 0.0421 | 4.0 | 0.0182 | 0.0087 | 0.0095 | 4.5 | 0.0190 | 0.0189 | 0.0165 | 5.0 | 0 | 0 | 0 |
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Table 5. Absolute value of maximum difference between positive and reverse stroke outputs in repeatability experiment
Angle /(°) | Standard deviation of positive stroke wavelength /nm | Standard deviation of reverse stroke wavelength /nm |
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-5.0 | 0.0350 | 0.0410 | -4.5 | 0.0133 | 0.0083 | -4.0 | 0.0093 | 0.0009 | -3.5 | 0.0061 | 0.0067 | -3.0 | 0.0012 | 0.0131 | -2.5 | 0.0158 | 0.0059 | -2.0 | 0.0048 | 0.0103 | -1.5 | 0.0153 | 0.0024 | -1.0 | 0.0069 | 0.0044 | -0.5 | 0.0127 | 0.0036 | 0 | 0.0164 | 0.0059 | 0.5 | 0.0043 | 0.0091 | 1.0 | 0.0138 | 0.0041 | 1.5 | 0.0130 | 0.0090 | 2.0 | 0.0145 | 0.0020 | 2.5 | 0.0104 | 0.0026 | 3.0 | 0.0195 | 0.0044 | 3.5 | 0.0091 | 0.0078 | 4.0 | 0.0051 | 0.0088 | 4.5 | 0.0097 | 0.0163 | 5.0 | 0.0059 | 0.0059 |
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Table 6. Calculation results of standard deviation of positive and reverse stroke
Type of tilt sensor | Measuring range /(°) | Sensitivity /[nm·(°)-1] | Distinguishability /(°) | Linear goodness of fitting |
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Long period fiber grating tilt sensor | -30--30 | 0.077 | 0.260 | 0.997 | Tapered phase shift fiber grating optical inclinometer | 30--90 | 0.023 | 0.430 | 0.995 | Mach-Zehnder interferometer inclinometer based on long period fiber grating and offset splices | -3--3 | 0.935 | | 0.978 | Proposed sensor | -5--5 | 0.359 | 0.003 | 0.999 |
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Table 7. Comparative analysis of comprehensive performance of tilt sensor