Energy efficiency improvement method of magnetic pulse welding based on auxiliary capacitance

Abstract

To solve the problem of energy loss caused by low energy utilization rate in the process of magnetic pulse welding (MPW), this paper presents a method to recover the energy after the first half wave of pulse current by using auxiliary capacitance. A detailed introduction of the working process of the improved discharge circuit was first carried out. Then experimental investigation of the current waveform of the main discharge circuit and analyzed numerically of the improved MPW system were investigated. The experimental results of the current waveform of the main discharge loop agree well with the simulation results, which verifies the feasibility of the proposed method. The simulation results show that the energy loss decreases from 95.3% before the improvement to 36% after the improvement, and the energy utilization rate increases by 261.5%. According to the welding window theory, the welding quality of this method is the same as that of the traditional method. It shows that this method can greatly improve the energy utilization rate of magnetic pulse welding without reducing the welding quality and verifies the effectiveness of this method.

1 Introduction

In the field of manufacturing, to meet the new development requirements of lightweight, low-cost, and structural function integration of industrial design, single structural materials are gradually changing to composite structural materials. Welding is a common means to change a variety of single materials into composite materials, but the traditional fusion welding technology has obvious defects, such as different materials having different thermal properties, which will lead to fusion welding defects [1, 2]. In addition, some specific alloys are sensitive to heat, for example, aluminum 7075 alloy is easy to crack at high temperature [3, 4]. Titanium has strong chemical activity at high temperatures [5, 6].Therefore, as a solid welding technology, magnetic pulse welding has attracted much attention in recent years. In solid welding, defects such as cracking, deformation and porosity caused by the liquid phase in fusion welding can be avoided [7]. With the deepening of the research, scholars found that the magnetic pulse welding process has the advantages of environmental friendliness, low welding temperature, fast welding speed, and high-quality welding parts [8].

In the process of magnetic pulse welding, the pulse current presents a sinusoidal oscillation attenuation trend, and the time interval of flyer plate movement in the welding process is in the first positive half of the current [9]. The welding ended after the first positive half of the current. This causes a large amount of energy waste, and the energy utilization rate is less than 5% [10]. This shortcoming limits the research, development and application of MPW, so how to improve the system’s energy efficiency becomes an important issue in the development of MPW technology. Khalil et al. designed an O-coil structure to improve coil efficiency. Compared with the I-coil, the peak current and current frequency increase by 10%, and the simulation results show that the impact velocity of the plate is higher [11]. Zhang et al. analyzed the optimization of the structural parameters of the E-coil in MPW and proposed a set of coil structural parameters to improve the magnetic pressure on the surface of the flyer plate and thus improve the energy utilization rate [12]. Deng et al. optimized magnetic pulse spot welding with the help of a field shaper. Numerical analysis showed that with the increase of the aperture, the impact velocity of the plate first increased and then decreased, and the system efficiency could be improved by modulating the aperture [13]. Li et al. designed and developed a modularized MPW system with adjustable frequency. This study found that when the discharge energy remained constant, the peak current and the deformation velocity of the fly plate were proportional to the discharge frequency, so increasing the discharge frequency could effectively improve the welding effect and the energy utilization rate of the system [14]. Li et al. analyzed the circuit parameters of the system and found that reducing the circuit inductance could improve the system efficiency, and proposed a scheme to replace the circular transmission cable with copper bar to reduce the total inductance of the circuit [10]. Li et al. designed a multi-weld coil to increase the welding area of a single weld and thus improve energy utilization [15].

In the above research, the main means to enhance the energy efficiency of the MPW system is to optimize the design of coil, field shaper, and circuit parameters. Although these methods can improve the system, there is still a lot of wasted energy, so the effect of improving the system’s efficiency is not significant. Therefore, an energy recovery scheme based on bypass capacitance is proposed in this paper, and the scheme is introduced.

2 MPW system

The equivalent circuit of the MPW system consists of two circuits: a charging circuit and a discharge circuit. The charging circuit is composed of a charging power supply and a capacitor bank. Its function is to provide the initial voltage to the discharging capacitor, that is, to provide energy. The discharge circuit consists of a capacitor bank and a drive coil, as shown in Fig. 1a. When the discharge loop is connected, the electric energy stored in the capacitor is released into the drive coil as a pulse current, generating a strong pulsed magnetic field B around it. According to Lenz’s law, the flyer plate and the drive coil will generate a huge repulsing electromagnetic force, and the flyer plate will quickly collide with the base plate under the driving force, as shown in Fig. 1b.

Fig. 1

MPW system diagram and pulse electromagnetic field diagram

When the relative velocity and collision angle of the two plates are appropriate, metallurgical bonding will be formed [16]. The electromagnetic force can be expressed as follows:

$$F=J\times B$$

(1)

When the flyer plate is displaced, the mutual inductance between the drive coil and the flyer plate will be affected, so the theoretical calculation of discharge current is very complicated. However, as the duration of the whole welding process is very short, the influence of this part can be ignored, and the discharge circuit can be equivalent to an RLC circuit, as shown in Fig. 2.

Fig. 2

Equivalent circuit of the discharge circuit

In Fig. 2, R is the total resistance of the circuit, including line resistance, coil resistance and internal resistance of switches and capacitors. L is the total inductance of the circuit, including line inductance, coil inductance, switching inductance, and capacitor stray inductance. C is the capacitance of the capacitor bank. Therefore, the discharge circuit equation is as follows:

$$RI+L\frac{dI}{dt}+\frac{1}{C}\int Idt=0$$

(2)

In this equation, resistance, inductance, and capacitance must satisfy the following:

$$R<2\sqrt{\frac{L}{C}}$$

(3)

At this time, the coil current is as follows:

$$I\left(t\right)=\frac{{U}_{0}}{{\omega }_{d}L}{e}^{-\mathrm{\alpha }t}sin{\omega }_{d}t$$

(4)

where ω_d is the equivalent angular frequency and α is the attenuation coefficient.

A typical discharge current waveform is shown in Fig. 3.

Fig. 3

Typical discharge current waveform

3 The improved MPW circuit

In the previous section, the pulse current equation and waveform of conventional MPW were introduced. When the current is in the first positive half cycle, the capacitor voltage has entered the negative half cycle. According to this characteristic, a high-power diode (D₁) and a pulse capacitor (C₂) are added at both ends of the capacitor. When the voltage of the discharge capacitor enters the negative half cycle, the D₁ enters the on state. To maximize the energy utilization rate, a high-power diode (D₂) is also connected in series on the main discharge circuit. When the main discharge current enters the negative half cycle, the D₂ enters the off state. The improved MPW circuit is shown in Fig. 4.

Fig. 4

Improved MPW circuit

In the initial stage of discharge, the improved circuit and the original circuit working principle are the same, closing Sop₁, making the discharge circuit conduction, generating pulse current on the drive coil, so that the fly plate under the drive coil induction pulse current, fly plate current and drive coil current opposite, so that between the fly plate and the drive coil produces a great electromagnetic repulsive force, which driving flyer plate deforms at high speed and collides with the base plate. This stage is hereinafter referred to as the first discharge stage. The difference is that when the voltage of the discharge capacitor is reversed, the bypass capacitor branch enters the on–off state, and the on–off of the branch will affect the current waveform of the main discharge circuit. This stage is hereinafter referred to as the second hotel stage. When the main circuit current decays to zero, the discharge capacitor will only discharge the bypass capacitor branch until the voltage of C₁ is equal to that of C₂. This phase lasts very short. This stage is hereinafter referred to as the third discharge stage.

The working process of the improved MPW circuit is divided into four stages, as shown in Fig. 5.

Fig. 5

Working process of improved MPW circuit

In charging stage, circuit breaker Sop₁ is closed, and the primary power supply charges the capacitor C₁ until the voltage of the capacitor C₁ equals the voltage of the primary power supply to U₀.

In the first discharge stage, after the end of charging, Sop₁ is turned off; Sop₂ is closed; the main discharge circuit is connected; and the capacitor C₁ begins to discharge. The circuit voltage equation and the instantaneous expression of the circuit current in this discharge stage are as follows:

$${U}_{C1}{\left(t\right)}_{t={0}^{+}}={U}_{0}$$

(5)

$$RI+L\frac{dI\left(t\right)}{dt}+\frac{1}{C}\int Idt-{U}_{0}=0$$

(6)

$$I\left(t\right)=\frac{{U}_{0}}{{\omega }_{d}L}{e}^{-\mathrm{\alpha }t}sin{\omega }_{d}t$$

(7)

In the second discharge stage, because the load is resistance-inductance load, the loop current lags behind the voltage of capacitor C₁, that is, when capacitor C₁ ends the first positive half cycle, the main discharge circuit is still in the first positive half cycle. At this time, the voltage of capacitor C₁ will increase in the reverse direction, and the high-power diode of the bypass capacitor branch will be in the state of positive voltage. The tube will be switched on, and capacitor C₁ will then charge capacitor C₂. The circuit voltage equation and node equation of the circuit at this stage are as follows:

$${R}_{1}{I}_{L}\left(t\right)+L\frac{{dI}_{L}\left(t\right)}{dt}-\frac{1}{{C}_{1}}\int {I}_{{c}_{1}}dt=0$$

(8)

$$\frac{1}{{C}_{1}}\int {I}_{{c}_{1}}dt+\frac{1}{{C}_{2}}\int {I}_{{c}_{2}}dt+{I}_{{c}_{1}}\left(t\right){R}_{2}=0$$

(9)

$${I}_{{c}_{2}}\left({\text{t}}\right)-{I}_{L}\left({\text{t}}\right)={I}_{{c}_{1}}\left({\text{t}}\right)$$

(10)

In the third discharge stage, when the current of the main discharge circuit decays to zero, the diode of the main discharge circuit will be turned off, that is, the main discharge circuit is disconnected. At this time, only C1 and C₂ circuits remain. Because the C₁ voltage is higher than the C₂ voltage at the moment the main discharge circuit is disconnected, C₁ will continue to discharge to C₂. The circuit voltage equation at this stage can still be expressed by Eq. (9), and the current equation becomes

$$-{I}_{{c}_{1}}\left(t\right)={I}_{{c}_{2}}\left(t\right)$$

(11)

That is

$$-{C}_{1}\frac{{dU}_{{C}_{1}}\left(t\right)}{dt}={C}_{2}\frac{{dU}_{{C}_{1}}\left(t\right)}{dt}$$

(12)

To make the energy utilization rate more clear, the energy provided by the primary power supply to discharge capacitor C₁ at the charging stage is defined as the total energy storage E_sys of the system. In the first and second discharge stages, the energy used to provide the flyer plate welding and the energy lost in the discharge process is E_sec, that is, the energy consumed by the system during a single welding process. At the end of welding, the energy stored in capacitors C₁ and C₂ is E_rec, which is the total energy recovered by the system. In the process of single welding, the effective work done by the system should be E_k done to the flyer plate by the electromagnetic force between the driving coil and the flyer plate during the discharge process. During single welding, the system energy loss is E_loss. Before improvement, the energy efficiency of the system can be expressed as follows:

$${\eta }_{1}=\frac{{E}_{k}}{{E}_{sys}}\times 100\%$$

(13)

The energy efficiency of the improved system can be expressed as follows:

$${\eta }_{2}=\frac{{E}_{k}}{{E}_{sec}}=\frac{{E}_{k}}{{E}_{sys}-{E}_{rec}}\times 100\%$$

(14)

The calculation method for each energy value is as follows:

$${E}_{sys}=\frac{1}{2}{C}_{1}{U}_{0}^{2}$$

(15)

$${E}_{rec}=\frac{1}{2}{C}_{1}{U}_{1}^{2}+\frac{1}{2}{C}_{2}{U}_{2}^{2}$$

(16)

$${E}_{\text{loss}}={E}_{sys}-{E}_{k}-{E}_{rec}$$

(17)

where U₁ is the voltage of capacitor C₁ and U₂ is the voltage of capacitor C₂ after the end of the third discharge stage

$${E}_{k}={\int }_{a}^{b}{\int }_{0}^{d}F\left(x,y\right){\text{dxdy}}$$

(18)

where d is the maximum displacement of each segment of the line element, a and b are the left and right ends of the cross-section of the welding zone respectively, and F is the electromagnetic force.

4 Establishment of a simulation model

Magnetic pulse welding is a very complicated physical process. Much data on the energy utilization rate of the calculation system are difficult to be obtained by artificial calculation or experiment, so it is necessary to establish a numerical model for this process. Each part of the numerical model established in this paper is made of a 1060 aluminum flyer plate, T2 copper base plate and chrome-zirconium copper (CuCrZr) driving coil. Because the coupling between multiple physical fields is involved, the two-dimensional model of magnetic pulse welding is established by using COMSOL Multiphysics finite element software. The model uses three modules: circuit, magnetic field, and solid mechanics.

4.1 Circuit module

This module is used for circuit analysis. The impulse current is solved by Kirchhoff’s current law and Kirchhoff’s voltage law. The current data solved by the circuit module will be transferred to the magnetic field module as input through the discharge coil for the calculation of electromagnetic force. In this model, the current data used by the circuit module is simulated by Simulink. The circuit parameters in the simulation process are shown in Table 1.

Table 1 Circuit parameters

4.2 Magnetic field module

The module is used for magnetic field analysis of welding equipment. Firstly, the spatial distribution of the magnetic field is solved by Maxwell’s equation, and then the electromagnetic force acting on the flyer plate is calculated and transferred to the solid mechanic’s module as an input load. In this module, the induced eddy current in the coil, channel, and flyer plate can be described by the following equation:

$$\nabla \times \mathbf{E}=-\frac{\partial \mathbf{B}}{\partial t}+\nabla \times \left(\mathbf{v}\times \mathbf{B}\right)$$

(19)

$$J=\gamma \mathbf{E}$$

(20)

where E is the electric field intensity, B is the magnetic flux density, v is the deformation speed of the flyer plate, J is the induced current density, and $\gamma$ is the conductivity of metal materials. The electromagnetic parameters in the simulation are shown in Table 2.

Table 2 Electromagnetic parameters of each material

4.3 Solid mechanics module

The module is mainly used for stress analysis of discharge coil and plastic deformation motion of flyer plate. The output will be fed back to the magnetic field module to realize the coupling calculation between the magnetic field and the structure. Table 3 shows the detailed mechanical parameters of the materials used in the simulation. The flyer plate will undergo plastic deformation motion under the action of the electromagnetic force, and its motion satisfies the following equation:

$$\nabla \cdot \sigma +{\mathbf{F}}_{\nu }=\rho \frac{{\partial }^{2}\mathbf{u}}{\partial {t}^{2}}$$

(21)

σ is the stress tensor of the flyer plate, F_v is the volume density vector of the electromagnetic force, ρ is the density of the flyer plate, and u is the displacement vector.

Table 3 Mechanical parameters of each material

The coupling mode of the three physical field modules is shown in Fig. 6.

Fig. 6

Coupling mode of multiple physical fields

5 Results and discussion

5.1 Choice of capacitance C ₂ capacity

In this magnetic pulse welding system, most of the energy loss is Joule heat; so to improve the system energy utilization, Joule heat should be reduced as much as possible. The values of resistance, inductance, and capacitor C₁ are fixed throughout the circuit, so the value of capacitor C₂ should be adjusted to reduce the Joule heat. Joule heat can be calculated by the following formula:

$$W=R{\int }_{0}^{t}{i}^{2}\left(\tau \right)d\tau$$

(22)

In this MPW system, there are two circuits, the main discharge circuit and the auxiliary circuit. Through simulation, the current waveforms of two loops can be obtained, and the capacitance value of capacitor C₂ can be changed to obtain a series of current waveforms, as shown in Fig. 7.

Fig. 7

Current waveform of each loop with capacitance C₂ changed

As can be seen from Fig. 7, with the increase of capacitance C₂, the peak current of the main discharge loop remains unchanged, but the duration of the second discharge stage gradually increases. The peak current of the auxiliary loop and the total duration of the second discharge stage and the third discharge stage is increasing gradually. As can be seen from Eq. (21), with the increase of capacitance C₂, the Joule heat generated by the whole system also increases, and the changing trend is shown in Fig. 8.

Fig. 8

Trend of Joule heat

Therefore, the smaller the capacity of capacitor C₂, the smaller the system energy loss. However, as the capacity of capacitor C₂ decreases, the voltage that C₂ finally bears will also increase, as shown in Fig. 9.

Fig. 9

Voltage variation trend of capacitor C₂

Because the higher the capacitor rated voltage, the higher the capacitor cost, taking into account the above factors, this paper finally determined the capacity value of C₂ as 80 µF.

5.2 Experimental analysis

In order to verify the feasibility of the improved MPW circuit proposed in this paper, we carry out an experimental analysis. In the experiment, the current waveforms of the main discharge circuit of the MPW system before and after improvement were captured, respectively, and compared with the current waveforms of the main discharge circuit obtained by simulation, as shown in Fig. 10. The waveform of the actual main discharge circuit before and after the improvement is roughly consistent with that of the simulated main discharge circuit. It is verified that the improved MPW circuit can realize that the current of the main discharge circuit can rapidly decay to near 0 after the first positive half cycle, so as to achieve the purpose of improving the energy efficiency of the MPW system.

Fig. 10

Comparison between experimental current waveform and simulation current waveform

5.3 Simulated analysis

Based on the initial circuit parameters of the past work and the selected capacitor C₂, the Simulink circuit simulation model and COMSOL Multiphysics simulation model are built. The main function of the Simulink simulation model is to take the data in the main discharge circuit as the input of the circuit module of the COMSOL Multiphysics model and calculate the energy E_rec recovered by the system through formula (16). COMSOL Multiphysics model is used to verify the feasibility of this method, that is, whether effective welding can be formed. The criterion is the Al-Cu welding window theory. In addition, the COMSOL Multiphysics model can also calculate the work E_k done by the electromagnetic force on the flyer plate through Eq. (17).

The simulation results show that the pulse current of the main discharge loop reaches its peak value at 12.55 µs after the discharge capacitor starts, and the peak current is 157.3 kA. When the main discharge circuit current reaches the peak, the circuit will enter the second discharge stage from the first discharge stage. The duration of the second discharge stage was 13.97 µs. When the system changes from a transient state to a steady state, the voltage of C₁ and C₂ is 5582.5 V. According to the calculation method of Eqs. (15) ~ (18), the energy distribution of the simulation system before and after circuit improvement can be obtained, as shown in Fig. 11.

Fig. 11

Energy distribution of simulation system before and after circuit improvement

According to the calculation method of Eqs. (13)–(14), the energy utilization rate of the system before and after improvement is 5.1% and 13.33%, respectively, and the energy utilization rate is increased by 261.5%. Energy loss decreased from 95.3 to 36% after improvement.

According to the welding window theory, the moving velocity Vc of the collision front point (CFP) and the collision angle β are respectively the horizontal axes and the vertical axis to form a rectangular coordinate system. When the welding process (V_C, β) falls in the rectangular coordinate system under a specific area, effective welding can be formed, and the area calls the welding window [17]. The collision front point and collision angle are shown in Fig. 12. The value range of the welding window is related to the material and geometric parameters of the plate. For different materials and plate thicknesses, the corresponding welding window is also different [18]. In this model, the thickness of the Cu plate and Al plate is 1 mm, and the materials are T2 Cu and 1060 Al. The lower limit of the welding window can be expressed by Eq. (23) [19].

Fig. 12

Schematic diagram of collision front point (CFP) and collision angle β

$$\beta =\sqrt{\frac{2.45\times {10}^{8}}{2700\cdot {V}_{c}^{2}}}$$

(23)

The upper limit of the welding window was obtained by extracting the upper limit curve data of MPW of the Cu-Al plate based on Vc and β [19]. The maximum impact angle is 31.9° [20]. Finally, data points (V_C, β) of 14-time points in a simulation were selected and compared with those before improvement. The welding window and simulation results are shown in Fig. 13.

Fig. 13

Welding window and simulation data

As shown in Fig. 11, Vc-β curves before and after improvement are basically consistent and located in the welding window, so the improved circuit with this method does not affect the final welding effect.

6 Conclusion

In this paper, the low energy utilization rate of traditional MPW circuits is introduced in detail, and a magnetic pulse welding energy efficiency improvement method based on auxiliary capacitance is proposed. The effect of auxiliary capacitance on energy loss and the improved energy distribution are studied by simulation. The efficiency of the optimized system is improved significantly. Therefore, the following conclusions are drawn:

• 1. The larger the capacity of the auxiliary capacitor, the more Joule heat is generated by the system, but the smaller the capacity of the auxiliary capacitor, the higher the voltage it will withstand. In order to improve the energy utilization rate of the system and ensure the stable operation of the circuit, the capacity of the auxiliary capacitor is set at 80 µF.

• 2. Through experimental analysis, the improved circuit can realize that the current of the main discharge circuit can rapidly decay to near 0 after the first positive half cycle, so as to achieve the purpose of improving the energy efficiency of MPW system.

• 3. Through simulation analysis, the energy loss of the improved circuit is reduced from 95.3 to 36%, and the energy utilization rate is increased by 261.5%. Greatly improved the system energy utilization rate.

• 4. According to the welding window theory, the welding quality of this method is analyzed. The results show that this method can improve the energy utilization rate of the system under the premise of guaranteeing the welding quality, and providing technical support for the industrialization of magnetic pulse welding