Pulsed arc plasma modeling method and equipment based on high-speed images

Abstract

The present invention provides a method and device for modeling pulse arc plasma based on high-speed images. The method includes: collecting pulse arc image data, voltage and current; calculating the brightness center position and pulse arc calculation matrix; gridding the pulse arc and obtaining a three-dimensional distribution of pulse arc plasma density; calculating the electron migration speed of each horizontal layer; calculating the three-dimensional distribution of conductivity and obtaining the three-dimensional distribution of electron collision frequency and electron temperature; calculating the total energy of pulse arc particles and the total macroscopic energy of pulse arc ， When the difference between the total energy of the particles and the total macroscopic energy meets the convergence condition, the modeling is completed. This solution has a simple modeling method, more realistic and effective model parameters, and is time-varying, making it widely applicable.

Description

Technical Field

[0001] The present invention relates to the fields of plasma modeling and simulation, image data processing and pulse arc data modeling, and in particular to a method for constructing a three-dimensional transient plasma model of a pulse arc based on high-speed images and related equipment. Background Art

[0002] Arc discharge pulses are widely used, for example, in plasma processing, materials processing, and welding. In plasma processing, arc discharge pulses can be used for surface treatment, cleaning, and modification; in materials processing, arc discharge pulses can be used for cutting, drilling, and marking; and in welding, arc discharge pulses can be used for welding and cutting. Each of these applications requires arc discharge pulses to generate high-energy plasma to achieve specific processing effects. Modeling and analyzing pulsed arcs is an important means of exploring the mechanisms underlying their characteristics and provides theoretical support for precise control of pulsed arcs.

[0003] In the past, when modeling pulsed arcs, finite element analysis methods such as magnetohydrodynamic theory were used. Although three-dimensional data could be obtained, the calculation model was complex, consuming huge computing resources, and a large number of parameters could not be accurately obtained during the process. In addition, most models were steady-state models or quasi-steady-state models, making it difficult to obtain continuous changes within the pulse cycle, which contradicts the rapid changes in pulsed arc current. For example, the Mayer model or the Cauchy model, although the calculation method was simple, the calculated model was a one-dimensional mean model, which could not obtain microscopic parameters such as plasma density and plasma temperature. Moreover, both of the above methods are divorced from the actual occurrence and development process of the pulsed arc, limiting the accuracy and effectiveness of the model.

[0004] Therefore, how to establish an accurate and effective three-dimensional transient plasma model of pulsed arc is an urgent problem to be solved and has great practical application significance. Summary of the Invention

[0005] In response to the shortcomings of the prior art, the present invention proposes a pulse arc plasma modeling method and device based on high-speed images. Specifically, the present invention discloses the following technical solutions:

[0006] In one aspect, the present invention provides a method for modeling pulsed arc plasma based on high-speed images, the method comprising:

[0007] Step 1: Initialize a high-speed camera for acquiring high-speed images and determine the pulse arc frequency;

[0008] Step 2: Collect multiple pulse arc image data within the pulse period, and simultaneously collect the voltage and current at the time of image data collection within the pulse period;

[0009] Step 3: Determine the pulse arc coordinate origin based on the pulse arc image data, and determine the coordinate system and the effective brightness range matrix with the pulse arc coordinate origin as the origin; perform mean processing on the effective brightness range matrix to obtain the pulse arc calculation matrix;

[0010] Step 4: Divide the pulse arc into a three-dimensional structure consisting of multiple concentric rings in the horizontal direction and multiple horizontal layers in the vertical direction, so as to perform three-dimensional gridding on the pulse arc; obtain the three-dimensional distribution of the pulse arc plasma density based on the pulse arc calculation matrix and the initial value of the plasma density;

[0011] Step 5: Calculate the electron migration velocity of each horizontal layer based on the three-dimensional distribution of pulse arc plasma density;

[0012] Step 6: Combine the results of step 5 to calculate the three-dimensional distribution of conductivity and obtain the three-dimensional distribution of electron collision frequency and electron temperature;

[0013] Step 7: Combine the results of step 6 to calculate the total energy of the pulse arc particles from the perspective of microscopic particles. W total , the total energy of the particle W total Includes total ion energy and total electron energy;

[0014] Step 8: Combine the results of step 6 to calculate the total macroscopic energy of the pulse arc W 等离子体 , the macroscopic total energy W 等离子体 Calculation based on energy balance and time cumulative effect;

[0015] Step 9: Determine the total energy of the particle W total and macroscopic total energy W 等离子体 Whether the percentage of the difference meets the convergence condition, if it does, then end; if not, adjust the initial value of the plasma density and return to step 4 until the convergence condition is met.

[0016] Preferably, in step 3, the pulse arc coordinate origin is determined by:

[0017] First calculate the brightness center position ( C x , C y ):

[0018] ;

[0019] ;

[0020] in,H arc ( k , w ) represents the first k Column, No. w the brightness of the row; X max is the maximum horizontal pixel coordinate of the pulse arc image, Y max is the maximum value of the longitudinal pixel coordinate of the pulse arc image;

[0021] by( C x , Y 阴 ) is the pulse arc coordinate origin, where, Y 阴 is the longitudinal coordinate of the upper surface of the cathode of the pulse arc emission source.

[0022] Preferably, in step 3, H arc ( k , w ) is calculated as follows:

[0023] ;

[0024] Right now H arc ( k , w ) represents the pulse arc image k Column, No. w The brightness of the row. R ( k , w )、 G ( k , w )、 B ( k , w ) represents the RGB three-color value matrix of each pulse arc image.

[0025] Preferably, in step 3, the pulse arc calculation matrix is ​​determined as follows:

[0026] First, in the coordinate system with the pulse arc coordinate origin as the origin, determine the effective brightness range matrix of the pulse arc J ( b , j ), b ∈[- H 边 ,1]∪[1, H 边 ], j ∈[1, H纵 ],in, H 纵 Indicates the number of pixels from the upper surface of the cathode of the pulse arc emission source to the lower surface of the anode of the pulse arc emission source in the longitudinal direction; H 边 Indicates that the pulse arc coordinate origin is the center ， Brightness decay to alpha W max The maximum horizontal coordinate of the pixel; W max express H arc ( k , w ) in the image; α represents the attenuation ratio; J ( b , j ) indicates the b Column, No. j The brightness value of the row; b、j Take an integer to represent the element subscript;

[0027] Secondly, perform mean processing on the effective brightness range matrix to obtain the pulse arc calculation matrix:

[0028] K ( i , j ) = [ J (- i , j )+ J ( i , j )]´0.5;

[0029] in, , i ∈[1, H 边 ], j ∈[1, H 纵 ] .

[0030] Preferably, in step 4, during the three-dimensional gridding process, the number of horizontal layers is H 纵 , the number of concentric rings is H 边 ;

[0031] The electron density matrix N( i , j ) represents the three-dimensional distribution of pulse arc plasma density, N( i , j ) is calculated as follows:

[0032] , i ∈[1, H 边 ], j ∈[1, H 纵 ];

[0033] in, n 0 is the initial value of plasma density, T abel for H 边 × H 边 Abel coefficient matrix, K( i , j ) is the pulse arc calculation matrix.

[0034] Preferably, in step 5, the electron migration speed distribution matrix v 迁 Represents the electron migration speed of each horizontal layer, among which the vertical j Electron migration speed in horizontal layers v 迁 ( j ) is calculated as:

[0035] ;

[0036] Among them, N ( i , j ) represents the electron density matrix, which represents the i Concentric rings, j electron density of horizontal layers; S ( i ) is the i The area of ​​the concentric rings, e is the electron charge, I arc It is the arc current corresponding to the moment when the pulse arc image exposure is generated.

[0037] Preferably, in step 6, the three-dimensional distribution of conductivity is reflected by the conductivity at various locations inside the pulse arc, and the conductivity at various locations inside the pulse arc is calculated as follows:

[0038] ;

[0039] Among them, δ ( i , j ) indicates the j The horizontal layer i The conductivity of the concentric rings, Δ l is the actual height corresponding to the length of each pixel in the z-axis direction, N ( i , j) represents the electron density matrix, v 迁 ( j ) is the longitudinal j The electron migration velocity distribution matrix of the horizontal layer, e is the electron charge, Δ U is the voltage drop of each vertical horizontal layer. l The value is equal to the vertical distance between the lower surface of the pulse arc emission source anode and the upper surface of the pulse arc emission source cathode and H 纵 The ratio, H 纵 Indicates the number of pixels from the upper surface of the cathode of the pulse arc emission source to the lower surface of the anode of the pulse arc emission source in the longitudinal direction.

[0040] Preferably, Δ U The calculation is as follows:

[0041] ;

[0042] in, U arc The arc voltage at the moment corresponding to the pulse arc image exposure is generated, U 阴极鞘层 is the cathode sheath voltage of the pulse arc emission source, U 阳极鞘层 is the anode sheath voltage of the pulse arc emission source. U 阴极鞘层 and U 阳极鞘层 The value of is related to the electrode material and has little to do with the arc current and frequency. It can be obtained by looking up the table.

[0043] Preferably, in step 6, the three-dimensional distribution of the electron collision frequency and the electron temperature is obtained by calculating the electron collision frequency and the electron temperature based on the following conductivity characteristics:

[0044] ;

[0045] in, f ei ( i , j ) is the electron collision frequency, lnΛ is the Coulomb logarithm, m e is the electron mass, Z i is the relative charge number of the plasma, T e ( i , j ) is the electron temperature.

[0046] Preferably, in step 7, the total energy of the pulse arc particles W total The calculation method is:

[0047] ;

[0048] in, i ∈[1, H 边 ], j ∈[1, H 纵 ], N ( i , j ) represents the electron density matrix, T e ( i , j ) is the electron temperature, Z i is the relative charge number of the plasma, V arc ( i , j ) represents the first j The horizontal layer i The volume of the concentric rings can be combined Figure 5 The pulse arc structure diagram and the actual size represented by each pixel are calculated.

[0049] Preferably, in step 8, the pulse arc macroscopic total energy W 等离子体 The calculation method is:

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] in, W 等离子体 ( t ) is the total energy of the pulse arc at the current moment t, W 等离子体 ( t -1) is the total energy of the pulse arc at the previous moment, Δ W 等离子体 ( t ) is the energy change within this time step, W input ( t ) is the input energy, W loss( t ) is the lost energy, W f ( t ) is the energy lost by the particle, W s ( t ) is the radiation loss energy, Δ t is the time step value, U arc ( t ) is the arc voltage at the current moment t, U 阴极鞘层 is the cathode sheath voltage of the pulse arc emission source, U 阳极鞘层 is the anode sheath voltage of the pulse arc emission source.

[0055] Preferably, the particles lose energy W f ( t ) is solved as follows: the statistical range of ion loss energy includes the layer corresponding to the upper surface, the layer corresponding to the lower surface and the layer corresponding to the side of the cylinder, and the particle loss energy W f ( t ) is calculated as follows:

[0056] ;

[0057] Among them, Shell represents the range composed of the layer corresponding to the upper surface of the pulse arc, the layer corresponding to the lower surface, and the layer corresponding to the side of the cylinder. is the electron flux density in the outermost layer of the pulse arc, is the ion flux density in the outermost layer of the pulse arc, T e ( i , j ) is the electron temperature, Indicates the surface area corresponding to the outermost layer of the pulse arc.

[0058] Preferably, W s ( t ) according to the energy loss W loss ( t ) is calculated as 15% of the

[0059] On the other hand, the present invention also provides a pulse arc plasma modeling device based on high-speed images, which includes: a timing control module, a pulse arc oscillation circuit, a high-speed camera, a host computer and a voltage and current measurement device;

[0060] The pulse arc oscillation circuit generates a pulse arc based on a timing control module, the high-speed camera is used to collect multiple pulse arc image data within a pulse period and upload them to a host computer, and the voltage and current measuring device is used to collect the voltage and current at the time of image data collection within the pulse period and upload them to the host computer;

[0061] The host computer includes at least a processor and a memory, and the processor calls computer instructions in the memory to execute the pulse arc plasma modeling method based on high-speed images as described above.

[0062] Preferably, the pulse arc oscillation generating circuit is composed of a pulse energy circuit, an arc striking circuit, an absorption protection circuit and a pulse arc emission source.

[0063] Preferably, the pulse energy circuit consists of a resistor R 0. Inductor L 1 and capacitor C 0 and bidirectional triode thyristor VT 0 structure, in which the bidirectional triode thyristor VT 0 is responsible for the conduction control of the control circuit; bidirectional triode thyristor VT 0 T1 pole connection inductance L One end of 1; the inductor L The other end of 1 is connected to the capacitor C 0 positive electrode; the capacitor C 0 negative connection resistance R 0 end; the resistor R The other end of 0 is grounded. VT The T2 pole of 0 is connected to the positive pole of the pulse arc emission source.

[0064] Preferably, the arc striking circuit is composed of an electrolytic capacitor C 1. Current limiting resistor R 1. Thyristor VT1 and power diode VD1; the positive electrode of thyristor VT1 is connected to the current limiting resistor R One end of 1; current limiting resistor R The other end of 1 is connected to the electrolytic capacitor C 1's positive electrode and the negative electrode of the power diode VD1; electrolytic capacitor C The cathode of thyristor VT1 and the anode of the power diode VD1 are grounded. The cathode of thyristor VT1 is connected to the anode of the pulse arc emission source.

[0065] Preferably, the absorption protection circuit includes a capacitor C 2. Resistance R 2 and varistor R v ;resistance R 2 and capacitor C 2 series, varistor Rv With resistor R 2 and capacitor C 2 series circuits are connected in parallel, i.e. varistor R v Connect one end of the resistor R 2 Keep away from the capacitor C 2, one end of the varistor R v The other end of the capacitor is grounded; C 2 Keep away from the resistor R One end of 2 is grounded.

[0066] Compared with the existing technology, this solution has at least the following advantages:

[0067] 1. The modeling method is simple and can obtain the plasma density, temperature and electron migration velocity distribution results of the three-dimensional pulse arc without using the finite element analysis method;

[0068] 2. The modeling process of this model is based on the real data of arc images, pulse arc voltage and current, so the model parameters are more realistic and effective;

[0069] 3. This model is time-varying and is a dynamic model within the entire cycle of the pulse arc. The obtained microscopic parameters also change dynamically. Theoretically, as long as the shooting speed is fast enough and the voltage and current sampling accuracy is high enough, even if the pulse arc frequency is very high, a non-steady-state three-dimensional model can be established. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0071] Figure 1 A schematic diagram of a model building method flow chart according to an embodiment of the present invention;

[0072] Figure 2 Schematic diagram of the structure of a pulse arc generation and measurement system according to an embodiment of the present invention;

[0073] Figure 3 This is a timing diagram of a pulse arc generation measurement system according to an embodiment of the present invention;

[0074] Figure 4 The principle of generating high-speed pulse arc images in a certain horizontal direction according to an embodiment of the present invention;

[0075] Figure 5Schematic diagram of a multi-layer structure of a pulse arc according to an embodiment of the present invention;

[0076] Figure 6 This is a schematic diagram of a 3kA pulse arc image according to an embodiment of the present invention;

[0077] Figure 7 Schematic diagram of the three-dimensional distribution of electron density corresponding to a 3kA pulse arc according to an embodiment of the present invention;

[0078] Figure 8 Schematic diagram of three-dimensional conductivity calculation results corresponding to a 3kA pulse arc according to an embodiment of the present invention;

[0079] Figure 9 This is a schematic diagram of the electron migration velocity along the z-axis corresponding to a 3kA pulse arc according to an embodiment of the present invention;

[0080] Figure 10 Schematic diagram of the three-dimensional distribution of electron temperature corresponding to a 3kA pulse arc according to an embodiment of the present invention. DETAILED DESCRIPTION

[0081] The following describes embodiments of the present invention in detail with reference to the accompanying drawings. It should be understood that the embodiments described are only a portion of the embodiments of the present invention, and not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0082] Those skilled in the art should be aware that the following specific embodiments or implementations are a series of optimized configurations listed in the present invention to further explain the specific content of the invention, and these configurations can be combined or used in conjunction with each other, unless the present invention explicitly states that some or a specific embodiment or implementation cannot be combined or used in conjunction with other embodiments or implementations. At the same time, the following specific embodiments or implementations are only intended to be optimized configurations and are not to be understood as limiting the scope of protection of the present invention.

[0083] In a specific embodiment, this solution establishes a three-dimensional distributed pulse arc microscopic parameter model with time-varying characteristics based on the arc image and voltage and current parameters within the pulse arc cycle. The specific process of the modeling method is as follows: Figure 1 shown.

[0084] In this embodiment, the generation and parameter measurement of the pulse arc rely on a pulse arc generation and measurement system, which consists of a pulse arc oscillation circuit, a high-speed camera, an oscilloscope, a host computer, and a voltage and current measurement device. The circuit topology is as follows: Figure 2The timing control module is responsible for controlling the pulse arc oscillation circuit, camera, and oscilloscope action timing. The specific timing control is as follows: Figure 3 The pulse arc is generated by the pulse arc oscillation circuit. The voltage and current signals of the pulse arc are collected by an oscilloscope and uploaded to the host computer system. A high-speed camera captures high-speed images of the pulse arc. The host computer system integrates the pulse arc image with the voltage and current signals to model the pulse arc.

[0085] In a more preferred embodiment, combined with Figure 2 As shown, the pulse arc oscillation generating circuit is composed of a pulse energy circuit, an arc striking circuit, an absorption protection circuit and a pulse arc emission source.

[0086] For the pulse energy circuit, the resistor R 0. Inductor L 1 and capacitor C 0 and bidirectional triode thyristor VT 0, where bidirectional triode thyristor VT 0 is responsible for the conduction control of the control loop. VT 0 T1 pole connection inductance L One end of 1; the inductor L The other end of 1 is connected to the capacitor C 0 positive electrode; the capacitor C 0 negative connection resistance R 0 end; the resistor R The other end of 0 is grounded. VT The T2 pole of 0 is connected to the positive pole of the pulse arc emission source.

[0087] Combined with the circuit structure of the pulse energy circuit, it can be seen that the resistance R 0. Inductor L 1 and capacitor C The voltage relationship of 0 satisfies equations (1) and (2):

[0088] (1)

[0089] (2)

[0090] Among them, U c Indicates capacitance C 0 voltage, U R Indicates resistance R 0 voltage, U L Inductance L 1 voltage. When the resistance of the circuit R 0. Inductor L 1 and capacitor CWhen 0 satisfies the relationship of formula (3), the main circuit produces a non-oscillating discharge process, and the oscillating current i(t) can be described as formula (4), U 0 is the pre-charge voltage of the main circuit capacitor, ω is the angular frequency of the second-order oscillation circuit, δ is the time constant, and the calculation formulas are:

[0091] (3)

[0092] (4)

[0093] (5)

[0094] (6)

[0095] The arc striking circuit is used to generate a low-current DC arc so that the medium in the electrode gap remains conductive before the pulse current is applied. In this embodiment, a specific circuit design is used as an example. The arc striking circuit consists of a 50mF / 220V electrolytic capacitor. C 1. Current limiting resistor with a resistance of 2.5Ω R 1. It consists of 1800V / 200A thyristor VT1 and power diode VD1. The positive electrode of thyristor VT1 is connected to the current limiting resistor. R One end of 1; current limiting resistor R The other end of 1 is connected to the electrolytic capacitor C 1's positive electrode and the negative electrode of the power diode VD1; electrolytic capacitor C The cathode of 1 and the anode of the power diode VD1 are grounded. The cathode of thyristor VT1 is connected to the anode of the pulse arc emission source. When thyristor VT1 is turned on, the electrolytic capacitor C 1Through current limiting resistor R 1 discharges, allowing current to flow through the positive and negative electrodes of the pulse spectrum emitter. Power diode VD1 protects the electrolytic capacitor. The time constant of the discharge process is 125ms, and the maximum current is 80A.

[0096] For the absorption protection circuit, including capacitor C 2. Resistance R 2 and varistor R v .resistance R 2 and capacitor C 2 series, varistor R v With resistor R 2 and capacitor C 2 series circuits are connected in parallel, i.e. varistor R v Connect one end of the resistor R2 Keep away from the capacitor C 2, one end of the varistor R v The other end of the capacitor is grounded; C 2 Keep away from the resistor R One end of 2 is grounded. C 2 and resistor R 2 is used to adjust the recovery voltage rise rate d after the pulse current passes through zero U / d t , varistor R v Used to limit the amplitude of the recovery voltage. The absorption protection circuit can prevent the positive and negative electrodes of the pulse spectrum generator from being broken down, thereby avoiding the emission of unplanned spectra, and also provide voltage protection for each device in the line.

[0097] The pulse arc emission source is mainly composed of an electromagnetic action mechanism and positive and negative electrodes. The electromagnetic action mechanism is operated by a timing control module according to the preset timing logic (refer to Figure 3 As shown in the figure), to control the arc between the positive and negative electrodes.

[0098] In this embodiment, combined with the above-mentioned pulse arc generation measurement system, the overall process of the pulse arc plasma modeling method is as follows: Figure 1 As shown, the details are as follows:

[0099] STEP 1: Determine the frequency of the pulse arc and adjust the inductance of the pulse energy circuit L 1 and capacitor C 0 value; determine the current level of the pulse arc, and C 0 is charged to the preset value; arc ignition circuit capacitance C 1. Charge to 200V; set the shooting speed of the high-speed camera, adjust the camera lens so that it faces the center of the gap between the positive and negative electrodes of the pulse arc emission source, and adjust the camera aperture so that the R, G, and B values ​​of the captured arc image are all less than the maximum bit value (for example, if the camera is 8-bit, the maximum value is 255; if the camera is 16-bit, the maximum value is 65535). If the camera aperture value is adjusted to the minimum and still exceeds the maximum bit value, add a grayscale film in front of the camera lens. The grayscale film has a consistent radiation intensity attenuation percentage within the visible light range.

[0100] STEP 2: Press Figure 3 The timing logic shown in the figure is used to conduct pulse arc experiment. The host computer collects the pulse period. p pulse arc image ".RAW" format file, pThe value is determined by the pulse frequency and camera shooting speed; the oscilloscope acquires the voltage and current values ​​within the pulse arc cycle. It is understood that the specific file format of the pulse arc image can adopt other common types besides the ".RAW" format, and the file format here is not to be understood as limiting the scope of protection of the present invention.

[0101] Combine Figure 3 As shown, the timing of this embodiment is set as follows: the thyristor VT1 is triggered as the timing start signal, after time t1, the electromagnetic action mechanism in the pulse arc emission source is triggered, and the electrode gap is turned on; at time t2, the high-speed camera is triggered, and the camera CCD is started to work, and then at time t3, the bidirectional triode thyristor VT 0 triggers, the pulse arc is put into operation; at time node t4, the bidirectional triode thyristor VT 0 is turned off and the pulse arc is extinguished.

[0102] We take 3kA pulse arc as an example, and the pulse arc image obtained is as follows Figure 6 shown.

[0103] STEP 3: By reading the ".RAW" format file, the RGB three-color value matrix of each pulse arc image can be obtained, specifically the matrix R ( k , w )、 G ( k , w )、 B ( k , w ),in, k ∈[1, X max ], w ∈[1, Y max ], X max is the maximum horizontal pixel coordinate of the arc image, Y max The maximum vertical pixel coordinate of the arc image. The coordinate origin can generally be set to the lower left corner (or upper right corner) of the image. Taking a 320 (total number of columns) x 240 (total number of rows) pixel matrix as an example, the origin is the pixel corresponding to the 1st column and the 1st row, and the origin coordinates are (1,1). X max is 320, Y max is 240, then R ( k , w ) also represents the k Column, No. w The pixel corresponding to the row R value,G ( k , w )and B ( k , w ) has a similar meaning. The grayscale of each pulse arc image is calculated. In this embodiment, the calculation standard refers to the photometric calculation standard of "Photometric / Digital ITU BT.709", and the pixel position is ( k , w ) of the arc brightness pixel matrix H arc ( k , w ) is calculated as follows:

[0104] (7)

[0105] Right now H arc ( k , w ) represents the pulse arc image k Column, No. w The brightness of the row.

[0106] Since the starting position of the pulse arc is random, it is necessary to determine the pulse arc brightness center in order to select the valid data range. H arc ( k , w ), calculate the pixel position of the brightness center position as ( C x , C y ), calculated as follows:

[0107] (8)

[0108] (9)

[0109] Determine the effective brightness range of the pulse arc: The basic characteristic of the pulse arc image is that its brightness gradually decreases from the center of the arc to both sides. We first determine the pulse arc coordinate origin, and then perform subsequent pulse arc image processing in a new coordinate system with the pulse arc coordinate origin as the origin. Then the effective brightness range can be determined as follows: ( C x , Y 阴 ) is the pulse arc coordinate origin O ; The range in the longitudinal direction is the cathode (ie Figure 2 the negative electrode) to the anode (i.e. Figure 2 The number of pixels on the surface below the positive electrodeH 纵 , Y 阴 express H arc ( k , w ) corresponds to the vertical pixel coordinate of the arc area closest to the cathode upper surface; the horizontal range is (- H 边 , H 边 ), H 边 Origin O Centered ， Arc brightness decays to W max The horizontal coordinate of the pixel where the attenuation ratio is 10% (i.e., α=10%), W max Represents the arc brightness pixel matrix H arc The maximum brightness value, that is, the maximum brightness value in the pulse arc image. It can be understood here that the attenuation ratio α can be selected and changed, for example, adjusted to 8%, 15%, etc. This embodiment takes 10% as an example.

[0110] Then, the pulse arc effective brightness range matrix can be obtained J ( b , j ), b ∈[- H 边 ,1]∪[1, H 边 ], j ∈[1, H 纵 ], b 、 j is the pixel number, which is an integer and not equal to 0. From the above derivation process, it can be seen that the matrix J Each element value in represents the pixel brightness at the corresponding position. The effective brightness range matrix at this time is J Has been converted to the pulse arc coordinate origin O In the coordinate system with as the origin.

[0111] In order to reduce the impact of asymmetric distribution of pulse arc, the arc brightness of the left and right halves is averaged, that is, the origin is O The pulse arc calculation matrix covering half of the arc pulse image is obtained by taking the average brightness of two pixels symmetrical in the horizontal direction as the center. K :

[0112] K ( i ,j ) = [ J (- i , j )+ J ( i , j )]´0.5, , i ∈[1, H 边 ], j ∈[1, H 纵 ] .

[0113] like C x、 C y、 Y 阴、 H 边 If it is not an integer, it will be rounded up. i and j Refers to the matrix element number, which is the corresponding position pixel number in this embodiment. It can only be an integer, not a decimal. Taking this as an example, the pulse arc calculation matrix K The horizontal range is from 1 to H 边 Pixels, vertically from 1 to H 纵 Pixels, therefore, in this embodiment, if C x、 C y、 Y 阴、 H 边 If the number is not an integer, it will be rounded up.

[0114] STEP 4: The pulse arc can be considered as a columnar body with symmetrical distribution of characteristics along the arc center. Its contribution to the brightness of each pixel of the arc image is proportional to the cumulative value of the plasma density corresponding to the pixel along a certain direction. In this embodiment, the arc column is gridded to facilitate the subsequent calculation of the three-dimensional distribution. That is, the three-dimensional grid is divided based on the pulse arc calculation matrix in STEP 3. Figure 4 、 Figure 5 As shown, in this embodiment, the column is divided into concentric rings in the horizontal direction and grid-divided into equal-height cylinders in the vertical direction. That is, the pulse arc column can be regarded as a three-dimensional structure with m horizontal layers in the vertical direction (z-axis direction) and n concentric rings in the horizontal direction (xOy plane). In this embodiment, the grid is divided in pixels, and m is H 纵 , n is H边 , that is, after gridding, the number of concentric rings is H 边 , the number of horizontal layers is H 纵 .

[0115] In the following description, the concentric rings are numbered from the inside to the outside, starting with i Indicates the number of pulse arc cylinders from the inside to the outside. i Layer concentric rings (reference Figure 4 shown), i The value range is [1, H 边 ], j Indicates the pulse arc cylinder from bottom to top j horizontal layer, j The value range is [1, H 纵 It is understandable that the horizontal layer starting position of the pulse arc cylinder can be the uppermost or lowermost end of the pulse arc. In this embodiment, the pulse arc calculation matrix K The position corresponding to the vertical pixel coordinate of 1 is the starting position of the horizontal layer, that is, the pulse arc coordinate origin O The layer is the starting layer; in addition, the innermost layer, the first ring, can be understood as a complete circle, or as the ring excluding the point on the y-axis. These understandings do not affect the calculation and use of this solution.

[0116] In this embodiment, the pulse arc calculation matrix K ( i,j ) performs an inverse Abel transform to obtain the matrix N( i,j ), N( i,j ) is the electron density matrix, which is calculated as shown in formula (10), where T abel for H 边 × H 边 The Abel coefficient matrix can be obtained by looking up the table.

[0117] N ( i , j ) = n 0 K ( i , j ) T abel (10)

[0118] In the above formula, n 0 is the initial value of the plasma density, then the matrix is the electron density matrix of the pulse arc, where n = H 边 ,m= H 纵 ,in n The value changes from small to large, corresponding to the horizontal change from the center of the pulse arc to the surrounding area; m The value increases from small to large, corresponding to the vertical change from the cathode surface to the anode surface. i, j ) represents the first i Concentric rings, j The electron density of the horizontal layer.

[0119] Continuing to take the 3kA pulse arc in this embodiment as an example, the corresponding three-dimensional distribution results of the electron density are as follows: Figure 7 shown.

[0120] STEP 5: After 3D meshing, the pulse arc column can be regarded as a 3D structure with m layers in the longitudinal direction (z-axis direction) and n layers in the horizontal direction (xOy plane), as shown in the following example: Figure 5 shown.

[0121] Voltage drop of each vertical layer Δ U are equal, and the calculation formula is as follows:

[0122] (11)

[0123] in, U arc The arc voltage at the moment corresponding to the pulse arc image exposure is generated, U 阴极鞘层 is the cathode sheath voltage of the pulse arc emission source, U 阳极鞘层 is the anode sheath voltage of the pulse arc emission source, U 阴极鞘层 and U 阳极鞘层 The value of is related to the electrode material and has little to do with the arc current and frequency. It can be obtained by looking up the table.

[0124] According to the law of conservation of current, the current in each longitudinal layer is also equal. I arc The arc current at the corresponding moment of the pulse arc image exposure is generated. The pulse arc voltage and current data are collected by the oscilloscope and transmitted to the host computer, which interpolates them according to the pulse arc image exposure time to obtain U arc 、 I arc .

[0125] The total current value passing through is the same and can be obtained through measurement. It can be understood that the total current value is the current value of the cathode of the pulse arc emission source, and the current value of each xOy horizontal layer is equal. In this embodiment, the current density calculation formula is as follows:

[0126] (12)

[0127] in, Q(i,j) represents the current density, N(i,j) is the electron density matrix (i.e., plasma density), e is the electron charge, v 迁 ( j ) is the electron migration speed.

[0128] For a vertical number j For the horizontal layer, the current calculation formula is as follows:

[0129] (13)

[0130] in, S ( i ) is on the horizontal plane xOy, i The area of ​​the concentric rings, H 边 Indicates ( C x , Y 阴 ) as the center ， The effective brightness range is attenuated to α W max The maximum horizontal coordinate of the pixel, W max Indicates the effective brightness range J ( b , j ). According to formula (13), the vertical number can be calculated as j The electron migration speed of the horizontal layer v 迁 ( j ),Right now: .

[0131] Furthermore, we can find m Electron migration speed of the layer v 迁 ( j ), j ∈[1, m ].

[0132] Still taking the 3kA pulse arc in this embodiment as an example, the calculation results of the electron migration velocity along the z-axis are as follows: Figure 9 shown.

[0133] STEP 6: For a vertical number j For the horizontal layer, i The conductivity calculation formula of the concentric rings is as follows:

[0134] (14)

[0135] Among them, Δ l The actual height corresponding to the length of each pixel in the z-axis direction is equal to L gap / m ,in L gap It represents the vertical distance between the lower surface of the positive electrode (anode) and the upper surface of the negative electrode (cathode).

[0136] According to the definition of conductivity in formula (15), the electron collision frequency can be further calculated as f ei ( i , j ) and electron temperature T e ( i , j ) distribution:

[0137] (15)

[0138] in f ei ( i , j ) is the electron collision frequency, in Hz; lnΛ is the Coulomb logarithm, which can be obtained by looking up the table; m e is the mass of an electron, which is 9.11×10 -31 kg; Z i is the relative charge number of the plasma, which can be obtained by looking up the table; T e ( i , j ) is the electron temperature, unit is eV.

[0139] Still taking the 3kA pulse arc in this embodiment as an example, the corresponding three-dimensional distribution of conductivity is calculated as follows: Figure 8 The three-dimensional distribution of electron temperature is shown in Figure 10 shown.

[0140] STEP 7: Based on the above results, calculate the total energy from the perspective of microscopic particles inside the pulse arc W total ,by W 离子 represents the total ion energy, W 电子 represents the total energy of electrons, N ( i , j ) represents the electron density matrix, T e ( i , j ) is the electron temperature matrix, Z i is the relative charge number of the plasma, V arc ( i , j ) represents the first j The horizontal layer i The volume of the concentric rings can be combined Figure 5 The total energy is calculated based on the pulse arc structure diagram and the actual size represented by each pixel. W total As shown in formula (16):

[0141] (16)

[0142] in, i ∈[1, H 边 ], j ∈[1, H 纵 ], i 、 j Take the integer.

[0143] STEP 8: Calculate the total energy of the pulse arc based on energy balance and time accumulation effect. Suppose the total energy of the pulse arc at the current time t is W 等离子体 ( t ), then it is equal to the total energy at the previous moment W 等离子体 ( t -1) plus the energy change Δ in this time step W 等离子体 ( t ), the change Δ W 等离子体 ( t ) is the input energy W input ( t ) and lost energy W loss (t ), where the input energy is calculated as (19), and the loss energy W loss ( t ) including particle loss energy W f ( t ) and radiation loss energy W s ( t ), as shown in formula (20). t is the time step value, that is, the shooting interval between two images of the high-speed camera.

[0144] (17)

[0145] (18)

[0146] (19)

[0147] (20)

[0148] The particle loses energy W f ( t ) is caused by the movement of the outermost particles (including electrons and ions) of the pulse arc to the outside of the boundary. Therefore, its statistical range includes the layer corresponding to the upper surface (the H 纵 horizontal layer), the layer corresponding to the lower surface (the first horizontal layer), and the layer corresponding to the side of the cylinder (the first horizontal layer of the entire cylinder). H 边 Layers of concentric rings), collectively known as the collective Shell, the Shell range is the outermost layer of the pulse arc, that is, the calculated i and j values ​​are within the Shell range (which can be expressed as ( i, j )∈Shell) is calculated as follows (21):

[0149] (twenty one)

[0150] Among them, Shell represents the range composed of the layer corresponding to the upper surface of the pulse arc, the layer corresponding to the lower surface, and the layer corresponding to the side of the cylinder. is the electron flux density in the outermost layer (i.e., Shell range) of the pulse arc, and the calculation formula is as follows (22), where For position ( i , j ) at the electron escape velocity; is the ion flux density of the outermost layer (i.e., Shell range) of the pulse arc, and the calculation formula is as follows (23), where For position (i , j ) at the ion escape velocity, m ion is the ion mass, T e ( i , j ) is the electron temperature, Indicates the surface area corresponding to the outermost layer of the pulse arc.

[0151] (twenty two)

[0152] (twenty three)

[0153] in, N ( i , j ) means at position ( i , j ), the electron density matrix at W s ( t ) represents the energy dissipated through radiation, conduction and other forms. This part of energy is the total dissipated energy (i.e., lost energy W loss It is understood that the particle loss energy given in this step is W f ( t ) is a preferred implementation method, the particle loss energy W f ( t ) can also be calculated by other estimation methods or table lookup methods, and the replacement of other conventional calculation methods can also achieve the calculation effect of this solution to a certain extent. Therefore, they should all be considered to fall within the scope of protection of the present invention.

[0154] STEP 9: Judgement W total and W 等离子体 ( t ) Whether the percentage difference meets the convergence condition b , in this example b Take 5%. If it is satisfied, go to step STEP10. The optimal calculation method for convergence judgment is as follows:

[0155] ;

[0156] If the convergence condition is not met, adjust the initial value of plasma density n 0, and start the calculation again from STEP 4 until the convergence condition is met.

[0157] STEP 10: Proceed to the next step of simulation modeling, or end the simulation.

[0158] The modeling method provided in this embodiment is simple, and the plasma density, temperature and electron migration velocity distribution results of the three-dimensional pulse arc can be obtained without using the finite element analysis method; during the modeling process, this scheme is based on the captured arc images and the real data of the pulse arc voltage and current, and the model parameters are more realistic and effective; the model constructed by this scheme is time-varying and is a dynamic model within the entire cycle of the pulse arc. The obtained microscopic parameters also change dynamically. In theory, as long as the shooting speed is fast enough and the voltage and current sampling accuracy is high enough, even if the pulse arc frequency is very high, a non-steady-state three-dimensional model can be established.

[0159] It should be noted that any process or method description in the flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or more executable instructions for implementing the steps of a specific logical function or process, and that the scope of the preferred embodiment of the present solution includes alternative implementations in which functions may be performed in a different order than shown or discussed, including performing functions in a substantially simultaneous manner or in a reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present solution belong.

[0160] The logic and / or steps represented in the flowchart or otherwise described herein may be embodied in any readable storage medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device).

[0161] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A pulse arc plasma modeling method based on high-speed images, characterized in that: The method comprises: Step 1: Initialize a high-speed camera for acquiring high-speed images and determine the pulse arc frequency; Step 2: Collect multiple pulse arc image data within the pulse period, and simultaneously collect the voltage and current at the time of image data collection within the pulse period; Step 3: Determine the pulse arc coordinate origin based on the pulse arc image data, and determine the coordinate system and the effective brightness range matrix with the pulse arc coordinate origin as the origin; perform mean processing on the effective brightness range matrix to obtain the pulse arc calculation matrix; Step 4: Divide the pulse arc into a three-dimensional structure consisting of multiple concentric rings in the horizontal direction and multiple horizontal layers in the vertical direction, so as to perform three-dimensional gridding on the pulse arc; obtain the three-dimensional distribution of the pulse arc plasma density based on the pulse arc calculation matrix and the initial value of the plasma density; Step 5: Calculate the electron migration velocity of each horizontal layer based on the three-dimensional distribution of pulse arc plasma density; Step 6: Combine the results of step 5 to calculate the three-dimensional distribution of conductivity and obtain the three-dimensional distribution of electron collision frequency and electron temperature; Step 7: Combine the results of step 6 to calculate the total energy of the pulse arc particles from the perspective of microscopic particles. W total , the total energy of the particle W total Includes total ion energy and total electron energy; Step 8: Combine the results of step 6 to calculate the total macroscopic energy of the pulse arc W 等离子体 , the macroscopic total energy W 等离子体 Calculation based on energy balance and time cumulative effect; Step 9: Determine the total energy of the particle W total and macroscopic total energy W 等离子体 Whether the percentage of the difference meets the convergence condition, if it does, then end; if not, adjust the initial value of the plasma density and return to step 4 until the convergence condition is met.

2. The method according to claim 1, characterized in that In step 3, the pulse arc coordinate origin is determined as follows: First calculate the brightness center position ( C x , C y ): ； ； in, H arc ( k , w ) represents the first k Column, No. w the brightness of the row; X max is the maximum horizontal pixel coordinate of the pulse arc image, Y max is the maximum value of the longitudinal pixel coordinate of the pulse arc image; by( C x , Y 阴 ) is the pulse arc coordinate origin, where, Y 阴 is the longitudinal coordinate of the upper surface of the cathode of the pulse arc emission source.

3. The method according to claim 2, characterized in that In step 3, the pulse arc calculation matrix is ​​determined as follows: First, in the coordinate system with the pulse arc coordinate origin as the origin, determine the effective brightness range matrix of the pulse arc J ( b , j ), b ∈[- H 边 ,1]∪[1, H 边 ], j ∈[1, H 纵 ],in, H 纵 Indicates the number of pixels from the upper surface of the cathode of the pulse arc emission source to the lower surface of the anode of the pulse arc emission source in the longitudinal direction; H 边 Indicates that the pulse arc coordinate origin is the center ， Brightness decay to alpha W max The maximum horizontal coordinate of the pixel; W max express H arc ( k , w ) in the image; α represents the attenuation ratio; J ( b , j ) represents the brightness value of the b-th column and the j-th row; b、j Take the integer; Secondly, perform mean processing on the effective brightness range matrix to obtain the pulse arc calculation matrix: K （ i , j ）= [ J （- i , j ）+ J （ i , j ）]×0.5； in, , i ∈[1, H 边 ], j ∈[1, H 纵 ] .

4. The method according to claim 3, characterized in that In step 4, during the three-dimensional gridding process, the number of horizontal layers is H 纵 , the number of concentric rings is H 边 ; The electron density matrix N( i , j ) represents the three-dimensional distribution of pulse arc plasma density, N( i , j ) is calculated as follows: ， i ∈[1， H 边 ]， j ∈[1， H 纵 ]； in, n 0 is the initial value of plasma density, T abel for H 边 × H 边 Abel coefficient matrix, K( i , j ) is the pulse arc calculation matrix.

5. The method according to claim 4, characterized in that In step 5, the electron migration speed distribution matrix v 迁 Represents the electron migration speed of each horizontal layer, among which the vertical j Electron migration speed in horizontal layers v 迁 ( j ) is calculated as: ； Among them, N ( i , j ) is the electron density matrix, S ( i ) is the i The area of ​​the concentric rings, e is the electron charge, I arc It is the arc current corresponding to the moment when the pulse arc image exposure is generated.

6. The method according to claim 4, characterized in that In step 6, the three-dimensional distribution of conductivity is represented by the conductivity at each location within the pulse arc. The conductivity at each location within the pulse arc is calculated as follows: ； Among them, δ ( i , j ) indicates the j The horizontal layer i The conductivity of the concentric rings, Δ l is the actual height corresponding to the length of each pixel in the z-axis direction, N ( i , j ) represents the electron density matrix, v 迁 ( j ) is the longitudinal j The electron migration speed of the horizontal layer, e is the electron charge, Δ U is the voltage drop of each vertical horizontal layer.

7. The method according to claim 6, characterized in that In step 6, the three-dimensional distribution of the electron collision frequency and the electron temperature is obtained by calculating the electron collision frequency and the electron temperature based on the following conductivity characteristics: ； in, f ei ( i , j ) is the electron collision frequency matrix, lnΛ is the Coulomb logarithm, m e is the electron mass, Z i is the relative charge number of the plasma, T e ( i , j ) is the electron temperature matrix.

8. The method according to claim 4, characterized in that In step 7, the total energy of the pulse arc particles W total The calculation method is: ; Among them, N ( i , j ) represents the electron density matrix, T e ( i , j ) is the electron temperature matrix, Z i is the relative charge number of the plasma, V arc ( i , j ) indicates the j The horizontal layer i The volume of the concentric rings.

9. The method according to claim 1, characterized in that In step 8, the pulse arc macroscopic total energy The calculation method is: ; ; ; ; in, W 等离子体 ( t ) is the total energy of the pulse arc at the current moment t, W 等离子体 ( t -1) is the total energy of the pulse arc at the previous moment, Δ W 等离子体 ( t ) is the energy change within this time step, W input ( t ) is the input energy, W loss ( t ) is the lost energy, W f ( t ) is the energy lost by the particle, W s ( t ) is the radiation loss energy, Δ t is the time step value, U arc ( t ) is the arc voltage at the current moment t, U 阴极鞘层 is the cathode sheath voltage of the pulse arc emission source, U 阳极鞘层 is the anode sheath voltage of the pulse arc emission source.

10. Pulsed arc plasma modeling equipment based on high-speed images, characterized in that The equipment includes: a timing control module, a pulse arc oscillation circuit, a high-speed camera, a host computer and a voltage and current measuring device; The pulse arc oscillation circuit generates a pulse arc based on a timing control module, the high-speed camera is used to collect multiple pulse arc image data within a pulse period and upload them to a host computer, and the voltage and current measuring device is used to collect the voltage and current at the moment of image data collection within the pulse period and upload them to the host computer; The host computer includes at least a processor and a memory, and the processor calls computer instructions in the memory to execute the pulse arc plasma modeling method based on high-speed images as described in any one of claims 1-9.

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