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Pyrometric measurements metrology of real-world objects temperature, for example, in metallurgy is still not error-free. Ultimately, these errors become the reasons for great industrial disasters. Analysis of the energy pyrometry method metrological challenges is given in the article.
Теги: objects spectrographic radiation efficiency pyrometry temperature measurement измерение температур пирометрия спектральная излучательная способность тел
Introduction
According to the long-standing tradition originating from the last century [1], pyrometry refers to the complex of methods for the temperature measurement of hot bodies on the basis of their heat radiation. And since pyrometry is the complex of methods, researchers have been studying the methods up until now, their development, improvement, solution of the problems caused by the implementation of used method. And they have not been trying to consider all methods together and, first of all, the challenges connected with these methods.
It is about time to generalize the challenges connected with all methods and see that all these challenges have one origin. It is time to understand that the pyrometry problems must be solved as a whole and then the particular problems will be solved too. And since the science name contains the root "...metry", for the most part problems solution is possible with the application of metrology.
Laws of Planck, Wien, Rayleigh-Jeans and Stefan-Boltzmann are well-known; they determine the value and spectral distribution of energy flux from hot body depending on its temperature. Pyrometry solves the inverse task – estimation of the body temperature on the basis of the value and/or spectral distribution of the energy flux radiated by it.
Three main methods for the solution of inverse task can be marked out. The first method – energy method, the temperature is estimated on the basis of the value of energy flux radiated by the object. The second and third methods – methods of spectral similarity and spectral ratio – estimate the temperature on the basis of spectral characteristics of radiated energy flux.
Let us consider the metrological challenges of energy method in more detail.
Metrology Challenges
of Energy Method
Energy method is based on the measurement of energy flux coming to the pyrometer detector and further transformation of the measured value into the value of the temperature of measured object.
Operation principle of the standard energy pyrometer implementing the energy method is described below. Hot object radiates the energy flux into the hemisphere where the pyrometer is located. Part of the flux gets on the pyrometer lens which collects it on the detector. Detector produces the electric signal which is proportional to the value of energy flux. Then, this signal is amplified by the electronic unit and transformed into the value of the temperature of measured object.
Energy method unified the methods of brightness pyrometry, radiation pyrometry and partial radiation pyrometry which were considered as separate methods before.
It should be noted here that energy method has one serious congenital defect. Energy flux depends not only on the object temperature but on its radiation capacity as well.
Radiation capacity of tangible objects is always less than one and therefore during measurements energy pyrometers always understate the result. In order to correct this understatement it is necessary to enter so-called coefficient of radiation (or coefficient of correction, corrective factor) to them which is connected with the radiation capacity of measured object. With the help of these coefficients pyrometers translate the measured brightness or radiation temperature into the actual temperature.
Where can we find information about the radiation coefficients? Predominantly, it can be found in the literary sources and user manuals for pyrometers. And right here two very serious metrological problems occur.
Challenge connected with the multiplicity of the values of radiation coefficients for energy pyrometers
Multiplicity of the values of radiation coefficient for energy pyrometers is explained by two reasons – "non-gray" character of radiation of many objects and dependence of the spectral radiation capacity on the object temperature which is manifested almost all the time.
Multiplicity of the values of radiation coefficients for energy pyrometers due to "non-gray" character of radiation
Situation which is described below is familiar to many process engineers and metrologists of large enterprises. The company purchased fully-contained production line from well-known western manufacturer (for example, rolling mill with the sheet width up to 2500 mm for the production of pipes). 3-4 energy pyrometers from the complete set of the mill, produced by one of the leading world companies, are used for the measurement of the temperature of laminated sheet. It is specified in the equipment user manual that it is necessary to set the radiation coefficient equal to 0.88, for example, in the pyrometers when working with the steel of certain brand.
In the course of time, one of these pyrometers breaks down and in order to replace it the other pyrometer with the same basic error and almost the same sighting parameter is purchased from the different manufacturer. However, installation of the new pyrometer with the entered value of 0.88 is accompanied by the occurrence of evident error in measurements. In order to eliminate this error it is necessary to enter the value 0.91 instead of 0.88. And users have the question: so what is the value of radiation coefficient for this brand of steel, 0.88 or 0.91? Searching for the answer to this question, workers find the third pyrometer produced by the third company at other workshop. But the measurements performed with it puzzle the metrologists and process engineers completely – it is necessary to enter the value of radiation coefficient equal to 0.69 to the third pyrometer in order to obtain the same result of the temperature measurement. There it is!
The values of radiation coefficients given in this example are random to certain degree and in every specific case they can have specific value. But the most important is that they are different for the same material under the same conditions but for different pyrometers. And this uncertainty causes the fair complaints from the pyrometer users.
Described situation is paradoxical – measurement of the same object under the same conditions using different pyrometers (but with the same values of instrumental error and sighting parameters) can give different results. And the difference between these measurement results exceeds the instrumental errors of pyrometers by several times.
There are several reasons for it but metrological analysis has not been given yet. Also, the way for the solution of this collision which is correct from the metrological point of view has not been found yet. Although, everything is simple from the metrological point of view – some additional errors are not taken into account and our task is to find them, describe mathematically (if they have not been described) and take into account correctly. Therefore, reasons for the occurrence of severe additional errors, which are not taken into account and take place during the measurements performed by pyrometers, and ways of their strict registration and minimization are considered below.
As it was shown above, radiation coefficient is the parameter which depends not only on the material but instrument as well. In other words, radiation coefficient of the same material under the same conditions can have different values for different instruments with various spectral sensitivities of radiation detectors.
In order to understand the reason for such behavior of radiation coefficient let us use the following figures. Dependence of the spectral radiation capacity of low-alloy steel on the radiation wavelength plotted on the basis of the data from the paper [2] is shown in Fig. 1. Since in original this dependence within the range of wavelengths of less than 1 µm was not measured, it is interpolated into the short wave region on the basis of the data given in the papers [3] and [4]. Accuracy of such interpolation is very low but for this case when it is necessary just to explain the origin of the radiation coefficient ε and its difference upon the use of different pyrometers in qualitative manner it will be enough.
It should be noted that the considered dependence of on is not constant, at least in the visible and near IR spectrum region. Objects which are characterized by such dependence on are called "non-gray objects" or "non-gray bodies".
The spectral sensitivity characteristics of three different radiation detectors are given in Fig. 2. The curve corresponds to the detector based on Si-photodiode with the cutting filter of infrared glass. The curve corresponds to the detector based on InGaAs-photodiode. The curve corresponds to the "solar-blind" thermal detector with the spectral sensitivity range of 7-8 µm to 12-13 µm.
In Fig. 3 the spectral sensitivity characteristics of the above-mentioned radiation detectors are superposed with the spectral radiation capacity of low-alloy steel from Fig. 1. It is evident that within the range of sensitivity of the first detector the spectral radiation capacity varies near the value of 0.7. Within the range of sensitivity of the second detector the spectral radiation capacity varies approximately from 0.65 to 0.6. And within the range of sensitivity of the third detector the spectral radiation capacity varies approximately from 0.27 to 0.22.
Thus, for "non-gray bodies", which the vast majority of metals refer to, the radiation coefficient turns out to depend on the spectral range where the energy pyrometer functions. And practically in all reference literature there is no information on the spectral ranges within which the measurements specified in the relevant tables were performed. Therefore, the user can easily enter the value of radiation coefficient to his pyrometer which corresponds to the pyrometer with different spectral range. If these values are different or the object is "non-gray" the method error will occur due to the entry of the inaccurate value of radiation coefficient, estimated (for brightness pyrometers) on the basis of the following correlation:
. (1)
Here, Тд is the actual value of the object temperature, is the value of the object temperature obtained upon the entry of inaccurate value of radiation coefficient, is the actual (corresponding to the used pyrometer) value of radiation capacity, and is the error of radiation coefficient entry, in other words, it is the difference between and value which was taken from the reference literature, с2 = 1,4380 · 10-2 м·К.
Calculation results of the value of additional method error connected with the entry of inaccurate value of radiation coefficient in accordance with the formula (1) are given in Tables 1-3. Calculations were performed for three temperatures (1600 K, 2000 K and 2600 K) and wavelengths of 0.6 µm, 1 µm, 1.5 µm, 2 µm, 5 µm, 8 µm and 12 µm. And the results which correspond to 10% error in the estimation of radiation capacity are specified in Table 1, 20% – in Table 2, 30% – in Table 3.
It appears from Tables 1-3 that if pyrometer functions on the wavelengths of 1.5-2 µm, for example, upon the error 10% during the estimation of radiation coefficient the mentioned additional error will be 1.5 to 3.3%, upon the error 20% – 2.9 to 6.2%, upon the error 30% – 4.2 to 8.7%. If pyrometer functions on the wavelength of 12 µm upon the error 10% during the estimation of radiation coefficient the mentioned additional error will be 11 to 17%, upon the error 20% – 19 to 28%, upon the error 30% – 26 to 36%. In other words, very often this additional error is significant and noticeably influences on the measurement result and sometimes it is even catastrophic! And user does not know the value of this error and most often does not even suspect about its existence! So this is the first mentioned metrological problem.
In practice, metrologists just close their eyes to this component of the error. And the reason for it lies in the fact that they usually do not know how to estimate the value of the radiation coefficient ε which is metrologically significant. Often, metrologists estimate the value ε on the basis of empiricism "adjusting" the coefficient, entered to pyrometer, till they obtain the value with which the pyrometer will give them measurement result corresponding to the value which process engineer or his management considers correct.
Incorrectness of the similar "adjustment" from the metrological point of view can be shown using such evident example. For example, we measure the low values of voltage in the printed-circuit wiring unit using the microvoltmeter for direct current. As it is known, upon the contact of copper probe with kovar pin rather large contact potential difference occurs (about 30 µV at the room temperature). It is obvious, if instead of deduction of this potential difference (corrected for the pin temperature) from the measurement result we will gradually "adjust" the microvoltmeter amplification coefficient within the specific limits until we receive the value corresponding to the actual value of measured parameter on display, we can forget the traceability of measurements in radio engineering. It is inadmissible to eliminate method errors by the "adjustment for correct result" not relying upon the measurement of influencing factor and awareness of its dependencies on different medium parameters.
To be continued.
According to the long-standing tradition originating from the last century [1], pyrometry refers to the complex of methods for the temperature measurement of hot bodies on the basis of their heat radiation. And since pyrometry is the complex of methods, researchers have been studying the methods up until now, their development, improvement, solution of the problems caused by the implementation of used method. And they have not been trying to consider all methods together and, first of all, the challenges connected with these methods.
It is about time to generalize the challenges connected with all methods and see that all these challenges have one origin. It is time to understand that the pyrometry problems must be solved as a whole and then the particular problems will be solved too. And since the science name contains the root "...metry", for the most part problems solution is possible with the application of metrology.
Laws of Planck, Wien, Rayleigh-Jeans and Stefan-Boltzmann are well-known; they determine the value and spectral distribution of energy flux from hot body depending on its temperature. Pyrometry solves the inverse task – estimation of the body temperature on the basis of the value and/or spectral distribution of the energy flux radiated by it.
Three main methods for the solution of inverse task can be marked out. The first method – energy method, the temperature is estimated on the basis of the value of energy flux radiated by the object. The second and third methods – methods of spectral similarity and spectral ratio – estimate the temperature on the basis of spectral characteristics of radiated energy flux.
Let us consider the metrological challenges of energy method in more detail.
Metrology Challenges
of Energy Method
Energy method is based on the measurement of energy flux coming to the pyrometer detector and further transformation of the measured value into the value of the temperature of measured object.
Operation principle of the standard energy pyrometer implementing the energy method is described below. Hot object radiates the energy flux into the hemisphere where the pyrometer is located. Part of the flux gets on the pyrometer lens which collects it on the detector. Detector produces the electric signal which is proportional to the value of energy flux. Then, this signal is amplified by the electronic unit and transformed into the value of the temperature of measured object.
Energy method unified the methods of brightness pyrometry, radiation pyrometry and partial radiation pyrometry which were considered as separate methods before.
It should be noted here that energy method has one serious congenital defect. Energy flux depends not only on the object temperature but on its radiation capacity as well.
Radiation capacity of tangible objects is always less than one and therefore during measurements energy pyrometers always understate the result. In order to correct this understatement it is necessary to enter so-called coefficient of radiation (or coefficient of correction, corrective factor) to them which is connected with the radiation capacity of measured object. With the help of these coefficients pyrometers translate the measured brightness or radiation temperature into the actual temperature.
Where can we find information about the radiation coefficients? Predominantly, it can be found in the literary sources and user manuals for pyrometers. And right here two very serious metrological problems occur.
Challenge connected with the multiplicity of the values of radiation coefficients for energy pyrometers
Multiplicity of the values of radiation coefficient for energy pyrometers is explained by two reasons – "non-gray" character of radiation of many objects and dependence of the spectral radiation capacity on the object temperature which is manifested almost all the time.
Multiplicity of the values of radiation coefficients for energy pyrometers due to "non-gray" character of radiation
Situation which is described below is familiar to many process engineers and metrologists of large enterprises. The company purchased fully-contained production line from well-known western manufacturer (for example, rolling mill with the sheet width up to 2500 mm for the production of pipes). 3-4 energy pyrometers from the complete set of the mill, produced by one of the leading world companies, are used for the measurement of the temperature of laminated sheet. It is specified in the equipment user manual that it is necessary to set the radiation coefficient equal to 0.88, for example, in the pyrometers when working with the steel of certain brand.
In the course of time, one of these pyrometers breaks down and in order to replace it the other pyrometer with the same basic error and almost the same sighting parameter is purchased from the different manufacturer. However, installation of the new pyrometer with the entered value of 0.88 is accompanied by the occurrence of evident error in measurements. In order to eliminate this error it is necessary to enter the value 0.91 instead of 0.88. And users have the question: so what is the value of radiation coefficient for this brand of steel, 0.88 or 0.91? Searching for the answer to this question, workers find the third pyrometer produced by the third company at other workshop. But the measurements performed with it puzzle the metrologists and process engineers completely – it is necessary to enter the value of radiation coefficient equal to 0.69 to the third pyrometer in order to obtain the same result of the temperature measurement. There it is!
The values of radiation coefficients given in this example are random to certain degree and in every specific case they can have specific value. But the most important is that they are different for the same material under the same conditions but for different pyrometers. And this uncertainty causes the fair complaints from the pyrometer users.
Described situation is paradoxical – measurement of the same object under the same conditions using different pyrometers (but with the same values of instrumental error and sighting parameters) can give different results. And the difference between these measurement results exceeds the instrumental errors of pyrometers by several times.
There are several reasons for it but metrological analysis has not been given yet. Also, the way for the solution of this collision which is correct from the metrological point of view has not been found yet. Although, everything is simple from the metrological point of view – some additional errors are not taken into account and our task is to find them, describe mathematically (if they have not been described) and take into account correctly. Therefore, reasons for the occurrence of severe additional errors, which are not taken into account and take place during the measurements performed by pyrometers, and ways of their strict registration and minimization are considered below.
As it was shown above, radiation coefficient is the parameter which depends not only on the material but instrument as well. In other words, radiation coefficient of the same material under the same conditions can have different values for different instruments with various spectral sensitivities of radiation detectors.
In order to understand the reason for such behavior of radiation coefficient let us use the following figures. Dependence of the spectral radiation capacity of low-alloy steel on the radiation wavelength plotted on the basis of the data from the paper [2] is shown in Fig. 1. Since in original this dependence within the range of wavelengths of less than 1 µm was not measured, it is interpolated into the short wave region on the basis of the data given in the papers [3] and [4]. Accuracy of such interpolation is very low but for this case when it is necessary just to explain the origin of the radiation coefficient ε and its difference upon the use of different pyrometers in qualitative manner it will be enough.
It should be noted that the considered dependence of on is not constant, at least in the visible and near IR spectrum region. Objects which are characterized by such dependence on are called "non-gray objects" or "non-gray bodies".
The spectral sensitivity characteristics of three different radiation detectors are given in Fig. 2. The curve corresponds to the detector based on Si-photodiode with the cutting filter of infrared glass. The curve corresponds to the detector based on InGaAs-photodiode. The curve corresponds to the "solar-blind" thermal detector with the spectral sensitivity range of 7-8 µm to 12-13 µm.
In Fig. 3 the spectral sensitivity characteristics of the above-mentioned radiation detectors are superposed with the spectral radiation capacity of low-alloy steel from Fig. 1. It is evident that within the range of sensitivity of the first detector the spectral radiation capacity varies near the value of 0.7. Within the range of sensitivity of the second detector the spectral radiation capacity varies approximately from 0.65 to 0.6. And within the range of sensitivity of the third detector the spectral radiation capacity varies approximately from 0.27 to 0.22.
Thus, for "non-gray bodies", which the vast majority of metals refer to, the radiation coefficient turns out to depend on the spectral range where the energy pyrometer functions. And practically in all reference literature there is no information on the spectral ranges within which the measurements specified in the relevant tables were performed. Therefore, the user can easily enter the value of radiation coefficient to his pyrometer which corresponds to the pyrometer with different spectral range. If these values are different or the object is "non-gray" the method error will occur due to the entry of the inaccurate value of radiation coefficient, estimated (for brightness pyrometers) on the basis of the following correlation:
. (1)
Here, Тд is the actual value of the object temperature, is the value of the object temperature obtained upon the entry of inaccurate value of radiation coefficient, is the actual (corresponding to the used pyrometer) value of radiation capacity, and is the error of radiation coefficient entry, in other words, it is the difference between and value which was taken from the reference literature, с2 = 1,4380 · 10-2 м·К.
Calculation results of the value of additional method error connected with the entry of inaccurate value of radiation coefficient in accordance with the formula (1) are given in Tables 1-3. Calculations were performed for three temperatures (1600 K, 2000 K and 2600 K) and wavelengths of 0.6 µm, 1 µm, 1.5 µm, 2 µm, 5 µm, 8 µm and 12 µm. And the results which correspond to 10% error in the estimation of radiation capacity are specified in Table 1, 20% – in Table 2, 30% – in Table 3.
It appears from Tables 1-3 that if pyrometer functions on the wavelengths of 1.5-2 µm, for example, upon the error 10% during the estimation of radiation coefficient the mentioned additional error will be 1.5 to 3.3%, upon the error 20% – 2.9 to 6.2%, upon the error 30% – 4.2 to 8.7%. If pyrometer functions on the wavelength of 12 µm upon the error 10% during the estimation of radiation coefficient the mentioned additional error will be 11 to 17%, upon the error 20% – 19 to 28%, upon the error 30% – 26 to 36%. In other words, very often this additional error is significant and noticeably influences on the measurement result and sometimes it is even catastrophic! And user does not know the value of this error and most often does not even suspect about its existence! So this is the first mentioned metrological problem.
In practice, metrologists just close their eyes to this component of the error. And the reason for it lies in the fact that they usually do not know how to estimate the value of the radiation coefficient ε which is metrologically significant. Often, metrologists estimate the value ε on the basis of empiricism "adjusting" the coefficient, entered to pyrometer, till they obtain the value with which the pyrometer will give them measurement result corresponding to the value which process engineer or his management considers correct.
Incorrectness of the similar "adjustment" from the metrological point of view can be shown using such evident example. For example, we measure the low values of voltage in the printed-circuit wiring unit using the microvoltmeter for direct current. As it is known, upon the contact of copper probe with kovar pin rather large contact potential difference occurs (about 30 µV at the room temperature). It is obvious, if instead of deduction of this potential difference (corrected for the pin temperature) from the measurement result we will gradually "adjust" the microvoltmeter amplification coefficient within the specific limits until we receive the value corresponding to the actual value of measured parameter on display, we can forget the traceability of measurements in radio engineering. It is inadmissible to eliminate method errors by the "adjustment for correct result" not relying upon the measurement of influencing factor and awareness of its dependencies on different medium parameters.
To be continued.
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