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以遥感卫星有源相控阵天线为对象,采用FBG传感器和波分复用方法组建准分布式监测网络。由于该天线为平面阵列天线,结构质量主要集中在天线阵面,将FBG传感器网络布设在天线阵表面。FBG传感器网络的布局方式如图1所示,在结构上每个测量点处可采用1个FBG测量主方向的热应变,或采用3个FBG组成1个应变花结构,同时测量0°、45°、90°三个方向的应变量;在每个测量点通过应变隔离封装方法布设1个只对温度敏感的FBG传感器,测量该位置的温度参数,用于解耦温度与应变传感信号。对于其它类型结构,需要根据结构几何特征设计传感器网络布局[13]。
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FBG传感器原理是利用Bragg光栅效应实现物理量的测量。Bragg光栅效应是指当被测物理量发生变化时光栅栅距会随之变化,进而由弹光效应使纤芯折射率会发生变化进而产生Bragg波长偏移,通过测量该波长偏移量就可以建立被测量与波长偏移量之间的关系。当一宽带光源进入光纤后,满足Bragg条件的光将被反射回来,其方程为:
$$ \lambda_{B}=2 n_{e f f} \varLambda $$ (1) 式中:neff为有效折射率;Λ为光栅周期。当光纤产生一个轴向应变时,会引起neff、Λ发生变化,进而使反射光的中心波长发生偏移。研究表明,当出现拉应变或者光纤遇热使光栅距增大时,其中心波长会增大,反之则会减小。
由于FBG同时对应变和温度敏感,其中心波长偏移量可表示为:
$$ \Delta \lambda = {K_\varepsilon }\Delta \varepsilon + {K_T}\Delta T $$ (2) 式中:∆λ为中心波长偏移量;Kε为应变灵敏度;∆ε为轴向应变变化量;KT为温度灵敏度; ∆T为温度变化量。
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由于FBG同时对应变和温度敏感,在热变形监测中,需要通过解耦方法消除温度变化对应变测量的影响[14]。
为此,采用温度参考光栅测量法进行温度解耦。如图1所示,光纤监测网络中各测量点处都有一个三向应变花和一个对应变不敏感的FBG温度传感器,分别测量该位置的应变和温度。温度和应变传感信号可表示为:
$$ \begin{gathered} {\text{ }}\Delta {\lambda _1} = {K_T}\Delta T \\ \Delta {\lambda _2} = {K_\varepsilon }\Delta \varepsilon + {K_T}\Delta T \\ \end{gathered} $$ (3) 在应变测量中,将FBG温度传感器的波长偏移量∆λ1代入公式(3)中的FBG应变传感器波长偏移量∆λ2计算公式中,可消除温度导致的传感信号变化量,得出相应的应变量,实现温度解耦。温度和应变解耦计算方程可表示为:
$$ \begin{gathered} {\text{ }}\Delta {T} = \frac{{\Delta {\lambda _1}}}{{{K_T}}} \\ \Delta \varepsilon = \frac{{\Delta {\lambda _2} - \Delta {\lambda _1}}}{{{K_\varepsilon }}} \\ \end{gathered} $$ (4) -
由于空间环境存在极端温度变化,而且FBG的温度灵敏度高于应变灵敏度,为精确解耦温度和应变传感信号,需要精确标定各FBG的温度和应变灵敏度[15-16]。
在温度灵敏度标定中,将FBG放入高精度温控箱,调节温控箱的工作温度以改变FBG环境温度,定义环境温度变化量为∆Tr;采用高精度光纤光栅解调仪采集光栅中心波长随温度变化的实时数据;通过观察FBG中心波长稳定情况,判断其所在区域是否受热平衡;将采集到的FBG中心波长数据与对应温度值进行线性拟合;通过公式(5)计算得出FBG温度灵敏度KT为:
$$ {K_T} = \frac{{\Delta {\lambda _1}}}{{\Delta {T_r}}} $$ (5) 在应变灵敏度标定中,根据被测结构材料类型制作试验件,将FBG应变传感器粘贴在试验件表面;粘贴时对FBG栅区施加预应力,且保证粘接剂厚度适中、分布均匀;同时在试验件表面粘贴电阻应变片作为应变测量基准 ,并粘贴FBG温度传感器用于温度解耦;将装有传感器的试验件安装到MTS拉伸试验机上,进行三次循环拉伸加载试验。以电阻应变片测量值作为FBG应变传感器的标定基准,根据公式(6)计算得出FBG的应变灵敏度Kε为:
$$ {K_\varepsilon } = \frac{{\Delta {\lambda _2} - \Delta {\lambda _1}}}{{{\varepsilon _r}}} $$ (6) 式中:∆λ1是FBG温度传感器的波长偏移量;∆λ2是FBG应变传感器的波长偏移量;εr是电阻应变片测量得到的应变基准值。
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为验证光纤光栅测量热应变的准确性。以遥感卫星有源相控阵天线的平面型结构为研究对象,在ANSYS SpaceClaim中建立该结构几何模型,模型尺寸为200 mm×100 mm×1 mm,材质采用合金材料模拟,主要参数如表1所示。
表 1 卫星天线结构有限元模型材料参数表
Table 1. Material parameters of finite element model of satellite antenna structure
Material parameter type Material parameter value Density/g·cm−3 2.81 Elastic modulus/GPa 71.7 Poisson's ratio 0.25 Thermal conductivity/W·m−1·K−1 173 Specific heat capacity/J·kg−1·K−1 960 Thermal expansion coefficient/℃−1 23.6×10−6 在ANSYS程序中采用壳单元以自由网格划分方法建立结构有限元模型,设置初始温度后,将稳态温度场导入瞬态热分析模块,将计算后的瞬态温度场导入瞬态力学分析模块,最后施加载荷和边界条件得到瞬态热力学耦合分析结果,计算分析流程如图2所示[17]。
图 2 卫星天线结构热应变场有限元计算流程
Figure 2. Finite element calculation process of thermal strain field of satellite antenna structure
根据图2计算流程对该结构进行仿真分析,设置参考温度为−120 ℃,计算得出结构在120 ℃的应变场如图3所示。
图 3 120 ℃均匀温度载荷下应变场分布特征
Figure 3. Characteristics of strain field distribution under uniform temperature load at 120 ℃
由图3可以看出,在均匀温度载荷作用下,该结构大部分区域的应变值一致,只有在结构边缘区域应变值升高。为得出结构在均匀温度载荷下应变场分布规律,对结构以40 ℃为间隔施加−120~120 ℃的温度载荷,并根据仿真结果绘制不同温度载荷下结构中轴线热应变变化曲线。得到结构应变场变化曲线如图4所示。
由图4得出,不同温度载荷下的结构应变场分布特征一致,变化曲线均呈现内凹形状,结构中心区域(20~180 mm范围内)应变量相同,边缘区域随着与结构中心距离增加,应变量逐渐增大。同时温度载荷越高,中心区域应变量越大,边缘区域应变增加量越明显。
原因是在均匀温度载荷作用下,结构各区域温度相同,由于热胀冷缩现象,结构各部分会产生相同的应变量,但在结构边缘区域,会出现应力集中情况,导致该区域内应变值较大。
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根据铝合金板在均匀热载荷作用下的应变场分析结果,设计搭建高低温环境光纤热应变监测系统,如图5所示。该系统由结构试样、FBG传感器、FBG解调仪、电阻应变片测量仪、高低温试验箱以及计算机组成。采用48通道高精度光纤光栅解调仪采集FBG传感信号;采用中航电测BAB120-3AA250-G500电阻应变片测量FBG应变传感器位置的应变量,并作为光纤测量的基准值。
图 5 高低温环境FBG传感器温度与应变监测试验系统。(a) 监测试验系统构成;(b) 监测试验系统实物照片:1.计算机 2.电阻应变片测量仪 3.FBG解调仪 4.高低温试验箱
Figure 5. FBG sensor temperature and strain monitoring system for high and low temperature environments. (a) Monitoring test system composition; (b) Physical photo of the monitoring test system: 1.PC 2.Strain gauges 3.FBG demodulator 4. Temperature test chamber
由仿真可以得到结构在中心区域的应变量相同,所以在该区域选取3个不同位置去验证FBG温度和热应变的测量精度。在试样中心轴依次布设3个测量点,测量点间距为60 mm,各测量点分别布设FBG应变传感器、FBG温度传感器和电阻应变片。FBG应变传感器采用全粘贴方式布设,FBG温度传感器通过应变隔离方式贴装。
为消除温度对电阻应变片的影响,试验采用热应变测量补偿方法提高电阻应变片测量精度(该方法有效性已在参考文献[18]中得到证实)。试验将硅酸钛材料制作为20 mm×20 mm×1 mm的方形薄板,并在表面布设电阻应变片作为补偿。理想情况下,粘贴在该材料上的补偿应变片仅受环境温度影响,不受材料因温度变化产生的热膨胀影响;粘贴在铝合金材料上的工作应变片不但受环境温度变化影响,而且受铝合金热膨胀影响。将工作应变片与补偿应变片通过半桥方式相连后共同放入高低温实验箱内进行试验,可消除电阻应变片因温度变化产生的热输出。
在实际情况下,硅酸钛材料热膨胀系数不为零,为精准测量铝合金结构热应变,需要对测量值进行补偿。补偿方法是将电阻应变片测量应变值与硅酸钛材料的理论热应变相加。硅酸钛材料在−200~20 ℃下平均线性热膨胀系数为0.26×10−6(1/ ℃),在20~200 ℃的平均线性热膨胀系数为0.32×10−6(1/ ℃)。试验将−120 ℃作为初始温度,经计算在−120~20 ℃范围内温度每增加10 ℃,测量补偿值增加2.6 με,在20~120 ℃范围内温度每增加10 ℃,测量补偿值增加3.2 με。经补偿后可消除硅酸钛材料热膨胀对补偿应变片的影响,实现铝合金结构热应变测量[18]。传感器布局及实物照片如图6所示。
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根据3次高低温循环试验数据,将试样温度分别与3个FBG温度传感器波长测量值线性拟合,结果如图7所示,同时将拟合数据进行汇总,结果如表2所示。
图 7 FBG温度传感器中心波长随温度变化关系。(a) 升温过程;(b) 降温过程
Figure 7. FBG temperature sensor center wavelength versus temperature. (a) Warming process; (b) Cooling process
表 2 FBG温度传感器灵敏度与线性度
Table 2. FBG temperature sensor sensitivity and linearity
Temperature Sensor Loading method Temperature sensitivity/pm·℃−1 Linearity FBG4 Heating 10.21 0.993 Cooling 10.18 0.992 FBG5 Heating 10.23 0.996 Cooling 10.25 0.991 FBG6 Heating 10.19 0.995 Cooling 10.21 0.996 分析图7数据得出,随着试样温度逐渐升高或降低,FBG温度传感器中心波长逐渐向长波或短波方向偏移,同时中心波长与结构温度变化量呈现良好的线性关系。经计算,3次高低温循环试验FBG温度传感器灵敏度平均值为10.21 pm/ ℃,线性度均大于0.99,不同传感器在不同阶段最大温度灵敏度偏差为0.06 pm/ ℃。
根据公式(4),由FBG温度传感器波长偏移量计算出试样温度值,并以试验箱温度为基准,对比分析温度测量精度,得到相对误差平均值为1.02%。对数据的重复性和迟滞性进行分析,得到FBG温度传感器的迟滞性误差为0.52%,重复性误差为0.69%。数据表明FBG温度传感器具有高精度和高稳定性,满足传感器在轨监测中高低温循环条件下的温度监测。
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在−120~120 ℃温度变化范围,试验分析3次高低温循环试验中FBG传感器的热应变测量精度。根据不同温度节点的FBG应变传感器和温度传感器数据,通过公式(4)进行温度解耦计算,得出各个温度节点的应变测量数据。利用温度解耦后FBG应变传感器测量得到的应变量与电阻应变片测量的应变数据,绘制出应变随温度变化关系如图8所示。
图 8 FBG应变传感器热应变测量值随温度变化关系。(a) FBG1;(b) FBG2;(c) FBG3
Figure 8. Thermal strain measurement of FBG strain transducer as a function of structure temperature. (a) FBG1; (b) FBG2; (c) FBG3
分析图8数据得出,随着试样温度逐渐升高或降低,粘贴在铝合金板不同位置的FBG应变传感器FBG1、FBG2、FBG3测得的热应变值均随着温度逐渐增加或减小。各位置FBG传感器的应变测量值与电阻应变片测量值变化趋势基本一致,是因为铝合金材料各项同性且分布均匀,同时该测量结果与前期数值仿真结果一致。
将FBG应变传感器测量得到的应变值与电阻应变片测量值对比,结果如表3数据所示。由表3数据得出,在−120~120 ℃的变温环境下,通过FBG传感器和温度解耦算法对应变进行测量,相对误差平均值为2.45%。对数据的重复性和迟滞性进行分析,得到FBG温度传感器的迟滞性误差为0.94%,重复性误差为0.56%。产生误差的主要原因是由于FBG传感器的粘贴胶层不一致,导致FBG传感器与电阻应变片测得的热应变值出现一定偏差。试验数据表明,利用FBG传感器和温度解耦方法测量热应变具有高精度,满足遥感卫星结构健康监测需求。
表 3 FBG应变传感器最大绝对误差与平均相对误差
Table 3. FBG strain sensor maximum absolute error and average relative error
Strain sensors Loading method Maximum absolute error/με Average relative error FBG1 Heating 68.6 2.38% Cooling 52.9 2.26% FBG2 Heating 49.5 2.65% Cooling 55.1 3.15% FBG3 Heating 64.7 1.95% Cooling 73.3 2.28% -
为验证光纤光栅针对局部热载荷下温度场和应变场重构的准确性。以遥感卫星有源相控阵天线的平面型结构为研究对象。模型尺寸为600 mm×600 mm×1 mm,材质采用合金材料模拟,主要参数如表1所示。采用壳单元以自由网格划分方法建立结构有限元模型,设置初始温度后,将稳态温度场导入瞬态热分析模块,在模型中心区域选择150 mm×150 mm矩形作为热加载区域,并设置加载时间以及热对流边界条件,将计算后的瞬态温度场导入瞬态力学分析模块,最后施加载荷和边界条件得到瞬态热力学耦合分析结果,计算分析流程如图2所示。
对遥感卫星结构进行仿真分析,设置参考温度为25 ℃,加热时间为258 s,使中心加热区域升高到100 ℃,计算得出温度场和应变场如图9所示。
图 9 100 ℃温度载荷作用下卫星天线温度场与应变场分布特征。(a) 温度场分布特征;(b) 应变场分布特征
Figure 9. Distribution characteristics of the temperature and strain fields of the satellite antenna under the temperature load of 100 ℃. (a) Distribution characteristics of the temperature field; (b) Distribution characteristics of the strain field
由图9(a)得出,瞬态热加载作用后,热量逐渐由加热中心向结构的边缘传导,所以温度分布沿着中心向四周呈现递减的趋势,并在结构边缘趋于稳定。由图9(b)得出,应变最大值在结构中心区域,在0~220 mm范围内应变值逐渐减小至区域最小值。
当结构中心区域加热到100 ℃后,继续施加热载荷20 min,得到结构温度云图和应变云图如图10所示。由图10得出,热加载时间在20 min内时结构中心区域具有最高的温度值和应变值,其热变形量最大。当热加载时间达到1 h以上时,卫星天线结构的温度场和应变场呈均匀分布特征。由于在轨卫星受太阳辐照时间一般在数小时以上,可采用较少数量的传感器监测结构的热变形,并结合计算数据推算其他位置的热变形量,这有利于降低监测系统的体积质量和功耗,并且不对热变形监测精度造成显著影响。
图 10 长时间高温环境下卫星天线温度场与应变场分布特征。(a) 温度场分布特征;(b) 应变场分布特征
Figure 10. Distribution characteristics of temperature and strain fields of satellite antenna under long time high temperature environment. (a) Distribution characteristics of temperature field; (b) Distribution characteristics of strain field
为得出局部热加载下温度场和应变场分布特征及变化规律,对加热区域以10 ℃为间隔施加30~100 ℃的温度载荷,并根据仿真结果绘制遥感卫星结构温度和热应变变化曲线。变化曲线的自变量为平板轴线上与加热区域中心点的距离(如图11所示),因变量为不同温度载荷下结构的温度和热应变,计算结果如图12所示。由图12可以得出,在30~100 ℃的加热范围内,温度随着距离增加而减小,同时在结构边缘区域达到稳定,不同温度载荷下的结构温度场变化趋势相近。
由图13得出,结构中心具有最大应变值;在0~220 mm范围内,应变量随距离增加而逐渐减小,在距中心点220 mm处达到区域最小值;在220~300 mm范围内,应变量随距离增加而小幅增大,应变增大量与热中心区域温度正相关,这一特征与图9(b)所示应变云图特征一致。
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场重构方法采用三次B样条插值对结构温度场和应变场进行拟合,该方法需要测得特定位置的温度和应变值,就可以实现结构温度梯度场和应变场的反演。在选择测量点时需要以结构数值分析应变场作为参考,应选取结构应变变化较大区域进行传感器布设,并且在变化缓慢和幅值较小区域减少测点。所以测点选取在应变极值区域、幅值变化较大区域和靠近固支端区域选取测点,从而在有限的测点条件下,使温度场和应变场的重构误差最小。
由仿真应变场作为参考,得出结构热应变场为中心轴对称图形,所以只需对结构的部分区域进行监测,即可重构出完整结构的温度场和应变场。测点共选取6个,分别为结构中心点、结构中轴上距中心220 mm的极小值点、中轴上距中心110 mm和270 mm的梯度最大点、结构对角线上距中心140 mm和280 mm的测点。
为验证该重构方法针对遥感卫星结构温度场和应变场的适用性,将结构划分为25个120 mm×120 mm单元,定义各单元形心为误差评价点,同时按照逆时针方向对单元节点进行编号,测量点和误差评价点如图14所示。
对于遥感卫星结构相控阵天线,影响性能的主要指标是测量点的均方根误差而非各点的相对误差。为了合理评价重构精度,标准采用各测量点的均方根误差与最大测量值的百分比,误差公式如下:
$$ \text{%} RMSE = 100 \cdot \sqrt {\frac{1}{m}\sum\limits_{i = 1}^m {{{\left(\frac{{\left| {x_i^{Reconstruction} - x_i^{FEM}} \right|}}{{x{{_{Max}^{FEM}}_{}}}}\right)}^2}} } $$ (7) 式中:m为误差评价点的总个数;xiReconstruction为重构场中的评价点数据;xiFEM为仿真场中的评价点数据;xMaxFEM为仿真场中最大温度值或应变值。选取数值分析得到的测量点离散温度数据和应变数据,采用插值方法对结构的温度场和应变场进行重构,并提取误差评价点数据xi,将该数据与数值仿真中评价点数据xiFEM通过公式(7)进行对比。在30~100 ℃局部温度载荷下,得到该方法温度场和应变场的重构误差如表4所示。
表 4 数值仿真中不同温度载荷下温度场与应变场重构误差
Table 4. Reconstruction error of temperature field and strain field at different temperatures
Temperature/℃ RMSE Temperature field Strain field 30 0.67% 1.06% 40 0.81% 1.35% 50 0.99% 1.45% 60 1.15% 1.56% 70 1.31% 1.69% 80 1.49% 1.86% 90 1.55% 1.92% 100 1.76% 2.23% Average value 1.22% 1.64% 经验证该方法重构温度场和应变场的平均误差分别是1.22%和1.64%,满足遥感卫星结构在轨运行中健康监测需求。
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为了验证非均匀热载荷下,光纤光栅对结构梯度温度场和应变场重构情况。根据卫星天线简化模型的热变形计算分析结果,设计搭建热变形光纤监测试验系统,主要包括:结构试样、FBG传感器、FBG解调仪、电阻应变片测量仪、热加载装置、多通道测温仪、温度调节控制器以及试验台和工装等。卫星天线结构试样尺寸为600 mm×600 mm×1 mm,材质为合金材料,材料热力学参数参照有限元模型参数选择。
试验系统构成及实物照片如图15所示。在试样中心选取150 mm×150 mm矩形区域贴装加热片和隔热保温层;采用萨妮SLD70型温度控制器实时控制加热区温度;采用48通道高精度光纤光栅解调仪采集FBG传感信号;采用电阻应变片测量结构的实时应变量;采用多通道测温仪测量结构的离散点温度;采用电阻应变片和Pt100型铂电阻温度传感器测量误差评价点的实时温度和应变量。
图 15 卫星天线热应变场光纤监测试验系统。(a)热应变场监测试验系统构成;(b) 热应变场监测试验系统实物照片:1.结构试样 2.电阻应变片测量仪 3.热加载装置 4.多通道测温仪 5. FBG解调仪 6.计算机
Figure 15. Satellite antenna thermal strain field fiber optic monitoring test system. (a) Thermal strain field monitoring test system composition; (b) Photos of the thermal strain field monitoring test system: 1. structural specimen 2.Strain gauges 3. Thermal loading device 4. Multi-channel pyrometer 5. FBG Demodulator 6.PC
在30~100 ℃局部温度载荷作用下,试验分析FBG传感器重构温度场和应变场与结构数值分析温度场和应变场。让热加载区域温度从30 ℃起以10 ℃为间隔逐步升高至100 ℃,待温度升高至100 ℃后,以10 ℃为步进从100 ℃降至30 ℃,试验循环加载3次。在每个温度节点采集FBG应变传感器和温度传感器数据,根据FBG传感器数据重构温度场和应变场,将重构温度场和应变场与数值仿真温度场和应变场通过公式(7)计算重构误差,重构误差如表5所示。由表5数据得出,该方法重构结构在局部热加载下的温度场和应变场的平均误差分别是2.31%与3.75%。误差产生的主要原因是模拟计算时,结构热传导与热扩散效应均按理想条件计算,但是在实际试验测量中,试样材料参数、试验仪器设备与环境条件等都与理想条件存在偏差,这将导致实际测量数据与模拟计算结果存在一定偏差。
表 5 不同温度下重构应变场与理论计算应变场重构误差
Table 5. Reconstruction errors between reconstructed strain field and theoretically calculated strain field at different temperatures
Temperature/℃ First cycle Second cycle Third cycle Temperature field Strain field Temperature field Strain field Temperature field Strain field Heating Cooling Heating Cooling Heating Cooling Heating Cooling Heating Cooling Heating Cooling 30 1.05% 1.09% 2.16% 2.21% 1.08% 1.16% 2.12% 2.18% 1.06% 1.12% 2.18% 2.15% 40 1.34% 1.39% 2.55% 2.57% 1.37% 1.31% 2.51% 2.61% 1.26% 1.34% 2.65% 2.58% 50 1.75% 1.72% 3.02% 3.06% 1.79% 1.85% 3.06% 3.12% 1.82% 1.86% 3.13% 3.15% 60 2.15% 2.19% 3.49% 3.52% 2.21% 2.26% 3.45% 3.55% 2.19% 2.12% 3.53% 3.59% 70 2.47% 2.45% 3.95% 3.82% 2.52% 2.47% 3.85% 3.82% 2.54% 2.46% 3.92% 3.84% 80 2.75% 2.65% 4.39% 4.35% 2.82% 2.75% 4.36% 4.45% 2.85% 2.79% 4.47% 4.39% 90 3.21% 3.37% 4.85% 4.82% 3.35% 3.19% 4.91% 4.92% 3.26% 3.23% 4.86% 4.89% 100 3.49% 3.49% 5.52% 5.52% 3.51% 3.50% 5.46% 5.48% 3.54% 3.54% 5.54% 5.54% Average 2.28% 2.29% 3.74% 3.73% 2.33% 2.31% 3.72% 3.77% 2.32% 2.31% 3.79% 3.77% 根据试验中光纤光栅温度测量值和应变测量值重构结构的温度场和应变场。拟合100 ℃温度载荷作用下的温度场与应变场如图16所示。
图 16 100 ℃温度载荷作用下的卫星天线。(a) 重构温度场;(b) 重构应变场
Figure 16. Satellite antenna under 100 °C temperature load. (a) Reconstructed temperature field; (b) Reconstructed strain field
根据重构温度场和应变场,提取误差评价点重构值,将该值与传感器测量值对比,对比结果如图17所示。
图 17 100 ℃温度载荷作用下测量值与重构值对比。(a) 温度场对比;(b) 应变场对比
Figure 17. Comparison of measured and reconstructed values under 100 ℃ temperature load. (a) Comparison of temperature fields; (b) Comparison of strain fields
由图17可以得出,结构中心区域(评价点17~25)各测点相对误差较小,结构边缘区域各测点(评价点1~16)相对误差较大。其主要原因是结构边缘与热源中心距离较远,使边缘测点受空气对流影响较大,导致FBG温度传感器在测量上有少量偏差。另外边缘区域由于夹具限制,使FBG应变传感器测点与试件表面的耦合质量较差,导致该区域应变测量精度较中心区域偏低。
在30~100 ℃局部温度载荷作用下,试验对比分析FBG传感器重构温度场和应变场与结构真实温度场和应变场。在每个温度节点采集FBG应变传感器和温度传感器数据,根据FBG传感器数据重构温度场和应变场,将Pt100测量的温度值和电阻应变片测量的应变值分别与重构温度场和应变场的误差评价点数值通过公式(8)进行比较,结果如表6所示。
表 6 不同温度下重构应变场与真实应变场重构误差
Table 6. Reconstruction error between reconstructed strain field and real strain field at different temperatures
Temperature/℃ First cycle Second cycle Third cycle Temperature field Strain field Temperature field Strain field Temperature field Strain field Heating Cooling Heating Cooling Heating Cooling Heating Cooling Heating Cooling Heating Cooling 30 1.58% 1.49% 3.76% 3.59% 1.49% 1.32% 3.59% 3.61% 1.32% 1.42% 3.61% 3.72% 40 1.76% 1.65% 4.79% 4.72% 1.57% 1.64% 4.97% 4.84% 1.78% 1.75% 4.82% 4.68% 50 2.53% 2.59% 5.58% 5.76% 2.69% 2.58% 5.65% 5.58% 2.42% 2.56% 5.52% 5.48% 60 2.97% 3.16% 6.75% 6.82% 2.78% 2.76% 6.93% 6.87% 2.87% 2.99% 6.83% 6.92% 70 3.46% 3.59% 7.35% 7.64% 3.24% 3.36% 7.75% 7.64% 3.37% 3.25% 7.59% 7.48% 80 3.98% 4.15% 7.82% 7.95% 3.87% 3.95% 7.92% 7.84% 3.88% 3.96% 7.89% 7.98% 90 4.62% 4.71% 8.05% 8.11% 4.78% 4.54% 8.16% 8.25% 4.54% 4.52% 8.13% 8.15% 100 5.48% 5.49% 8.42% 8.43% 5.12% 5.12% 8.38% 8.36% 5.43% 5.42% 8.32% 8.35% Average 3.30% 3.35% 6.57% 6.63% 3.19% 3.16% 6.67% 6.62% 3.20% 3.23% 6.59% 6.60% $$ \text{%} R M S E = 100 \cdot \sqrt {\frac{1}{m}\sum\limits_{i = 1}^m {{{\left(\frac{{\left| {x_i^{Reconstruction} - x_i^{Real}} \right|}}{{x_{Max}^{Real}}}\right)}^2}} } $$ (8) 式中:xiReal为评价点的实测数据;xMaxReal为实测数据中最大温度值或应变值。
由表6数据可以得出,当结构中心热源温度升高时,温度场和应变场的重构误差均有小幅增大。原因是结构整体温度升高时,与周围环境温差增大,热对流现象增强,导致温度场重构误差增加。根据光纤光栅温度解耦原理,温度测量误差的增大会间接导致应变测量误差增大,从而导致结构应变场重构误差增大。
经分析在3次高低温循环试验中,通过FBG重构结构温度场和应变场的平均误差分别是为3.24%、6.61%,重构误差在升温和降温过程中各阶段最大偏差量分别为0.19%和0.29%。试验中最大的绝对误差出现在100 ℃温度加载条件下的边缘区域,温度和应变的最大绝对误差分别为6.6 ℃和35 με。测量结果均在误差容许的范围内,满足遥感卫星结构在轨监测需求。
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遥感卫星在实际服役过程中,可能会同时存在温度载荷和机械载荷两个方面的作用。为了验证该方法针对热力耦合情况下的适用性,在热应变场监测试验系统的基础上,进行卫星天线结构的热力耦合作用分析试验。
试验开始前将室温下结构状态设为系统基准状态,通过温控器调节热加载区域温度为40 ℃、70 ℃和100 ℃,并将试件中心直径50 mm区域定义为力加载区。试验过程中,将200 g砝码放置在力加载区,使试件受到垂直地面向下的压力,待结构稳定后,测量并记录此时FBG传感器中心波长、应变片数值及Pt100温度数值。以200 g为单位增加砝码直至砝码总质量达到1000 g,再依次取下砝码,各阶段重复测量并纪录传感器数值。
根据试验得到的分布式光纤光栅数据重构结构温度场和应变场,将该数据与实际应变片和Pt100实际测量值进行对比,根据公式(8)得出各阶段重构误差如表7所示。
表 7 热力耦合下结构温度场与应变场重构误差
Table 7. Reconstruction errors of structural temperature and strain fields under thermodynamic coupling
Weight quality/g 40 ℃ temperature load 70 ℃ temperature load 100 ℃ temperature load Temperature field Strain field Temperature field Strain field Temperature field Strain field Weight gain Weight loss Weight gain Weight loss Weight gain Weight loss Weight gain Weight loss Weight gain Weight loss Weight gain Weight loss 0 1.82% 1.76% 4.65% 4.68% 3.48% 3.62% 7.28% 7.16% 5.35% 5.48% 8.34% 8.35% 200 1.75% 1.88% 4.98% 4.91% 3.56% 3.51% 7.65% 7.66% 5.45% 5.54% 8.87% 8.68% 400 1.79% 1.94% 5.34% 5.24% 3.51% 3.48% 8.05% 8.12% 5.47% 5.48% 9.35% 9.18% 600 1.86% 1.84% 5.79% 5.85% 3.42% 3.55% 8.72% 8.85% 5.52% 5.64% 9.94% 9.82% 800 1.95% 1.82% 6.12% 6.24% 3.35% 3.52% 9.25% 9.22% 5.46% 5.62% 10.26% 10.14% 1000 1.84% 1.89% 6.53% 6.59% 3.48% 3.42% 9.56% 9.61% 5.54% 5.58% 10.85% 10.76% Average 1.84% 1.86% 5.57% 5.59% 3.47% 3.52% 8.42% 8.44% 5.47% 5.56% 9.60% 9.49% 由表7数据可以得出,在不同温度载荷作用下,对结构施加不同大小的力,不影响结构温度场重构精度。在相同温度载荷下,随着对结构施加力的增大,会使应变场重构误差增加,同时热加载区温度越高,重构误差增加越明显。主要原因是在结构边缘区域以及力加载处由于应力集中,使FBG传感器应变测量值不够精确,当施加的力越大,这种现象越明显。
经计算,结构在热力耦合作用下,该方法重构结构温度场和应变场的误差分别为3.62%、7.85%。试验中在增重和减重的过程中,各阶段温度场和应变场重构误差最大偏差量仅为0.15%、0.19%。试验数据表明,利用FBG传感器和温度解耦方法,对结构热力耦合情况下的温度场和应变场重构具有较高精度。在此基础上,结合逆有限元法等变形场重构算法,可以实现热变形场测量并达到较高精度,该方法有潜力用于卫星结构热变形在轨监测。
Remote sensing satellite structure in-orbit thermal strain Bragg fiber grating monitoring method
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摘要: 遥感卫星结构在轨服役期间易受空间极端温度变化与微重力环境影响容易产生热应变,严重影响探测精度,而现有方法难以实现热应变在轨监测。针对这一问题,提出具有温度解耦功能的热应变光纤光栅监测方法。采用数值模拟方法开展结构热应变计算分析,得到结构整体和局部热加载下温度场和应变场分布特征及变化规律。设计构建热应变光纤监测试验系统,对卫星天线结构模拟试件进行热加载光纤测量试验,测试分析热应变光纤监测精度,验证了方法的有效性。研究结果表明,在−120~120 ℃温度变化范围,利用光纤布拉格光栅传感器和温度解耦方法监测温度和热应变的相对误差分别为1.02%和2.45%;在30~100 ℃局部热加载作用下,结构温度场和应变场的重构误差分别为3.24%和6.61%。该方法在卫星结构在轨监测领域中具有良好的应用价值与前景。Abstract: Remote sensing satellite structures are susceptible to thermal strain during in-orbit service due to extreme temperature changes in space and microgravity environment, which seriously affects the detection accuracy. However, the existing methods are difficult to achieve thermal strain monitoring in orbit. To solve this problem, a thermal strain fiber grating monitoring method with temperature decoupling function is proposed. The thermal strain of the structure is calculated and analyzed by numerical simulation, and the change of temperature and strain fields under overall and local thermal loading are obtained. A thermal strain fiber optic monitoring test system is designed and constructed, thermal loading fiber optic measurement test on satellite antenna structure specimens is conducted, the accuracy of structural thermal strain fiber optic monitoring is tested and analyzed, and the effectiveness of the method is verified. Research results show that in the temperature variation range of −120-120 ℃, the monitoring accuracy of temperature and thermal strain by fiber Bragg grating sensor and temperature decoupling method are 1.02% and 2.45%, respectively. The reconstruction errors of the structural temperature and strain fields are 3.24% and 6.61% under the action of local thermal loading from 30 ℃ to 100 ℃, respectively. The method has the prospect of application in satellite structure in-orbit health monitoring.
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图 5 高低温环境FBG传感器温度与应变监测试验系统。(a) 监测试验系统构成;(b) 监测试验系统实物照片:1.计算机 2.电阻应变片测量仪 3.FBG解调仪 4.高低温试验箱
Figure 5. FBG sensor temperature and strain monitoring system for high and low temperature environments. (a) Monitoring test system composition; (b) Physical photo of the monitoring test system: 1.PC 2.Strain gauges 3.FBG demodulator 4. Temperature test chamber
图 9 100 ℃温度载荷作用下卫星天线温度场与应变场分布特征。(a) 温度场分布特征;(b) 应变场分布特征
Figure 9. Distribution characteristics of the temperature and strain fields of the satellite antenna under the temperature load of 100 ℃. (a) Distribution characteristics of the temperature field; (b) Distribution characteristics of the strain field
图 15 卫星天线热应变场光纤监测试验系统。(a)热应变场监测试验系统构成;(b) 热应变场监测试验系统实物照片:1.结构试样 2.电阻应变片测量仪 3.热加载装置 4.多通道测温仪 5. FBG解调仪 6.计算机
Figure 15. Satellite antenna thermal strain field fiber optic monitoring test system. (a) Thermal strain field monitoring test system composition; (b) Photos of the thermal strain field monitoring test system: 1. structural specimen 2.Strain gauges 3. Thermal loading device 4. Multi-channel pyrometer 5. FBG Demodulator 6.PC
表 1 卫星天线结构有限元模型材料参数表
Table 1. Material parameters of finite element model of satellite antenna structure
Material parameter type Material parameter value Density/g·cm−3 2.81 Elastic modulus/GPa 71.7 Poisson's ratio 0.25 Thermal conductivity/W·m−1·K−1 173 Specific heat capacity/J·kg−1·K−1 960 Thermal expansion coefficient/℃−1 23.6×10−6 表 2 FBG温度传感器灵敏度与线性度
Table 2. FBG temperature sensor sensitivity and linearity
Temperature Sensor Loading method Temperature sensitivity/pm·℃−1 Linearity FBG4 Heating 10.21 0.993 Cooling 10.18 0.992 FBG5 Heating 10.23 0.996 Cooling 10.25 0.991 FBG6 Heating 10.19 0.995 Cooling 10.21 0.996 表 3 FBG应变传感器最大绝对误差与平均相对误差
Table 3. FBG strain sensor maximum absolute error and average relative error
Strain sensors Loading method Maximum absolute error/με Average relative error FBG1 Heating 68.6 2.38% Cooling 52.9 2.26% FBG2 Heating 49.5 2.65% Cooling 55.1 3.15% FBG3 Heating 64.7 1.95% Cooling 73.3 2.28% 表 4 数值仿真中不同温度载荷下温度场与应变场重构误差
Table 4. Reconstruction error of temperature field and strain field at different temperatures
Temperature/℃ RMSE Temperature field Strain field 30 0.67% 1.06% 40 0.81% 1.35% 50 0.99% 1.45% 60 1.15% 1.56% 70 1.31% 1.69% 80 1.49% 1.86% 90 1.55% 1.92% 100 1.76% 2.23% Average value 1.22% 1.64% 表 5 不同温度下重构应变场与理论计算应变场重构误差
Table 5. Reconstruction errors between reconstructed strain field and theoretically calculated strain field at different temperatures
Temperature/℃ First cycle Second cycle Third cycle Temperature field Strain field Temperature field Strain field Temperature field Strain field Heating Cooling Heating Cooling Heating Cooling Heating Cooling Heating Cooling Heating Cooling 30 1.05% 1.09% 2.16% 2.21% 1.08% 1.16% 2.12% 2.18% 1.06% 1.12% 2.18% 2.15% 40 1.34% 1.39% 2.55% 2.57% 1.37% 1.31% 2.51% 2.61% 1.26% 1.34% 2.65% 2.58% 50 1.75% 1.72% 3.02% 3.06% 1.79% 1.85% 3.06% 3.12% 1.82% 1.86% 3.13% 3.15% 60 2.15% 2.19% 3.49% 3.52% 2.21% 2.26% 3.45% 3.55% 2.19% 2.12% 3.53% 3.59% 70 2.47% 2.45% 3.95% 3.82% 2.52% 2.47% 3.85% 3.82% 2.54% 2.46% 3.92% 3.84% 80 2.75% 2.65% 4.39% 4.35% 2.82% 2.75% 4.36% 4.45% 2.85% 2.79% 4.47% 4.39% 90 3.21% 3.37% 4.85% 4.82% 3.35% 3.19% 4.91% 4.92% 3.26% 3.23% 4.86% 4.89% 100 3.49% 3.49% 5.52% 5.52% 3.51% 3.50% 5.46% 5.48% 3.54% 3.54% 5.54% 5.54% Average 2.28% 2.29% 3.74% 3.73% 2.33% 2.31% 3.72% 3.77% 2.32% 2.31% 3.79% 3.77% 表 6 不同温度下重构应变场与真实应变场重构误差
Table 6. Reconstruction error between reconstructed strain field and real strain field at different temperatures
Temperature/℃ First cycle Second cycle Third cycle Temperature field Strain field Temperature field Strain field Temperature field Strain field Heating Cooling Heating Cooling Heating Cooling Heating Cooling Heating Cooling Heating Cooling 30 1.58% 1.49% 3.76% 3.59% 1.49% 1.32% 3.59% 3.61% 1.32% 1.42% 3.61% 3.72% 40 1.76% 1.65% 4.79% 4.72% 1.57% 1.64% 4.97% 4.84% 1.78% 1.75% 4.82% 4.68% 50 2.53% 2.59% 5.58% 5.76% 2.69% 2.58% 5.65% 5.58% 2.42% 2.56% 5.52% 5.48% 60 2.97% 3.16% 6.75% 6.82% 2.78% 2.76% 6.93% 6.87% 2.87% 2.99% 6.83% 6.92% 70 3.46% 3.59% 7.35% 7.64% 3.24% 3.36% 7.75% 7.64% 3.37% 3.25% 7.59% 7.48% 80 3.98% 4.15% 7.82% 7.95% 3.87% 3.95% 7.92% 7.84% 3.88% 3.96% 7.89% 7.98% 90 4.62% 4.71% 8.05% 8.11% 4.78% 4.54% 8.16% 8.25% 4.54% 4.52% 8.13% 8.15% 100 5.48% 5.49% 8.42% 8.43% 5.12% 5.12% 8.38% 8.36% 5.43% 5.42% 8.32% 8.35% Average 3.30% 3.35% 6.57% 6.63% 3.19% 3.16% 6.67% 6.62% 3.20% 3.23% 6.59% 6.60% 表 7 热力耦合下结构温度场与应变场重构误差
Table 7. Reconstruction errors of structural temperature and strain fields under thermodynamic coupling
Weight quality/g 40 ℃ temperature load 70 ℃ temperature load 100 ℃ temperature load Temperature field Strain field Temperature field Strain field Temperature field Strain field Weight gain Weight loss Weight gain Weight loss Weight gain Weight loss Weight gain Weight loss Weight gain Weight loss Weight gain Weight loss 0 1.82% 1.76% 4.65% 4.68% 3.48% 3.62% 7.28% 7.16% 5.35% 5.48% 8.34% 8.35% 200 1.75% 1.88% 4.98% 4.91% 3.56% 3.51% 7.65% 7.66% 5.45% 5.54% 8.87% 8.68% 400 1.79% 1.94% 5.34% 5.24% 3.51% 3.48% 8.05% 8.12% 5.47% 5.48% 9.35% 9.18% 600 1.86% 1.84% 5.79% 5.85% 3.42% 3.55% 8.72% 8.85% 5.52% 5.64% 9.94% 9.82% 800 1.95% 1.82% 6.12% 6.24% 3.35% 3.52% 9.25% 9.22% 5.46% 5.62% 10.26% 10.14% 1000 1.84% 1.89% 6.53% 6.59% 3.48% 3.42% 9.56% 9.61% 5.54% 5.58% 10.85% 10.76% Average 1.84% 1.86% 5.57% 5.59% 3.47% 3.52% 8.42% 8.44% 5.47% 5.56% 9.60% 9.49% -
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