CN103344358B - Low-temperature fine metal wire non-contact temperature measuring method in complex setting - Google Patents

Low-temperature fine metal wire non-contact temperature measuring method in complex setting Download PDF

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CN103344358B
CN103344358B CN201310168167.4A CN201310168167A CN103344358B CN 103344358 B CN103344358 B CN 103344358B CN 201310168167 A CN201310168167 A CN 201310168167A CN 103344358 B CN103344358 B CN 103344358B
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mrow
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temperature
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CN103344358A (en
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徐学军
林永忠
周睿
陆钻贞
孙洪洋
吕添
张哲�
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Huazhong University of Science and Technology
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Huazhong University of Science and Technology
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Abstract

Disclosed in the invention is a low-temperature fine metal wire non-contact temperature testing method. The method comprises the following steps: step one, utilizing a non-contact temperature measuring device to carry out measurement so as to obtain a measurement distance, background temperature, a target offset, and an emission rate of a static annealing metal wire in a current environment and obtain n groups of reference values Wmk and measurement values Tmk, and carrying out calculation to obtain a corresponding error; step two, utilizing the non-contact temperature measuring device to carry out measurement so as to obtain a measurement temperature T measurement of a moving annealing metal wire in a current environment; step three, according to an interpolation algorithm carrying out calculation to obtain an error by changing one parameter; step four, obtaining a comprehensive offset deltaT0 causing generation of the annealing temperature measurement value; and step five, on the basis of a formula: T actuality =T measurement + deltaT0, carrying out calculation by using the formula so as to obtain T actuality approaching the actual value of the surface temperature of the copper wire. According to the invention, a defect of large offset existing in measurement of a temperature measurement value of a fine metal wire in a high-speed motion state at a low-temperature section in the non-contact temperature measurement filed can be overcome, thereby ensuring the measurement precision of the fine metal wire in a high-speed motion state at a low-temperature section by a non-contact temperature measurement instrument.

Description

Non-contact temperature measurement method for low-temperature fine metal wire under complex background
Technical Field
The invention belongs to the field of temperature measurement and control, and particularly relates to a non-contact temperature measurement method for a low-temperature fine metal wire under a complex background. The complex background of the invention means that the temperature of the water vapor around the surface of the copper wire is lower than the surface temperature of the copper wire, but far higher than the normal temperature, which brings serious interference to non-contact temperature measurement; lower temperature refers to a condition at a temperature below 550 ℃ and fine wire refers to a wire having a cross-sectional diameter of less than 5 mm.
Background
Because the copper wire moves at a high speed, the wire diameter is small, the emissivity is high, the direct contact type accurate measurement of the annealing temperature of the copper wire is difficult to realize, and if the temperature of the copper wire is to be accurately measured, a non-contact type measurement scheme suitable for the high-speed moving metal wire under the complex condition needs to be researched and discussed.
In the prior art, a metal wire thermal radiation extraction technology under the background of water vapor infrared absorption and radiation noise and a metal wire infrared image tracking detection technology of high-speed movement and severe shaking in a limited image field are mainly adopted.
In the metal wire thermal radiation extraction technology, the copper wire annealing section is usually protected by water vapor (inert gases such as nitrogen are used, but the cost is high), and the water vapor is generally normal pressure steam and surrounds the copper wire in a water mist shape. Firstly, water vapor has an absorption effect on the thermal infrared radiation of the copper wire; ② the temperature of the normal pressure water vapor is close to 100 ℃, and the self thermal infrared radiation thereof forms noise background interference.
In the metal wire infrared image tracking detection technology, in order to reduce background radiation interference as much as possible, a detection target is generally required to occupy more than 2/3 of an image field, but as a copper wire moves at a high speed and is accompanied by severe jitter, the detection target image is easily lost frequently. The annealing temperature control mode is changed from the existing constant heating current and the existing wire drawing and outgoing speed regulation and control into the constant wire drawing and outgoing speed and the heating current regulation and control.
In a limited image field, when the measured temperature is high (more than 700 ℃), the temperature measurement accuracy has no obvious relation with the filling rate of the thermometer to the image field, namely the temperature measurement accuracy has insensitivity to the filling rate of the image field. When the measured temperature is low (less than 550 ℃), the temperature measurement accuracy is related to the filling rate of the image field of the thermometer, and the research on the aspect is not available at home and abroad, so that a method for measuring the low temperature below 550 ℃ by using a non-contact thermometer is proposed.
The correction model for the low-temperature measurement of the thin metal wire is not complete at home, the correction model comprises the correction of 4 influence factors of the measurement distance, the background temperature, the target offset and the emissivity on the temperature measurement value, the influence degree of each influence factor on the deviation of the non-contact temperature measurement value is compared, the respective error correction coefficient (weighting coefficient) is determined, and reference is provided for the industrial application of the non-contact temperature measurement in the field of high-speed moving metal wires.
Disclosure of Invention
The invention provides a non-contact temperature measuring method for a low-temperature thin metal wire under a complex background, aiming at enabling a temperature measured value of the high-speed moving thin metal wire at a low-temperature section to approach to a true value of the high-speed moving thin metal wire.
The invention provides a metal wire temperature measuring method which is characterized by comprising the following steps:
step 1, a non-contact temperature measuring device is used for measuring and obtaining the static retreat of the current environmentFour parameters of the fire wire, including the distance measured as l0Background temperature u0Target offset amount p0And emissivity of λ0Let k be the measurement number, k be 1,2,3,.. the n, n be the number of measurements, and m be l, u, λ, and p, respectively; adjusting one parameter each time, keeping the other three parameters unchanged, and respectively obtaining n groups of reference values W by adopting a contact type temperature measuring instrument and a non-contact type temperature measuring instrumentmkAnd the measured value TmkAnd W ismkRemain unchanged, i.e. Wlk=Wuk=Wλk=Wpk(ii) a The corresponding error Δ T is calculatedmk=Tmk-WmkWherein m is represented by l, u, λ and p, respectively;
step 2, measuring the measured temperature T of the annealing metal wire moving under the current environment by using a non-contact temperature measuring deviceMeasuring
Step 3, calculating to obtain an error delta T caused by changing one parameter according to an interpolation algorithmmAnd m is represented by l, u, p and λ:
ΔTm=ΔTm1+f[Tm1,Tm2](Tmeasuring-Tm1)+f[Tm1,Tm2,Tm3](TMeasuring-Tm1)(TMeasuring-Tm2)+…+f[Tm1,Tm2,…,Tmn](TMeasuring-Tm1)(TMeasuring-Tm2)…(TMeasuring-Tm,n-1),
Wherein, <math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mi>mi</mi> </msub> <mo>,</mo> <msub> <mi>T</mi> <mi>mj</mi> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&Delta;T</mi> <mi>mi</mi> </msub> <mo>-</mo> <msub> <mi>&Delta;T</mi> <mi>mj</mi> </msub> </mrow> <mrow> <msub> <mi>T</mi> <mi>mi</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>mj</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math>
<math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>mk</mi> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> <mo>-</mo> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>3</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>mk</mi> </msub> <mo>]</mo> </mrow> <mrow> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>mk</mi> </msub> </mrow> </mfrac> </mrow> </math>
and 4, acquiring comprehensive deviation of the measured value of the annealing temperature caused by 4 influence factors of the measured distance, the background temperature, the target offset and the emissivity:
ΔT0=ωpΔTpuΔTuλΔTλlΔTl
wherein, <math> <mrow> <msub> <mi>&omega;</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>p</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>&omega;</mi> <mi>u</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>u</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> </mrow> </math>
<math> <mrow> <msub> <mi>&omega;</mi> <mi>&lambda;</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>&omega;</mi> <mi>l</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>.</mo> </mrow> </math>
step 5 using formula TReality (reality)=TMeasuring+ΔT0And calculating to obtain the temperature T approximate to the true value of the surface temperature of the copper wireReality (reality)
Compared with the prior art, the invention has the following technical effects:
the invention can correct the defect of overlarge temperature measurement value deviation of the high-speed moving thin metal wire in the low-temperature section in the non-contact temperature measurement field so as to ensure the measurement precision of the non-contact temperature measuring instrument on the high-speed moving thin metal wire in the low-temperature section.
When the temperature is measured, the measuring distance is adjusted under the condition that the fine metal wire is not completely filled with an image field, and the optimal value of the measuring distance under different wire diameters is obtained; reducing the area of the background temperature appearing in the image field, and correcting the interference of the background temperature on the real temperature of the surface of the thin metal wire; when the emissivity is changed, the real temperature of the surface of the thin metal wire under the influence of different emissivities can be corrected; when the measuring target shakes or shifts, the measuring error caused by the shift distance can be corrected.
By integrating the correction method, the correction weight of each influence factor is set, and the temperature measurement value of the high-speed moving thin metal wire in the low-temperature section can approach the true value of the thin metal wire.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a graph of measured distance versus measured temperature for each temperature segment;
FIG. 3 is a graph of the approximation of the measured temperature to the true temperature under the influence of a background temperature;
FIG. 4 is a graph of emissivity versus measured temperature for each temperature segment;
FIG. 5 is an experimental schematic of the effect of target offset distance on measured temperature;
FIG. 6 is a plot of target offset distance versus measured temperature for each temperature segment;
FIG. 7 is a composite error contribution coefficient profile;
FIG. 8 is a weight example of each influence factor in the non-contact thermometry correction model.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings. It should be noted that the description of the embodiments is provided to help understanding of the present invention, but the present invention is not limited thereto. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, the method of the present invention comprises the steps of:
(1) acquiring 4 influence factors of a measuring distance, a background temperature, a target offset and an emissivity when a metal wire is static in the current environment to cause the deviation of an annealing temperature measuring value;
recording the measurement distance l under the current environment0Background temperature u0Target offset amount p0Emissivity of lambda0The changing measurement distances are acquired separately in the following mannerError Δ T caused by llkError Δ T due to change in background temperatureukError delta T caused by changing emissivityλkAnd error Δ T caused by changing the target offsetpk
The method comprises the following steps of (I) analyzing and correcting the influence factors of the measured distance:
in non-contact temperature measurement, the measurement error increases with the distance, and the measured target surface temperature becomes smaller.
Setting the background temperature u0Target offset p0Emissivity lambda0Keeping the surface temperature of the copper wire constant, adjusting the measuring distance l, and respectively measuring the surface temperature of the same copper wire by using a non-contact type temperature measuring instrument and a contact type temperature measuring instrument to obtain n groups of measured values T of the surface temperature of the copper wirelkWith a reference value WlkWherein n is the number of measurements, k is the measurement serial number, and k is 1,2, 3. To ensure the precision, n can be 6-8 groups of values, WlkThe value range of (A) is preferably 300-550 ℃.
Calculating to obtain the error delta T corresponding to each group of valueslk=Tlk-WlkWherein k is 1,2, 3. Wherein, i and j are serial numbers of two adjacent measurements, i.e. j equals i + 1;
<math> <mrow> <mi>f</mi> <mo>[</mo> <mo>=</mo> <msub> <mi>T</mi> <mi>li</mi> </msub> <mo>,</mo> <msub> <mi>T</mi> <mi>lj</mi> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&Delta;T</mi> <mi>li</mi> </msub> <mo>-</mo> <msub> <mi>&Delta;T</mi> <mi>lj</mi> </msub> </mrow> <mrow> <msub> <mi>T</mi> <mi>li</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>lj</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> is a first order difference quotient;
<math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>l</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>lk</mi> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>l</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <msub> <mi>T</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> <mo>-</mo> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>l</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>l</mi> <mn>3</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>lk</mi> </msub> <mo>]</mo> </mrow> <mrow> <msub> <mi>T</mi> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>lk</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> is a k-order difference quotient;
(II) analyzing and correcting background temperature influence factors:
since not only the measurement target but also radiation energy of background temperature enters the detector in the instantaneous effective field of view, the environmental radiation energy is a main factor for generating measurement errors of the target surface temperature.
In the case of relatively ideally controlling other error-influencing factors, as shown in fig. 3, the non-contact type temperature measuring instrument and the thermocouple have the same trend of change, and the higher the target surface temperature is, the larger the background temperature error influence index is, and the larger the temperature error is.
Setting the measurement distance l0Target offset p0And emissivity lambda0Keeping the temperature constant, adjusting the background temperature u, adjusting the annealing current during each measurement, and measuring the surface temperature of the same copper wire by using a contact type temperature measuring instrument to obtain the surface temperature of the copper wire, namely the reference value Wuk=WlkMeasuring the surface temperature of the same copper wire by using a non-contact type temperature measuring instrument to obtain a measured value T of the surface temperature of the copper wire at the momentukK is a measurement serial number, k is 1,2,3, and n is the measurement times;
calculating to obtain the error delta T corresponding to each groupuk=Tuk-WukWherein, let i, j denote the serial number of two adjacent measurements, i.e. j ═ i + 1;
<math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mi>ui</mi> </msub> <mo>,</mo> <msub> <mi>T</mi> <mi>uj</mi> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&Delta;T</mi> <mi>ui</mi> </msub> <mo>-</mo> <msub> <mi>&Delta;T</mi> <mi>uj</mi> </msub> </mrow> <mrow> <msub> <mi>T</mi> <mi>ui</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>uj</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> is a first order difference quotient;
<math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>u</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>u</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>uk</mi> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>u</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>u</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <msub> <mi>T</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> <mo>-</mo> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>u</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>u</mi> <mn>3</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>uk</mi> </msub> <mo>]</mo> </mrow> <mrow> <msub> <mi>T</mi> <mrow> <mi>u</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>uk</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> k-order difference quotient;
(III) emissivity influence factor analysis and correction process:
as can be seen from fig. 4, the temperature measurement value is approximately linearly changed with the change of emissivity, and it can be seen that the higher the temperature is, the larger the slope of the linear fit is, i.e. the measured temperature is also larger with the change of emissivity, which indicates that the higher the temperature is, the larger the emissivity has to affect the measurement error.
Setting the measurement distance l0Target offset p0Background temperature u0Keeping constant, adjusting emissivity lambda, adjusting annealing current during each measurement, and measuring the surface temperature of the same copper wire by using a contact type temperature measuring instrument to obtain the reference value Wλk=WlkMeasuring the surface temperature of the same copper wire by using a non-contact type temperature measuring instrument to obtain a measured value T of the surface temperature of the copper wire at the momentλkK is a measurement serial number, k is 1,2,3, and n is the measurement times; calculating to obtain the error delta T corresponding to each group of values3k=T3k-W3kWherein, let i, j denote the serial number of two adjacent measurements, i.e. j ═ i + 1;
<math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mi>j</mi> </mrow> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&Delta;T</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&Delta;T</mi> <mrow> <mn>3</mn> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> is a first order difference quotient;
<math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mn>31</mn> </msub> <mo>,</mo> <msub> <mi>T</mi> <mn>32</mn> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mi>k</mi> </mrow> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mn>31</mn> </msub> <mo>,</mo> <msub> <mi>T</mi> <mn>32</mn> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> <mo>-</mo> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mn>32</mn> </msub> <mo>,</mo> <msub> <mi>T</mi> <mn>33</mn> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mi>k</mi> </mrow> </msub> <mo>]</mo> </mrow> <mrow> <msub> <mi>T</mi> <mn>31</mn> </msub> <mo>-</mo> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mi>k</mi> </mrow> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> is a k-order difference quotient;
(IV) analyzing and correcting the target offset influence factor:
for a metal wire moving at a high speed, particularly in the continuous annealing processing of an online copper wire, the vibration of the metal wire is one of important factors influencing the temperature measurement precision. The target offset is the distance of the center of the cross section of the metal wire deviating from the target aiming point of the non-contact type temperature measuring instrument.
Referring to fig. 5, a wire having a wire diameter of 1mm is horizontally placed with respect to a thermometer, and an extension line of a center line of the wire is an X-axis, wherein the X-axis represents a distance of a measurement target deviated in a direction parallel to the wire, the Y-axis represents a distance of a measurement target deviated in a direction perpendicular to the wire, a positive number represents that an aiming point is located above the wire in an actual case, and a negative number represents that the aiming point is located below the wire. The relationship of the aiming point perpendicular to the wire deflection distance and the measured temperature is shown in fig. 6.
It is understood from fig. 6 that the higher the measured temperature, the larger the error due to the target deviation. The influence of vibration errors in an ideal temperature section of copper wire annealing is very large, errors caused by aiming deviation need to be reduced in application, the vibration amplitude of a metal wire needs to be controlled as much as possible from machine hardware, when the response frequency of a non-contact type temperature measuring instrument and the vibration frequency of a copper wire are much smaller, the measuring accuracy is higher, and the target vibration error frequency is lower.
Setting the measuring distance, background temperature and emissivity to be constant, and recording the measuring distanceIs 10Background temperature u0Emissivity of lambda0Adjusting target offset p, adjusting annealing current during each measurement, and measuring the surface temperature of the same copper wire by using a contact type temperature measuring instrument to obtain the surface temperature of the copper wire, namely a reference value Wpk=WlkMeasuring the surface temperature of the same copper wire by using a non-contact type temperature measuring instrument to obtain a measured value T of the surface temperature of the copper wire at the momentpkK is a measurement serial number, k is 1,2,3, and n is the measurement times;
calculating to obtain the error delta T corresponding to each group of valuespk=Tpk-WpkWherein k is 1,2, 3.
Wherein, let i, j denote the serial number of two adjacent measurements, i.e. j ═ i +1
<math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mi>pi</mi> </msub> <mo>,</mo> <msub> <mi>T</mi> <mi>pj</mi> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&Delta;T</mi> <mi>pi</mi> </msub> <mo>-</mo> <msub> <mi>&Delta;T</mi> <mi>pj</mi> </msub> </mrow> <mrow> <msub> <mi>T</mi> <mi>pi</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>pj</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> Is a first order difference quotient;
<math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>pk</mi> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> <mo>-</mo> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mn>3</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>pk</mi> </msub> <mo>]</mo> </mrow> <mrow> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>pk</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math> is a k-order difference quotient;
(2) measuring the measured temperature T of the annealing metal wire moving under the current environment by using a non-contact temperature measuring deviceMeasuring
(3) According to Newton's interpolation algorithm, the error caused by changing one of the parameters is obtained, and the error caused by changing the measurement distance l is respectively obtainedError correction value Δ T oflError correction value delta T caused by changing background temperatureuError correction value delta T caused by changing emissivityλError correction value delta T caused by changing target offsetp
According to the Newton interpolation algorithm, an error correction model caused by changing the measurement distance is obtained as follows:
ΔTm=ΔTm1+f[Tm1,Tm2](Tmeasuring-Tm1)+f[Tm1,Tm2,Tm3](TMeasuring-Tm1)(TMeasuring-Tm2)+…+f[Tm1,Tm2,…,Tmn](TMeasuring-Tm1)(TMeasuring-Tm2)…(TMeasuring-Tm,n-1),
Wherein, <math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mi>mi</mi> </msub> <mo>,</mo> <msub> <mi>T</mi> <mi>mj</mi> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&Delta;T</mi> <mi>mi</mi> </msub> <mo>-</mo> <msub> <mi>&Delta;T</mi> <mi>mj</mi> </msub> </mrow> <mrow> <msub> <mi>T</mi> <mi>mi</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>mj</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </math>
<math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>mk</mi> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> <mo>-</mo> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>3</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>mk</mi> </msub> <mo>]</mo> </mrow> <mrow> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>mk</mi> </msub> </mrow> </mfrac> </mrow> </math>
the required delta T can be obtained by carrying out curve fitting through a Newton interpolation algorithmmAnd m is represented by l, u, λ and p, respectively.
And 4, acquiring comprehensive deviation of the measured value of the annealing temperature caused by 4 influence factors of the measured distance, the background temperature, the target offset and the emissivity:
on one hand, in order to make the calculation result of the model more accurate, many experimental measurements are required to obtain actual data so as to obtain a proper model. On the other hand, in order to obtain a model more favorable for engineering calculation, besides the approximate estimation of some influencing factors, the error minimization needs to be achieved by matching from other aspects such as the aspect of device hardware. And setting the influence degrees of different factors in the model, namely error influence weights, and establishing a metal wire non-contact temperature measurement comprehensive correction model.
For a high-speed vibrating wire, the comprehensive correction model can be expressed by the following formula:
ΔT0=ωpΔTpuΔTuλΔTλlΔTl
wherein; delta T0Indicating combined correction value, omega, for non-contact temperature measurementp,ωu,ωλ,ωlError influence coefficients which are 4 influence factors of the measured distance, the background temperature, the emissivity and the target offset respectively, namely error influence weights under different conditions, determine the proportion of each factor when the measured temperature error is calculated.
<math> <mrow> <msub> <mi>&omega;</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>p</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>&omega;</mi> <mi>u</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>u</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> </mrow> </math>
<math> <mrow> <msub> <mi>&omega;</mi> <mi>&lambda;</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>&omega;</mi> <mi>l</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>&Delta;T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>.</mo> </mrow> </math>
As can be seen from fig. 7, the variation of different conditions with temperature is not obvious, but it can be obviously obtained that the influence of the target offset on the measurement error is the largest, and then the influence caused by the change of emissivity, and the error caused by the change of background temperature and measurement distance is relatively small, and the influence coefficients of different conditions on the measurement error are obtained through comprehensive consideration of experimental results.
Step 5 using formula TReality (reality)=TMeasuring+ΔT0And calculating to obtain the temperature T approximate to the true value of the surface temperature of the copper wireReality (reality)
Example (c):
as shown in table one, the reference temperature is a reference temperature value measured by a thermocouple on the surface of a section of copper wire, i.e. column 1 of table one.
When the background temperature is 20 ℃, the emissivity is 1 and the target offset is 0, the measurement distance is changed, and the value measured by the infrared colorimetric thermometer is column 2 of the first table.
The correction algorithm for obtaining the influence of the measuring distance on the temperature measurement of the infrared colorimetric thermometer by the Newton interpolation algorithm is as follows:
ΔTl=8+0.077(Tmeasuring-323)+2.78×10-3(TMeasuring-323)(TMeasuring-375)-2.61×10-5(TMeasuring-323)(TMeasuring-375)(TMeasuring-402)
When the measurement distance is 500mm, the emissivity is 1 and the target offset is 0, the background temperature is changed, and the value measured by the infrared colorimetric thermometer is column 3 of the first table.
The correction algorithm for obtaining the influence of the background temperature on the temperature measurement of the infrared colorimetric thermometer by the Newton interpolation algorithm is as follows:
ΔTu=-36+1.8(Tmeasuring-367)-3.21×10-2(TMeasuring-367)(TMeasuring-387)-2.22×10-4(TMeasuring-367)(TMeasuring-387)(TMeasuring-427)
When the measurement distance is 500mm, the background temperature is 20 ℃, and the target offset is 0, the emissivity is changed, and the value measured by the infrared colorimetric thermometer is column 4 of the first table.
The correction algorithm for obtaining the influence of the emissivity on the temperature measurement of the infrared colorimetric thermometer by the Newton interpolation algorithm is as follows:
ΔTλ=-25+0.077(Tmeasuring-356)+8.08×10-3(TMeasuring-356)(TMeasuring-408)-7.17×10-5(TMeasuring-356)(TMeasuring-408)(TMeasuring-429)
When the measurement distance is 500mm, the background temperature is 20 ℃, and the emissivity is 1, the target offset is changed, and the value measured by the infrared colorimetric thermometer is column 5 of the first table.
The correction algorithm for obtaining the influence of the target offset on the temperature measurement of the infrared colorimetric thermometer by the Newton interpolation algorithm is as follows:
ΔTp=95-0.33(Tmeasuring-236)-0.037(TMeasuring-236)(TMeasuring-320)+8.80×10-4(TMeasuring-236)(TMeasuring-320)(TMeasuring-299)
The second table shows the coefficients of the error influence under different conditions, and the weight omega of each influence factor in the radiation temperature measurement correction model for the high-speed vibration metal wire can be obtainedp=0.69,ωu=0.10,ωλ=0.12,ωl0.09 as shown in fig. 8, and reflects the influence of the error on the final error. Then the measured value T obtained in the above way is usedMeasuringCorrection amount DeltaTp,ΔTu,ΔTλ,ΔTlAnd corresponding additional weight ωp,ωu,ωλ,ωlSubstituting the formula into the formula to obtain the corrected value of the non-contact temperature measurement value of the fine metal wire at lower temperature under the complex background.
TReality (reality)=TMeasuring+ΔT0=TMeasuringpΔTpuΔTuλΔTλlΔTl
The above description is a preferred embodiment of the present invention, but the present invention should not be limited to the disclosure of the embodiment and the drawings. Therefore, it is intended that all equivalents and modifications which do not depart from the spirit of the invention disclosed herein are deemed to be within the scope of the invention.
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Claims (1)

1. A method of measuring the temperature of a wire, the method comprising the steps of:
step 1, measuring four parameters of the static annealing metal wire under the current environment by using a non-contact temperature measuring device, wherein the four parameters comprise a measuring distance l0Background temperature u0Target offset amount p0And emissivity of λ0Let k be a measurement serial number, k be 1,2,3,., n, n be the measurement times, and m be the measurement distance l, the background temperature u, the emissivity λ, and the target offset p after adjustment, respectively; regulating one of the ginseng at a timeCounting, keeping the other three of the four parameters unchanged, and respectively adopting a contact type temperature measuring instrument and a non-contact type temperature measuring instrument to obtain n groups of reference values WmkAnd the measured value TmkAnd W ismkRemain unchanged, i.e. Wlk=Wuk=Wλk=Wpk(ii) a The corresponding error Δ T is calculatedmk=Tmk-Wmk(ii) a The target offset refers to the distance of the center of the cross section of the metal wire deviating from a target aiming point of the non-contact type temperature measuring instrument;
step 2, measuring the measured temperature T of the annealing metal wire moving under the current environment by using a non-contact temperature measuring deviceMeasuring
Step 3, calculating to obtain the error caused by changing one of the parameters according to an interpolation algorithm, and respectively obtaining the error correction value delta T caused by changing the measurement distance llError correction value delta T caused by changing background temperatureuError correction value delta T caused by changing emissivityλError correction value delta T caused by changing target offsetpLet m be represented as l, u, λ and p, respectively, and the error correction model is:
ΔTm=ΔTm1+f[Tm1,Tm2](Tmeasuring-Tm1)+f[Tm1,Tm2,Tm3](TMeasuring-Tm1)(TMeasuring-Tm2)+…+f[Tm1,Tm2,…,Tmn](TMeasuring-Tm1)(TMeasuring-Tm2)…(TMeasuring-Tm,n-1),
Wherein,i. j represents the serial number of two adjacent measurements, i.e. j ═ i + 1;
<math> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>mk</mi> </msub> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> <mo>-</mo> <mi>f</mi> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>3</mn> </mrow> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>T</mi> <mi>mk</mi> </msub> <mo>]</mo> </mrow> <mrow> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>mk</mi> </msub> </mrow> </mfrac> </mrow> </math>
and 4, acquiring comprehensive deviation of the measured value of the annealing temperature caused by 4 influence factors of the measured distance, the background temperature, the target offset and the emissivity: delta T0=ωpΔTpuΔTuλΔTλlΔTl
Wherein, <math> <mrow> <msub> <mi>&omega;</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>p</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> <msub> <mi>&omega;</mi> <mi>u</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>u</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> </mrow> </math>
<math> <mrow> <msub> <mi>&omega;</mi> <mi>&lambda;</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> <msub> <mi>&omega;</mi> <mi>l</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>p</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>u</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>&lambda;</mi> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <mi>&Delta;</mi> <msub> <mi>T</mi> <mi>l</mi> </msub> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> </mrow> </math>
step 5 using formula TReality (reality)=TMeasuring+ΔT0And calculating to obtain the temperature T approximate to the true value of the surface temperature of the metal wireReality (reality)
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