Study on emissivity measurement of different types of coal and gangue using the matching method
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摘要: 煤和矸石的种类、表面纹理结构、变质和发育程度等因素都会对其发射率产生较为显著影响，精准的发射率参数设置对红外仪测温及煤和矸石红外图像的识别至关重要。针对该问题，提出了一种基于匹配法的煤和矸石发射率测量方法，即采用表面热电偶与红外热像仪相结合的方式测量煤和矸石发射率。用密闭的电热炉对被测煤和矸石进行均匀加热，待被测煤和矸石均匀受热且稳定后，用表面热电偶对被测煤和矸石的选定区域进行真实温度测定（标定为T1），然后用红外热像仪对被测煤和矸石选定的同一区域进行温度测定（标定为T2），最后对红外热像仪的发射率进行调试，当T2=T1时，得出的发射率即为被测煤和矸石在该温度下的真实发射率。实验结果表明：① 等温条件下，煤和矸石表面越粗糙，其发射率数值越大，表明煤和矸石表面的粗糙度是制约两者产生不同发射率的内在因素。② 4种不同种类煤和矸石发射率随温度的增大呈幂函数降低，且拟合函数相关系数R2达0.98以上，验证了匹配法应用于煤和矸石发射率测量的可行性。③ 采用反代法得出在不同温度条件下实测值与理论值的误差率均小于3%，验证了实验中测量的煤和矸石发射率的准确性。Abstract: The type, surface texture, metamorphic degree, and developmental stage of coal and gangue significantly influence their emissivity. Accurate settings for emissivity parameters are essential for infrared temperature measurements and the identification of coal and gangue in infrared images. This study proposed a method for measuring the emissivity of coal and gangue based on the matching method. The approach integrated surface thermocouples with infrared thermography to assess emissivity. Samples were uniformly heated in a closed electric furnace, and once the temperature stabilized, a surface thermocouple measured the actual temperature of a selected area (denoted as T1). Concurrently, the infrared thermography system measured the temperature of the same area (denoted as T2). The emissivity of the infrared thermography system was calibrated until T2 equaled T1. At this point, the calculated emissivity reflected the true emissivity of the coal and gangue at that temperature. The experimental results indicated that: (1) Under isothermal conditions, greater surface roughness of coal and gangue correlated with higher emissivity values, suggesting that surface roughness is a fundamental factor restricting the emissivity of these materials. (2) The emissivity of four different types of coal and gangue decreased with increasing temperature, following a power function, with the fitting function's correlation coefficient (R2) exceeding 0.98, thereby confirming the feasibility of the matching method for measuring emissivity. (3) The inverse method revealed that the error rates between the measured and theoretical values under varying temperature conditions were all below 3%, validating the accuracy of the measured emissivity of coal and gangue.
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图 1 匹配法测量煤矸发射率的实验平台
Figure 1. Experimental device for measuring emissivity by matching metho
图 3 煤和矸石发射率测试流程
Figure 3. Determination of coal gangue emission rate by matching method
图 5 煤和矸石发射率与温度的拟合曲线
Figure 5. Fitting curve of emissivity and temperature of different coal and gangue types
表 1 无烟煤表面不同区域发射率
Table 1. Emissivity of different areas on anthracitel surface
检测区域 温度T/℃ 发射率均值 A 70 0.926 B 0.920 C 0.921 
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表 2 无烟煤的发射率
Table 2. Emissivity of anthracite
温度/℃ 实验/次 发射率均值 1 2 3 4 5 6 7 8 9 10 70 0.92 0.94 0.89 0.94 0.94 0.90 0.92 0.92 0.93 0.94 0.924 90 0.93 0.91 0.92 0.93 0.91 0.89 0.94 0.92 0.88 0.91 0.914 110 0.92 0.90 0.89 0.91 0.87 0.92 0.92 0.91 0.90 0.89 0.903 130 0.89 0.92 0.92 0.88 0.90 0.87 0.89 0.88 0.87 0.91 0.893 150 0.89 0.86 0.86 0.92 0.87 0.87 0.90 0.88 0.89 0.86 0.880 170 0.86 0.88 0.93 0.92 0.85 0.85 0.87 0.86 0.87 0.88 0.877
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表 3 黑色砂岩的发射率
Table 3. Emissivity of black sandstone
温度/℃ 实验/次 发射率均值 1 2 3 4 5 6 7 8 9 10 70 0.96 0.95 0.95 0.93 0.98 0.95 0.97 0.93 0.93 0.95 0.950 90 0.96 0.96 0.95 0.94 0.94 0.95 0.97 0.94 0.95 0.94 0.950 110 0.97 0.96 0.93 0.94 0.94 0.94 0.95 0.93 0.96 0.94 0.946 130 0.94 0.93 0.95 0.93 0.93 0.91 0.96 0.95 0.95 0.96 0.941 150 0.95 0.92 0.94 0.94 0.94 0.93 0.91 0.96 0.95 0.93 0.937 170 0.91 0.89 0.92 0.93 0.93 0.95 0.95 0.94 0.93 0.94 0.929
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表 4 不同温度下煤和矸石的发射率范围
Table 4. Emissivity range of different coal and gangue types at different temperatures
试样种类 温度范围/℃ 发射率 无烟煤 70～170 0.877～0.924 灰色砂岩 0.891～0.963 黑色砂岩 0.939～0.955 黑色页岩 0.844～0.910 白色砂岩 0.881～0.932
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表 5 煤和矸石发射率的函数拟合结果
Table 5. Function fitting results of emissivity of different coal and gangue types
试样种类 拟合函数 参数选取 拟合优度/R2 a b c 无烟煤 $ \varepsilon (T) = a{T^b} $ 1.181 1 −0.062 1 —— 0.98 黑色砂岩 $ \varepsilon (T) = a + b{T^c} $ 0.952 2 −8.104 7−9 3.026 6 0.98 灰色砂岩 $ \varepsilon (T) = a{T^b} $ 1.304 1 −0.075 18 —— 0.98 白色砂岩 $ \varepsilon (T) = a{T^b} $ 1.204 7 −0.063 9 —— 0.99 黑色页岩 $ \varepsilon (T) = a + b{T^c} $ 0.914 3 −9.553 4−9 3.473 3 0.98
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表 6 煤和矸石发射率实测值与基于拟合函数的理论计算值
Table 6. Measured value and theoretical calculation value of the fitting function
温度/℃ 无烟煤 黑色砂岩 灰色砂岩 白色砂岩 黑色页岩 实测值 理论值 实测值 理论值 实测值 理论值 实测值 理论值 实测值 理论值 170 0.877 0.859 0.929 0.915 0.891 0.886 0.881 0.868 0.844 0.830 150 0.880 0.865 0.937 0.927 0.902 0.895 0.888 0.875 0.870 0.860 130 0.893 0.873 0.941 0.936 0.915 0.904 0.899 0.883 0.887 0.881 110 0.903 0.882 0.946 0.942 0.920 0.916 0.906 0.892 0.896 0.896 90 0.914 0.893 0.950 0.947 0.940 0.930 0.920 0.904 0.910 0.905 70 0.924 0.907 0.950 0.950 0.963 0.948 0.932 0.918 0.910 0.910
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表 7 室温条件下煤和矸石的发射率预测值
Table 7. Emissivity prediction value of different coal gangue types at ambient condition
温度/℃ 预测值/ε 无烟煤 白色砂岩 黑色砂岩 灰色砂岩 黑色页岩 25 0.967 0.981 0.952 1.000 0.914
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表 8 基于反代法的不同温度下无烟煤发射率验证
Table 8. Error rate of anthracite emissivity at different temperatures
发射率 实测值T0/℃ 理论值Tr/℃ 误差率/% 0.924 70 71.86 2.657 0.914 90 90.89 2.700 0.903 110 110.92 2.743 0.893 130 130.94 2.771 0.880 150 150.96 2.800 0.877 170 170.99 2.843
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表 9 基于反代法的不同温度下灰色砂岩发射率验证
Table 9. Error rate of gray sandstone emissivity at different temperatures
发射率 实测值T0/℃ 理论值Tr/℃ 误差率/% 0.963 70 71.43 2.042 0.94 90 90.62 2.314 0.92 110 110.70 2.429 0.915 130 130.82 2.600 0.902 150 150.91 2.729 0.891 170 170.96 2.800
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