Numerical simulation method for the effect of power source polarity on nugget formation in resistance spot welding

Abstract

The present application relates to a kind of numerical simulation method of resistance spot welding power supply polarity influence on nugget morphology, belong to welding numerical simulation technical field.The formation process of nugget under two polarities is simulated, and the influence of the change of polarity on nugget size and offset phenomenon is verified.The welding plate is made of two kinds of heterogeneous materials, and the power supply polarity refers to the positive and negative directions of current through the welding plate.The advantages are as follows:it fills the research gap of the influence of power supply polarity on resistance spot welding joint.The nugget morphology under different polarities can be presented more intuitively through simulation results, which provides accurate reference for experimental research, improves test efficiency and reduces test cost.

Description

Technical Field

[0001] This invention relates to the field of resistance spot welding simulation technology, and in particular to a numerical simulation method for the influence of resistance spot welding power supply polarity on the weld nugget shape. Background Technology

[0002] The formation of a spot weld nugget is the result of the combined action of electricity, heat, and force. The current passing through the welding plate generates heat that melts the plate, and the electrode pressure causes the nugget to form a plastic ring, producing the necessary plastic deformation.

[0003] The fundamental reason for weld nugget displacement is the unequal heat generation and dissipation of the two weld plates during the heating process in the welding zone. The weld nugget shifts towards the side with more heat generation and slower heat dissipation. When spot welding plates of different thicknesses, the thicker plate has higher resistance and generates more heat, while its heat generation center dissipates heat slowly because it is far from the electrode. The thinner plate is the opposite, which leads to weld nugget displacement. When resistance spot welding dissimilar materials, the material with poor electrical conductivity has higher resistance and generates more heat, and at the same time, its thermal conductivity is poor and dissipates heat slowly. In contrast, the material with better electrical conductivity is the opposite. This causes the welding temperature field to shift towards the material with poor electrical conductivity, and consequently, the weld nugget also shifts.

[0004] Resistance spot welding is an important processing method in industrial production. The quality of the joint is crucial to the overall quality of the product. Therefore, for many years, numerous researchers both domestically and internationally have dedicated themselves to studying how to ensure the joint quality of resistance spot welds. In resistance spot welding of non-uniform thickness plates and dissimilar materials, weld nugget misalignment is a significant issue. Weld nugget misalignment results in the weld nugget's size on the workpiece-to-workpiece mating surface being smaller than its maximum diameter. It also causes the weld penetration rate of thinner plates in non-uniform thickness plates or materials with low resistivity in dissimilar materials to fall below the specified value, leading to decreased weld strength, reduced weld load-bearing capacity, and weld quality that fails to meet requirements. Therefore, studying the weld nugget misalignment characteristics and improving weld nugget misalignment is of great significance.

[0005] Most domestic and international research on resistance spot welding is limited to evaluating the mechanical properties and metallographic structure of the weld. Currently, there is almost no research on the influence of power supply polarity on the weld nugget offset. With the development of numerical simulation technology, this technology can provide great help to spot welding processes and actual production. Summary of the Invention

[0006] The purpose of this invention is to provide a numerical simulation method for the influence of power supply polarity on the weld nugget morphology in resistance spot welding. This fills a research gap in the impact of power supply polarity on resistance spot welded joints, provides accurate reference for experimental research, improves experimental efficiency, and reduces experimental costs. This invention achieves a precise assessment of the influence of power supply polarity on the morphology and size of the weld nugget by numerically simulating weld nugget formation under two polarity conditions.

[0007] The above-mentioned objective of this invention is achieved through the following technical solution:

[0008] A numerical simulation method for the influence of power supply polarity on the weld nugget morphology in resistance spot welding is proposed. This method simulates the weld nugget formation process under two different polarities, verifying the impact of polarity changes on the weld nugget size and offset. Welding plates one and two are made of two dissimilar materials. The power supply polarity refers to the opposite direction of current flow through the welding plates, including two polarities: Polarity I, where welding plate one is positive and welding plate two is negative; and Polarity II, where welding plate two is positive and welding plate one is negative. The method includes the following steps:

[0009] Step 1: Modeling: Based on the specifications of the electrodes used in the welding test and the dimensions of the welding plate, a three-dimensional geometric model is constructed using SolidWorks software. The model consists of upper and lower electrode caps and the welding plate, and the model is then imported into ABAQUS.

[0010] Step 2: Assign material properties: Assign corresponding material properties to each component of the upper and lower electrode caps and welding plates respectively;

[0011] Step 3: Set simulation parameters and conditions: Under polarity I conditions, set boundary conditions and loads according to the welding test parameters, and mesh the model;

[0012] Step 4: Solution and Analysis: Simulate the formation process of the melt nugget and measure the size and offset of the simulated melt nugget.

[0013] Step 5: Solve and analyze by changing the power supply polarity: Change polarity I in Step 3 to polarity II, that is, set the degrees of freedom of the lower electrode in the X and Y directions to 0, set the Z-axis direction to the default, set the upper electrode to be completely fixed with displacement and rotation angles of 0, set the potential of the upper end face of the upper electrode to 0, apply current as a load to the lower end face of the lower electrode, apply upward pressure to the lower end face of the lower electrode and hold it; after setting, submit the job to simulate and measure the size and offset of the melt core simulation results.

[0014] Step Six: Comparative Analysis of Simulation Results: Compare the results obtained in Step Four with the results obtained in Step Five;

[0015] Step 7, Experimental Measurement and Comparison: The plates welded under polarity I and polarity II conditions will be cut, ground, polished and etched along the centerline of the weld nugget. Then the weld nugget of the plates will be characterized and measured, and the size and offset of the weld nugget under the two polarities will be compared.

[0016] Step 8: Result Comparison: Compare the comparison results obtained in Step 7 with the comparison results obtained in Step 6.

[0017] The material properties described in step two include density, Young's modulus, Poisson's ratio, yield stress, thermal conductivity, coefficient of thermal expansion, specific heat capacity, and electrical conductivity. These material properties change with temperature and are obtained using simulation software JmatPro. The molten welded plates one and two are still considered to be isotropic and ideal homogeneous materials.

[0018] The three-dimensional geometric model is simplified to a 1 / 4 finite element model. The symmetry interface conditions of the finite element software are used to reduce the computational difficulty and facilitate computational convergence.

[0019] Due to the difference in electrical and thermal conductivity, heterogeneous materials will produce the Peltier effect when resistance spot welding. The Peltier effect is that when current passes through a circuit composed of different conductors, heat absorption or heat release will occur at different joints. If the polarity of the power supply is changed to reverse the current, the heat-absorbing joint will release heat, and the heat-releasing joint will absorb heat.

[0020] The formula for calculating the Seebeck effect potential difference:

[0021]

[0022] Peltier effect formula:

[0023] Q=I(π X -π Y )

[0024] Where π is the Peltier coefficient, S A and S B The values ​​represent the Seebeck coefficients of the two materials used in welding plates one and two, respectively; I represents the current; Q represents the heat generated; and V represents the potential difference. Peltier coefficient = Seebeck coefficient × absolute temperature.

[0025] V = IR ≈ ST

[0026] π = ST

[0027] Where V represents the potential difference, I represents the current, R represents the resistance, S represents the Seebeck coefficient, and T represents the temperature;

[0028] Transient heat conduction governing equations:

[0029]

[0030] Where x, y, and z are axial coordinates, K, ρ, and c are thermal conductivity, density, and specific heat, respectively, Q is the heat generated, T is the temperature, and t is the time. The heat generated during resistance spot welding is mainly Joule heating.

[0031] Q = I 2 Rt

[0032] Where Q is the heat generated, I is the current, R is the resistance, and t is the time.

[0033] The simulation parameters and conditions set in step three are as follows: In the initial analysis step, the initial ambient temperature is 293K, the lower electrode is completely fixed, and the displacement and rotation angles are both 0. For ease of calculation, the selected model is a 1 / 4 axisymmetric model, and symmetric interface conditions are set for the two sides; the potential of the lower end face of the lower electrode is set to 0; in the pre-pressure analysis step, a downward pressure is applied to the upper end face of the upper electrode and held; in the energization analysis step, the current is applied as a load to the upper end face of the upper electrode, surface film cooling conditions are set in the electrode cooling water action area, and air heat dissipation boundary conditions are set for the contact surface between the electrode and the plate and the air.

[0034] The simulation results comparison analysis described in step six is ​​to compare the weld nugget size and offset obtained under polarity I with those obtained under polarity II to verify the influence of power supply polarity on the weld nugget shape of resistance spot welding.

[0035] The beneficial effects of this invention are as follows: Most current research on resistance spot welding, both domestically and internationally, is limited to evaluating the mechanical properties and metallographic structure of the weld, with almost no research on the influence of power supply polarity on weld nugget displacement. With the development of numerical simulation technology, this invention utilizes this technology to greatly assist in spot welding processes and actual production. Through simulation analysis using the method of this invention, it provides accurate references for experimental research, improves experimental efficiency, reduces experimental costs, and fills the research gap on the influence of power supply polarity on spot welded joints. It has strong practicality. Attached Figure Description

[0036] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate the invention and are used to explain it, but do not constitute an undue limitation of the invention.

[0037] Figure 1 This is a schematic diagram of the logic flow of the present invention;

[0038] Figure 2 This is a schematic diagram of the model of the present invention;

[0039] Figure 3 This is a simulation result diagram under polarity I conditions of the present invention;

[0040] Figure 4 The figure shows the simulation results under polarity II conditions of the present invention. Detailed Implementation

[0041] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0042] See Figures 1 to 3 As shown, the numerical simulation method of the present invention for the influence of resistance spot welding power supply polarity on the weld nugget morphology mainly verifies the effect of polarity change on weld nugget size and offset phenomenon by simulating the weld nugget formation process under two polarities. The simulation results can intuitively present the weld nugget morphology under different polarities, providing accurate reference for experimental research, improving experimental efficiency, and reducing experimental costs.

[0043] The welding plates use two materials, Material 1 and Material 2. The power supply polarity refers to the positive and negative directions of the current passing through the welding plates, including two polarities: Polarity I, where Material 1 is the positive electrode and Material 2 is the negative electrode; and Polarity II, where Material 2 is the positive electrode and Material 1 is the negative electrode. The process includes the following steps:

[0044] Step 1: Modeling: Based on the specifications of the electrodes used in the welding test and the dimensions of the welding plate, a three-dimensional model is constructed using SolidWorks software. The model consists of upper and lower electrode caps and the welding plate, and the model is then imported into ABAQUS.

[0045] Step 2: Assign material properties: Assign corresponding material properties to the upper and lower electrode caps and each component of the welding plate.

[0046] Step 3: Set simulation parameters and conditions: Under polarity I conditions, set boundary conditions and loads according to the welding test parameters, and mesh the model.

[0047] Step 4: Solution and Analysis: Simulate the formation process of the melt nugget and measure the size and offset of the simulated melt nugget.

[0048] Step 5: Solve and analyze by changing the power supply polarity: Change polarity I in Step 3 to polarity II. That is, set the degrees of freedom of the lower electrode in the X and Y directions to 0, set the Z-axis direction to the default, set the upper electrode to be completely fixed with zero displacement and rotation angle, set the potential of the upper end face of the upper electrode to 0, apply current as a load to the lower end face of the lower electrode, apply upward pressure to the lower end face of the lower electrode and hold it. After setting, submit the job to simulate and measure the size and offset of the melt core simulation results.

[0049] Step Six: Comparison and Analysis of Simulation Results: Compare the results obtained in Step Four with the results obtained in Step Five.

[0050] Step 7, Experimental Measurement and Comparison: The plates welded under polarity I and polarity II conditions will be cut, ground, polished and etched along the centerline of the weld nugget. Then the weld nugget of the plate will be characterized and measured, and the size and offset of the weld nugget under the two polarities will be compared.

[0051] Step 8: Result Comparison: Compare the comparison results obtained in Step 7 with the comparison results obtained in Step 6.

[0052] The material properties described in step two include physical properties such as density, thermal conductivity, coefficient of thermal expansion, specific heat capacity, and electrical conductivity. These material properties change with temperature and are obtained using simulation software JmatPro. The melted materials one and two are still considered to be isotropic and ideal homogeneous materials.

[0053] The three-dimensional geometric model is simplified to a 1 / 4 finite element model. The symmetry interface conditions of the finite element software can reduce the computational difficulty and facilitate computational convergence.

[0054] Due to the difference in electrical and thermal conductivity, heterogeneous materials will produce the Peltier effect during resistance spot welding. The Peltier effect is that when current passes through a circuit composed of different conductors, heat absorption or release will occur at different joints. If the polarity of the power supply is changed to reverse the current, the heat-absorbing joint will release heat, and the heat-releasing joint will absorb heat.

[0055] The formula for calculating the Seebeck effect potential difference:

[0056]

[0057] Peltier effect:

[0058] Q=I(π X -π Y )

[0059] Where π is the Peltier coefficient, S A and S B These are the Seebeck coefficients for the two materials, I is the current, Q is the heat generated, and V represents the potential difference; Peltier coefficient = Seebeck coefficient × absolute temperature.

[0060] V = IR ≈ ST

[0061] π = ST

[0062] Where V represents the potential difference, I represents the current, R represents the resistance, S represents the Seebeck coefficient, and T represents the temperature;

[0063] Transient heat conduction governing equations:

[0064]

[0065] Where x, y, and z are axial coordinates, K, ρ, and c are thermal conductivity, density, and specific heat, respectively, Q is the heat generated, T is the temperature, and t is the time. The heat generated during resistance spot welding is mainly Joule heating.

[0066] Q = I 2 Rt

[0067] Where Q is the heat generated, I is the current, R is the resistance, and t is the time.

[0068] The simulation parameters and conditions set in step three are as follows: In the initial analysis step, the initial ambient temperature is 293K, the lower electrode is completely fixed, and the displacement and rotation angles are both 0. For ease of calculation, a 1 / 4 axisymmetric model is selected, and symmetric interface conditions are set for the two sides; the potential of the lower end face of the lower electrode is set to 0; in the pre-pressure analysis step, a downward pressure is applied to the upper end face of the upper electrode and held; in the energization analysis step, current is applied as a load to the upper end face of the upper electrode, surface film cooling conditions are set in the electrode cooling water action area, and air heat dissipation boundary conditions are set for the contact surfaces between the electrode and the plate and the air.

[0069] Step six involves comparing the simulation results obtained under polarity I with those obtained under polarity II to verify the influence of power supply polarity on the shape of the resistance spot weld nugget.

[0070] Example:

[0071] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0072] This embodiment relates to a numerical simulation method for the influence of power supply polarity on the weld nugget shape in resistance spot welding. The main process includes: modeling, assigning material properties, setting simulation parameters and conditions, solving and analyzing, solving and analyzing by changing power supply polarity, comparing and analyzing simulation results, experimental measurement and comparison, and comparing results.

[0073] See Figures 1 to 4The diagram shows a flowchart of the numerical simulation method for the influence of resistance spot welding power source polarity on the weld nugget shape provided in this embodiment. The numerical simulation method for the influence of resistance spot welding power source polarity on the weld nugget shape in this embodiment includes:

[0074] Step S1: Modeling: Based on the specifications of the electrodes used in the welding test and the dimensions of the welding plate, a three-dimensional geometric model is constructed using SolidWorks software. The model consists of upper and lower electrode caps and the welding plate, and the model is then imported into ABAQUS.

[0075] Figure 2 This is a schematic diagram of the model provided in this embodiment. Figure 2 1 is the upper electrode cap, 2 and 3 are welding plates one and two, 4 is the lower electrode cap, 5 is the upper end face of the upper electrode, and 6 is the lower end face of the lower electrode.

[0076] The three-dimensional geometric model in this embodiment is simplified to a 1 / 4 finite element model. The upper and lower electrode caps 1 and 4 are both spherical electrodes with a radius of curvature R = 100 mm. The welding plates 1 and 2, i.e., 2 and 3, are both cuboids with a length of 45 mm, a width of 45 mm, and a thickness of 1.2 mm.

[0077] Step S2: Assign material properties: Assign corresponding material properties to the upper and lower electrode caps and the first and second welding plates, respectively.

[0078] The upper and lower electrode caps are made of chromium-zirconium copper, and the welding plates one and two are made of stainless steel SUS301 and duplex steel DP780, respectively. Their density, Young's modulus, Poisson's ratio, yield stress, thermal conductivity, coefficient of thermal expansion, specific heat capacity, and electrical conductivity were obtained by simulation software JmatPro and assigned to each component.

[0079] Step S3: Set simulation parameters and conditions: Under polarity I conditions, set boundary conditions and loads according to the welding test parameters, and mesh the model.

[0080] In the initial analysis step, the initial ambient temperature was 293K. The lower electrode was completely fixed with zero displacement and rotation angle. For ease of calculation, a 1 / 4 axisymmetric model was selected, and symmetric interface conditions were set for the two sides. The potential of the lower end face of the lower electrode was set to 0. In the pre-pressure analysis step, a downward pressure was applied to the upper end face of the upper electrode and held. In the energization analysis step, current was applied as a load to the upper end face of the upper electrode. Surface film cooling conditions were set in the electrode cooling water action area, and air heat dissipation boundary conditions were set for the contact surfaces between the electrode and the weldment and the air.

[0081] Non-uniform mesh generation was adopted, with smaller mesh sizes used in the main functional areas and relatively larger mesh sizes used in other areas, improving computational efficiency while ensuring accurate calculation results. The mesh used eight-node linear hexahedral reduced integration elements, with 12,324 mesh elements for the test plate and 4,224 mesh elements for both the upper and lower electrodes.

[0082] Referring to the actual resistance spot welding process, five analysis steps need to be set: initial, pre-pressure, pressurization, energization, and pressure maintenance. Each analysis step is determined according to the actual spot welding process parameters: pre-pressure analysis step 0.1s, pressurization analysis step 0.1s, energization analysis step 0.24s, and pressure maintenance analysis step 0.2s.

[0083] Step S4, Solution Analysis: Simulate the formation process of the melt nugget and measure the size and offset of the melt nugget simulation results.

[0084] Measure the diameter of the melt core from the simulation results, observe the direction of melt core offset, and measure the amount of melt core offset.

[0085] Step S5, Solving and analyzing the power supply polarity: Change polarity I in step three to polarity II for simulation, and measure the size and offset of the simulation result of the melt core.

[0086] In step three, the X and Y degrees of freedom of the lower electrode are set to 0, the Z-axis direction is set to the default, the upper electrode is completely fixed with both displacement and rotation angles at 0, the potential of the upper end face 5 of the upper electrode is set to 0, and current is applied as a load to the lower end face of the lower electrode, applying upward pressure and maintaining it. That is, in Figure 2 Current and pressure are applied to position 6 on the lower end face of the lower electrode. The upper electrode cap 1 is set to be completely fixed, the lower electrode cap 4 is set to have 0 degrees of freedom in the X and Y directions, and the Z-axis direction is set to default. The potential on the upper end face 5 of the upper electrode is set to 0.

[0087] Step S6: Comparison and analysis of simulation results: Compare the results obtained in step four with the results obtained in step five.

[0088] The measured melt core size and offset after simulation under polarity I condition are compared with those measured after simulation under polarity II condition. Figure 3 The region within the dashed line represents the melt nucleus formed under polarity I conditions. Figure 4 The area within the dashed line represents the molten nucleus formed under polarity II conditions.

[0089] Step S7, Experimental Characterization and Measurement: The plates welded under polarity I and polarity II conditions will be cut, ground, polished and etched along the centerline of the weld nugget. Then the weld nugget of the plate will be characterized and measured to compare the size and offset of the weld nugget under the two polarities.

[0090] Welding was performed on plates under two polarity conditions with welding parameters of 7.5 kA current, 4 kN electrode pressure, and 0.24 s welding time. The plates were cut, ground, polished and etched along the center line of the weld nugget. The weld nugget was then characterized and the diameter and offset of the weld nugget were measured. The differences in weld nugget size and offset under the two polarity conditions were compared.

[0091] The welding parameters described above are consistent with the simulation parameters.

[0092] Step S8, Result Comparison: Compare the comparison results obtained in Step 7 with the comparison results obtained in Step 6.

[0093] The experimental results and simulation results in this embodiment show good agreement, proving the influence of the polarity of the resistance spot welding power supply on the weld nugget shape. It also verifies the accuracy and effectiveness of the numerical simulation method for the influence of the polarity of the resistance spot welding power supply on the weld nugget shape.

[0094] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made to the present invention should be included within the scope of protection of the present invention.

Claims

1. A numerical simulation method for the effect of power source polarity on nugget shape in resistance spot welding, characterized by: The influence of the change of the polarity on the nugget size and the offset phenomenon is verified by simulating the nugget formation process of resistance spot welding under two polarities; the power polarity refers to the positive and negative directions of the current through the welding plates, including two polarities: polarity I is that the welding plate one is the positive electrode and the welding plate two is the negative electrode, and polarity II is that the welding plate two is the positive electrode and the welding plate one is the negative electrode, including the following steps: Step one, modeling: according to the specifications of the electrode used in the welding test and the size of the welding plates, a three-dimensional geometric model is constructed by using the solidworks software, the model is composed of upper and lower electrode caps and welding plates, and the model is imported into ABAQUS; Step two, attribute of material: the corresponding material properties are respectively assigned to the upper and lower electrode caps and the welding plates; Step three, setting simulation parameters and conditions: under the condition of polarity I, the boundary conditions and loads are set according to the welding test parameters, and the model is meshed; Step four, solution analysis: the nugget formation process is simulated, and the size and offset of the nugget simulation results are measured; Step five, change the power polarity and solve the analysis: change the polarity I in step three to polarity II, that is, set the freedom degrees of the lower electrode X and Y directions in step three to 0, set the Z axis direction to default, set the upper electrode to be completely fixed, the displacement and rotation angle are both 0, set the potential of the upper end surface of the upper electrode to 0, apply the current as the load to the lower end surface of the lower electrode, and apply the upward pressure to the lower end surface of the lower electrode and keep it; after setting, submit the job for simulation, measure the size and offset of the nugget simulation results; Step six, comparison and analysis of simulation results: compare the results obtained in step four with the results in step five; Step seven, test measurement and comparison: after welding under the conditions of polarity I and polarity II, cut, polish and polish the plates along the nugget center line, then characterize and measure the plate nugget, and compare the nugget size and offset under the two polarities; Step eight, comparison of results: compare the comparison results obtained in step seven with the comparison results obtained in step six.

2. The numerical simulation method of the effect of the polarity of a resistance spot welding power source on nugget formation according to claim 1, characterized by: The material properties in step two include density, Young's modulus, Poisson's ratio, yield stress, thermal conductivity, thermal expansion coefficient, specific heat capacity and electrical conductivity, which change with temperature, and are obtained by using the simulation software JmatPro; the melted welding plate one and the welding plate two are still considered as isotropic ideal homogeneous materials.

3. The numerical simulation method of the effect of polarity on nugget shape of resistance spot welding power source according to claim 1, characterized in that: The three-dimensional geometric model is simplified to a 1 / 4 finite element model, the symmetric interface condition of the finite element software is used to reduce the calculation difficulty, which is conducive to the convergence of the calculation.

4. The numerical simulation method of the effect of polarity on nugget shape of resistance spot welding power source according to claim 1, characterized in that: The setting of the simulation parameters and conditions in step three is as follows: in the initial analysis step, the initial temperature of the environment is 293 K, the lower electrode is completely fixed, the displacement and rotation angle are both 0, the selected model is a 1 / 4 axisymmetric model for the convenience of calculation, and symmetric interface conditions are set for the two side surfaces; the potential of the lower end surface of the lower electrode is set to 0; in the pre-pressing analysis step, a downward pressure is applied to the upper end surface of the upper electrode and is maintained; in the current-carrying analysis step, the current is applied as a load to the upper end surface of the upper electrode, surface film cooling conditions are set in the area acted on by the electrode cooling water, and air heat dissipation boundary conditions are set for the contact surfaces of the electrode and the plate with air.

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