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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:
$ {\lambda _{\rm{B}}} = 2{n_{{\rm{eff}}}}\mathit{\Lambda } $
(1) 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]:
$ \Delta {\lambda _{\rm{B}}} = {\lambda _{\rm{B}}}(1 - {P_\varepsilon })\varepsilon $
(2) 式中, ε为测量点受应力后的应变量; Pε为弹光系数。
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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。
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:
$ \left\{ \begin{array}{l} \text{d}x = (\begin{array}{*{20}{c}} {\Delta {\lambda _{{\rm{B}}, 1}}}& \cdots &{\Delta {\lambda _{{\rm{B}}, 6}}} \end{array})\cdot{(\begin{array}{*{20}{c}} {{C_{{x_1}}}}& \cdots &{{C_{{x_6}}}} \end{array})^{\rm T}}\\ \text{d}y = (\begin{array}{*{20}{c}} {\Delta {\lambda _{{\rm{B}}, 1}}}& \cdots &{\Delta {\lambda _{{\rm{B}}, 6}}} \end{array})\cdot{(\begin{array}{*{20}{c}} {{C_{{y_1}}}}& \cdots &{{C_{{y_6}}}} \end{array})^{\rm T}}\\ \text{d}z = (\begin{array}{*{20}{c}} {\Delta {\lambda _{{\rm{B}}, 1}}}& \cdots &{\Delta {\lambda _{{\rm{B}}, 6}}} \end{array})\cdot{(\begin{array}{*{20}{c}} {{C_{{z_1}}}}& \cdots &{{C_{{z_6}}}} \end{array})^{\rm T}} \end{array} \right. $
(3) 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。
$ D{\rm{ = }}\sqrt {{{\left( {{\rm{d}}x} \right)}^2}{\rm{ + }}{{\left( {{\rm{d}}y} \right)}^2}{\rm{ + }}{{\left( {{\rm{d}}z} \right)}^2}} $
(4) 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。
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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。
Table 1. Comparison between simulated and measured value
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 2. Comparison between simulation results and visual measurement results D
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 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。
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。
用于数字化标定的光纤光栅应变检测系统
Fiber Bragg grating strain detection system for digital calibration
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摘要: 在装配过程中因工件不同摆放方式或夹持方式造成表面形变,为了减小其引起基准点、对接位置等的偏差,采用光纤光栅传感器应变检测方法,设计了基于光纤布喇格光栅(FBG)的3维应变场实时监测系统。通过正交结构FBG应变片组实时监测工件的应变场分布变化,并利用ANSYS仿真分析了工件受力后表面形变偏移量分布。结果表明,仿真分析与视觉检测绝对误差为0.72mm,应变检测与视觉检测结果的绝对误差为0.52mm,均在误差范围内; 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。通过建立3维应变场与工件形变偏移量之间关系,实现了形变偏移量补偿并辅助精密装配。该系统在大型工件数字化精密装配中具有重要作用。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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Key words:
- fiber optics /
- fiber Bragg grating /
- strain field detection /
- 3-D reconstruction /
- digital calibration
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Table 1. Comparison between simulated and measured value
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 2. Comparison between simulation results and visual measurement results D
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 -
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