Calibration results and analysis of thin-film gauges calibrated with the transfer method
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摘要: 针对常用于薄膜热电阻热流传感器（简称薄膜热流计）的两步法标定步骤多、误差源多等问题，在解决吸收薄膜必要性、标定时间和标定热流范围的基础上实现了薄膜热流计的对比标定。在对比标定薄膜热流计时，基体材料的热物性参数乘积以及热电阻的电阻–温度系数被处理成简单的传感器灵敏度系数，使得标定实验只是重复简单的步骤，有效减少了误差源；针对通过对比标定获得的多支薄膜热流计灵敏度系数差异大的问题，在分析其测温原理的基础上通过去除热电阻的电阻-温度系数，得到同一批次生产的多支薄膜热流计较为一致的修正灵敏度系数。薄膜热流计对比标定结果的扩展不确定度不超过6.5%，明显优于二步法标定结果的扩展不确定度约10.7%，提升了薄膜热流计测热结果的可信度。Abstract: Considering the fact that there are more error sources in the measured heat flux with thin-film gauges when the two-stage approach is applied to determine the thermal product and resistance-temperature factor, the transfer method is applied to directly calibrate thin-film gauges, in which the thermal product and resistance-temperature factor are treated as the sensitivity coefficients. To get the consistent calibration results of different thin-film gauges fabricated in a batch, the sensitivity coefficients are divided by the resistance-temperature factors of the thin-film gauges, and then the correction sensitivity coefficients are consistent. With the transfer calibration technique, the calibration results of thin-film gauges show a good linearity with a relative expanded uncertainty below 6.5%, which is lower than that reported in other researches, in which the two-stage approach is used to calibrate thin-film gauges.
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Key words:
- thin-film resistance /
- heat flux /
- calibration /
- sensitivity /
- uncertainty analysis
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图 3 薄膜热流计的对比标定原始数据与计算结果
Figure 3. The typical profiles of a thin-film gauge’s calibration data and calculation result
图 4 薄膜热流计计算热流结果的修正
Figure 4. The corrected results of the calculated heat flux measured with a thin-film gauge
表 1 其他7支薄膜热流计的标定结果
Table 1. The calibration results of other 7 thin-film gauges
编号 Sensitivity
/（Ω·s–0.5·kW–1.m2）Maximum
non-linearity /%Resistance-temperature
factor /（Ω·℃-1）Correction sensitivity
/（℃·s–0.5·W–1.m2）1 0.03451 0.414 0.1207 0.2859 2 0.02183 0.295 0.0787 0.2773 3 0.02133 0.069 0.0767 0.2782 4 0.02352 0.172 0.0824 0.2856 5 0.03519 0.373 0.1224 0.2874 6 0.02817 0.525 0.0982 0.2868 7 0.02627 0.246 0.0921 0.2852 
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表 2 薄膜热流计对比标定结果的不确定度估计
Table 2. Estimation of uncertainties for the calibration results of a thin-film gauge
Uncertainty source Type Uncertainty （%） Ⅰ Transfer standard ECR B 0.6 Ⅱ Gardon gauge A 0.606① Ⅲ Non-uniformity and time stability of the laser beam A 2.8② Ⅳ Position alignment B 0.1 Ⅴ Data acquisition unit B 0.5 Ⅵ High-temperature paint B 1.0 Ⅶ Current source B 0.5 Ⅷ Non-linearity A 0.536③ Relative expanded uncertainty（κ=2④） The thin-film gauge 6.44 Relative expanded uncertainty（κ=2④） [13-14] 10.72 注： ①定期利用ECR对水冷Gardon计进行校准，保证了水冷Gardon计可溯源至工业级最高的功率计标准，通过校准数据的线性拟合得到源于水冷 Gardon计自身的不确定度0.606%。
②由于不同的感应面尺寸和传感器在标定系统中移动时的定位精度等问题，标定光斑的均匀性直接影响标定结果的准确性，因此利用面阵CCD相机 对标定光斑进行拍照，进而分析得到标定光斑功率分布均匀性和时间稳定性的不确定度为2.8%。
③来自于图4。
④κ=2表示不确定度因素符合正态分布，置信概率为95%。
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