Study on the error analysis and correction method of temperature measurement using compensation wire of thermocouple

1 Introduction

According to relevant literature reports, Japan already has a thermocouple with compensation wire temperature measurement error correction table for users to correct the measured value when using it to obtain accurate measurement results; however, it has not been published publicly so far, and there is no similar report published in China. In recent scientific research, the author also found that when thermocouples are equipped with compensation wires for temperature measurement, the temperature of the connection point has a significant impact on the temperature measurement results, especially when the connection point temperature is greater than 50℃, the error is so large that it is unacceptable for measurements in general industrial fields, and further discussions have been conducted on this.

This paper summarizes the temperature measurement principle of thermocouples with compensating wires, and conducts error analysis. The "practical temperature error correction table" for the commonly used nickel-chromium-nickel-silicon (aluminum) thermocouples with copper-constantan compensating wires is calculated and compared with the error correction values ​​obtained using the thermocouple graduation table. The deviation is very small and can meet the requirements of most industrial and scientific research fields.

2 Thermocouple temperature measurement principle and temperature measurement error analysis using compensation wire

2.1 The principle of temperature measurement using thermocouples and compensation wires

The connection method of thermocouple and compensation wire is shown in Figure 2-1. In the figure, a and b are two thermocouple wires, a' and b' are two compensation wires. According to the law of thermocouple connection wires, the total thermoelectric potential of the loop is:

Within a certain temperature range of tn, the following formula holds true:

Substituting formula (2-2) into formula (2-1), we get:

The above formula (2-3) shows that the use of compensation wires a′ and b′ is equivalent to moving the reference end of the thermocouple to the temperature t0. This is the theoretical basis for using compensation wires to measure temperature with thermocouples.

2.2 Error analysis of temperature measurement using thermocouples and compensation wires

From the above analysis, it can be seen that the establishment of formula (2-3) is conditional, that is, the temperature tn is required to be a certain value, or within a certain range. For the thermocouple with compensation wire temperature measurement system shown in Figure 2-1, using the principle of potential superposition, formula (2-1) is rewritten as:

Formula (2-5) shows that the total thermoelectric potential of the temperature measurement system is equivalent to the algebraic sum of the thermoelectric potential eab (t, tn, t0) of thermocouples a and b and an additional thermoelectric potential δε, where δe expresses the difference between the thermoelectric potential of the couple wire and the compensation wire. For actual temperature measurement systems, the display often gives not the thermoelectric potential mv value, but the temperature value ℃, that is, converting formula (2-5) into:

It should be noted that in formula (2-6), the temperature processor converts the thermoelectric potential mv values ​​of the compensation lines a′, b′ and the thermocouple wires a, b into temperature values ​​℃ according to the mv-℃ relationship of the thermocouple wires a, b, thus causing temperature measurement errors.

For the sake of accuracy and practicality, this paper directly uses the temperature value of tn to correct the temperature measurement error. The basic idea is to find the part of the δt value that increases or decreases when the processor treats the thermoelectric potential of the compensation line as the thermoelectric potential of the thermocouple wire as the temperature value. The specific calculation process is shown in the calculation method shown in Figure 2-2. For the convenience of description, the thermocouple and compensation line are specifically nickel-chromium-nickel-silicon (aluminum) with copper-constantan compensation line in the calculation process.

3 Practical computer thermocouple compensation wire temperature measurement error correction method and program

3.1 Practical thermocouple v-℃ piecewise polynomial fitting formula

As computers are increasingly used for measurement and control in various fields, people widely use thermocouple v-℃ segmented polynomial fitting formulas. The nth segment of the thermocouple v-℃ curve segmented diagram shown in Figure 3-1 has the following cubic polynomial:

Substituting formula (3-2) into formula (3-1), we get:

Where a(n), b(n) and c(n) are segmentation coefficients, x0(n), y0(n) are the thermoelectric potential volts and temperatures °C at the segmentation starting points, and v is the thermoelectric potential volt value.

From formula (3-3), we can see that as long as we know the value of the thermoelectric potential v (volt) and the segment number n where v is located, we can calculate the temperature value y℃.

3.2 Computer program for temperature error correction

According to the temperature error calculation method shown in Figure 2-2, the commonly used nickel-chromium-nickel-silicon (aluminum) thermocouple is selected, and copper-constantan is used as the compensation wire. The error correction value of tn between -50℃ and 150℃ is calculated by computer using v-℃ piecewise polynomial and fortran language programming. Figure 3-2 is the main program flowchart, and Figures 3-3 and 3-4 are the tv(v) value temperature-thermoelectric potential solution subprogram flowchart and kt(℃) value thermoelectric potential-temperature calculation subprogram flowchart respectively.

Table 3-1 is a practical temperature error correction table obtained by calculation, and Table 3-2 is a comparison of the error correction values ​​calculated by the computer and the error correction values ​​obtained by the thermocouple graduation table.

4 Conclusions

(1) The practical temperature error correction value of the nickel-chromium-nickel-silicon (aluminum) thermocouple equipped with copper-constantan compensating wire provided in this paper is very small compared with the error correction value obtained using the thermocouple graduation table, which can meet the requirements of use in most industrial and scientific research fields.

(2) The computer correction method introduced in this paper can be used to correct the temperature measurement error of other types of thermocouples equipped with compensation wires, and this method can also be used directly to participate in online temperature measurement error correction.

(3) When using nickel-chromium-nickel-silicon (aluminum) with copper-constantan as compensation wire to measure temperature, the temperature of the connection point is more suitable between 0 and 50°C. If the temperature exceeds 50°C, the compensation wire temperature measurement error should be corrected according to the use requirements. Generally, the manual stipulates that the compensation wire operating temperature is 0 to 100°C. For the convenience of users, it is best to provide the error correction value at the same time.