Plasma arc welding heat source model considering backward offset of small hole and modeling method of plasma arc welding heat source model

Abstract

The invention discloses a plasma arc welding heat source model considering small hole backward offset and a modeling method thereof, and the modeling method comprises the following steps: S1, obtaining a welding seam picture, and fitting to obtain a polynomial equation of a fusion region boundary line of a welding seam cross section and a longitudinal section; s2, the effective heating radius of plasma arc welding is obtained through calculation; s3, calculating to obtain the offset of the center line of the welding seam; s4, rotating around the center line of the welding seam to obtain the geometrical shape of the heat source; s5, considering the size factor to establish a heat source power density distribution formula; s6, forming a heat source model, performing sensitivity analysis on the heat source model, and determining a regression equation of an ellipse factor and a size factor; and S7, a heat source parameter optimization problem mathematical model is established, the ellipse factor and the size factor are determined, and the plasma arc welding heat source model considering the small hole backward offset is obtained. According to the method, the number of parameter variables of the heat source model is small, small hole backward offset is considered, and technical support can be provided for welding simulation of small hole type plasma arc welding.

Description

Technical Field

[0001] The invention relates to the field of welding technology, and in particular to a plasma arc welding heat source model taking into account a keyhole backward offset 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 weldment before putting it into actual use. For some large or complex welded components, the cost of experimental research is high and the time cycle is long, so researchers began to use finite element models to simulate the welding process in order to obtain suitable welding process parameters. The welding process itself is a temperature-phase change-stress coupling problem, and the 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 simulation of welding process depends largely on the heat source model, which not only contains the thermal information of welding process, but also is associated with parameters such as welding strength, welding stress, deformation, etc. Since the heat flux density distribution and real-time temperature evolution in welding process are difficult to measure, the heat source parameters are often adjusted by comparing the weld shape to match the boundary of the actual weld.

[0004] Plasma arc welding is widely used in the welding production of medium and thick plates due to its advantages of high energy density distribution and large weld depth-to-width ratio. However, the keyhole stability of keyhole plasma arc welding is poor, and the welding process parameters need to be adjusted to maintain the welding stability. For the welding simulation of keyhole plasma arc welding, the heat source models currently established all design the keyhole axis as an axisymmetric cylinder or cone, and do not consider the influence of the backward offset of the keyhole channel on the welding heat transfer process. Zhang Xiaoyu et al. considered the influence of the keyhole backward offset and established a "double ellipsoid + cone" combined volume heat source model that dynamically adjusts with the keyhole shape, which can better reflect the influence of the keyhole channel of the keyhole plasma arc on the welding heat conduction. Although the combined heat source can flexibly approximate the shape of the welding pool and can achieve higher accuracy than a single heat source, it also increases the heat source model parameters, including the shape parameters of the single heat source model and the power distribution coefficient that determines the power proportion of each part of the heat source. The adjustment and determination of these parameters require repeated trial and error and adjustment according to the actual shape of the welding pool, which greatly depends on the experience of the experimenter and increases the uncertainty in the welding simulation process. Therefore, considering the phenomenon that the keyhole deviates backward from the axis of the welding gun during plasma arc welding, it is of great significance to establish an integrated heat source model with fewer heat source model parameters and accurately predict the molten pool profile and temperature distribution during plasma arc welding to improve the efficiency and accuracy of numerical simulation of plasma arc welding.

[0005] In addition, residual stress and metallurgical transformation caused by nonlinear thermal cycles during welding can lead to damaging effects. An important tool for predicting the behavior of welded structures is numerical simulation. However, any volumetric heat source model has several heat source parameters that need to be determined, and the relationship between these parameters is very small. Determining the optimal parameters of the heat source becomes an important step in welding simulation. Most researchers use trial and error, but it is very time-consuming and cannot guarantee the optimal value. 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 deviation of the keyhole.

[0007] The technical solution of the present invention is as follows:

[0008] On the one hand, a method for modeling a plasma arc welding heat source model considering a keyhole backward offset is provided, comprising the following steps:

[0009] S1: obtaining a weld image, and performing grid processing on the weld image, and obtaining a polynomial equation of a fusion zone boundary line of a weld cross section and a longitudinal section based on a least squares polynomial curve fitting;

[0010] S2: Calculating and obtaining 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, the evolution of small holes and the solid-liquid phase change, the offset of the weld centerline is calculated;

[0012] S4: According to the effective heating radius and the offset of the weld centerline, the geometric shape of the heat source is obtained by rotating around the weld centerline;

[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 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;

[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 the 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 equation.

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

[0021]

[0022]

[0023] Where: k 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 gravitational acceleration; 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 distribution in the front quadrant and the rear quadrant 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 planes of the front and rear quadrants respectively; bh 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 in the parallel welding direction, 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 molten pool width; x 1w 、x 2w 、x 3w are the fitting coefficients of the molten width; D(h,f) is the molten 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 both error weight coefficients; W e and D e are the measured weld width and 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 taking into account the backward offset of the keyhole is also provided, which is established using any of the modeling methods of the plasma arc welding heat source model taking into account the backward offset of the keyhole described above.

[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. The variable parameters are relatively small, and the influence of the backward offset of the keyhole on the welding heat transfer process is taken into account. 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 drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative labor.

[0046] Figure 1 It is a structural schematic diagram of the heat source geometric model of the present invention;

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

[0048] Figure 3 It is a schematic diagram of heat source verification results in a specific embodiment;

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

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

[0051] The present invention is further described below in conjunction with the accompanying drawings and embodiments. 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 generally understood by those of ordinary skill in the art to which this application belongs. The words "including" or "comprising" and the like used in the disclosure of the present invention mean 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] On the one hand, the present invention provides a method for modeling a plasma arc welding heat source model taking into account a keyhole backward offset, comprising the following steps:

[0053] S1: Obtain a weld image, grid the weld image, and obtain a polynomial equation of a fusion zone boundary line of a weld cross section and a longitudinal section based on a least squares polynomial curve fitting.

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

[0059] In a specific embodiment, the coordinate axis is precisely divided into grids of equal proportions using AutoCAD software and superimposed on the weld image, so that any point on the fusion zone boundary that coincides with the grid line is used as a data point for curve fitting. Then, the polynomial equation of the fusion zone boundary line of the weld cross section and longitudinal section is obtained using MATLAB software based on the least squares polynomial curve fitting, and the result is as follows:

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

[0061] fx =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, the evolution of keyholes and the solid-liquid phase change, the weld centerline offset is calculated.

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

[0067]

[0068] Where: k 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 gravitational acceleration; 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 by 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 distribution in the front quadrant and the rear quadrant 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 planes of the front and rear quadrants 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 in the parallel welding direction, 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, and 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 formula of the front quadrant and the rear quadrant shown in formulas (5)-(6). In this way, the heat source model of the present invention only includes three variables: polynomial fitting coefficient, ellipse factor and 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 parameters of the heat source model 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 molten pool width; x 1w 、x 2w 、x 3w are the fitting coefficients of the molten width; D(h, f) is the molten 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 direction of the molten pool is obtained by the linear difference method, that is, the molten width and depth of the molten pool are obtained. The relevant process is as follows: Figure 2 The actual plasma arc welding and the corresponding melting depth results obtained by 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] minE=ω1(W e -W s ) 2 +ω2(D e -D s ) 2 (16)

[0090] h∈[h1,h2] (17)

[0091] f∈[f1,f2] (18)

[0092] hf∈R (19)

[0093] Where: minE is the objective function; ω1 and ω2 are both 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 equal to 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 are optimized using the Genetic Algorithm Toolbox (GAOT) of MATLAB software. The goal of the optimization is to obtain the same actual molten pool shape through numerical simulation and obtain the same thermal cycle as the experiment. The maximum temperature of several points near the molten pool is monitored in the numerical simulation and compared with the experimental points. At least 15 generations are iterated during the optimization process to ensure the accuracy of the calculation. The result obtained is that when the ellipse factor h is 1.7433 and the size factor f is 1.05, the optimal solution is 0.60872.

[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 modeling methods for the plasma arc welding heat source model that takes into account the backward offset of the keyhole described above.

[0098] In a specific embodiment, in order 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, and the weld shape of the steady-state process is compared with the actual weld. The results are as follows: Figure 3 The simulated penetration depth and width are 6 mm and 5.7 mm respectively, while the actual weld penetration depth and width are 6 mm and 6.2 mm respectively, and the overall cross-sectional area error is 6.7%. From the comparison results, the simulated results of the distribution of the weld metal molten zone and HAZ are basically consistent with the experiment, which shows that the simulated PAW welding of the present invention 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 away from the center of the weld, the lower the peak temperature of the measuring point. Compared with the peak temperature of the test measuring point, the relative error of the finite element temperature field analysis results is calculated. It can be seen that the relative error of the finite element simulation results is less than 5%, and the peak temperature measured in the test is higher than the result obtained by simulation calculation, but the overall change trend is consistent. The measured temperature is slightly higher than the simulated value mainly because the convection and heat conduction process inside the molten pool are ignored in the simulation process. In actual welding, more arc heat can be transferred to the workpiece, resulting in the difference between the measured temperature and the simulated value.

[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. From the distribution of the longitudinal residual stress along the weld direction at a distance of 12 mm from the weld, it can be seen that the longitudinal residual stress is distributed in a hump shape, and the residual tensile stress value near the central section reaches a maximum of 535.35 MPa, which is slightly higher than the yield strength of the parent material at room temperature (499.5 MPa). This may be because the material at this location has undergone work hardening during welding, resulting in an increase in its yield strength, so the longitudinal residual stress also increases.

[0102] Depend on Figure 5It can be seen that the transverse residual stress along the weld direction is distributed in a cap-shaped manner, and the maximum tensile residual stress appears in the middle of the weld. The maximum tensile residual stress is 392.13MPa, which is less than its yield strength at room temperature and much less than the longitudinal residual stress at the same position. At the same time, it is observed that at the beginning and end of welding, both the transverse residual stress and the longitudinal residual stress have a certain degree of uneven distribution, and the gradient of change is large. This is mainly attributed to the unstable arc starting and arc ending at the beginning and end of welding, which causes the heat input changes in these two parts, thereby causing the change of 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 small hole deviating backward from the axis of the welding gun during the actual plasma arc welding process. The genetic algorithm used in its application 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 numerical simulation of plasma arc welding.

[0105] The above description is only a representative embodiment of the present invention and does not limit the present invention in any form. Any technician familiar with the profession, without departing from the scope of the technical solution of the present invention, uses the above-disclosed technical contents to make some changes or modifications to the embodiments are equivalent embodiments of the present invention. However, any simple modification, 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: obtaining a weld image, and performing grid processing on the weld image, and obtaining a polynomial equation of a fusion zone boundary line of a weld cross section and a longitudinal section based on a least squares polynomial curve fitting; S2: Calculating and obtaining the effective heating radius of plasma arc welding according to the polynomial equation; S3: Considering the heat transfer and flow in the molten pool, the evolution of small holes and the solid-liquid phase change, the offset of the weld centerline is calculated; S4: According to the effective heating radius and the offset of the weld centerline, the geometric shape of the heat source is obtained by rotating around the weld centerline; 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 elongated by the ellipse factor to represent the molten pool characteristics in the actual welding process; Considering the size factor, a heat source power density distribution formula of the front quadrant and the rear quadrant is established; 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 the regression equations of the ellipse factor and the size factor; 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 is 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 equation.

3. The modeling method of the plasma arc welding heat source model considering the backward offset of the keyhole according to claim 1 is characterized in that: In step S3, the weld centerline offset is calculated by the following formula: Where: k 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 gravitational acceleration; 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 distribution in the front quadrant and the rear quadrant 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 planes of the front and rear quadrants 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 in the parallel welding direction, 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.

5. The method for modeling a plasma arc welding heat source model considering keyhole backward offset according to claim 4, characterized in that: In step S6, the regression equation of the ellipse factor and the size factor is expressed as: Where: W(h,f) is the molten pool width; x 1w 、x 2w 、x 3w are the fitting coefficients of the molten width; D(h,f) is the molten pool depth; x 1d 、x 2d 、x 3d are the fitting coefficients of penetration depth.

6. The method for modeling a plasma arc welding heat source model considering keyhole backward offset according to claim 5, characterized in that: In step S7, the mathematical model of the heat source parameter optimization problem is: min E=ω1(W e -IN 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 both error weight coefficients; W e and D e are the measured weld width and 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.

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

8. 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.

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

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