Plasma arc welding heat source model and modeling method considering keyhole backward deviation

Abstract

The present invention discloses a plasma arc welding heat source model and modeling method that considers keyhole backward offset. The modeling method includes the following steps: S1: obtaining a weld image and fitting a polynomial equation for the fusion zone boundary line of the weld cross section and longitudinal section; S2: calculating the effective heating radius of the plasma arc welding; S3: calculating the weld centerline offset; S4: rotating around the weld centerline to obtain the geometric shape of the heat source; S5: establishing a heat source power density distribution formula considering the size factor; S6: constructing a heat source model and performing a sensitivity analysis on it to determine the regression equations of the ellipse factor and the size factor; S7: establishing a mathematical model for the heat source parameter optimization problem, determining the ellipse factor and the size factor, and obtaining the plasma arc welding heat source model that considers keyhole backward offset. The heat source model of the present invention has fewer parameter variables and considers keyhole backward offset, and can provide technical support for welding simulation of keyhole plasma arc welding.

Description

Technical Field

[0001] The present invention relates to the field of welding technology, and in particular to a plasma arc welding heat source model taking keyhole backward offset into consideration and a modeling method thereof. Background Art

[0002] The welding process is often accompanied by the generation of residual stress and deformation of components, which will affect the welding quality. This has prompted researchers to study and analyze the welds before putting them into actual use. For some large or complex welded components, experimental research is costly and time-consuming, so researchers began to use finite element models to simulate the welding process in order to obtain appropriate welding process parameters. The welding process itself is a temperature-phase change-stress coupling problem, and welding residual stress and deformation are the result of the coupling of temperature, phase change and thermal stress. However, because the influence of stress and phase change on the temperature field is very weak, the finite element calculation of welding residual stress and deformation often ignores the influence of phase change, and mainly analyzes the thermal stress caused by the uneven temperature field.

[0003] The accuracy of finite element simulations of welding processes depends largely on the heat source model. This model not only incorporates thermal information from the welding process but also correlates with parameters such as weld strength, weld stress, and deformation. Because the heat flux distribution and real-time temperature evolution during welding are difficult to measure, heat source parameters are often adjusted by comparing the weld shape to match the actual weld boundary.

[0004] Plasma arc welding is widely used in the welding of medium and thick plates due to its high energy density distribution and large weld depth-to-width ratio. However, keyhole stability in keyhole plasma arc welding is poor, requiring control of welding process parameters to maintain weld stability. For keyhole plasma arc welding simulations, currently established heat source models design the keyhole axis as an axisymmetric cylinder or cone, failing to account for the effect of the keyhole channel's backward offset on the weld heat transfer process. Zhang Xiaoyu et al. considered the effect of keyhole backward offset and established a combined "double ellipsoid + cone" volumetric heat source model that dynamically adjusts to the keyhole shape. This model better reflects the influence of the keyhole channel on weld heat conduction in keyhole plasma arc welding. Although the combined heat source can flexibly approximate the weld pool shape and achieve higher accuracy than a single heat source, it also increases the number of heat source model parameters, including the shape parameters of the single heat source model and the power distribution coefficient that determines the power contribution of each heat source component. Adjusting and determining these parameters requires repeated trial and error based on the actual weld pool shape, which relies heavily on the experimenter's experience and increases uncertainty in the welding simulation process. Therefore, considering the phenomenon of the keyhole deviating backward from the welding gun axis during plasma arc welding, establishing an integrated heat source model with fewer parameters and accurately predicting the weld pool profile and temperature distribution during the plasma arc welding process is of great significance for improving the efficiency and accuracy of plasma arc welding numerical simulations.

[0005] Furthermore, residual stresses and metallurgical transformations caused by nonlinear thermal cycling during welding can lead to damaging effects. Numerical simulation is an important tool for predicting the behavior of welded structures. However, any volumetric heat source model requires several heat source parameters to be determined, and the correlation between these parameters is minimal. Therefore, determining the optimal heat source parameters becomes a crucial step in welding simulation. Most researchers use trial-and-error methods, but this is time-consuming and does not guarantee optimal values. Summary of the Invention

[0006] In view of the above problems, the present invention aims to provide a plasma arc welding heat source model and a modeling method thereof that takes into account the backward offset of the keyhole.

[0007] The technical solutions of the present invention are as follows:

[0008] In one aspect, a method for modeling a plasma arc welding heat source model taking into account keyhole backward offset is provided, comprising the following steps:

[0009] S1: Obtain a weld image, perform grid processing on the weld image, and obtain polynomial equations of fusion zone boundaries of the weld cross section and longitudinal section based on least squares polynomial curve fitting;

[0010] S2: Calculating the effective heating radius of plasma arc welding according to the polynomial equation;

[0011] S3: Considering the heat transfer and flow in the molten pool, keyhole evolution, and solid-liquid phase transition, the weld centerline offset is calculated.

[0012] S4: obtaining a geometric shape of the heat source by rotating around the weld centerline according to the effective heating radius and the weld centerline offset;

[0013] S5: Assuming that the heat flux power density along the depth direction has an exponential decay, the heat source is divided into a front quadrant and a rear quadrant, and the rear quadrant is elongated by an ellipse factor to represent the characteristics of the molten pool during the actual welding process; considering the size factor, the heat source power density distribution formula of the front quadrant and the rear quadrant is established;

[0014] S6: forming a heat source model by using the polynomial equation and the heat source power density distribution formula, and performing sensitivity analysis on the heat source model to determine regression equations of the ellipse factor and the size factor;

[0015] S7: Establish a mathematical model for the heat source parameter optimization problem, determine the ellipse factor and the size factor in combination with the regression equation, and obtain the plasma arc welding heat source model that takes the keyhole backward offset into consideration.

[0016] Preferably, in step S1, the polynomial equations of the fusion zone boundary lines of the weld cross section and longitudinal section are:

[0017] f x =a1z m +a2z m-1 ......+a m z+a0 (1)

[0018] f y =b1z n +b2z n-1 ......+b n z+b0 (2)

[0019] Where: f x and f y are the cross-sectional radius and longitudinal section radius of the weld in the thickness direction respectively; z is the position of the molten pool center in the weld thickness; a1, a2, a m , a0 and b1, b2, b n , b0 are fitting coefficients; m and n are the orders of the polynomial equations.

[0020] Preferably, in step S3, the weld centerline offset is calculated by the following formula:

[0021]

[0022]

[0023] Where: υ is the offset of the weld centerline; z is the position of the molten pool center on the weld thickness; δ is the workpiece thickness; γ is the offset parameter; p is the pressure; H is the thermal enthalpy; t is the time; represents the partial derivative of a vector; ρ is the density; V is the velocity vector; k is the thermal conductivity; T is the temperature; T m is the melting point of the metal material; is the gradient symbol; f l and f s are the volume fractions of liquid and solid phase respectively; L a is the latent heat of solid-liquid phase change; V0 is the welding speed; Q(x,y,z) is the total heat at (x,y,z); w is the speed in the z direction; u1 is the dynamic viscosity; K is the permeability; F z is the electromagnetic force in the z direction; g is the acceleration due to gravity; β is the thermal expansion coefficient; u is the velocity in the x direction; F x is the electromagnetic force in the x direction; v is the velocity in the y direction; F y is the electromagnetic force in the y direction.

[0024] Preferably, in step S5, the heat source power density distribution formulas of the front quadrant and the rear quadrant are:

[0025]

[0026] in:

[0027] b h 2 =f y 2 ,a f 2 =f x 2 ,a r 2 =ha f 2 (11)

[0028]

[0029] Q=ηIU a (14)

[0030] Where: q f (x,y) and q r (x, y) are the heat source power density distributions in the front and rear quadrants respectively; Q f and Q r are the total heat of the front quadrant and the rear quadrant respectively; f is the size factor; a f and a rare the shape and size parameters of the horizontal plane of the front quadrant and the back quadrant respectively; b h is the radius of the minor axis of the ellipse; x and y are the positions of the molten pool boundary in the perpendicular and parallel welding directions, respectively; h is the ellipse factor; Q is the total heat; η is the thermal efficiency; I is the welding current; U a is the welding working voltage.

[0031] Preferably, in step S6, the regression equation of the ellipse factor and the size factor is expressed as:

[0032]

[0033] Where: W(h,f) is the width of the molten pool; x 1w 、x 2w 、x 3w are the fitting coefficients of the melt width; D(h,f) is the melt pool depth; x 1d 、x 2d 、x 3d are the fitting coefficients of penetration depth.

[0034] Preferably, in step S7, the mathematical model of the heat source parameter optimization problem is:

[0035] min E=ω1(W e -W s ) 2 +ω2(D e -D s ) 2 (16)

[0036] h∈[h1,h2] (17)

[0037] f∈[f1,f2] (18)

[0038] h,f∈R (19)

[0039] Where: minE is the objective function; ω1 and ω2 are error weight coefficients; W e and D e are the measured weld width and weld depth respectively; W s and D s are the simulated melt width and melt depth respectively; h1 and h2 are the lower and upper limits of the ellipse factor respectively; f1 and f2 are the lower and upper limits of the size factor respectively; R is a real number set.

[0040] Preferably, the error weight coefficients ω1 and ω2 are both 1.

[0041] Preferably, in step S7, optimization iteration is performed based on a genetic algorithm to determine the ellipse factor and the size factor.

[0042] On the other hand, a plasma arc welding heat source model considering keyhole backward offset is also provided, which is established using any of the above-mentioned modeling methods for the plasma arc welding heat source model considering keyhole backward offset.

[0043] The beneficial effects of the present invention are:

[0044] The plasma arc welding heat source model described in the present invention only includes three variables: polynomial fitting coefficient, ellipse factor and size factor. It has fewer variable parameters and takes into account the influence of the backward offset of the keyhole on the welding heat transfer process. It can accurately simulate the welding of keyhole plasma arc welding. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] 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.

[0046] Figure 1 Schematic diagram of the heat source geometric model of the present invention;

[0047] Figure 2 Schematic diagram of a process for performing sensitivity analysis on heat source model parameters in a specific embodiment;

[0048] Figure 3 A schematic diagram of heat source calibration results in a specific embodiment;

[0049] Figure 4 is a thermal cycle curve in a specific embodiment;

[0050] Figure 5 Schematic diagram of the longitudinal residual stress and transverse residual stress distribution results in a specific embodiment; (a) is a schematic diagram of the longitudinal residual stress results, and (b) is a schematic diagram of the transverse residual stress results. DETAILED DESCRIPTION

[0051] The present invention is further described below with reference to the accompanying drawings and examples. It should be noted that, in the absence of conflict, the embodiments in this application and the technical features in the embodiments can be combined with each other. It should be noted that, unless otherwise specified, all technical and scientific terms used in this application have the same meanings as those commonly understood by those of ordinary skill in the art to which this application belongs. The use of similar words such as "include" or "comprising" in the present invention means that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0052] In one aspect, the present invention provides a method for modeling a plasma arc welding heat source model taking into account keyhole backward offset, comprising the following steps:

[0053] S1: Acquire a weld image, perform grid processing on the weld image, and obtain polynomial equations of fusion zone boundary lines of the weld cross section and longitudinal section based on least squares polynomial curve fitting.

[0054] In one specific embodiment, the weld seam image is directly gridded. In another specific embodiment, the coordinate axes are divided into grids of equal proportions and superimposed on the weld seam image, thereby indirectly gridding the weld seam image.

[0055] In a specific embodiment, the polynomial equations of the fusion zone boundary lines of the weld cross section and longitudinal section are respectively:

[0056] f x =a1z m +a2z m-1 ......+a m z+a0 (1)

[0057] f y =b1z n +b2z n-1 ......+b n z+b0 (2)

[0058] Where: f x and f y are the cross-sectional radius and longitudinal section radius of the weld in the thickness direction respectively; z is the position of the molten pool center in the weld thickness; a1, a2, a m , a0 and b1, b2, b n , b0 are fitting coefficients; m and n are the orders of the polynomial equations.

[0059] In one specific embodiment, AutoCAD software was used to precisely divide the coordinate axes into a grid of equal proportions and overlay it onto a weld image. Any point on the fusion zone boundary that coincided with a grid line was used as a data point for curve fitting. MATLAB software was then used to perform a least squares polynomial curve fit to obtain the polynomial equations for the fusion zone boundary lines in the cross-sectional and longitudinal sections of the weld. The results are shown below:

[0060] f y =1.279-1.179z+1.641z 2 -0.7488z 3 +0.1443z 4 -0.009679z 5 (20)

[0061] f x =1.522-2.024z+2.534z 2 -0.9855z 3 +0.1535z 4 -0.007635z 5 (twenty one)

[0062] It should be noted that the order of the polynomial equation is determined by the correlation coefficient R 2 Determination, correlation coefficient R 2 The closer the value is to 1, the more accurate the result.

[0063] S2: Calculate the effective heating radius of plasma arc welding according to the polynomial equation.

[0064] In this step, the effective heating radius is calculated by the polynomial equation, which can reflect the volume distribution of the plasma arc welding heat flux along the thickness direction of the weldment.

[0065] S3: Considering the heat transfer and flow in the molten pool, keyhole evolution, and solid-liquid phase transition, the weld centerline offset is calculated.

[0066] In a specific embodiment, the weld centerline offset is calculated by the following formula:

[0067]

[0068] Where: υ is the offset of the weld centerline; z is the position of the molten pool center on the weld thickness; δ is the workpiece thickness; γ is the offset parameter; p is the pressure; H is the thermal enthalpy; t is the time; represents the partial derivative of a vector; ρ is the density; V is the velocity vector; k is the thermal conductivity; T is the temperature; T m is the melting point of the metal material; is the gradient symbol; f l and f s are the volume fractions of liquid and solid phases respectively; L a is the latent heat of solid-liquid phase change; V0 is the welding speed; Q(x,y,z) is the total heat at (x,y,z); w is the speed in the z direction; u1 is the dynamic viscosity; K is the permeability; F z is the electromagnetic force in the z direction; g is the acceleration due to gravity; β is the thermal expansion coefficient; u is the velocity in the x direction; F x is the electromagnetic force in the x direction; v is the velocity in the y direction; F y is the electromagnetic force in the y direction.

[0069] S4: According to the effective heating radius and the weld centerline offset, the geometric shape of the heat source is obtained by rotating around the weld centerline.

[0070] In a specific embodiment, the heat source geometry is established as Figure 1 shown.

[0071] S5: Assuming that the heat flux power density along the depth direction has an exponential decay, the heat source is divided into a front quadrant and a rear quadrant, and the rear quadrant is elongated with an ellipse factor to represent the molten pool characteristics in the actual welding process; considering the size factor, the heat source power density distribution formula of the front quadrant and the rear quadrant is established.

[0072] In a specific embodiment, the heat source power density distribution formulas of the front quadrant and the rear quadrant are respectively:

[0073]

[0074] in:

[0075] b h 2 =f y 2 ,a f 2 =f x 2 ,a r 2 =ha f 2 (11)

[0076]

[0077] Q=ηIU a (14)

[0078] Where: q f (x,y) and q r (x, y) are the heat source power density distributions in the front and rear quadrants respectively; Q f and Q r are the total heat of the front quadrant and the rear quadrant respectively; f is the size factor; a f and a r are the shape and size parameters of the horizontal plane of the front quadrant and the back quadrant respectively; b h is the radius of the minor axis of the ellipse; x and y are the positions of the molten pool boundary in the perpendicular and parallel welding directions, respectively; h is the ellipse factor; Q is the total heat; η is the thermal efficiency; I is the welding current; U a is the welding working voltage.

[0079] In the above embodiment, by assuming that the heat flux power density along the depth direction has an exponential decay, the heat source is divided into the front quadrant and the rear quadrant, and the rear quadrant is stretched by the ellipse factor to represent the characteristics of the molten pool in the actual welding process; the size factor is then multiplied by the heat source volume to adjust the heat source power density. The power density based on the double ellipsoid heat source model is integrated and substituted into the polynomial equation describing the molten pool profile in the thickness direction to obtain the heat source power density distribution formulas for the front quadrant and the rear quadrant shown in equations (5) and (6). In this way, the heat source model of the present invention only includes three variables: the polynomial fitting coefficient, the ellipse factor, and the size factor.

[0080] S6: A heat source model is formed by the polynomial equation and the heat source power density distribution formula, and a sensitivity analysis is performed on the heat source model to determine the regression equations of the ellipse factor and the size factor.

[0081] In order to determine the accuracy of the heat source model parameters, it is necessary to analyze the sensitivity of the parameters to determine the weight of each parameter. At the same time, through the analysis of the sensitivity function, a preliminary estimation and regression of the heat source model parameters can be made.

[0082] In a specific embodiment, the regression equation of the ellipse factor and the size factor is expressed as:

[0083]

[0084] Where: W(h,f) is the width of the molten pool; x 1w 、x 2w 、x 3w are the fitting coefficients of the melt width; D(h,f) is the melt pool depth; x 1d 、x 2d 、x 3d are the fitting coefficients of penetration depth.

[0085] In a specific embodiment, the APDL command stream of ANSYS is used to load the heat source for temperature field calculation. After obtaining the steady-state temperature field, the cross-section node temperature is extracted using MATLAB and matched with the node coordinate information. The coordinate difference of the peak temperature of 1400°C (melting point) in the width and depth directions of the molten pool is obtained by the linear difference method, that is, the molten pool width and depth are obtained. The relevant process is as follows: Figure 2 As shown. The corresponding weld width and depth results obtained by actual plasma arc welding and finite element numerical simulation are substituted into formula (11) for fitting, and the results are shown as follows:

[0086]

[0087] S7: Establish a mathematical model for the heat source parameter optimization problem, determine the ellipse factor and the size factor in combination with the regression equation, and obtain the plasma arc welding heat source model that takes the keyhole backward offset into consideration.

[0088] In a specific embodiment, the mathematical model of the heat source parameter optimization problem is:

[0089] min E=ω1(W e -W s ) 2 +ω2(D e -D s ) 2 (16)

[0090] h∈[h1,h2] (17)

[0091] f∈[f1,f2] (18)

[0092] h,f∈R (19)

[0093] Where: minE is the objective function; ω1 and ω2 are error weight coefficients; W e and D e are the measured weld width and weld depth respectively; W s and D s are the simulated melt width and melt depth respectively; h1 and h2 are the lower and upper limits of the ellipse factor respectively; f1 and f2 are the lower and upper limits of the size factor respectively; R is a real number set.

[0094] In a specific embodiment, the error weight coefficients ω1 and ω2 are both 1.

[0095] In a specific embodiment, optimization iterations are performed based on a genetic algorithm to determine the ellipse factor and the size factor.

[0096] In a specific embodiment, the heat source parameters were optimized using the Genetic Algorithm Toolbox (GAOT) in MATLAB software. The optimization goal was to achieve the same actual melt pool shape through numerical simulation while also achieving the same thermal cycle as the experiment. The maximum temperature at several points near the melt pool was monitored in the numerical simulation and compared with the experimental points. The optimization process was repeated at least 15 times to ensure computational accuracy. The optimal solution, 0.60872, was obtained when the ellipse factor h was 1.7433 and the size factor f was 1.05.

[0097] On the other hand, the present invention also provides a plasma arc welding heat source model that takes into account the backward offset of the keyhole, which is established using any of the above-mentioned modeling methods for the plasma arc welding heat source model that takes into account the backward offset of the keyhole.

[0098] In a specific embodiment, to verify the accuracy of the heat source model described in the present invention, small-hole plasma arc welding was performed on 1.4835 stainless steel. During the test, four thermocouples were used to measure the temperature field of the plate. At the same time, the blind hole method was used to measure the residual stress of the weld joint.

[0099] First, the morphology of the fusion zone is analyzed: the heat source parameters are written as an APDL command stream that can be recognized by ANSYS. The command stream is called to simulate and calculate the temperature field during the welding process. The weld shape of the steady-state process is compared with the actual weld shape. The results are as follows: Figure 3 The simulated weld penetration and width were 6 mm and 5.7 mm, respectively, while the actual weld penetration and width were 6 mm and 6.2 mm, respectively. The overall cross-sectional area error was 6.7%. The simulated distribution of the weld metal molten zone and HAZ was basically consistent with the experimental results, indicating that the simulated PAW welding method is reliable and effective.

[0100] Then, the thermal cycle curves were analyzed: To further explore the accuracy of the heat source parameters, the experimental thermal cycle and numerical results were analyzed. Figure 4 As shown. Figure 4 It can be seen that the farther from the weld center, the lower the peak temperature of the measuring point. Comparing the peak temperatures at the experimental measuring points with the relative error of the finite element temperature field analysis results shows that the relative errors of the finite element simulation results are all less than 5%. The experimentally measured peak temperatures are all higher than those calculated, but the overall trend is consistent. The measured temperatures are slightly higher than the simulated values ​​primarily because the convection and heat conduction processes within the molten pool are ignored during the simulation. During actual welding, more arc heat can be transferred to the workpiece, resulting in the difference between the measured and simulated temperatures.

[0101] Finally, the welding residual stress is analyzed: the longitudinal residual stress and transverse residual stress distribution along the welding direction on the upper surface of the weldment when cooled to room temperature are compared with the actual measurement results. Figure 5 As shown in the figure, the longitudinal residual stress distribution along the weld seam at a distance of 12 mm shows a hump-shaped distribution. The residual tensile stress near the central section reaches a maximum of 535.35 MPa, slightly higher than the yield strength of the parent material at room temperature (499.5 MPa). This may be due to work hardening of the material at this location during welding, which increases its yield strength and, consequently, the increase in longitudinal residual stress.

[0102] Depend on Figure 5It can be seen that the transverse residual stress along the weld seam is distributed in a cap-shaped manner, with the maximum tensile residual stress occurring in the middle of the weld seam. The maximum tensile residual stress is 392.13 MPa, which is less than its yield strength at room temperature and far less than the longitudinal residual stress at the same location. At the same time, observations show that both the transverse and longitudinal residual stresses exhibit a certain degree of uneven distribution at the start and end of welding, with large gradients. This is mainly attributed to the unstable arc starting and ending at the beginning and end of welding, which causes changes in heat input in these two locations, leading to changes in residual stress.

[0103] There is a certain deviation between the stress value obtained by simulation and the actual value. This is because the stress caused by phase change in the welding process and the calculation accuracy error are ignored in the simulation calculation process. However, the overall change trend is consistent, indicating that the simulation calculation results of the present invention have good reliability.

[0104] In summary, the heat source model of the present invention has few heat source parameters and can reflect the characteristic of the keyhole deviating backward from the welding gun axis during the actual plasma arc welding process. When applied, the genetic algorithm can quickly and accurately obtain the correct heat source parameters, thereby efficiently obtaining accurate results during welding simulation. The present invention is of great significance for improving the calculation efficiency and accuracy of plasma arc welding numerical simulation.

[0105] The above description is merely a representative embodiment of the present invention and does not constitute any form of limitation to the present invention. Any technical personnel familiar with the present invention who, without departing from the scope of the technical solution of the present invention, makes some changes or modifications to the embodiments disclosed above using the technical contents disclosed above are equivalent embodiments of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for modeling a plasma arc welding heat source model considering keyhole backward offset, characterized in that: The following steps are involved: S1: Obtain a weld image, perform grid processing on the weld image, and obtain polynomial equations of fusion zone boundaries of the weld cross section and longitudinal section based on least squares polynomial curve fitting; S2: Calculating the effective heating radius of plasma arc welding according to the polynomial equation; S3: Considering the heat transfer and flow in the molten pool, keyhole evolution, and solid-liquid phase transition, the weld centerline offset is calculated. S4: obtaining a geometric shape of the heat source by rotating around the weld centerline according to the effective heating radius and the weld centerline offset; S5: Assuming that the heat flux power density along the depth direction has an exponential decay, the heat source is divided into the front quadrant and the rear quadrant, and the rear quadrant is stretched by the ellipse factor to represent the molten pool characteristics in the actual welding process; Establishing heat source power density distribution formulas for the front quadrant and the rear quadrant taking into account size factors; S6: A heat source model is formed by the polynomial equation and the heat source power density distribution formula, and a sensitivity analysis is performed on the heat source model to determine the regression equation of the ellipse factor and the size factor; the regression equation of the ellipse factor and the size factor is expressed as follows: Where: W(h,f) is the width of the molten pool; x 1w 、x 2w 、x 3w are the fitting coefficients of the melt width; h is the ellipse factor; f is the size factor; D(h,f) is the melt pool depth; x 1d 、x 2d 、x 3d are the fitting coefficients of penetration depth; S7: Establish a mathematical model for the heat source parameter optimization problem, determine the ellipse factor and the size factor in combination with the regression equation, and obtain the plasma arc welding heat source model that takes the keyhole backward offset into consideration.

2. The method for modeling a plasma arc welding heat source model considering keyhole backward offset according to claim 1, characterized in that: In step S1, the polynomial equations of the fusion zone boundary lines of the weld cross section and longitudinal section are respectively: f x =a1z m +a2z m-1 ......+a m z+a0 (1) f y =b1z n +b2z n-1 ......+b n z+b0 (2) Where: f x and f y are the cross-sectional radius and longitudinal section radius of the weld in the thickness direction respectively; z is the position of the molten pool center in the weld thickness; a1, a2, a m , a0 and b1, b2, b n , b0 are fitting coefficients; m and n are the orders of the polynomial equations.

3. The method for modeling a plasma arc welding heat source model considering keyhole backward offset according to claim 1, characterized in that: In step S3, the weld centerline offset is calculated using the following formula: Where: υ is the offset of the weld centerline; z is the position of the molten pool center on the weld thickness; δ is the workpiece thickness; γ is the offset parameter; p is the pressure; H is the thermal enthalpy; t is the time; represents the partial derivative of a vector; ρ is the density; V is the velocity vector; k is the thermal conductivity; T is the temperature; T m is the melting point of the metal material; is the gradient symbol; f l and f s are the volume fractions of liquid and solid phases respectively; L a is the latent heat of solid-liquid phase change; V0 is the welding speed; Q(x,y,z) is the total heat at (x,y,z); w is the speed in the z direction; u1 is the dynamic viscosity; K is the permeability; F z is the electromagnetic force in the z direction; g is the acceleration due to gravity; β is the thermal expansion coefficient; u is the velocity in the x direction; F x is the electromagnetic force in the x direction; v is the velocity in the y direction; F y is the electromagnetic force in the y direction.

4. The method for modeling a plasma arc welding heat source model considering keyhole backward offset according to claim 1, characterized in that: In step S5, the heat source power density distribution formulas of the front quadrant and the rear quadrant are respectively: in: b h 2 =f y 2 ,a f 2 =f x 2 ,a r 2 =ha f 2 (11) Q=ηIU a (14) Where: q f (x,y) and q r (x, y) are the heat source power density distributions in the front and rear quadrants respectively; Q f and Q r are the total calories of the front quadrant and the back quadrant respectively; a f and a r are the shape and size parameters of the horizontal plane of the front quadrant and the back quadrant respectively; b h is the radius of the minor axis of the ellipse; x and y are the positions of the molten pool boundary in the vertical welding direction and the position in the parallel welding direction respectively; υ is the offset of the weld centerline; f x and f y are the cross-sectional radius and longitudinal section radius of the weld in the thickness direction, respectively; Q is the total heat; η is the thermal efficiency; I is the welding current; U a is the welding working voltage.

5. The method for modeling a plasma arc welding heat source model considering keyhole backward offset according to claim 1, characterized in that: In step S7, the mathematical model of the heat source parameter optimization problem is: minE=ω1(W e -W s ) 2 +ω2(D e -D s ) 2 (16) h∈[h1,h2] (17) f∈[f1,f2] (18) h,f∈R (19) Where: minE is the objective function; ω1 and ω2 are error weight coefficients; W e and D e are the measured weld width and weld depth respectively; W s and D s are the simulated melt width and melt depth respectively; h1 and h2 are the lower and upper limits of the ellipse factor respectively; f1 and f2 are the lower and upper limits of the size factor respectively; R is a set of real numbers.

6. The method for modeling a plasma arc welding heat source model considering keyhole backward offset according to claim 5, characterized in that: The error weight coefficients ω1 and ω2 are both set to 1.

7. The method for modeling a plasma arc welding heat source model considering keyhole backward offset according to claim 1, characterized in that: In step S7, optimization iteration is performed based on a genetic algorithm to determine the ellipse factor and the size factor.

8. A plasma arc welding heat source model considering keyhole backward offset, characterized in that: The heat source model of plasma arc welding is established by adopting the modeling method of any one of claims 1 to 7 that takes into account the backward offset of the keyhole.

Images