CN115116770B - Arc plasma parameter diagnosis method under sinusoidal curved surface contact - Google Patents
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01H—ELECTRIC SWITCHES; RELAYS; SELECTORS; EMERGENCY PROTECTIVE DEVICES
- H01H1/00—Contacts
- H01H1/0015—Means for testing or for inspecting contacts, e.g. wear indicator
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- H05H1/0012—Investigating plasma, e.g. measuring the degree of ionisation or the electron temperature using electromagnetic or particle radiation, e.g. interferometry
- H05H1/0037—Investigating plasma, e.g. measuring the degree of ionisation or the electron temperature using electromagnetic or particle radiation, e.g. interferometry by spectrometry
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- H—ELECTRICITY
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- H05H—PLASMA TECHNIQUE; PRODUCTION OF ACCELERATED ELECTRICALLY-CHARGED PARTICLES OR OF NEUTRONS; PRODUCTION OR ACCELERATION OF NEUTRAL MOLECULAR OR ATOMIC BEAMS
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- H05H1/0006—Investigating plasma, e.g. measuring the degree of ionisation or the electron temperature
- H05H1/0081—Investigating plasma, e.g. measuring the degree of ionisation or the electron temperature by electric means
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01H—ELECTRIC SWITCHES; RELAYS; SELECTORS; EMERGENCY PROTECTIVE DEVICES
- H01H1/00—Contacts
- H01H1/0015—Means for testing or for inspecting contacts, e.g. wear indicator
- H01H2001/0031—Means for testing or for inspecting contacts, e.g. wear indicator by analysing radiation emitted by arc or trace material
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Abstract
The invention discloses a method for diagnosing arc plasma parameters under a sinusoidal curved surface contact, belonging to the method for diagnosing arc plasma parameters; the method comprises the following steps: firstly, setting a GAMMA correction coefficient, calibrating parameters of a bimodal narrow-band filter matched with a color CCD camera by using a tungsten band lamp, and shooting arc light under a sinusoidal curved contact; the upper computer obtains arc radiation intensity data, determines the position, the opening distance and the arc area of the anode and cathode of the sinusoidal curved contact, establishes an arc image coordinate system, and determines the contour line function of the anode and cathode surfaces; further utilizing a contour line function to carry out rectangular space transformation on projection radiation power data of the sinusoidal curve contact gap, selecting the center position of an arc column, and carrying out Abel inverse transformation; and finally, calculating by using a colorimetry to obtain an electron temperature and electron density distribution result. The invention solves the problem that the radiation intensity of the arc under the sine curve contact structure can not be subjected to Abel conversion.
Description
Technical Field
The invention relates to an arc plasma parameter diagnosis method, in particular to a sinusoidal curve contact arc plasma parameter diagnosis method.
Background
The electric arc is used as a thermal plasma, the temperature and the density of the thermal plasma are important thermodynamic parameters for representing the transport characteristics and the evolution trend of the plasma, and the thermal plasma is an important basis for guiding the structural design of the power switch.
The commonly used arc plasma parameter diagnosis method is divided into: contact diagnosis, non-contact diagnosis, etc.;
The common method of contact diagnosis is a probe method, wherein the probe consists of an insulated wire with an exposed tail end, the tail end of the probe stretches into plasma to be measured during measurement, different currents are collected by the probe after different direct-current bias voltages are applied, and characteristic parameters of the plasma are obtained by analyzing a current/voltage characteristic curve. However, the probe method itself forms a non-negligible disturbance to the arc plasma, and the measurement position cannot be guaranteed to be effective all the time when the plasma is in a rapid evolution process.
The most commonly used non-contact diagnostic method is a spectroscopic method, which has no disturbance to the arc plasma, and the plasma density and temperature can be obtained by analyzing and calculating the radiation intensity of the arc spectrum. But this method does not allow plasma diagnostics of the arc under the curved contact gap.
The sinusoidal curved surface contact is a contact structure with stronger capability of breaking high-frequency electric arc in a short gap, the cathode contact and the anode contact are formed by linear cutting according to sinusoidal curves, the surface of an electrode is smooth and continuous, the surface area of the electrode is larger than that of a flat contact with the same contact diameter, the electric arc ablation is lighter, the breaking capability is stronger, and the sinusoidal curved surface contact has obvious performance advantages especially for fast-changing medium-high-frequency vacuum electric arc.
And the distribution rule of the arc plasma parameters under the sinusoidal surface contact is diagnosed and analyzed by utilizing a spectrum analysis method, so that the selection and optimization of the sinusoidal surface contact structure parameters and the material parameters are facilitated. In the past diagnosis process of arc plasma, the arc column is used as the premise of regular cylindrical shape, the follow-up calculation process is carried out, and no test method capable of diagnosing plasma parameters of the arc column under the bending clearance of the sinusoidal curved contact is available.
Disclosure of Invention
Aiming at the problems, the invention provides a parameter diagnosis method for arc plasma under a sinusoidal contact, which is based on a spectrum continuous theory, utilizes a color camera to obtain the bremsstrahlung intensity of an arc in cooperation with a bimodal optical filter, combines the structural characteristics of the sinusoidal contact to perform spatial transformation of radiation intensity data, and finally obtains the parameter distribution of the density and the temperature of the arc plasma in a sinusoidal contact gap.
The diagnosis method of arc plasma parameters under the sinusoidal curved contact comprises the following specific steps:
Setting a GAMMA correction coefficient, and carrying out parameter calibration on an optical system formed by matching a color CCD camera with a bimodal narrow-band filter with center wavelengths of lambda 1 and lambda 2 by using a tungsten band lamp;
Parameter calibration means: calibrating analog-to-digital conversion proportionality coefficients K λ1 and K λ2 of each optical channel through a standard temperature source;
Shooting arc light under the sinusoidal curved contact by using an optical system after calibrating parameters;
Reading a 'RAW' format file by an upper computer to obtain RGB tristimulus values corresponding to arc light in a sinusoidal curve contact gap, and obtaining projection radiation powers I λ1 (X, Y) and I λ2 (X, Y) with central wavelengths of lambda 1 and lambda 2;
Determining the position, the opening distance and the arc area of a cathode and an anode of a sinusoidal curved contact in arc radiation intensity data, establishing an arc image coordinate system, and determining a cathode surface contour line function Y C and an anode surface contour line function Y A of the surface of the sinusoidal curved contact;
Then there is
A g is a pixel value corresponding to the bending amplitude of the curved contact in the arc image, T g is a pixel value corresponding to one bending period, and D gap is a pixel value corresponding to the contact opening distance.
Fifthly, utilizing the shape characteristics of the sinusoidal contact expressed by the contour line function to carry out rectangular space transformation on projection radiation power data of the sinusoidal contact gap, and recording two central wavelengths lambda 1 and lambda 2, and corresponding projection radiation power distribution functionsAnd/>
The specific transformation process is as follows:
Firstly, calculating the P coordinate (x P,yP) of any pixel point of the cathode surface by using a cathode surface contour line function Y C;
Let the tangent equation be l 1 and the normal equation be l 2, if there is
Y C'|x＝xP denotes the slope of the cathode profile function at point P.
Then, calculating the center position G point coordinate (x G,yG) when the plasma jet of the cathode spot at the P point reaches the anode;
The method comprises the following steps: first, the direction of the plasma jet of the cathode spot at point P is along l 2, and the intersection point G of l 2 and the anode surface contour function Y A, that is, the center position of the plasma flow occurring at point P when reaching the anode, the G-point coordinate (x G,yG) can be found by the equation of simultaneous l 2 and Y A.
Then, the point P and the point G are connected, the line segment PG is divided into N equidistant line segments, and the projection radiation power of each point on the line segment PG corresponds to one column of rectangular projection radiation power data.
And finally, repeating the steps for each pixel point on the cathode surface of the sinusoidal contact, and finally, completely converting the original curved distribution projection radiation power data into rectangular projection radiation power data.
Distribution functionAnd/>Wherein X, Y is an integer coordinate value, X ε [ X left,Xright],Y∈[Ycath,Yano];Xleft、Xright ] is a left boundary and a right boundary coordinate value of projection radiation power data of the arc respectively, and Y cath、Yano is a cathode boundary and an anode boundary coordinate value of the projection radiation power data of the arc respectively.
Step six, utilizing projection radiation power distribution functions of central wavelengths lambda 1 and lambda 2 And/>Selecting the center position of an arc column; performing data interpolation according to the order of the Abel inverse transformation, and performing the Abel inverse transformation;
The specific calculation process is as follows:
step 601, calculating a direction vector of a projected radiation power center with a center wavelength lambda 1
Wherein r (X, Y) is the vector diameter of the point (X, Y) relative to the origin O, the numerator is the sum of the projection radiation power of the center wavelength lambda 1 of each point and the vector multiplication of the direction of the point, and the denominator is the sum of the projection radiation power of the center wavelength lambda 1 of each pointI.e. the direction vector of the center of gravity of the projection radiation power with the center wavelength lambda 1 of each point.
Step 602, similarly calculating the direction vector of the projection radiation power center with the center wavelength lambda 2
Step 603, calculating a vector diameter r ce of the center of gravity position of the arc column by using two direction vectors, wherein the vector diameter r ce is as follows:
In step 604, the pixel coordinate corresponding to the vector r ce is (X ce,Yce), and x=x ce is selected as the luminance center line of the arc column.
Step 605, comparing the values of (X right-Xce) and (X ce-Xleft), taking the minimum value of X arc, and redefining the projection radiation power of the central wavelengths lambda 1 and lambda 2 And/>
X∈[Xce-Xarc,Xce+Xarc],Y∈[Ycath,Yano]。
Step 606, setting an order N Abel of the Abel inverse transform, wherein the value represents the number of equivalent circles dividing the arc plane after x=x ce is taken as the brightness center of the arc column.
Step 607, utilizing the redefined projected radiation powerAnd/>Calculate projection radiance matrix/>And/>
Is provided with
Wherein n=n Abel,m＝Yano-Ycath;
if the calculated coordinates are not integers, adopting a linear fitting method to take the projection radiation power value according to the coordinate values.
Step 608, for projection radiation brightness matrixAnd/>Performing Abel inverse transformation;
And/> A radiation power distribution matrix with central wavelengths of lambda 1 and lambda 2 inside the curved contact arc; wherein T N is a coefficient matrix of N Abel×NAbel, and is obtained through table lookup.
And step seven, calculating by using a colorimetric method to obtain an electron temperature and electron density distribution result.
For radiation power distribution matrixAnd/>The following calculation is performed for each element of (a):
electron temperature T e(gij) is calculated as follows:
h is the Planck constant; c is the speed of light; k B is boltzmann constant;
electron density n e(hij) is calculated as follows:
k is a constant, e is an electron charge, ε 0 is a dielectric constant, c is a speed of light, m e is a mass of electrons,/> Is the correction factor of bremsstrahlung, i.e., biberman factor.
Then the electron temperature profile T e(gij) and electron density profile n e(hij) of the arc in the sinusoidal contact gap are obtained).
The invention has the advantages that:
1. the invention relates to a method for diagnosing arc plasma parameters under a sinusoidal contact, which considers the influence mechanism of sinusoidal contact structural parameters on the arc plasma emission process, solves the problem that the arc radiation intensity under the sinusoidal contact structure cannot be subjected to ABEL conversion by using a method that the cathode surface normal corresponds to the columnar arc longitudinal direction, enables a measurement result to be closer to a physical process, and provides a solution for plasma parameter measurement under a special contact structure.
2. The invention relates to a method for diagnosing parameters of arc plasma under a sinusoidal curved contact, which has a simple structure and comprises a CCD color camera, a bimodal narrow-band filter and related calculation programs, so that the undisturbed measurement of the parameters of the arc plasma can be realized.
Drawings
FIG. 1 is a flow chart of a method for diagnosing parameters of arc plasma under a sinusoidal contact;
FIG. 2 is a graph showing the relationship between the internal radiation power of the electric arc and the digital quantity of the upper computer;
FIG. 3 is a graph showing RGB trichromatic response of a color CCD camera system employed in the present invention;
FIG. 4 is a diagram of a sinusoidal contact structure and embodiment of the present invention;
FIG. 5 is a schematic diagram of a contour function and a spatial transformation method according to the present invention;
FIG. 6 is a graph showing the results of the invention for arc electronic temperature diagnostics under sinusoidal contacts;
FIG. 7 is a graph showing the results of the invention for arc electron density diagnostics under sinusoidal contacts.
Detailed Description
The invention is described in further detail below with reference to the drawings and examples.
The diagnosis method of arc plasma parameters under the sinusoidal contact, as shown in figure 1, comprises the following specific steps:
Setting a GAMMA correction coefficient, and carrying out parameter calibration on an optical system formed by matching a color CCD camera with a bimodal narrow-band filter with center wavelengths of lambda 1 and lambda 2 by using a tungsten band lamp;
parameter calibration means: analog-to-digital conversion scaling factor for each optical channel And/>Calibrating through a standard temperature source;
The calculation formula is as follows:
Wherein R (T), G (T) and B (T) are RGB tristimulus values corresponding to a tungsten zone center pixel in a tungsten zone lamp image; i W(T,λ1) is the radiation power of the tungsten band lamp at a brightness temperature T in the wavelength range of lambda 1; i W(T,λ2) is the radiation power of the tungsten band lamp at a brightness temperature T in the wavelength range of λ 2; And/> The transmittance of the filter at two center wavelengths lambda 1、λ2; /> Is the photoelectric response coefficient of the radiant energy at the center wavelengths lambda 1 and lambda 2, respectively, on the R, B, G three-color pixel.
The present embodiment sets the GAMMA correction coefficient to 1.0.
Shooting arc light under the sinusoidal curved contact by using an optical system after calibrating parameters;
Reading a 'RAW' format file by an upper computer to obtain RGB tristimulus values corresponding to arc light in a sinusoidal curve contact gap, and obtaining projection radiation power with center wavelengths of lambda 1 and lambda 2 And/>
The calculation formula is as follows:
The projection radiation power of a pixel position (XY) in the CCD camera at the center of two wavelengths along the y-axis direction is respectively set as an observation point corresponding to a pixel And/>Then there is
Wherein R (X, Y), G (X, Y) and B (X, Y) are RGB tristimulus values corresponding to the pixel;
Determining the position, the opening distance and the arc area of the anode and cathode of the sinusoidal contact in arc radiation intensity data, establishing an arc image coordinate system, and determining the contour line function of the surface of the sinusoidal contact;
A two-dimensional rectangular coordinate system is established in the arc image, the pixel is taken as a minimum scale unit, the pixel where the starting point of the sinusoidal contour of the sinusoidal curved surface contact cathode is located is taken as an original point, the horizontal direction of the arc image is taken as an x-axis, and the vertical direction of the arc image is taken as a y-axis.
The cathode surface contour line function is Y C, the anode surface contour line function is Y A, then there are
A g is a pixel value corresponding to the bending amplitude of the curved contact in the arc image, T g is a pixel value corresponding to one bending period, and D gap is a pixel value corresponding to the contact opening distance.
Fifthly, utilizing the shape characteristics of the sinusoidal contact expressed by the contour line function to carry out rectangular space transformation on projection radiation power data of the sinusoidal contact gap, and recording two central wavelengths lambda 1 and lambda 2, and corresponding projection radiation power distribution functionsAnd/>
The specific transformation process is as follows:
Firstly, calculating the P coordinate (x P,yP) of any pixel point of the cathode surface by using a cathode surface contour line function Y C;
Let the tangent equation be l 1 and the normal equation be l 2, if there is
Representing the slope of the cathode contour function at point P.
Then, calculating the center position G point coordinate (x G,yG) when the plasma jet of the cathode spot at the P point reaches the anode;
The method comprises the following steps: first, the direction of the plasma jet of the cathode spot at point P is along l 2, and the intersection point G of l 2 and the anode surface contour function Y A, that is, the center position of the plasma flow occurring at point P when reaching the anode, the G-point coordinate (x G,yG) can be found by the equation of simultaneous l 2 and Y A.
Then, the point P and the point G are connected, the line segment PG is divided into N equidistant line segments, and the projection radiation power of each point on the line segment PG corresponds to one column of rectangular projection radiation power data.
And finally, repeating the steps for each pixel point on the cathode surface of the sinusoidal contact, and finally, completely converting the original curved distribution projection radiation power data into rectangular projection radiation power data.
X, Y in the distribution functions J λ1 (X, Y) and J λ2 (X, Y) are integer coordinate values, X ε [ X left,Xright],Y∈[Ycath,Yano];Xleft、Xright ] is the left boundary and right boundary coordinate value of the projection radiation power data of the arc respectively, and Y cath、Yano is the cathode boundary and anode boundary coordinate value of the projection radiation power data of the arc respectively.
Step six, utilizing projection radiation power distribution functions of central wavelengths lambda 1 and lambda 2 And/>Selecting the center position of an arc column; performing data interpolation according to the order of the Abel inverse transformation, and performing the Abel inverse transformation;
The specific calculation process is as follows:
step 601, calculating a direction vector of a projected radiation power center with a center wavelength lambda 1
Wherein r (X, Y) is the vector diameter of the point (X, Y) relative to the origin O, the numerator is the sum of the projection radiation power of the center wavelength lambda 1 of each point and the vector multiplication of the direction of the point, and the denominator is the sum of the projection radiation power of the center wavelength lambda 1 of each pointI.e. the direction vector of the center of gravity of the projection radiation power with the center wavelength lambda 1 of each point.
Step 602, similarly calculating the direction vector of the projection radiation power center with the center wavelength lambda 2
Step 603, calculating a vector diameter r ce of the center of gravity position of the arc column by using two direction vectors, wherein the vector diameter r ce is as follows:
In step 604, the pixel coordinate corresponding to the vector r ce is (X ce,Yce), and x=x ce is selected as the luminance center line of the arc column.
Step 605, comparing the values of (X right-Xce) and (X ce-Xleft), taking the minimum value of X arc, and redefining the projection radiation power of the central wavelengths lambda 1 and lambda 2 And/>
X∈[Xce-Xarc,Xce+Xarc],Y∈[Ycath,Yano]。
Step 606, setting an order N Abel of the Abel inverse transform, wherein the value represents the number of equivalent circles dividing the arc plane after x=x ce is taken as the brightness center of the arc column.
Step 607, utilizing the redefined projected radiation powerAnd/>Calculate projection radiance matrix/>And/>
Is provided with
Wherein n=n Abel,m＝Yano-Ycath;
if the calculated coordinates are not integers, adopting a linear fitting method to take the projection radiation power value according to the coordinate values.
Step 608, for projection radiation brightness matrixAnd/>Performing Abel inverse transformation;
And/> A radiation power distribution matrix with central wavelengths of lambda 1 and lambda 2 inside the curved contact arc; wherein T N is a coefficient matrix of N Abel×NAbel, and is obtained through table lookup.
And step seven, calculating by using a colorimetric method to obtain an electron temperature and electron density distribution result.
For radiation power distribution matrixAnd/>The following calculation is performed for each element of (a):
electron temperature T e(gij) is calculated as follows:
h is the Planck constant 6.62607X -34 J.s; c is the speed of light; k B is boltzmann constant 1.38065 ×10 - 23J·K-1;
electron density n e(hij) is calculated as follows:
k is a constant, e is an electron quantity of 1.6X10 -19C,ε0 is a dielectric constant of 8.85419X 10 -12C·v-1·m-1, c is a light velocity of 2.99793X 10 8m·s-1,me is a mass of 9.10956X 10 -31 kg of electrons,/> Is the correction factor of bremsstrahlung, i.e., biberman, and the hydrogen-like atoms selected in this example can be approximately 1.
Then the electron temperature profile T e(gij) and electron density profile n e(hij) of the arc in the sinusoidal contact gap are obtained).
Examples:
the continuous spectrum radiation of the switching arc includes bremsstrahlung and composite radiation; bremsstrahlung is electromagnetic radiation emitted during the process of electron collision or change of kinetic energy when passing through ions, and compound radiation refers to the energy radiated during the process of electron capture by ions. In contrast to bremsstrahlung, the composite radiation is very weak in the arc, and can be ignored.
The expression of bremsstrahlung is as follows:
The radiation power emitted by a plasma having an electron temperature of T e per unit volume of E λ at a unit solid angle at a unit length interval of wavelength λ is expressed in terms of electron density in terms of unit w·m -4·Sr-1.ne and in terms of unit m -3.
The arc is considered to be symmetrically distributed in a columnar shape, and the light transmittance is good because the density of the plasma is relatively thin. Let a certain horizontal plane of arc radial radiation power distribution be E λ (r), I (x) be the projected radiation power received by the sensor in a certain direction (set as y-axis forward direction), where r is the arc radius, as shown in fig. 2. Meanwhile, taking the bandpass effect of the optical device and the actual CCD sensor on visible light into consideration, let V (x) be the digital quantity converted by the CCD sensor according to the received radiation power, then there are
Where K ad is the analog-to-digital conversion coefficient and G is the attenuation coefficient of the radiation power through the optical system. GAMMA is a GAMMA correction coefficient representing the nonlinear processing of incident light by a CCD digital imaging system for image display, and can be set in a camera. Lambda H and lambda L are the upper and lower cut-off limits of the visible light band centered on lambda. S r represents the area of the observed point corresponding to the CCD pixel, omega E represents the solid angle of the radiation of the measured object, and Q (lambda) is the spectral response curve of the optical element and the CCD sensor.
Since the diameter of the observed point is smaller than the distance from the observed point to the lens and the area of the observed point corresponding to the CCD pixel, and the spectral characteristics of the optical filter are approximately rectangular, the solid angle ΔΩ E, the area ΔS and the wavelength difference Δλ (λ H-λL) can be considered to be very small, Q (λ) can be approximately a constant Q, and the symmetry of E λ (r) can be considered, so that the formula (2) can be simplified as follows:
Wherein the method comprises the steps of
P＝K[G·Q·Δλ·ΔS·ΔΩ]γ (4)
For the function in columnar symmetrical distribution, for conveniently solving E λ (r), abel transformation is carried out on the formula (3) to obtain:
Equation (5) is solved by using an Abel linearization integration method, and the arc cross section in columnar distribution is subdivided into N concentric rings with equal widths, and the values on each ring are approximately equal, as shown in figure 2.
The projection radiation power I (x k) is now the weighted sum of E λ (r) over all circles in the positive direction along the y-axis, i.e.:
Matrix S ik is a weighted value matrix, each value S ik in the matrix represents the contribution of E λ (r) on the ith ring to the kth I (y k), and the matrix T ki is obtained by inverting the upper triangular matrix S ik, so that E λ(ri with radial distribution can be obtained):
The first expression brought in (3) is available:
If the constants P and gamma are known, the radial radiation power distribution E λ(ri can be calculated from the digital quantity V (y) acquired by the actual CCD camera system.
In (1), T e is distributed in the index term and the coefficient term, and n e is only present in the coefficient term, and by using this feature, n e can be eliminated first, and then n e can be obtained by taking T e into the radiation power formula. The electron temperature T e is determined using the radiation powers of the two center wavelengths. Setting radial radiation power in two wave bandsAnd/>Can be expressed as:
In combination (1), the electron temperature T e(ri is obtained by dividing the two formulae in formula (9):
and then substituting T e(ri) into any one of the formulas (9) to obtain electron density n e(ri), namely:
In order to accurately and effectively acquire the radiation power of two central wavelengths, the arc light of the arc is measured by adopting a mode of matching a color CCD (Charge-Coupled Device) high-speed camera with a double-peak narrow-band filter.
In the image shot by the color CCD camera, each pixel corresponds to R, G, B tristimulus values, so that more than two types of radiation power superposition results with center wavelengths can be provided, and after the photosensitive characteristics of the camera are obtained, the radiation power with two more accurate center wavelengths can be obtained by matching with the filtering effect of the double-peak narrow-band filter. The RGB three-color response curve of the color high-speed camera Phantom v7.3 used in the invention is shown in FIG. 3, the wavelength corresponding to the peak value of the response curve is R color at the highest, G color in the middle and B color at the lowest.
As can be seen by analyzing the three-color response curves of the camera, the red R response curve and the blue B response curve have the highest degree of distinction, and the response amplitudes of other colors at the respective response peaks are lower; therefore, the two selected center wavelengths lambda 1、λ2 are 451nm and 635nm respectively, and the screening of the radiation power of lambda 1、λ2 at two wavelengths is realized by using a bimodal narrow-band filter, and the parameter characteristics of the bimodal filter are shown in table 1.
Table 1 optical parameters of bimodal filters
In order to facilitate connection with the lens of the high-speed camera, the optical filter is mounted in an adapter ring which can be screwed with the lens.
The integral of the radiation power at two central wavelengths along the Y-axis direction is respectively as follows, which is set at the observation point corresponding to a pixel with the position of (X, Y) in the CCD of the cameraAnd/>Then there is
R (X, Y), G (X, Y) and B (X, Y) are RGB tristimulus values corresponding to the pixel, and can be obtained from an 'RAW' format file recorded by a camera, wherein the RAW format file of the camera is original data of converting captured light source signals into digital signals by a CMOS or CCD image sensor, and the GAMMA coefficient GAMMA in an optical system is set to be 1.0 for simplifying calculation and analysis processes.And/>The transmittance of the filter at two center wavelengths lambda 1、λ2, respectively. /(I)/>The photoelectric response coefficients of the radiation energy with the center wavelengths lambda 1 and lambda 2 on the R, B, G three-color pixel are obtained through a camera parameter manual. /(I)And/>Is the analog-to-digital conversion scaling factor with center wavelengths lambda 1 and lambda 2. Any two equations in the simultaneous equation (12) can be solved to obtain/>And/>In the solving process, three equation sets of R and G, R and B and G and B are simultaneously solved in a distribution mode, and the average value of the results is obtained, so that errors generated in the calculating process and an optical system can be reduced.
Analog-to-digital conversion scaling factor for each optical channel when measuring electron temperature and electron density using equation (3)And/>Unknown, first should be calibrated by a standard temperature source. The tungsten strip lamp is a radiation source using tungsten strip as heating element, and its brightness temperature is a single value function of energizing current in a certain wavelength range. The optical channel is calibrated by adopting a tungsten strip lamp, I (lambda) in the formula (12) is replaced by monochromatic radiation intensity of the tungsten strip lamp with the temperature T at the wavelength lambda, and the expression is as follows:
Wherein c 1 and c 2 are respectively a blackbody first radiation constant and a blackbody second radiation constant, the values of which are 2hc 2 and hc/k B, respectively, h is Planck constant, c is light velocity, k B is Boltzmann constant, and the formula (12) has
Wherein R (T), G (T) and B (T) are RGB tristimulus values corresponding to a tungsten zone center pixel in a tungsten zone lamp image; i W(T,λ1) is the radiation power of the tungsten band lamp at its brightness temperature in the wavelength range lambda 1; i W(T,λ2) is the radiation power of the tungsten band lamp at its brightness temperature in the wavelength range lambda 2; And/> The transmittance of the filter at two center wavelengths lambda 1、λ2; /> Is the photoelectric response coefficient of the radiant energy at the center wavelengths lambda 1 and lambda 2, respectively, on the R, B, G three-color pixel.
When the arc experiment is carried out, the aperture, focal length, resolution, shooting speed and distance between the camera and a shooting target are kept to be the same as those of the tungsten strip lamp correction experiment.
When the tungsten strip lamp is used for correction, the constant direct current power supply of the tungsten strip lamp is ensured, and the tungsten strip lamp is continuously electrified for more than half an hour under the current supply, so that the tungsten strip lamp and the environment are in a heat balance state. The linearity of the correction coefficient obtained by the least square method is higher, which shows that the radiation brightness input by the two channels and the digital quantity output by the two channels are close to linear relation, and the effectiveness of the deduction process and the simplification process of the formula is proved, as shown in table 2.
TABLE 2 analog-to-digital conversion scaling factor and linearity for optical channels
For sinusoidal contacts, the shape of the arc column is curved, and the shape of the arc column is not columnar arc under the flat contact, so that the Abel transformation cannot be directly performed, as shown in fig. 4. If the arc irradiance data in the sinusoidal contact gap is "flattened" directly, larger calculation errors will occur, which are caused by the plasma emission process that ignores the arc. The electric field direction at any position of the surface of the curved contact electrode is the normal direction of the position, the normal direction is the center direction of the plasma to the gap jet flow, and the brightness intensity of the arc plasma radiation is in positive correlation with the plasma density, so that the arc radiation brightness in the sinusoidal curved contact gap is converted.
Establishing a two-dimensional rectangular coordinate system in an arc image, taking a pixel as a minimum scale unit, taking a pixel where a sinusoidal contour starting point of a sinusoidal curved surface contact cathode is located as an original point, taking the horizontal direction of the arc image as an x-axis, the vertical direction of the arc image as a Y-axis, a cathode surface contour line function as Y C and an anode surface contour line function as Y A, wherein the two-dimensional rectangular coordinate system is formed by the steps of
A g is a pixel value corresponding to the bending amplitude of the curved contact in the arc image, T g is a pixel value corresponding to one bending period, and D gap is a pixel value corresponding to the contact opening distance.
And carrying out rectangular space transformation on projection radiation power data of the sinusoidal contact gaps by utilizing the shape characteristics of the sinusoidal contact expressed by the contour line function, and finally, completely transforming the projection radiation power data which are originally distributed in a bending way into rectangular projection radiation power data. Corresponding to the two central wavelengths lambda 1 and lambda 2, the projection radiation power distribution function can be obtained respectivelyAnd/>
Since the center position of the arc column is required to be specified for the shot arc image to perform the subsequent Abel transformation, the arc image is obtained byAnd/>Respectively calculating the brightness centers of two arc columns with the central wavelengths of lambda 1 and lambda 2, and taking the x-axis coordinate of the average value as the brightness center line of the arc column; by comparing the projection radiation power distribution function/>And/>The difference between the left boundary coordinate value and the right boundary coordinate value of the arc column brightness central line is taken as a minimum value of X arc, and the projection radiation power/>, of the central wavelengths lambda 1 and lambda 2, is redefinedAnd/>
The order N Abel of the Abel inverse transform is set as the number of equivalent circles dividing the arc plane.
By means ofAnd/>Calculate projection radiance matrix/>And/>And performing Abel inverse transformation to obtain a radiation power distribution matrix/>, with central wavelengths of lambda 1 and lambda 2, inside the curved contact arcAnd/>Matrix/>And/>The electron temperature distribution case T e(gij) and the electron density distribution case n e(ri) are calculated separately).
By using the method, the plasma parameter diagnosis is carried out on the sinusoidal curved surface contact made of copper with the bending amplitude of 3mm, the bending period of 2 and the contact diameter of 40mm, and the electron temperature and electron density diagnosis results are shown in fig. 6 and 7. The diagnostic time was 3mm, and the arc current amplitude was 5kA.
The plasma parameter amplitude obtained by the method is similar to the results obtained by other measuring means, and the parameter distribution conditions of the vicinity of the arc cathode and anode and the arc column accord with the common arc microcosmic rule, thereby explaining the effectiveness of the method. The arc plasma parameter distribution characteristics under the sinusoidal contact obtained by the method can be used for guiding the structural parameter design of the sinusoidal contact.
Claims (5)
1. A method for diagnosing parameters of arc plasma under a sinusoidal contact is characterized by comprising the following specific steps:
Firstly, setting a GAMMA correction coefficient, and carrying out parameter calibration on an optical system formed by matching a color CCD camera with a bimodal narrowband filter with center wavelengths of lambda 1 and lambda 2 by using a tungsten band lamp; shooting the arc light under the sinusoidal curved contact by using an optical system after calibrating parameters;
The parameter calibration means: analog-to-digital conversion scaling factor for each optical channel And/>Calibrating through a standard temperature source;
The calculation formula is as follows:
Wherein R (T), G (T) and B (T) are RGB tristimulus values corresponding to a tungsten zone center pixel in a tungsten zone lamp image; i W(T,λ1) is the radiation power of the tungsten band lamp at its brightness temperature in the wavelength range lambda 1; i W(T,λ2) is the radiation power of the tungsten band lamp at its brightness temperature in the wavelength range lambda 2; And/> The transmittance of the filter at two center wavelengths lambda 1、λ2; /> The photoelectric response coefficients of the radiation energy with the center wavelengths of lambda 1 and lambda 2 on the R, B, G three-color pixel element are respectively;
Then, the upper computer reads the 'RAW' format file to obtain RGB tristimulus values corresponding to arc light in a sinusoidal curve contact gap, obtains arc radiation intensity data with center wavelengths of lambda 1 and lambda 2, further determines the position, the opening distance and the arc area of the anode and cathode of the sinusoidal curve contact, establishes an arc image coordinate system, and calculates a contour line function of the surface of the sinusoidal curve contact;
Then, the projected radiation power data of the sinusoidal contact gap is subjected to rectangular space transformation by utilizing the shape characteristics of the sinusoidal contact expressed by the contour line function, and two central wavelengths lambda 1 and lambda 2 are recorded, and corresponding projected radiation power distribution functions J λ1 (X, Y) and Selecting the center position of the arc column by using the two distribution functions; performing data interpolation according to the order of the Abel inverse transformation, and performing the Abel inverse transformation;
The rectangular space transformation specifically comprises the following steps:
i) Calculating the P coordinate (x P,yP) of any pixel point on the cathode surface by using the contour line function Y C of the cathode surface;
Let the tangent equation be l 1 and the normal equation be l 2, if there is
Representing the slope of the cathode contour function at point P;
II), calculating the center position G point coordinate (x G,yG) when the plasma jet of the cathode spot at the P point reaches the anode;
the method comprises the following steps: firstly, the direction of the plasma jet of the cathode spot at the point P is along the direction of l 2, and the intersection point G of l 2 and the anode surface contour line function Y A is the central position when the plasma flow generated at the point P reaches the anode, and the coordinate (x G,yG) of the point G is obtained by the equation of the simultaneous l 2 and Y A;
III), connecting the point P with the point G, dividing the line segment PG into N equidistant line segments, and enabling the projection radiation power of each point on the line segment PG to be a column corresponding to the rectangular projection radiation power data;
IV), repeating the steps for each pixel point on the cathode surface of the sinusoidal curved contact, and finally, completely converting the original curved distributed projection radiation power data into rectangular projection radiation power data;
Distribution function And/>Wherein X, Y is an integer coordinate value, X epsilon [ X left,Xright],Y∈[Ycath,Yano];Xleft、Xright ] is a left boundary and a right boundary coordinate value of projection radiation power data of the arc respectively, and Y cath、Yano is a cathode boundary and an anode boundary coordinate value of the projection radiation power data of the arc respectively;
And finally, calculating by using a colorimetry to obtain an electron temperature and electron density distribution result.
2. The method of claim 1, wherein the arc radiation intensity data with center wavelengths of λ 1 and λ 2 is projected radiation powerAnd/>
The calculation formula is as follows:
The projection radiation power of a pixel position (X, Y) in the CCD camera at the center of two wavelengths along the Y-axis direction is respectively set as the observation point corresponding to a pixel And/>Then there is
Wherein R (X, Y), G (X, Y) and B (X, Y) are RGB tristimulus values corresponding to the pixel.
3. The method for diagnosing arc plasma parameters under a sinusoidal contact according to claim 1, wherein an arc image coordinate system is established, and a contour function of the sinusoidal contact surface is calculated; the method comprises the following steps:
Firstly, a two-dimensional rectangular coordinate system is established in an arc image, a pixel is used as a minimum scale unit, a pixel where a sinusoidal contour starting point of a sinusoidal curved surface contact cathode is located is used as an original point, the horizontal direction of the arc image is used as an x-axis, and the vertical direction of the arc image is used as a y-axis;
then, the cathode surface contour function is calculated as Y C and the anode surface contour function is calculated as Y A, then there are
A g is a pixel value corresponding to the bending amplitude of the curved contact in the arc image, T g is a pixel value corresponding to one bending period, and D gap is a pixel value corresponding to the contact opening distance.
4. The method for diagnosing parameters of arc plasma under a sinusoidal contact as recited in claim 1, wherein the specific process of selecting the center position of the arc column and performing the Abel inverse transformation is as follows:
step 601, calculating a direction vector of a projected radiation power center with a center wavelength lambda 1
Wherein r (X, Y) is the vector diameter of the point (X, Y) relative to the origin O, the numerator is the sum of the projection radiation power of the center wavelength lambda 1 of each point and the vector multiplication of the direction of the point, and the denominator is the sum of the projection radiation power of the center wavelength lambda 1 of each pointNamely, the direction vector of the center of the projection radiation power gravity center with the center wavelength lambda 1 of each point;
step 602, similarly, calculating the direction vector of the projection radiation power center with the center wavelength lambda 2
Step 603, calculating a vector diameter r ce of the center of gravity position of the arc column by using two direction vectors, wherein the vector diameter r ce is as follows:
Step 604, the pixel coordinate corresponding to the vector r ce is (X ce,Yce), and x=x ce is selected as the arc column brightness center line;
Step 605, comparing the values of (X right-Xce) and (X ce-Xleft), taking the minimum value of X arc, and redefining the projection radiation power of the central wavelengths lambda 1 and lambda 2 And/>
X∈[Xce-Xarc,Xce+Xarc],Y∈[Ycath,Yano]；
Step 606, setting an order N Abel of Abel inverse transformation, wherein the value represents the number of equivalent circles for dividing an arc plane after x=X ce is taken as the brightness center of an arc column;
step 607, utilizing the redefined projected radiation power And/>Calculate projection radiation brightness matrixAnd/>
Is provided with
Wherein n=n Abel,m＝Yano-Ycath;
If the calculated coordinates are not integers, adopting a linear fitting method to take the projection radiation power value according to the coordinate values;
Step 608, for projection radiation brightness matrix And/>Performing Abel inverse transformation;
And/> A radiation power distribution matrix with central wavelengths of lambda 1 and lambda 2 inside the curved contact arc; wherein T N is a coefficient matrix of N Abel×NAbel, and is obtained through table lookup.
5. The method for diagnosing parameters of arc plasma under a sinusoidal contact as recited in claim 1, wherein the specific process of calculating the electron temperature and electron density distribution by colorimetry is as follows:
For radiation power distribution matrix And/>The following calculation is performed for each element of (a):
electron temperature T e(gij) is calculated as follows:
h is the Planck constant; c is the speed of light; k B is boltzmann constant;
electron density n e(hij) is calculated as follows:
k is a constant, e is an electron charge, ε 0 is a dielectric constant, c is a speed of light, m e is a mass of electrons,/> Is the correction factor of bremsstrahlung, i.e., biberman factor;
Then the electron temperature profile T e(gij) and electron density profile n e(hij) of the arc in the sinusoidal contact gap are obtained).
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