Analysis of the Parallel Seam Welding Process by Developing a Directly Coupled Multiphysics Simulation Model

Abstract

Parallel seam welding (PSW) is the most commonly employed encapsulation technology to ensure hermetic sealing and to safeguard sensitive electronic components. However, the PSW process is complicated by the presence of multiphysical phenomena and nonlinear contact problems, making the analysis of the dynamics of the PSW process highly challenging. This paper proposes a multiphysics simulation model based on direct coupling, enabling the concurrent coupling of the electric field, temperature field, and structural field to facilitate the analysis of the thermal and electrical dynamics within the PSW process. First, this paper conducts an in-depth theoretical analysis of thermal and electrical contact interactions at all contact interfaces within the PSW process, taking into account material properties related to temperature. Second, the acquired data are integrated into a geometric model encompassing electrode wheels and ceramic packaging components, facilitating a strongly coupled multiphysics simulation. Finally, the experimental results show that the simulated weld area deviates by approximately 6.5% from the actual values, and the highest component temperature in the model exhibits an approximate 10.8% difference from the actual values, thus validating the accuracy of the model. This directly coupled multiphysics simulation model provides essentially a powerful tool for analyzing the dynamic processes in the PSW process.

1. Introduction

In the realm of hermetic packaging for integrated circuits, parallel seam welding stands out as one of the most prevalent encapsulation techniques employed in microelectronic devices due to its outstanding characteristics, which include high reliability, superior sealing performance, cost-effectiveness, and high productivity, setting it apart from storage welding, reflow soldering process, and laser welding [1,2,3]. In contrast to storage welding, which produces a large weld area, and laser welding, which produces a high heat-affected zone, high-quality welding in small dimensions is realized in parallel seam welding due to the fineness of the weld area and the low heat-affected zone, which is essential for the protection of sensitive components in microelectronics. It has been widely used in many industrial applications, such as the aerospace, defense, and automotive industries. Early-stage research primarily focused on comprehending the influence of equipment and apparatus on parallel seam welding, including the effects of electrode wheels, fixtures, cover plates, and their associated process parameters, through the utilization of process experimentation methods [4,5,6,7,8,9,10]. However, due to the complexity and transience of the welding process, satisfactory results in the analysis of the internal thermal–electric processes of parallel seam welding are challenging to attain through exclusive reliance on pure theoretical or experimental research. The rapid development in finite element numerical analysis methods has provided powerful tools to address this issue [11].

The main challenges in modeling the process are representation of the multiphysics involved in the process and their interaction, which requires a high level of coupling among the thermal, electrical, metallurgical, and mechanical fields and consideration of the electrical, thermal, and mechanical contact conditions [12,13]. Early simulation work primarily focused on conducting heat transfer analyses of parallel seam welding, without considering thermal–electric coupling [14,15,16]. Hu et al. [17] established a coupled simulation model using the finite element method for the physical processes of the parallel seam welding process, taking contact behavior into account. However, this model used a unidirectional sequential coupling, neglecting the mutual coupling of thermal, electrical, and structural effects. The surface welding area was uniformly divided into multiple geometric subunits, and the PSW process was simulated by progressively applying Joule heating to the welding area. Furthermore, many subsequent studies have extended this coupling approach and applied it to investigate additional physical phenomena [18,19]. For example, Huang et al. [20] studied the stress evolution in parallel seam welding using the moving heat source method by controlling the number of cut-cover plate edges and the duration of the heat source action. Currently, there is still no work focusing on a comprehensive analysis of the dynamic changes within the parallel seam welding process, mainly due to the absence of consideration for the strong coupling between the electrical, thermal, and structural fields, and the insufficient discussion of thermal/electrical contact interactions at the interface.

In this study, a directly coupled multiphysics simulation model simulating the PSW process is developed. A direct coupling between the electric field, temperature field, and structural field was established by this model, which considers the thermal/electrical contact interactions at the interface and the material properties that vary with temperature. This model was experimentally validated in this paper, confirming its accuracy. Finally, an analysis of the thermal and electrical dynamic processes of parallel seam welding was conducted. This paper provides valuable insights into the analysis of the parallel seam welding process, including the dynamic distributions in the electric field, temperature field, and structural field.

2. Development of the Parallel Seam Welding Simulation Model

Parallel seam welding is a packaging technique used to replace traditional soldering methods with pre-placed solder material. Extensive control over sealing parameters is provided, making it particularly suitable for the welding of coated lids and metal solder rings. The foundation of parallel seam welding lies in resistance welding, which is accomplished through Joule heating. During the seam welding process, temperatures exceeding 1000 °C are typically reached at the contact points, leading to the instant melting and bonding of the coating on the lid and solder ring. A pulsed current is generated, and a series of overlapping weld spots are formed by the electrodes as they move along the contact positions, achieving hermetic sealing. The parallel seam welding process can be divided into three stages. Firstly, the electrode is pressed down to make contact with the lid, creating a contact resistance between the electrode and the lid. The contact point serves as the heat generation area. Then, spot welding is performed to secure the lid before welding. Subsequently, the device is moved by the fixture, and the pulsed current is generated by the power source while the surface of the lid is rolled on by the electrode. Two weld spots are created by each pulse. The weld seam for sealing is formed by overlapping weld spots, which are created by the application of multiple pulses. Finally, the power is turned off, and the electrode is lifted to complete the encapsulation of a device. The schematic diagram of the parallel seam welding process is shown in Figure 1.

In rotational sealing, a square or circular lid is required. Spot welding is performed before the welding process to position the lid. Then, the fixture drives the entire device to rotate counterclockwise by 210°. During the rotation, the pulsed current generated by the power source forms a series of overlapping weld spots at the contact positions between the electrodes and the lid. Finally, a closed weld seam is formed, completing the entire sealing process. The process is shown in Figure 2.

The coupling logic relationships among the various physical fields involved in the entire process are shown in Figure 3. Based on the Figure 3, it can be understood that the physical fields involved in the entire parallel seam welding process can be classified into three categories: electric field, thermal field, and structural field. A localized high-temperature region is generated through Joule heating, which is the result of the combined action of welding current and contact resistance at the contact point. The heat in the high-temperature region is propagated to the surrounding areas through thermal conduction, resulting in an overall temperature rise. The resistivity of the resistive heating region and the distribution of the current are affected by the temperature rise in the device. Thermal deformation and thermal stress within the structure are also induced, thereby further impacting the heat transfer characteristics and current density at the contact location. Because the thermal and electrical properties of the materials in the structure are varied with increasing temperature, the conduction of the thermal and electric fields is also affected. The distribution of the thermal field and electric field is also affected by the displacements and rotations of the structure.

The heating and heat transfer within the electrodes and devices in parallel seam welding are shown in Figure 4. The Joule heat generated at the contact point is conducted to the electrode wheel and the bottom of the device. At the same time, there is convective heat transfer between the surfaces of the electrode wheel and the device and the surrounding environment. Since the device is placed in an aluminum alloy fixture, some of the heat is conducted to the fixture. Additionally, there is a contact thermal resistance between the device and the fixture at the contact interface.

2.1. Theoretical Descriptions of Electrical, Thermal, and Structural Fields

2.1.1. Theoretical Analysis of the Thermo–Electric Field

The simulation of the electrical and thermal fields is the focus of this parallel seam welding process simulation model. When a closed circuit is formed by the electrode and the cover plate through which the current passes, Joule heating is generated due to the conductor’s resistance and contact resistance. Most of the heat is transferred throughout the device to the metal fixture through thermal conduction, while a small portion is dissipated through natural convection and thermal radiation to the surrounding environment. The basic governing equations for the thermo–electric process in parallel seam welding follow.

Laplace’s equation is satisfied by the electric potential distribution inside the conductor, when its cross-section is passed by a current. Therefore, the governing equation for computing the potential can be described as [21]:

$$\frac{\partial }{\partial \chi }\left(\frac{1}{\rho }\frac{\partial \varphi }{\partial \chi }\right)+\frac{\partial }{\partial y}\left(\frac{1}{\rho }\frac{\partial \varphi }{\partial y}\right)+\frac{\partial }{\partial z}\left(\frac{1}{\rho }\frac{\partial \varphi }{\partial z}\right)=0$$

(1)

where $x$, $y$, and $z$ represent the coordinates in the Cartesian coordinate system, $\rho$ is the resistivity, and $\phi$ is the electric potential. By solving this governing equation, the distribution of the electric potential can be obtained.

According to the principle of Joule heating, Equation (2) can be described as:

$$q=I^{2}Rt$$

(2)

where $I$ is the current, $R$ is the resistivity of the material, and $t$ is the time during which the current flows through the conductor.

According to the principle of Ohm’s law, Equation (3) can be described as:

$$I=\frac{\varphi }{R}$$

(3)

Furthermore, due to Equation (3), Equation (2) can be rewritten as:

$$q=\frac{{\varphi }^{2}t}{R}$$

(4)

The parallel seam welding process is a typical three-dimensional transient heat conduction problem of internal heat sources. The governing equation for the transient temperature field distribution, which involves electrical resistance heat, can be described as [22]:

$$\frac{\partial }{\partial \chi }\left({\lambda }_x\frac{\partial T}{\partial \chi }\right)+\frac{\partial }{\partial y}\left({\lambda }_y\frac{\partial T}{\partial y}\right)+\frac{\partial }{\partial z}\left({\lambda }_z\frac{\partial T}{\partial z}\right)+q=\rho C_{\rho }\frac{\partial T}{\partial t}$$

(5)

where $\rho$ is the material’s density, $C_{\rho }$ is heat capacity, $T$ is temperature, $t$ is time, and ${\lambda }_x$, ${\lambda }_y$, ${\lambda }_z$ is the thermal conductivity of the material in different directions. The material properties ${\rho }_{pcb}$ and $C_{pcb}$ are temperature dependent.

2.1.2. Theoretical Analysis of Thermal and Electrical Contact Interaction

The resistance during parallel seam welding mainly includes the electrode resistance $R_e$, the lid resistance $R_c$, the ring resistance $R_f$, the electrode/lid contact resistance $R_i$, and the lid/ring contact resistance $R_j$. The schematic diagram of the material body resistance and contact resistance during the parallel seam welding process of ceramic packaging is shown in Figure 5. Among them, the contact resistance $R_i$ is crucial for the completion of soldering and sealing in parallel seam welding, as the formation process of the welding spot and the distribution of the temperature field are affected by it.

There is electrical contact in the parallel seam welding process, and in order to take into account the surface interaction of the electrical contact, it is necessary to specify the electrical contact conductance per unit area in the electrical analysis. In this model, the electrical contact resistances $R_i$ and $R_j$ are taken into account by setting the electrical contact conductance value (ECC) for the contact element. In electrical conduction analysis, the ECC is given in units of $\mathrm{S}/{\mathrm{m}}^2$, and its defining equation can be written as [23]:

$$ECC=\frac{1}{\rho l}$$

(6)

where $\rho$ is the resistivity corresponding to the total contact resistance at the electrical contact interface and $\mathcal{l}$ is the characteristic length of the contact layer, which refers to the size of the microstructure formed between the two contact surfaces.

Owing to few existing reports on simulating the parallel seam welding process, the contact resistances of electrode/lid and lid/ring are not explicitly given. In this paper, the contact resistance is calculated by using the dissimilar metal-to-metal contact resistivity equation, which can be written as [24]:

$$\rho =\left({\rho }_1+{\rho }_2\right)\left[\frac{1}{4}{\left(\frac{\pi {\sigma }_{YS}}{\eta P}\right)}^{\frac{1}{2}}+\frac{3\pi }{16{\eta }^{\frac{1}{2}}}\right]$$

(7)

where ${\rho }_1$ and ${\rho }_2$ are the intrinsic resistivities of the two metals, $\pi$ is the contact surface roughness, $P$ is the contact pressure, and ${\sigma }_{YS}$ is the yield strength of the softer metal.

The electrical contact resistance of the contact interface at 20 °C is calculated by these equations, as shown in

Table 1. Electrical contact resistance of electrode/lid and lid/ring interfaces.

Temperature ($\mathbf{°}\mathbf{C}$)	Electrode/Lid ($\mathbf{S}/{\mathbf{m}}^2$)	Lid/Ring ($\mathbf{S}/{\mathbf{m}}^2$)
20	3.78 × 109	2.14 × 108

.

During the seam welding process, the heat generated at the welding point on the lid is conducted to the bottom device. A contact thermal resistance exists between the lid and the ring. The thermal contact resistance is taken into account by setting the thermal contact conductance value (TCC) for the contact element. TCC is used to describe the thermal contact thermal conductivity value, and its unit is $\mathrm{W}/{\mathrm{m}}^2°\mathrm{C}$. The electrical and thermal conductivity of the contact layer at higher temperatures is calculated via the Wiedemann–Franz law [25,26], which can be written as:

$$\frac{\lambda }{\sigma }=LT$$

(8)

where $L$ is Lorentz’s constant, which is 2.44 × 10⁻⁸ $\mathrm{W}\Omega {\mathrm{K}}^{-2}$, and $T$ is the absolute temperature.

The electrical conductivity and thermal conductivity of the contact layer can be converted into the electrical contact conductance and thermal contact thermal conductivity in this model [27], which can be expressed as:

$$\frac{\lambda }{\sigma }=\frac{TCC}{ECC}=LT$$

(9)

The thermal contact resistance of the contact interface is calculated from these equations, as shown in

Table 2. Thermal contact resistance of lid/ring interfaces.

Temperature ($\mathbf{°}\mathbf{C}$)	Lid/Ring ($\mathbf{W}/\mathbf{m}·\mathbf{°}\mathbf{C}$)
20	1.58 × 103

.

2.1.3. Temperature-Dependent Material Properties

Specific heat, density, and thermal conductivity are necessary material parameters for thermal simulations. However, when thermoelectric coupling simulation is performed, the resistivity of the material at different temperatures is required to be provided to calculate the potential distribution, current density, and Joule heating, in addition to the material parameters required for the thermal simulations described above.

The material used for the ceramic is 92% Al₂O₃, and its physical properties are shown in

Table 3. Physical properties of 92% Al₂O₃.

Temperature ($\mathbf{°}\mathbf{C}$)	Density ($\mathbf{kg}/{\mathbf{m}}^3$)	Specific Heat ($\mathbf{J}/\mathbf{kg}·\mathbf{°}\mathbf{C}$)	Thermo Conductivity ($\mathbf{W}/\mathbf{m}·\mathbf{°}\mathbf{C}$)	Electrical Resistivity (${10}^7\mathsf{\Omega }\mathbf{m}$)
20	3700	840	21	—
100		—	16.8
200		—	13.2
400		—	10.2
600		1250	8.3
800		1390	6.8

[28]. The ring is made of 4J29 alloy, also known as Kovar alloy. Its thermal expansion coefficient is similar to that of borosilicate glass. Because of its excellent welding performance, it is often used in electric vacuum devices. The physical properties of the welding ring are shown in

Table 4. Physical properties of 4J29.

Temperature ($\mathbf{°}\mathbf{C}$)	Density ($\mathbf{kg}/{\mathbf{m}}^3$)	Specific Heat ($\mathbf{J}/\mathbf{kg}·\mathbf{°}\mathbf{C}$)	Thermo Conductivity ($\mathbf{W}/\mathbf{m}·\mathbf{°}\mathbf{C}$)	Electrical Resistivity (${10}^7\mathsf{\Omega }\mathbf{m}$)
20	8170	480	18.84	3.8
100		510	20.04	4.6
200		520	21.57	5.4
400		540	23.11	7.1
600		560	22.62	9.7
800		580	25.5	10.3
1000		610	28.83	10.3
1200		640	32.16	10.3
1400		670	35.48	10.3

[29,30]. The lid and pins are made of 4J42 alloy, which also exhibits a thermal expansion coefficient matching that of glass and ceramics. It is commonly used in the electric vacuum industry, and its physical properties are shown in

Table 5. Physical properties of 4J42.

Temperature ($\mathbf{°}\mathbf{C}$)	Density ($\mathbf{kg}/{\mathbf{m}}^3$)	Specific Heat ($\mathbf{J}/\mathbf{kg}·\mathbf{°}\mathbf{C}$)	Thermo Conductivity ($\mathbf{W}/\mathbf{m}·\mathbf{°}\mathbf{C}$)	Electrical Resistivity (${10}^7\mathsf{\Omega }\mathbf{m}$)
20	8120	470	27.39	2.6
100		510	27.68	3.3
200		590	27.55	4.2
400		580	20.27	8.1
600		560	21.93	9.8
800		580	25.47	10.3
1000		610	29	10.3
1200		640	32.54	10.3
1400		670	36.06	10.3

. The solder between the ring and ceramic is AgCu28, and its physical properties are shown in

Table 6. Physical properties of AgCu28.

Temperature ($\mathbf{°}\mathbf{C}$)	Density ($\mathbf{kg}/{\mathbf{m}}^3$)	Specific Heat ($\mathbf{J}/\mathbf{kg}·\mathbf{°}\mathbf{C}$)	Thermo Conductivity ($\mathbf{W}/\mathbf{m}·\mathbf{°}\mathbf{C}$)	Electrical Resistivity (${10}^7\mathsf{\Omega }\mathbf{m}$)
20	9900	277	420	0.165
100
200
400
600
800

[31]. The electrodes are manufactured from a tungsten–copper alloy, and these properties are embodied, including high-temperature stability, wear resistance, electrical conductivity, and thermal conductivity. The electrode’s physical properties are shown in

Table 7. Physical properties of WCu20.

Temperature ($\mathbf{°}\mathbf{C}$)	Density ($\mathbf{kg}/{\mathbf{m}}^3$)	Specific Heat ($\mathbf{J}/\mathbf{kg}·\mathbf{°}\mathbf{C}$)	Thermo Conductivity ($\mathbf{W}/\mathbf{m}·\mathbf{°}\mathbf{C}$)	Electrical Resistivity (${10}^7\mathsf{\Omega }\mathbf{m}$)
20	15,400	186	220	0.5
100
200
400
600
800

[32,33].

2.2. Geometric Model and Boundary Conditions

2.2.1. Geometric Model

The dimensions of the electrode structure are shown in Figure 6a. The electrode material used in this study is a tungsten–copper alloy (WCu20), and the electrode angle is 4°, which is the angle between the inclined plane of the electrode and the horizontal plane. The device encapsulated by parallel seam welding is the CSOP-8 ceramic package. Since its cover plate is square, the rotational seam welding process can be used for sealing. The dimensions of the package shell are 14.7 × 6 × 2.3 mm, and the corresponding cover plate dimensions are 5.56 × 5.65 × 0.1 mm, as shown in Figure 6b.

Considering the strong coupling in the seam welding process, the direct coupling method with coupling field elements is employed. Coupling field elements are a special type of element used to simulate the interactions between multiple physical fields. Multidomain problems are solved through coupled field elements, where interactions between different domains are crucial. For example, changes in deformation or stress distribution due to the interaction of thermal conductivity and structural mechanics, or the temperature rise of an object due to Joule heating caused by electrical conductivity, and thus the resistivity and current density of the object are affected. These issues are often difficult to address by treating each domain individually, as interactions between different domains may be overlooked. Various multifield problems are solved through the use of coupled field elements, thus the realism and accuracy of the simulation will be better.

The model is set up as follows: frictional contact with a coefficient of friction of 0.1 is applied between the two electrodes and the cover plate. The remaining contact pairs are set as tied contacts, including the contact between the lid and the ring, and the contact between the ring and the ceramic. To balance computational accuracy and efficiency, the mesh near the contact regions is refined to a size of 0.1 mm, while the mesh in other areas is relatively coarse. The mesh size in the ceramic and pin regions is set to 0.2 mm. The total number of elements is 24,852, and the total number of nodes is 34,904. The specific mesh distribution is shown in Figure 7.

2.2.2. Boundary Conditions

For the CSOP-8 ceramic package, the parameters used in the parallel seam welding process follow: welding current of 184 A, pulse width of 2 ms, pulse repetition time of 140 ms, welding speed of 1.6 mm/s, electrode pressure of 3 N, and counterclockwise rotation angle of the fixture at 210°. Convection heat transfer to air is specified on all the lateral surfaces of the electrode and the device that are not in contact. The coefficient of heat transfer is set at 11.3 W/m²K, with an ambient temperature of 29 °C. A higher convective heat transfer coefficient of 300 W/m²K is applied to the bottom of the device.

A rotary sealing process is used in CSOP-8 ceramic packages, and the electrodes are pressed against the midpoint of the cover plate on both sides. Then, the fixture drive is rotated counterclockwise and the two electrodes are driven to rotate in opposite directions by the friction in the contact position. Included in the overall motion of the mechanism are three rotational pairs, for the bottom fixed plate and the two electrodes, and two pairs of translations: downward and upward for the electrodes. The MPC184 multipoint constraint element is added to the finite element model. A rotary joint is added to the bottom of the ceramic so that the rotational freedom of the bottom surface around the z-axis is established. General joints are added to both sides of the two electrodes and rotational movements around the z-axis and translational movements along the x-axis are established. A schematic diagram showing the motion subloading is provided in Figure 8.

3. Model Validation

The comparison of the simulation results for the temperature distribution in the welded joints under a single pulse with the actual experimental results is shown in Figure 9. The actual photographs of the soldered joints show that unmelted gold plating is present with the center area while the gold plating in the peripheral area has been melted, which is in good agreement compared to the simulation results. The width of the actual welded joint is 744.51 $\mathsf{\mu }\mathrm{m}$, and the height of the actual welded joint is 253.64 $\mathsf{\mu }\mathrm{m}$. The width of the welded joint obtained by the model is 739.8 $\mathsf{\mu }\mathrm{m}$, and the height of the welded joint is 238.6 $\mathsf{\mu }\mathrm{m}$. The calculated area of the welded joint in the model is shown to differ from its actual measured value by 6.53%, and the simulated dimensions of the welded joint are very much in line with the experimental results.

By comparing the two, it can be seen that a “crescent” shape is presented in the temperature distribution in the cover solder joints, and the temperature in the outer area is higher than the center. Actual photographs of the soldered joints show that unmelted gold plating is present, while the gold plating in the peripheral areas has melted, which is in good agreement with the simulation results. Due to the conical shape of the electrode, the pressure distribution at the contact interface with the cap is not uniform, with a higher pressure in the center and a lower pressure at the periphery. The contact resistance is unevenly distributed, with the occurrence of low resistance in the center and high resistance in the periphery, resulting in greater melting in the peripheral region than in the center.

The comparison of the measured temperature of the device at a rotation of 194° during soldering with the simulation results is shown in Figure 10. The infrared temperature measurement showed that the highest temperature in the ceramic was 106.1 °C, while the calculated ceramic temperature in the model was 117.57 °C, resulting in a difference of 10.8% compared to the actual value, and the accuracy of the model calculations is verified.

In this paper, parallel seam welding experiments were performed using the same process parameters as the simulation model for three simultaneous experiments. Welding joint area and maximum component temperature were chosen as indicators for calculating the error for the model validation. The data for these experiments were averaged to obtain more scientific experimental data. The experimental data were compared with the model data to obtain the error and thus verify the accuracy of the model, as shown in

Table 8. Summary of model validation.

Metric	Welding Mode	Actual Value	Simulated Value	Error
Welding joint area	Parallel seam welding	148,237.45 μm2	138,565.28 μm2	6.5%
Maximum component temperature	Parallel seam welding	106.1 °C	117.57 °C	10.8%

.

4. Results and Discussion

4.1. Analysis of the Electric Field

During the parallel seam welding process, the distribution of the current density at different angles of device rotation is shown in Figure 11. It can be observed that due to the constraints of current paths, there is a significant current density at the two contact regions between the electrode and the cover plate when the current flows from one electrode to the other through the electrode–cover plate interface. Moreover, during the welding process, the current density is continuously varied as the electrodes are rolled on the cover plate. Particularly, the maximum value for the current density is reached when the device is rotated to 45° and the contact point is moved to the rounded corner of the cover. It is attributed to the fact that the contact area between the electrodes and the cover plate is reduced in the rounded region, causing a reduction in the cross-sectional area of the current path and an increase in the current density. Conversely, when the contact point is moved to the straight edge of the cover, the contact area is increased, resulting in the current density being reduced.

The peak current density variations in the circuit throughout the welding process and the current density variations during the pulse-width phase (2 ms) under three specific pulses are shown in Figure 12. It can be observed that the current density in the circuit is significantly increased, when the corner of the lid plate is approached a second time by the contact point, and then it is rapidly reduced after passing through the corner area. This phenomenon is attributed to the dynamic change in contact area during the welding process, where the current density at the contact location is significantly influenced. Furthermore, for each pulse, the current density is also varied over the pulse width, although the magnitude of these variations is relatively small.

The variation in maximum voltage in the welding process is shown in Figure 13. With the change in the contact point during the welding process, the maximum voltage of each pulse is also varied continuously, and a certain periodicity similar to the current density is exhibited. The voltage is significantly higher when the electrode is located at the rounded corner of the cover plate compared to the straight edge of the cover plate. From Figure 13b, in the comparison of pulses A and D, the voltage is gradually increased during each pulse-width interval (2 ms), which the change in resistance during the seam welding process is illustrated. Since the resistivity of the metallic material is raised with the increase in temperature, the resistance in the circuit is enlarged, thus leading to an increase in the voltage between the electrodes during the pulse-width phase.

4.2. Analysis of Weld-Point Temperature

The temperature distribution in the welded joints on the lid at different times during the parallel seam welding process is shown in Figure 14. At the beginning of welding, the contact point is located at the midpoint of the cover plate’s sides. When the seal is rotated, the position of the contact points is varied along the edges of the cover plate and a series of weld joints are formed under the influence of the pulsed current. At 2.40 and 5.20 s, the temperature of the solder joint at the fillet of the cover plate is significantly increased. Reduction in the contact area between the electrode and the fillet of the cover plate causes an increase in the current density and the temperature at the center of the welded joint. However, as the contact area is increased after passing through the fillet, the current density is reduced and the temperature at the center of the solder joint decreases.

From Figure 14, it is not difficult to find that the shape of the weld joint has been constantly changing during the rotation of the device. When the solder joint is located on the straight edge of the lid, a semi-elliptical shape is presented. When the solder joint moves to the rounded corner of the lid, the semi-elliptical shape is transformed into a fan shape. Due to the uneven distribution of the current density, the outer temperature of each weld point is higher than the inner temperature.

4.3. Analysis of Overall Transient Temperature

The overall transient temperature distribution during parallel seam welding is shown in Figure 15. In the initial stage of welding, the fastest temperature rise is experienced by the lid of the device, with a higher central temperature and an elliptical distribution. The heat generated at the contact points is conducted to the device and the electrode. The temperature of the device was raised above 117 °C at 3.52 s, while the temperature of the electrodes reached about 50 °C. In the subsequent process, the temperature of the ceramic tube shell stabilized at approximately 110–140 °C until the end of the welding. The temperature of the pins is influenced by heat conduction, with higher temperatures near the ceramic and relatively lower temperatures farther from the ceramic position.

Throughout the entire welding process, it can be observed that the temperature of the lid is significantly higher than that of other components, with the central temperature typically falling within the range 180–220 °C. The lid is the main area of welding, and it is manually placed on the welding ring before welding. Due to the lack of close contact between the lid and the weld ring, significant contact thermal resistance is present and rapid heat transfer in the weld region is impeded, resulting in most of the heat being concentrated in the lid. Additionally, the thickness of the Kovar lid is only 0.1 mm and its mass and heat capacity are lower compared to ceramics. When the total heat of welding absorbed by the device is kept constant, higher rises in temperature occur in the objects with lower mass and heat capacity. Significant temperature gradients are exhibited in the device along its longitudinal axis, which can lead to the occurrence of significant stress concentrations within the ceramic.

5. Conclusions

In this study, a multiphysics simulation model for the analysis of the thermal–electric dynamic physical processes in parallel seam welding is established using the direct coupling method. A direct coupling between the electric field, temperature field, and structural field was established by this model, which considers the thermal/electrical contact interactions at the interface and the material properties that vary with temperature. The experimental results show that the simulated weld area deviates by approximately 6.5% from the actual values, and the highest component temperature in the model by approximately 10.8% from the actual values, thus validating the accuracy of the model. The thermal–electric physical fields are analyzed based on the information provided by the established model, including dynamic current, pulse voltage, weld-point temperature, shape, and the overall thermal behavior of the device. This directly coupled simulation model can be utilized for the analysis of the fundamental physical processes in parallel seam welding and serves as a powerful tool in the design of process parameters.

Owing to the complexity of modeling, excessive computational time was incurred in the simulation model described in this article, which stands as the primary limitation in the model. Further research is required to address this aspect. Focusing on a sensitivity analysis of crucial parameters and undertaking process optimization design based on this model will be the main focal points in our future work.