Structural Parameter Design of Magnetic Pulse Welding Coil for Dissimilar Metal Joints: Numerical Simulation, Parameter Optimization, and Experiments

Abstract

As a main component of the magnetic pulse welding (MPW) system, the working coil exerts a great influence on the electromagnetic force and its distribution, which, in turn, affects the quality of the MPW joints. This study proposes a structural parameter optimization of the MPW coil, with the objective of achieving a higher induced current density on the flyer plate. The optimal Latin hypercube sampling technique (OLHS), Kriging approximate model, and the Non-Linear Programming by Quadratic Lagrangian (NLPQL) algorithm were employed in the optimization procedure, based on the finite element model built in LS-DYNA. The results of the sensitivity analysis indicated that all the selected parameters of the coil had a specific influence on the induced current density in the flyer plate. The optimized coil structure serves to refine the pulse current flowing path within the coil, effectively reducing the current loss within the coil. Additionally, the structure reduces the adverse effect of the current within the coil on the induced current within the flyer plate. Numerical results show the peak-induced current of the flyer plate increasing by 25.72% and the maximum Lorentz force rising by 58.10% at 25 kJ with the optimized coil structure. The experimental results show that with the same 25 kJ discharge energy, the optimized coil could increase the collision velocity from 359.92 m/s to 458.93 m/s. Moreover, 30 kJ of discharge energy should be needed to achieve the failure mode of base material failure with the original coil, while only 15 kJ should be applied to the optimized coil. These findings verify the optimization model and give some outline for coil design.

1. Introduction

In response to the demand for lightweight design in the automotive industry, aerospace industry, and appliance industry, there is a growing focus on research into hybrid structures comprising lightweight materials, including high-strength steel, aluminum, and copper [1,2]. However, a challenge emerged due to the incompatibility of thermophysical and conductive properties between dissimilar metal materials in transitional welding technology [3]. In contrast, solid-state welding technologies, including friction welding [4], friction stir welding [5], ultrasonic welding [6], explosive welding [7], and magnetic pulse welding (MPW) [8], have been demonstrated to be effective in joining dissimilar materials without melting the materials. MPW employs the process of element diffusion, which occurs as a result of high-speed collisions under the influence of electromagnetic force (EMF), in order to achieve metallurgical bonding between dissimilar metals [9,10]. Consequently, MPW results in the formation of heterogeneous metal joints with high mechanical strength, devoid of brittle metal compounds and heat-affected zones [11]. In comparison to conventional techniques such as resistance welding, MPW technology demonstrated superior connection strength, enhanced production efficiency, and more favorable environmental performance [12].

Therefore, many researchers have studied the welding mechanism of the MPW joints. Zhang et al. [13] proposed that within the welding interface, the principal bonding mechanism of the magnetic pulse welding (MPW) process was interatomic element diffusion induced by high pressure and concentration gradients. Stern et al. [14] attributed the bonding between the connecting sheets to local melting and solidification in the aluminum–copper welding interface. Lee et al. [15] proposed that the high interfacial bonding strength of the magnetic pulse welded steel/aluminum alloy lap joint originated from the multi-phase intermediate layer and grain-refined aluminum layer. In order to further enhance the welding performance, considerable effort has been directed toward process development and micro-structure improvement for the MPW process. Kore et al. [16] demonstrated that optimizing the coil size and standoff distance could enhance the shear strength of Al/Al MPW joints. Zhu et al. [17] investigated the effects of temperature on Al/Mg MPW joints and found that when the temperature was above 150 °C, the formation of excessive Al₁₂Mg₁₇ intermetallic compounds resulted in a reduction in joint mechanical strength. The mechanical tests on Al/Fe MPW joints under high-speed tension and cyclic loading conditions demonstrated that brittle intermetallic compounds at the welding interface were the primary cause of joint failure under high strain rate loading [18].

The aforementioned studies primarily focused on examining the impact of process parameters and microstructures on the mechanical performance of the MPW joint. Additionally, the coil serves as the indispensable component responsible for conducting current and generating electromagnetic force during the welding process [19,20], thereby largely determining the quality of the welded joint. In order to meet the requirements of complex workpiece geometries, Aizawa et al. [21] proposed a one-layer E-shaped flat coil as a means of joining dissimilar plate metals through the MPW method. Shotri et al. [22] proposed a novel O-shaper flat coil to join the overlapping dissimilar metallic sheets. The uniform pressure electromagnetic actuator (UPEA) has been frequently employed in the joining of dissimilar plate metals due to its capacity to apply uniform pressure across the entire welding area [23,24]. Manogaran et al. [25] employed a monolayer I-shaped flat inductor to achieve magnetic pulse spot welding. Moreover, the importance of the field shaper has been highlighted in reducing the mechanical load on the coil and extending its operational lifespan [26].

Currently, the systematic parameter design for the coil structure in MPW sheet connections has not yet been reported, while the coil is crucial for improving welding performance and reducing energy loss. The objective of this study was to investigate the impact of structural parameters of the coil, including the width of the side arm, bottom width, and thickness, on the induced current density in the flyer plate of Al–copper MPW joints. Initially, the finite element model of magnetic pulse welding was established and verified through experiments. Subsequently, the sampling was conducted in accordance with the optimal Latin hypercube sampling method, and sensitivity analysis was performed on the basis of the sampling results. Based on this approach, a response approximation model was developed utilizing the Kriging approximation technique. Furthermore, the optimal structural parameters were identified through the application of the quadratic Lagrangian non-linear programming (NLPQL) algorithm. Through the numerical simulation analysis conducted on both the optimum coil and the original coil, the current paths of the coils and the induced currents in the flyer plate were analyzed. Finally, the velocity test, shear test, and weldability test were conducted with both types of coils to evaluate the welding performance.

2. Original Coil Design and Numerical Simulation

2.1. Principle of MPW Process

The discharge process in MPW can be represented by a simplified resistor–inductor–capacitor (RLC) oscillating circuit. At the outset, a pre-determined voltage was applied to the capacitor. Upon closure of the discharge switch, a high-frequency current was observed to flow through the coil, resulting in the generation of a transient magnetic field that induced eddy currents in the flyer plate. This phenomenon propelled the flyer plate toward the base plate at a high velocity [27,28]. The single-turn E-shaped copper MPW coil employed in this investigation is illustrated in Figure 1a, comprising five discernible regions: the current input area; current output area; working arm; side arm; and bottom. The current entered the coil from the upper portion, traversed the lateral and inferior arms, and exited from the central region. The narrower width of the working arm resulted in a significant increase in current density, which is conducive to welding metal sheets [29,30].

The MPW experiments were carried out using the PST 48/16 electromagnetic forming equipment (produced by PST products GmbH, Alzenau, Germany), which is illustrated in Figure 1b. This device has a rated voltage of 16 kV, a constant capacitance of 408 μF, and a maximum discharge energy of 48 kJ. The Photonic Doppler Velocimeter (PDV) measuring equipment was used to continuously and contactlessly capture the velocity and displacement of the flyer plate by measuring the frequency shift between the laser generator and the velocity measured point. The measurement results were then used to effectively verify the accuracy of the numerical simulation.

Figure 1c shows the discharge current curve obtained through the Rogowski coil measurement. As the current oscillated and decayed rapidly, the deformation of the flyer plate caused by the driving force was mostly completed before the first half-wave of the MPW process, which occurs within 0–30 μs. As a result, only the first half-wave of the discharge current was incorporated into the finite element model that follows. Based on the working principle of MPW, the discharge current curve was fitted by the following equations:

(1)$i(t)={\displaystyle \frac{U_c}{\omega L}}{e}^{-\beta t}\mathit{sin}\omega t$

(2)$\beta ={\displaystyle \frac{R}{2L}}$

(3)$\omega =\sqrt{{\displaystyle \frac{1}{\mathit{LC}}}-{\displaystyle \frac{R^2}{4L^2}}}$

where i(t) and U_c represent the discharge current (kA) and the discharge voltage (kV); ω represents the oscillatory frequency of the RLC circuit (rad/s); β is the current attenuation coefficient; L is the system inductance and C represent the discharge capacitance [31]. In this paper, the discharge energy of 25 kJ was adopted. By fitting the current curve via the above equations, the discharge circuit parameters of the MPW system are shown in Table 1.

2.2. Finite Element Model and Simulated Results

In order to simulate the complex electromagnetic–mechanical–thermal coupled multi-physics process, the LS-DYNA software (LS-DYNA 971) was employed to simulate the MPW process between the AA1060 and T2 copper sheet. The numerical model is illustrated in Figure 2. In the transient electromagnetic field analysis, all elements were assumed to be isotropic and homogeneous. As a result of the high-frequency discharge current and skin effect, the current density and electromagnetic force were concentrated near the surface of the conductive materials. The MPW process simulation model was discretized into 227,230 solid hexahedral elements. To guarantee the precision of the simulation, the deformation zone of the flyer plate was subdivided into more refined hexahedral solid elements (1 × 1 mm² of 3 layers), whereas the base plate (2 × 2 mm² of 1 layer) and the external region of the flyer plate (2 × 2 mm² of 3 layers) were partitioned into coarser hexahedral solid elements, with the objective of reducing the overall number of elements and enhancing the efficiency of the modeling calculations.

The material properties of each component are presented in Table 2. In order to analyze the behavior of the AA1060 flyer plate during the transient high strain rate deformation process, the Johnson–Cook plasticity model was employed, taking into account the effects of temperature, strain rate, and plastic strain [32,33]. The relative parameters were derived from Liang’s experimental procedure, as detailed in Table 3, where A is the stress value at the reference temperature; n is the hardening coefficient; B, C, and m are constants related to the material. The rigid blocks positioned between the base and flyer plate served to create a 1.4 mm gap for acceleration purposes. Meanwhile, the insulator positioned beneath the aforementioned flyer plate effectively simulated the insulation gap that would be present between the flyer plate and the coil. In order to prevent the occurrence of rigid body displacements within the model, rigid body displacement boundary constraints were applied to the coil, the insulator, and the rigid body blocks. The input and output ports of the discharge current are located on the lateral surfaces of the current input and output areas of the coil, respectively.

In order to validate the simulation model, Figure 3 presents a comparison of the velocity–displacement profile at the central point of the flyer plate and the morphology of the welded joints between the simulated and experimental results. Figure 3a shows that the measured velocity–displacement curves are in good agreement with the simulated velocity–displacement curves throughout the deformation of the 1.4 mm deformation gap. As illustrated in Figure 3b, the configuration of the weld region in the numerical simulation exhibited a high degree of correlation with the outcomes derived from the experimental investigation. As a consequence of the malleability of the aluminum, considerable warping deformation was observable on both sides of the width of the flyer plate. These findings demonstrated that the margin of error between the experimental and numerical results was within an acceptable range.

In accordance with the tenets of magnetic pulse welding, the initial focus of an analysis of the welding process is the distribution of current density in the coil and the metal sheets, that is to say, the simulation results of the electromagnetic field. As illustrated in Figure 4a, the coil working arm has a significantly reduced cross-section in comparison to the rest of the part, resulting in a significant current density concentration throughout the working arm. Furthermore, the maximum value of current density in the working arm is predominantly concentrated in the corresponding position of the flyer sheet, especially around the side edges. Similarly, the maximum value of current density in the aluminum plate is primarily distributed in the corresponding position of the coil working arm within the aluminum welding region. Furthermore, the current induced in the aluminum sheet by the coil side arm cannot be omitted. In the copper sheet, the induced current is predominantly generated by the secondary induction of the induced current on the aluminum sheet.

The current density vs. time relationships in four selected elements from the coil section and the center of the aluminum sheet were illustrated in Figure 4b,c. Discharge current curves during the MPW process were also presented in the analysis of deviations of current density. With regard to the coil, the current density of each element exhibits a trend that is essentially aligned with the discharge current, displaying an initial increase followed by a subsequent decline. Furthermore, the current density of the edge position element is markedly higher than that of the central position element.

The evolution of induced currents in aluminum sheets can be separated into four distinct stages. In the first stage, the aluminum sheet remained undeformed. During this period, the induced current within the aluminum sheet rose exponentially in conjunction with the discharge current in the coil. In the second stage, the increasing current density in the aluminum sheet decelerated due to the augmented distance from the coil subsequent to the deformation of the aluminum sheet. In the third stage, the current density in the aluminum plate demonstrated a declining trend as the plate underwent further deformation. This is due to the fact that the distance between the aluminum sheet and the coil increased at a rate that outpaced the growth of the discharge current in the coil, thereby counteracting its effect. In the fourth stage, the deformation of the aluminum plate ceased while the discharge current in the coil remained at a high level. Thereafter, the current density in the aluminum plate increased further and eventually decreased gradually as the discharge current decreased.

As illustrated in Figure 5, the deformation process of the flying plate in the simulation can be described as follows: the flying plate began to plastically deform under the influence of magnetic pressure at 7 μs and subsequently collided with the base plate in the central region at 12 μs. Subsequent to the collision, the contact area between the two welded plates transitioned from line contact mode to face contact mode, with the collision angle undergoing a continuous change. The collision between the two plates was completed at approximately 19 μs.

3. Parameter Optimization Analysis

3.1. Design Responses, Variables, and Optimization Methodology

The structural parameters exert a considerable influence on the magnitude of the induced current within the flyer sheet due to the edge effect and concentration of the discharge current on the coil. Consequently, a parameter optimization analysis of the coil’s structural parameters was conducted with the objective of increasing the induced current in the flyer sheet. Some structural parameters, such as the input and output surfaces, which have a limited impact on the current density within the working arm, were excluded. Furthermore, as the width of the working arm was contingent upon user specifications and proportional to the weld seam width, it was excluded from the optimization process.

The following schematic diagram in Figure 6 illustrates the dimensions of the coil shape and the design variables. The coil has an overall height of 130 mm, an overall width of 169 mm, and a working arm width of 4 mm. The design space of the side arm width (A) and the bottom width (B) was set with a minimum of 4 mm to ensure the current concentration effect (exceeding working arm width). In order to maintain the structural form and ensure the presence of epoxy resin-filled clearance between the side arms and the working arm, the range value of side arm width (A) was set at 4 mm to 81 mm. In order to guarantee that the plate induction area exceeds 4 mm × 30 mm, the range value of the bottom width (B) was set at 4 mm to 99 mm. The overall thickness of the E-shaped section (C) ranged from 4 mm to 10 mm based on magnetic pulse welding experiment outcomes.

The numerical simulation results indicate that the induced current i₂ was predominantly distributed within the welding area when the flyer plate exhibited no deformation, reaching a maximum value at the center of the welding area.

(4)$i_2={\displaystyle \frac{l{\mu }_0}{2\pi R}}[{\displaystyle \frac{U_c}{L}}{e}^{-\beta t}\cos \omega t-{\displaystyle \frac{U_c\delta }{\omega L}}{e}^{-\beta t}\sin \omega t]$

where l is the width of the welded plate; μ₀ is the dielectric constant. Both the tip effect and the skin effect have an impact on the induced current. As a result, merely using i₂ is not enough to describe the magnitude of the local eddy current in the central area of the flying plate. Hence, the objective was to define the magnitude of the current density (ρ) in the central element of the welding area on the flyer plate at 5 μs as the optimization objective in this analysis.

(5)$\rho ={\displaystyle \frac{l{\mu }_0}{2\pi RA}}[{\displaystyle \frac{U_c}{L}}{e}^{-\beta t}\cos \omega t-{\displaystyle \frac{U_c\delta }{\omega L}}{e}^{-\beta t}\sin \omega t]$

where A is the equivalent current flow area in the central zone of the flying plate. The design space for each parameter and optimization response is outlined below:

(6)$\left\{\begin{array}{ll}\max \hfill & \rho \hfill \\ \mathrm{s}.\mathrm{t}.\hfill & 4 \mathrm{mm}\le A\le 81 \mathrm{mm}\hfill \\ & 4 \mathrm{mm}\le B\le 99 \mathrm{mm}\hfill \\ & 4 \mathrm{mm}\le C\le 10 \mathrm{mm}\hfill \end{array}\right.$

Figure 7 illustrates the optimization flow chart of the MPW coil based on the specified design parameters, scope, space, and optimization objectives. The optimization process commenced with the utilization of the Optimal Latin Hypercube sampling technique (OLHS) [34,35] to sample structural parameters. Subsequently, the MPW simulation model was computed using LS-DYNA commercial software (LS-DYNA 971), with the objective and constraint function values simulated. Then, a sensitivity analysis was conducted to generate Pareto effect diagrams [36,37]. A Kriging model [38,39] was constructed to create a surrogate model for the current density response. The Non-Linear Programming by Quadratic Lagrangian (NLPQL) algorithm [40,41] was employed to obtain the optimization solution for the coil. Finally, an experimental validation was conducted on the optimized coil.

3.2. Approximation Model and Sensitivity Analysis

Sixty sampling points were obtained using the optimal Latin hypercube sampling method. The numerical simulation results for all sampling points were used to evaluate the parameter sensitivity and construct an approximate model of the response. Sensitivity analysis results between optimization parameters (including their interaction terms) and the response are shown in Figure 8. The figure shows that coil thickness C has a significant main effect on the optimization response. Additionally, the interaction terms of side arm width A and bottom width B had a significant interaction effect on the optimization response. Figure 9 shows the Kriging fitting surface of different parameters along the induced current density response. The root mean square errors of the Kriging models are all less than 0.05 and meet the accuracy requirements of the optimization. From the approximate model it can be seen that coil thickness has the greatest effect on the induced current density of the aluminum sheet. Side arm width and base width have less effect on the single variable of response and mainly show interaction effects. This is in agreement with the results of the sensitivity analysis.

3.3. Parameter Optimization Results

According to the approximate model developed, the optimal combination of structural parameters obtained using the sequential quadratic programming method (NLPQL) is as follows: a side arm width A of 64.294 mm; a bottom width B of 86.544 mm; and a coil thickness C of 4.0 mm. Figure 10 and Figure 11 show the simulation results under the baseline coil design and the optimal coil design at 5μs. Compared to the original coil, the optimum coil has a significantly shorter working arm length, an increased distance between the working arm and the side arm, and a greatly reduced coil thickness. On the one hand, the flow path of the discharge current in the coil is greatly shortened, effectively reducing the loss of the discharge current in the coil. By reducing the thickness of the coil and shortening the length of the working arm, the induced current is further concentrated in the weld area of the aluminum sheet. By increasing the distance between the working arm and the side arm, disadvantages such as induced current shunting due to the inductive effect of the side arm on the aluminum sheet and the reverse electromagnetic force are reduced.

The maximum value of current density within the aluminum sheet in the optimized coil in comparison to the original coil demonstrates an increase from 2.142 × 10¹⁰ A/m² to 2.693 × 10¹⁰ A/m² by 25.77%. Meanwhile, the maximum value of the Lorentz force exerted by the flyer plate is 2.005 × 10¹¹ N/m³ and 3.170 × 10¹¹ N/m³ in the original and optimized coils, respectively, indicating an increase of 58.10%. Furthermore, the numerical simulation results for the optimal coil exhibited a 1.917% discrepancy in comparison to the prediction results obtained from the optimization search, thereby providing additional evidence in support of the accuracy of the numerical simulation and the reliability of the optimization method.

Figure 12 presents a comparison of the cloud view of the collision velocity distribution in the welded region of the aluminum plate, both before and after the optimization process. As a consequence of the optimized coil structure that increases the induced current and Lorentz force in the aluminum sheet, the collision time of the plate was advanced to 10 μs. Furthermore, the collision velocity at the center point of the welding area has also been significantly enhanced. Following a collision in the central region, the new collision points in the optimized design exhibit a high collision velocity as the collision point expands to both sides of the weld region. In contrast, the original design demonstrates a lower collision velocity in comparison to the initial collision velocity. It is worth mentioning that at this moment in the original design, a reverse rebound velocity was also present at the center of the aluminum plate.

Figure 13 presents a comparison of the curves of current density, Lorentz force, and velocity as a function of time for different elements distributed along the longitudinal direction in the central region of the aluminum sheet in the original design and the optimized design. As illustrated in the figure, the optimally designed coil structure has the effect of enhancing all current density, the electromagnetic force, and the velocity at each element in the welding central region of the aluminum sheet.

4. Experimental Analysis

In order to evaluate the welding ability enhancement of the optimized coil design, several comparison experiments were conducted. Figure 14 presents a comparison of flyer plate speed profiles between the original and optimized coils at a discharge energy of 25 kJ. The figure demonstrates a discernible enhancement in flyer plate velocity resulting from the optimized coil. For a given gap of 1.4 mm, the recorded collision moments were 9.08 μs and 10.86 μs, respectively. At the specific moments, the flyer plate speeds were 359.5 m/s and 458.83 m/s, respectively, representing a 27.63% increase in speed.

To compare the welding ability of the original and optimal coils, magnetic pulsed welding tests were conducted using AA 1060 metal sheet and T2 Cu metal sheet at various energies with the original and optimal coils. For high reproducibility of experimental data, tests were repeated three times at each energy. As depicted in Figure 15a, the LANSANS tensile tester was used for mechanical tests on welded joints with a loading speed of 2 mm/min. To minimize torque influence in the test, 2.4 mm thickness plates were attached to the clamping parts of the specimens. The mechanical results of joints welded by the original and optimal coils under different discharge energies are shown in Figure 15b,c, respectively. With the increasing discharge energy, the joint’s load-bearing capacity and the deformation displacement also showed an upward trend. Once the maximum tensile load surpasses the strength of the aluminum plate, the tensile load of the joint ceases to grow any further as the discharge energy keeps rising.

During the tensile test, MPW joints underwent gradual tensile loading until failure. Based on the deformation pattern, failure modes were classified into two types: fracture at the welded zone and the base material. Figure 16a illustrates a comparison of the tensile force vs. displacement relationship of welded joints by the original and optimized coils at a discharge energy of 15 kJ. The welded joints that had been subjected to the original coil exhibited a welded zone failure pattern. In particular, the aluminum and copper plates were observed to have undergone complete separation at the weld seam, leaving a white trace on the copper plate. This trace had an elliptical, circular shape and was located at the joint where the magnetically pulsed plates were initially welded together. In other areas, the requisite metallurgical bond was not established due to collision velocities or angles that did not meet the necessary solderability conditions. In contrast, the welded joint subjected to the optimized coil exhibited a distinct base material failure pattern, whereby the aluminum plate fractured at the neck shrinkage, while the weld remained intact and did not pull out. This observation indicates that the tensile strength of the joint was greater than that of the weaker aluminum plate in the base material.

In addition to the evaluation of the weldability with the original and optimized coils, Figure 16 illustrates the mean peak tensile loads of magnetic pulse weld joints at various energies, together with the corresponding failure modes. The graph demonstrates that the welded joints subjected to the optimized coil exhibit a markedly higher peak tensile force than the original coil at the same energy level. It is noteworthy that the optimized coil achieved a reliable joint with only 10 kJ of discharge energy, whereas the original coil required 15 kJ for the same outcome. Furthermore, a base material failure mode occurred at 15 kJ of discharge energy with the optimized coil, whereas the same failure mode required 30 kJ of discharge energy with the original coil. In comparison to the original coil, the optimized one conserved 40% of the discharge energy, thereby demonstrating the beneficial impact of optimal structural parameters on energy conservation. In conclusion, the optimized coil structure could achieve welded joints with high performance and significantly lower discharge energy, which can be a useful guideline for engineering applications.

5. Conclusions

Considering the great influence of coil structure on the electromagnetic force within the flyer plate, this study performed a structural parameter design of magnetic pulse welding coil for dissimilar metal joints through numerical simulation, parameter optimization, and experimental approach. The conclusions are outlined below:

(1) According to the sensitivity analysis, coil thickness has the greatest effect on the induced current density in the aluminum sheet, while the side arm width and base width show less impact on the single variable of response and mainly show interaction effects. The optimal structural combination is a side arm width of 64.294 mm, base width of 86.544 mm, and coil thickness of 4.0 mm;

(2) In comparison to the baseline design, numerical results show that the optimized coil structure appeared to have a 25.72% increase in the peak-induced current of the flyer plate and a 58.10% increase in the maximum Lorentz force. According to the PDV measurement, the optimized coil was observed to increase the collision velocity of the flyer plate from 359.92 m/s to 458.93 m/s;

(3) The optimized coil structure serves to optimize the discharge current flow path within the coil, which might be one of the reasons for effectively reducing the current loss within the coil. Additionally, the structure reduces the adverse effect of the current within the coil on the induced current within the flyer plate;

(4) The optimized coil achieved a reliable joint with only 10 kJ of discharge energy, whereas the original coil required 15 kJ for the same outcome. Furthermore, a base material failure mode was realized at 15 kJ of discharge energy with the optimized coil, whereas the same failure mode required 30 kJ with the original coil.

Author Contributions

Y.Q., conceptualization, methodology, investigation, formal analysis, validation, writing—original draft, writing—review and editing, visualization; C.J., methodology, investigation, formal analysis, validation, writing—original draft, writing—review and editing; Y.J., conceptualization, methodology, investigation, formal analysis, validation, writing—review and editing; H.J., conceptualization, methodology, formal analysis, validation, review and editing; J.C., conceptualization, data curation, formal analysis, funding acquisition, supervision, resources, writing—review and editing; G.L., conceptualization, methodology, funding acquisition, supervision, resources, project administration. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The raw/processed data required to reproduce these findings cannot be shared at this time owing to technical or time limitations.

Conflicts of Interest

Author Junjia Cui was employed by the company Shenzhen Huashun Intelligent Equipment Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Footnotes

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Figures and Tables

Figure 1. Schematic diagram, experiment equipment, and the discharge current of MPW technology: (a) principle of discharge process; (b) MPW equipment and Photonic Doppler Velocimeter equipment; (c) discharge current and the fitted current curve.

Figure 2. FE model of the MPW process.

Figure 3. Comparison between experimental and simulated results: (a) velocity–displacement curve; (b) weldment appearance.

Figure 4. Electromagnetic field simulation results of (a) current density cloud diagram within coil and Al/Cu sheets at 5 μs and (b,c) current density–time history in the central area of the coil and the Al sheet.

Figure 5. Structural field simulation results of the flyer plate during the welding process: (a) effective plastic strain cloud diagram; (b) displacement in Z-direction.

Figure 6. Schematic diagram of the coil shape dimensions and design variables: (a) configuration and dimensions of coil (unit: mm); (b) diagram of coil design parameters.

Figure 7. Optimization flow chart of MPW coil.

Figure 8. Pareto diagram of the optimized parameters of the coil.

Figure 9. Kriging fitting surface of different parameters along inducted current density response: (a) the side arm width A and the bottom width B; (b) the side arm width A and the thickness C; (c) the bottom width B and the thickness C.

Figure 10. Simulation results under the baseline coil design at 5μs: (a) discharge current density and Lorentz force distribution within the coil; (b) current density distribution within the Al sheet; (c) current density distribution within the copper sheet; (d) Lorentz force distribution within the Al sheet.

Figure 11. Simulation results under the optimal coil design at 5 μs: (a) discharge current density and Lorentz force distribution within the coil; (b) current density distribution within the Al sheet; (c) current density distribution within the copper sheet; (d) Electric field distribution within the Al sheet; (e) Lorentz force distribution within the Al sheet.

Figure 12. Velocity clouds comparison of Al sheet before and after optimization.

Figure 13. Comparison of simulation results: (a) schematic diagram of different node locations, (b) current density–time curve; (c) Lorentz force–time curve; (d) velocity–time curve.

Figure 14. Comparison of welding speed profiles before and after optimization: (a) welding speed–time curve; (b) physical coil before and after optimization.

Figure 15. Experimental results of (a) diagram of the actual tensile tester and clamping of the welded parts, (b) tensile test results of welded joints welded by original coil, (c) tensile test results of welded joints welded by optimal coil.

Figure 16. Mechanical experiment results for original and optimized coils: (a) tensile force–displacement performance of the joints at 15 kJ; (b) Weldability test results under different energy.

Table 1

Discharge circuit parameters of the MPW system.

Inductance(L)/H	Resistance(R)/Ω	Attenuation Coefficient(β)/s−1	Oscillatory Frequency(ω)/(rad/s)	Capacitance(C)/F
2.14 × 10−7	6.98 × 10−3	1.63 × 104	1.07 × 105	408 × 10−6

Table 2

Material properties of each component.

Component	Materials	Elastic Modules (GPa)	Poisson’s Ratio	Density(kg/m3)	Electrical Conductivity(s/m)
Coil	Chromium Zirconium Copper	97	0.30	8900	5.71 × 107
Base plate	T2 red copper	119	0.46	8960	5.71 × 107
Flyer plate	AA 1060	70	0.33	2740	1.80 × 107
Rigid block	Epoxy resin	/	/	/	0
Insulator	Epoxy resin	/	/	/	0

Table 3

Model parameter values for the Johnson–Cook model of AA 1060.

A (MPa)	B (MPa)	C	n	m
324	114	0.002	0.42	1.34

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