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系统总体设计如图 1所示。系统采用宽带光源为系统提供初始信号光,光通过光纤进入光纤耦合器,再进入FBG阵列段,分布在工件上的FBG阵列将各个测试点位上的应变物理量转化为FBG波长偏移量。FBG阵列分布满足在不同梯度上均匀排布的要求,图 1中3条曲率变化不同的虚线表征梯度,将FBG阵列在3条特征梯度线上进行分布排列。这些回波再次通过光纤耦合器从而进入解调仪,由解调仪完成对回波光谱的解算,最终将各点位的数据转换成应变场分布数据。这些应变场分布数据可以根据不同的位置再验算成对应标准工件中3维坐标,在与标准数模中的坐标进行比较差分运算,从而获得数字装配校正数据。
在工件受自身重力或外力产生形变的时候,工件表面会产生变形,从而导致FBG栅格受到影响,回波波长产生偏移,并且可以通过波长偏移量计算表面形变特性。设工件厚度为h,测试位置尺寸为l,变形量为Δl,当测试环境的温度恒定时,FBG探测点上的波长偏移与该点位上的应变符合(可由参考文献[19]中(2)式在温度补偿后化简得到):
$ \Delta {\lambda _{\rm{B}}} = \left( {1 - {P_{\rm{e}}}} \right)\frac{{\Delta l}}{l}{\lambda _{\rm{B}}} $
(1) 式中,λB为FBG的回波波长;ΔλB为FBG的回波波长偏移量;Pe为等效弹光系数。当黏贴在工件表面的FBG阵列跟随工件面形变化时,通过检测分析各个FBG位置的波长偏移量ΔλB,就能够完成各个位置应变量ε(即Δl/l)的计算。通过应变量变化完成对标准点3维坐标偏移量的计算,实现对工件标准点的校正。
设复杂面形待测件的数模标准点集合为U(x, y, z),则当工件装配状态改变时,实际工件标准点集合为U′(x, y, z)。在工件装配过程中, 为了保证状态改变产生的形变不造成装配超差现象,需要获得实际标准点集合与数模标准点集合的偏差集合ΔU(x, y, z),该集合通过应变场测试数据反演得到,有:
$ \left\{ {\begin{array}{*{20}{l}} {{U^\prime }(x,y,z) = U(x,y,z) - \Delta U(x,y,z)}\\ {\Delta U(x,y,z) = f(\varepsilon ) \cdot U(x,y,z)} \end{array}} \right. $
(2) 式中,f(ε)表示应变-坐标位置转换函数。最终,可以解算获得实际标准点的坐标为:
$ {U^\prime }(x,y,z) = \left[ {\begin{array}{*{20}{l}} 1&{ - f(\varepsilon )} \end{array}} \right] \cdot U(x,y,z) $
(3) -
系统采用THORLABS公司的ASE宽带光源,1分2光纤耦合器,SOIL公司的BSIL-GS602型光纤光栅解调仪,表面黏贴型FBG传感探头。将FBG探头按照待测工件曲率分布梯度线均匀分布在待测表面上。工件的材质为合金铝,实验系统如图 3所示。
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将FBG阵列按照所设计的结构形式进行排布,每条梯度线上分布3个探头,以顶点右侧面载力的测试数据为例,9个探头的应变测试数据如表 1所示。数据分析表中分别给出仿真分析值、应变测试验算值以及光学扫描测试值。
Table 1. Strain data of FBG
FBG
No.wavelength
shift/
nmsimulation
result/
mmmicro-
displacement/
mmoptical scan
test value/
mmrelative
error/
%1 0.048 0.005 0.006 0.0055 9.1 2 1.324 0.214 0.244 0.2237 8.7 3 0.154 0.021 0.024 0.0221 8.6 4 0.624 0.137 0.141 0.1359 3.8 5 2.547 0.512 0.533 0.5047 5.6 6 0.445 0.120 0.132 0.1415 6.7 7 0.414 0.125 0.118 0.1288 8.4 8 1.643 0.351 0.347 0.3621 4.2 9 0.158 0.042 0.046 0.0429 7.2 如表 1所示,工件不同位置上对外加施力点的波长响应是不同的,其反映的微应变量也存在很大差异,故其微位移量也是根据不同位置而具有不同特性的。FBG序号从耦合器进入端开始顺序标识(No.1~No.9)。在以顶点右侧面载力条件下,斜线向下的曲率分布的3根FBG探头而言,5号波长偏移量最大,达到2.547nm,形成0.523mm的微位移,3号与7号亦有变化,但由此可见微位移改变量并不完全取决于距施力点的距离,与工件面形曲面位置也有关,该曲率梯度线上微位移量平均误差为0.012mm。底面曲率分布的3根FBG探头而言,6号波长偏移量最大,达到0.445nm,形成0.132mm的微位移,3号与9号变化基本一致,可见在平面条件下,应变场主要受到施力点与测试点距离的影响,该曲率梯度线上微位移量平均误差为0.009mm。直线向上的曲率分布的3根FBG探头而言,8号波长偏移量最大,达到1.643nm,形成0.347mm的微位移,7号与4号、1号应变量与位移量相近,可见曲面位置上对微位移量的影响主要由曲率决定。实验中测得最大波长偏移量为1.324nm, 2.547nm和1.643nm,其分别对应的位移偏移量为0.244mm,0.523mm和0.347mm。将应变验算数据与光学精密测量数据对比可知,其相对误差均小于10%,应变数据可以有效反应结构形变。由实验数据可知,系统微位移量与应变FBG获取的波长偏移量具有函数关系,即可通过解调计算波长偏移量值实现对复杂面形应变场的检测。
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根据FBG阵列获取的应变场分布测试数据可知,不同位置的外部施力会使工件产生变形,形变的量级受作用力大小、施力位置、曲面形态等所决定。根据波长偏移量与微位移量测试数据绘制的函数曲线如图 4所示。
在此基础上,对FBG阵列的位移偏移量测试数据与仿真数据进行误差分析,结果如图 5所示。
如图 5可知,第1组FBG阵列(No.1~No.3)中位移偏移量平均误差是0.016nm,第2组FBG阵列(No.4~No.6)中位移偏移量平均误差是0.009nm,第3组FBG阵列(No.7~No.9)中位移偏移量平均误差是0.009nm。分析认为,包含拱面的测试数据误差相对较大,而平面部分的测试数据误差较小,系统总体平均误差符合要求。
基于FBG的复杂面形应变场检测系统研究
Research on strain field detection system for complex surface based on FBG
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摘要: 为了实时采集在受力条件下复杂面形的应变分布,为复杂面形结构的健康程度评估提供数据支撑,设计了一种基于光纤传感网络的复杂面形应变分布实时检测系统。系统由光纤激光器、耦合器、解调仪、光纤传感阵列组成,采用与光学扫描检测数据对比的方法,进行了多种不同施力条件下待测件应变分布的理论分析和仿真计算;实验中采用4组光纤光栅传感器在待测面上正交排布的形式,针对5.0mm铝板进行了测试,并与仿真数据进行了对比。结果表明,应变分布与施力位置、大小、表面结构均有关;实验测得最大波长偏移量为1.324nm,2.547nm和1.643nm,其分别对应的位移偏移量为0.244mm,0.523mm和0.347mm,与激光扫描法标定数据对比,相对均小于10%。该测试数据能够反映面形变化趋势,符合设计要求。Abstract: In order to collect the real-time strain distribution of complex surface shapes, and provide data support for the health assessment of complex surface structures, the strain field detection system for complex surface was designed with fiber-optic sensor network. The system consisted of a fiber laser, a coupler, a demodulator, and a fiber sensing array. The method was compared with the optical scanning detection data, and the theoretical analysis and simulation calculation of the strain distribution were carried out under many different conditions. The strain distribution of the device under test with a variety of different force conditions was simulated and analyzed. The results show that the strain distribution is related to the applied position, size and surface structure. A 5.0mm aluminum plate was tested and compared with simulation data in the experiment. Four groups of fiber grating sensors were placed on the surface to be measured in an orthogonal structure arrangement. The test results show that the maximum wavelength offsets are 1.324nm, 2.547nm, and 1.643nm, and the corresponding shift offsets are 0.244mm, 0.523mm, and 0.347mm, respectively. Compared with the calibration data of laser scanning method, the offset of this method is relatively less than 10%. The test data can reflect the trend of surface shape change, and it meets the design requirements.
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Key words:
- fiber optics /
- strain field inversion /
- offset function /
- fiber grating /
- complex surface shape
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Table 1. Strain data of FBG
FBG
No.wavelength
shift/
nmsimulation
result/
mmmicro-
displacement/
mmoptical scan
test value/
mmrelative
error/
%1 0.048 0.005 0.006 0.0055 9.1 2 1.324 0.214 0.244 0.2237 8.7 3 0.154 0.021 0.024 0.0221 8.6 4 0.624 0.137 0.141 0.1359 3.8 5 2.547 0.512 0.533 0.5047 5.6 6 0.445 0.120 0.132 0.1415 6.7 7 0.414 0.125 0.118 0.1288 8.4 8 1.643 0.351 0.347 0.3621 4.2 9 0.158 0.042 0.046 0.0429 7.2 -
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