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Volume 44 Issue 5
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Fiber Bragg grating strain detection system for digital calibration

  • 1.

    School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun 130013, China

  • 2.

    Key Laboratory of Optoelectric Measurement and Optical Information Transmission Technology of Ministry of Education, Changchun University of Science and Technology, Changchun 130013, China

  • Corresponding author: LIU Zhichao, liuzhichao@cust.edu.cn ; 
  • Received Date: 2019-10-30
    Accepted Date: 2019-11-07
  • To reduce the deviation of the datum marks and the docking positions of tested workpieces owing to variations in their placements or the use of different clamping methods during assembly processes, a real-time monitoring system of three-dimensional (3-D) strain field was designed based on fiber Bragg grating (FBG). The correspondence between the 3-D strain field and the 3-D spatial coordinates of the workpiece was established, and the calculation method of the workpiece deformation offset was derived. Two FBG sensors were placed in a perpendicular to each other on the workpiece in the form of an FBG strain gauge group to monitor the strain field changes of the workpiece in real time. Numerical analyses were performed to study the workpiece deformations caused by pressure. In addition, the same pressure was applied at different positions of the workpiece and caused the surface of the workpiece to be deformed. Accordingly, the slope of the strain line becomes dense near the edge or at the clamping position, while the slope of the gradient distribution becomes larger than it would be if there were no force. The experimental FBG sensor response is shown to be consistent with the response characteristics of the applied force at the vertical and axial FBG sensors. The absolute error of the simulation analysis is 0.72mm. The absolute error of the strain detection is 0.52mm. Comparing the simulation results, strain detection results, and the visual detection results, the sample deviation of 0.19mm was observed. It can be seen that by establishing the relationship between the 3-D strain field and the workpiece deformation offset, the deformation offset compensation can be realized and the precision assembly is assisted. This system plays an important role in the digital precision of the assembly of large-sized workpieces.
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    XU O, LU S, FENG S, et al. Novel fiber-laser-based fiber Bragg grating strain sensor with high-birefringence Sagnac fiber loop mirror[J].Chinese Optics Letters, 2008, 6(11):818-820. doi: 10.3788/COL20080611.0818
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    GUO Y X, LI X, KONG J Y, et al. Sliding type fiber Bragg grating displacement sensor[J].Optics & Precision Engineering, 2017, 25(1):50-58.
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    YANG K M, HE J, LIAO Ch R, et al. Femtosecond laser inscription of fiber Bragg grating in twin-core few-mode fiber for directional bend sensing[J].Journal of Lightwave Technology, 35(21):4670-4676. doi: 10.1109/JLT.2017.2750407
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    MULLE M, YUDHANTO A, LUBINEAU G, et al. Internal strain assessment using FBGs in a thermoplastic composite subjected to quasi-static indentation and low-velocity impact[J].Composite Structures, 2019, 215(32):305-316.
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    ALANANY Y M, TAIT M J. Fiber-reinforced elastomeric isolators for the seismic isolation of bridges[J].Composite Structures, 2017, 160(7):300-311.
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    YU C W, LEI S C, CHEN W S, et al. Downhole fiber optic temperature-pressure innovative measuring system used in Sanshing geothermal test site[J].Geothermics, 2018, 74(31):190-196.
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    LEAL-JUNIOR A G, DÍAZ C A R, FRIZERA A, et al. Simultaneous measurement of pressure and temperature with a single FBG embedded in a polymer diaphragm[J].Optics & Laser Technology, 2019, 112(93):77-84.
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    QU D M, SUN G K, LI H, et al.Optical fiber sensing and reconstruction method for morphing wing flexible skin shape.Chinese Journal of Scientific Instrument, 2018, 39(2):460-40(in Chinese).
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    WU J, CHEN W M, SHU Y J, et al. Analysis on strain transfer of a pasted FBG strain sensor [J].Acta Photonica Sinica, 2015, 44(7):0706002(in Chinese). doi: 10.3788/gzxb20154407.0706002
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    ZHANG J J, WU Z T, PAN G F, et al. Design of low frequency and high sensitivity fiber Bragg grating vibration sensor[J].Acta Photonica Sinica, 2014, 43(s1):0128001(in Chinese).
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    OSÓRIO J H, CHESINI G, SERRÃO V A, et al. Simplifying the design of microstructured optical fibre pressure sensors[J].Scientific Reports, 2017, 7(1):372-381. doi: 10.1038/s41598-017-00409-z
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    SUN L, HAO H, ZHANG B B, et al. Strain transfer analysis of embedded fiber Bragg grating strain sensor[J].Journal of Testing and Evaluation, 2016, 44(6): 2312-2320.
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    XIAO H, ZHANG Y N, SHEN L Y, et al.Research on curvature serialization in the curve reconstruction algorithm based on fiber Bragg gratings[J].Chinese Journal of Scientific Instrument, 2016, 37(5): 993-999 (in Chinese).
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    SUN B Ch, LI J Zh, ZHANG W T. Fiber Bragg grating sensor[J].Optical Fiber Sensing and Structural Health Monitoring Technology, 2019, 26(4):77-148.
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    BOTSIS J, HUMBERT L, COLPO F, et al.Embedded fiber Bragg grating sensor for internal strain measurement sin polymeric materials[J].Optics and Lasers in Engineering, 2005, 43(3):491-510.
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    PALUMBO G, TOSI D, IADICICCO A, et al. Analysis and design of chirped fiber Bragg grating for temperature sensing for possible biomedical applications[J].IEEE Photonics Journal, 2018, 10(3):1-15.
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    ZHANG Y Sh, ZHANG W G, ZHANG Y X, et al. Simultaneous measurement of curvature and temperature based on LP11 mode Bragg grating in seven-core fiber [J].Measurement Science & Technology, 2017, 28(5):055101.
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    YUCEL M, TORUN M. Simplified fiber Bragg grating-based temperature measurement system design with enhanced high signal-to-noise ratio[J].Microwave & Optical Technology Letters, 2018, 60(4):965-969.
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    SKVORTSOV M I, WOLF A A, DOSTOVALOV A V, et al. Distributed feedback fiber laser based on a fiber Bragg grating inscribed using the femtosecond point-by-point technique[J].Laser Physics Letters, 2018, 15(3):035103. doi: 10.1088/1612-202X/aa9cca
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Fiber Bragg grating strain detection system for digital calibration

    Corresponding author: LIU Zhichao, liuzhichao@cust.edu.cn; 
  • 1. School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun 130013, China
  • 2. Key Laboratory of Optoelectric Measurement and Optical Information Transmission Technology of Ministry of Education, Changchun University of Science and Technology, Changchun 130013, China
  • Received Date: 2019-10-30
  • Accepted Date: 2019-11-07
  • Available Online: 2020-09-25

Abstract: To reduce the deviation of the datum marks and the docking positions of tested workpieces owing to variations in their placements or the use of different clamping methods during assembly processes, a real-time monitoring system of three-dimensional (3-D) strain field was designed based on fiber Bragg grating (FBG). The correspondence between the 3-D strain field and the 3-D spatial coordinates of the workpiece was established, and the calculation method of the workpiece deformation offset was derived. Two FBG sensors were placed in a perpendicular to each other on the workpiece in the form of an FBG strain gauge group to monitor the strain field changes of the workpiece in real time. Numerical analyses were performed to study the workpiece deformations caused by pressure. In addition, the same pressure was applied at different positions of the workpiece and caused the surface of the workpiece to be deformed. Accordingly, the slope of the strain line becomes dense near the edge or at the clamping position, while the slope of the gradient distribution becomes larger than it would be if there were no force. The experimental FBG sensor response is shown to be consistent with the response characteristics of the applied force at the vertical and axial FBG sensors. The absolute error of the simulation analysis is 0.72mm. The absolute error of the strain detection is 0.52mm. Comparing the simulation results, strain detection results, and the visual detection results, the sample deviation of 0.19mm was observed. It can be seen that by establishing the relationship between the 3-D strain field and the workpiece deformation offset, the deformation offset compensation can be realized and the precision assembly is assisted. This system plays an important role in the digital precision of the assembly of large-sized workpieces.

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引言

  • 光纤布喇格光栅(fiber Bragg grating，FBG)传感器是将被测信息转化为共振波长的移动继而得到所测数据，多用来测量温度和应力变化，同时还可方便地将多只光纤空分复用连结成网，以达到更好的信息传递效果，在应变检测方面具有广泛的应用，对我国工业、民生以及国防建设具有重大意义，并逐渐成为主流的发展方向之一[1-3]。

    国内外许多学者对各种结构的光纤形状传感方法开展了一定研究。2011年，MULLE等人提出了利用重力效应的FBG应变与振动传感器设计，传感器的灵敏度高于传统应变与振动传感器[4]。ALANANY等人利用多芯光纤传感方法开发了一种结构形状测量系统[5]。近年来，光纤光栅的传感阵列在对曲面面形的应变测量和3维重建方面应用广泛[6]，2018年，光纤传感网络应用在曲面面性测试的研究越来越多，LEAL-JUNIOR等人研究了弯曲形状的传感以及跟踪运动的飞机吊臂结构的光纤布喇格光栅传感器[7]; 同年，QU等人分析了光纤光栅波长漂移与柔性蒙皮弯曲曲率的关系，建立了柔性蒙皮曲率标定实验系统，验证了变形机翼柔性蒙皮形状光纤传感实时监测的技术可行性[8]。

    FBG传感器在航天、航海、桥梁传感等应用广泛[9-11]，具有抗电磁干扰、灵敏度高、尺寸小、重量轻等优点，在结构工程测量应变方面更有优势[11-15]。针对不同工件进行检测时，由于外界因素产生应变而导致变形及偏移时，若不进行偏移量补偿，则导致基准测量不准，进而影响装配质量等问题。本文中基于FBG传感器对应变场检测系统进行了深入研究，结合视觉测量系统，得到施力点与工件表面微应变及空间变形偏移量之间关系，补偿空间偏移量，得到校正模型并实现了提高装配精度的目的。

1.   系统设计

    1.1.   理论分析

  • 当一束光进入光纤光栅时，对于FBG传感来说，波长λB为入射光通过光栅反射波波峰处波长，即中心波长[16]。中心波长λB只与光纤纤芯的有效折射率neff和光纤光栅周期Λ有关, 且满足公式：

    针对工件微应变进行研究，当环境温度保持恒定时，温度对FBG传感器所产生的影响可忽略不计，只考虑测量点的微应变，则中心波长偏移量ΔλB可表示为[17]：

    式中, ε为测量点受应力后的应变量; Pε为弹光系数。

    • 1.2.   系统结构

  • 系统由宽带光源、3dB耦合器、光纤光栅解调仪、压力器等组成。系统整体测量方案如图 1所示。光由宽带光源射出，经3dB耦合器进入FBG光纤传感器，所测信号经3dB耦合器耦合后，解调结果在光纤光栅解调仪上实时显示。该测试方案针对待测件的3维应变场分布进行检测。当工件受压力等因素产生变形后，导致粘贴在其表面的FBG中心波长发生偏移，再通过MATLAB软件运算处理得到工件受压时应变片的3维应变场变化趋势。

    Figure 1.  Schematic of the test scheme of the system

    系统包括实验测试系统以及软件数据分析系统。实验系统部分包括通过FBG传感器检测到的中心波长偏移量变化, 从而计算出应变值，结合视觉测量技术测量工件变形空间偏移量，建立应变与工件形变偏移量之间关系，以补偿形变偏移量对数字化标定的影响。

    中心波长偏移量ΔλB与空间偏移距离D之间关系以超定方程AC=Y表示[18]，其中A为6个FBG应变传感器实时监测得到的中心波长偏移量ΔλB的集合，C为实数系数, Y为受力点受压后在不同方向上的空间偏移距离值的集合。应用MATLAB计算C值，下式表示3维应变场中FBG应变传感器组所监测到的中心波长偏移量ΔλB与工件表面在不同方向上因不同因素所产生的形变偏移量之间的关系，即：

    式中，ΔλB, 1~ΔλB, 6是指1号~6号FBG应变传感器所监测得到的中心波长偏移量; dx为空间偏移值D的x轴分量; dy为空间偏移值D的y轴分量; dz为空间偏移值D的z轴分量。

    应用MATLAB计算不同方向上实数系数C值为：Cx1=0.0205;Cx2=0.0316;Cx3=0.0455;Cx4=0.0094;Cx5=-0.0711;Cx6=-0.024;Cy1=0.0019;Cy2=0.0032;Cy3=0.0033;Cy4=0.0007;Cy5=-0.0071;Cy6=0.0062;Cz1=0.0366;Cz2=-0.017;Cz3=0.0486;Cz4=0.0107;Cz5=-0.1226;Cz6=0.0393。对任意FBG而言，正交应变片阵列监测得到的中心波长偏移量ΔλB是通过实验可测得量。当被测点位置发生变化时，FBG所监测到的中心波长偏移量ΔλB亦随之改变，代入(3)式即可得到工件受外力作用影响时，x轴、y轴、z轴3维方向上的形变偏移量，将3维方向上计算的dx, dy, dz值代入(4)式可得工件表面空间变形程度。

2.   仿真分析

  • 为了对比工件表面受力时面形变形程度，利用ANSYS软件对工件进行仿真分析[19]。对大小为300mm×250mm×2mm的工件进行仿真，材质为各项同性的6061型铝合金薄板，密度ρ=2.89g/m3; 弹性模量E=68.9GPa; 泊松比ν=0.330[20]。在静态结构命令下施加约束和压力。约束条件同实际实验条件; 接触面为直径2mm的圆，施力器对圆柱施力，施力面积相对于整体结构来说较小，因此可以将受力面看作是点施力。对工件所施压力均不会导致塑性变形，以保证仿真精确度。针对被测工件受相同压力的条件下，监测表面应变和形变偏移量的变化趋势。当在特征点即被测工件中点施加大小为50N压力时，仿真效果如图 2所示。

    Figure 2.  Simulation results following compression at the characteristic point

3.   实验

  • 建立基于FBG传感器的3维应变场监测系统，实验装置实物图如图 3所示。实验中所用FBG应变传感器型号为Acrylate SNF-28e;6个传感器带宽均为0.195nm; 边模抑制比为18.75dB; 栅区长度为10mm; 反射率高达92.5%，其中心波长分别是：1548.015nm, 1535.479nm, 1542.419nm, 1532.147nm, 1545.193nm, 1539.064nm。

    Figure 3.  Experimental setup for strain detection

    实验中所用宽带光源为光纤光栅解调仪内部自带光源，光谱宽度为C波段：1525nm~1565nm，光源平坦度不大于2dBm。光纤光栅解调仪选用深圳中科传感科技有限公司制造的，型号为中科传感SA-1型机器，解调范围为1525nm~15650nm，最小分辨率为0.5pm。被测件为6061-T651铝合金板，尺寸为300mm×250mm×2mm，在本次实验中，与被测工件直接接触的施力物体为一根半径为2mm的金属施力杆，受力面尺寸较小可看作点施力。

    在不发生塑性变形的条件下，观察工件在不同压力下不同位置所受微应变με变化。FBG传感器反射谱中心波长偏移量ΔλB与被测点产生微应变με成正比。记录各施力点处相同压力时，FBG传感器所产生的中心波长变化值，不同被测点每10s取中心波长偏移量值，即ΔλB的大小，并连续记录10组数据，计算10组数据的平均数作为最终中心波长偏移量的大小，以保证测量精度。

    利用Handscan手持双目扫描仪辅助应变监测系统，实验中所用Handscan手持双目扫描仪精度0.05mm; 扫描速率为18000个测量点/s[21]。将靶标点按最优位置粘贴在工件上，利用Handscan手持双目扫描仪扫描靶标点，在软件VXelements上得到靶标点3维空间位置，然后扫描整个被测面表面面形。由于实验误差的存在，极个别点会略有偏差，但并不影响实验结果。利用MATLAB处理扫描结果，计算出施力前后定位点空间偏移距离D大小。当被测工件受压时除受压点外其余点最大空间偏移距离D=1.372mm。应变检测与视觉检测空间偏移量结果的绝对误差为0.52mm，误差不超过1mm在误差范围内。

4.   实验结果分析

  • 通过对实验数据的拟合，可以方便、准确地分析工件在压力作用下的应力变化。结合微分思想，利用样条插值法拟合数据，当压力器施压力为固定值，对被测工件受力范围内的待测点进行分析。

    比较表 1中各组微应变不难看出，实验中FBG应变片组在相同受力下监测被测工件应变最大变化量为16.9με; 利用ANSYS对被测工件进行分析后得到的在相同受力条件下应变变化量为19.6με。通过与仿真应变数据对比得到实验所测应变误差小于30με，两组数据合并后的方差为5.4mm2。通过ANSYS仿真分析得到的空间偏移量与视觉测量获得的工件表面空间偏移量结果对比如表 2所示。

    FBG ANSYS simulation/με strain measurement/με
    1 25.4 13.2
    2 28.4 15.6
    3 23.6 18.1
    4 28.1 1.2
    5 11.8 9.6
    6 8.8 8.4

    Table 1.  Comparison between simulated and measured value

    coordinate/cm simulation D/mm vision D/mm
    (2, 2) 0.156 0.729
    (4, 2) 0.162 0.832
    (6, 2) 0.153 0.714
    (8, 2) 0.134 1.372
    (2, 4) 0.184 1.036
    (4, 4) 0.188 0.932
    (6, 4) 0.175 0.934
    (8, 4) 0.151 0.738
    (2, 6) 0.209 0.837
    (4, 6) 0.211 0.937
    (6, 6) 0.193 0.942
    (8, 6) 0.165 0.828
    (4, 8) 0.225 0.944
    (6, 8) 0.205 0.945
    (8, 8) 0.174 0.816

    Table 2.  Comparison between simulation results and visual measurement results D

    被测工件施力前后坐标点处视觉测量数据对比ANSYS仿真结果的空间变形量D较大，其原因在于Handscan视觉扫描仪实际扫描操作中存在一定的粗大误差，所以导致视觉扫描结果的空间变形量D大于仿真结果，仿真分析与视觉检测绝对误差为0.72mm，通过计算得到两组数据合并后的方差为0.015mm2，因此，所测结果与仿真结果对比后误差在规定范围内。

    如图 4所示，仿真结果中工件因受力所产生的空间偏移量值整体变化趋势较为平缓，视觉测量结果中不同受力点产生的偏移量较大，但最大值不超过2mm，对比仿真结果、应变检测结果和视觉检测结果，样本偏差为0.19mm，标准方差为2.141，由应变传感器反演出的受力区域内的空间偏移量值在仿真结果与视觉测量结果之间，变化趋势与视觉测量结果相似，符合实验预期效果。通过ANSYS仿真结果、视觉扫描结果和FBG应变传感器监测所得的空间变形量D对比分析，证明利用FBG应变传感器组网监测工件的方法具有可行性。

    Figure 4.  Variations of the spatial offset D values at various measurement points

    根据以上实验结果不难看出，本文中所设计的基于FBG组网的3维应变场测试系统具有结构简单、精度高、能在复杂环境下应用等优点，尤其是对大尺寸工件的装配过程中的变形监测，利用此系统能得到工件表面应变，进而计算出偏移量，以便在装配过程中补偿工件偏移量。对比同类应变场监测系统，本文中所设计的基于FBG应变传感的3维应变场监测系统主要针对3维应变场进行监测，且该监测系统可实现对应变变化的实时监测，通过所建立的数学模型，可快速发现工件在装配过程中可能会产生的形变问题。结合FBG传感器特性，在应变场监测及数字化装配等方面提供了一个新方法。

5.   结论

  • 光纤传感方法在面形应变监测及数字化装配方面具有良好的应用前景，并可拓展应用于不同面形应变场检测等众多领域。本文中基于FBG传感技术，验证了利用FBG传感技术对被测面形因受压力等不同因素而引起面形表面应力变化的监测可行性，以及验证了光纤光栅所测微应变与受力点坐标之间的关系。当通过应变片监测到工件任意位置因压力、自身重力等不同因素而发生变形时，根据光纤光栅解调仪解调出FBG组网的中心波长变化量，即可得到工件变形处的形变偏移量，从而完成偏移量补偿，提高了数字化装配精度。

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