A Short Review of Electromagnetic Attractive Forming and Its Applications

Abstract

Electromagnetic attractive forming (EMAF), as an emerging branch of electromagnetic forming (EMF), has attracted increasing attention due to its unique capacity to shape workpieces toward the coil, offering distinct advantages in forming small-diameter tubes, repairing surface dents, and strengthening hole fasteners. This review systematically classifies and elaborates on the two main approaches for generating electromagnetic attractive force: (1) methods based on dual-frequency discharge and (2) methods based on low-frequency discharge. For each category, the working principles, key technological configurations, experimental verifications, and application scenarios are comprehensively discussed. The dual-frequency discharge approach, implemented through sequential dual-capacitor, dual-coil, and novel single-power circuits, enables controllable attractive forces for sheet/tube forming and hole-fastener strengthening. The low-frequency discharge approach, utilizing ferromagnetic effects, attractive screen, or current-phase-difference mechanisms, extends EMAF to ferromagnetic and non-ferromagnetic materials. Finally, the existing challenges and future research directions are outlined, aiming to provide clear research guidance for the in-depth development and practical engineering application of EMAF technology.

1. Introduction

With the increasing demand for lightweight, high-performance metal components in advanced manufacturing sectors such as aerospace and new energy vehicles, lightweight materials represented by aluminum alloys, magnesium alloys, and titanium alloys have found widespread application [1]. However, these materials often present forming challenges at room temperature, including poor formability and significant springback [2,3,4]. Against this backdrop, electromagnetic forming (EMF) technology—an advanced, high-strain-rate, non-contact manufacturing process—has garnered significant attention from both academia and industry in recent years [5,6]. This is due to its unique advantages in enhancing material formability [7,8,9] and improving forming precision [10,11,12].

Based on the relationship between the direction of the applied electromagnetic force and the relative motion of the workpiece, this technology is primarily divided into two branches: electromagnetic repulsive forming (EMRF) and electromagnetic attractive forming (EMAF). EMRF process refers to the workpiece being shaped away from the coil, driven by a repulsive electromagnetic force towards a die positioned away from the coil. For instance, when the coil is positioned inside the tube, the tube undergoes expansion due to the repulsive force [13,14], as shown in Figure 1a; conversely, when the coil is positioned externally, the tube undergoes compression in diameter under the influence of the repulsive force [15,16], as shown in Figure 1b.

Currently, this approach constitutes the dominant paradigm in electromagnetic forming research since the repulsive electromagnetic force is easy to obtain. It has undergone extensive and in-depth investigation across sheet metal forming [17,18], stamping [19,20], tube expansion [21,22], compression [23,24] and joining [25,26,27] applications, achieving relative technological maturity. Regarding electromagnetic repulsive forming technology, Psyk et al. [28] have published a comprehensive and detailed review.

In contrast, the EMAF process—where the workpiece is shaped towards the coil—remains in its nascent research phase since it is challenging to generate an attractive force on the workpiece. Yet its distinctive process potential is attracting increasing scholarly interest. Its core technical feature lies in the mutual attraction between the coil and workpiece, enabling the workpiece to be rapidly deformed toward the coil. This characteristic effectively addresses certain application limitations inherent in traditional repulsive forming. For instance, in component repair, positioning the coil externally around surface indentations on sheet metal allows the generated attractive force to directly flatten defects, offering novel approaches for damage restoration. More crucially, attractive forming offers irreplaceable advantages when confronting specialized geometries. A typical application is the expansion forming of small-diameter, thin-walled tube components: the extremely limited internal cavity space makes it impractical to accommodate coils for driving expansion, rendering traditional internally driven repulsive forming processes unfeasible. Attractive forming offers a perfect solution in such scenarios. By simply positioning the coil externally around the tube and precisely controlling the distribution of attractive forces, efficient expansion can be achieved, as shown in Figure 1c. This breakthrough resolves the long-standing technical bottleneck in electromagnetic forming for small-sized components.

Given the unique principles and irreplaceable application scenarios of electromagnetic attractive forming, it is crucial to systematically review its developmental trajectory. Through a comprehensive analysis of the relevant literature, this paper identified that existing EMAF research naturally falls into two categories based on the physical mechanisms for generating attractive force: (1) method based on a dual-frequency discharge and (2) method based on a low-frequency discharge. The aim is to systematically elaborate on the fundamental principles, key technological breakthroughs, experimental validations, and application scenarios of each approach, while thoroughly analyzing their existing challenges. Finally, the paper will provide an outlook on future development trends. The goal is to offer clear research guidance to promote in-depth research and industrial application of electromagnetic attractive forming technology.

2. Principle of Electromagnetic Forming

The fundamental principle of the electromagnetic forming process is shown in Figure 2a, where the sheet forming is taken as an example. When a pulsed strong current i_c flows into the coil, it will generate a rapidly fluctuating strong magnetic field B in the surrounding space. This induces eddy current J within the adjacent conductive workpiece. The interaction between the eddy current and the magnetic field produces a pulsed electromagnetic force F, driving the workpiece to undergo high-speed deformation [29,30]. The electromagnetic force density acting on the workpiece can be expressed as [31,32]:

$$\mathbf{F}=\mathbf{J}\times \mathbf{B}$$

(1)

Given the symmetry between the coil and workpiece, the electromagnetic force density in cylindrical coordinates can be expressed as [33,34]:

F_r = J_phi × B_z

(2)

F_z = −J_phi × B_r

(3)

Here, F_r is the radial electromagnetic force, F_z is the axial electromagnetic force, J_phi represents the circumferential eddy current density, while B_z and B_r denote the axial magnetic flux density and radial magnetic flux density, respectively. In sheet forming, the F_z is the main driving force to cause deformation, while in tube forming, the F_r is the main driving force.

Figure 2b presents the equivalent circuit diagram of electromagnetic forming. In this circuit, the capacitor C discharges through the coil, generating the coil current i_c, which in turn induces the eddy current i_w in the workpiece. The coil is treated as a series connection of inductance L_c and resistance R_c, while the workpiece is represented as a series combination of inductance L_w and resistance R_w. Mutual inductance M exists between the coil and the workpiece. Furthermore, the coil and workpiece together can be equivalently represented as a series connection of inductance L_eq and resistance R_eq. According to circuit theory, the current flowing through the coil i_c can be expressed as:

$$i_{\mathrm{c}}={\displaystyle \frac{U_0}{{\omega }_{\mathrm{d}}{L}_{\mathrm{a}}}}{e}^{-\alpha t}\sin ({\omega }_{\mathrm{d}}t)$$

(4)

$$\alpha ={\displaystyle \frac{R_{\mathrm{eq}}}{2L_{\mathrm{eq}}}}$$

(5)

$${\omega }_{\mathrm{d}}=\sqrt{{\displaystyle \frac{1}{L_{\mathrm{eq}}C}}-{({\displaystyle \frac{R_{\mathrm{eq}}}{2L_{\mathrm{eq}}}})}^2}$$

(6)

where α is the attenuation coefficient, ω_d is the oscillation angular frequency. Typically, the current waveform shows as a damped oscillating sine wave, as shown in Figure 2c.

The electromagnetic forces typically manifest as a repulsive force, driving the workpiece to deform in a direction away from the coil. Based on Equation (1), the fundamental approach to altering the direction of the electromagnetic force to achieve attractive forming lies in regulating the direction of the eddy current density J or the magnetic flux density B. The following section will systematically review the electromagnetic attractive forming methods developed in existing research. It is worth noting that the numerical modeling approaches for electromagnetic attractive forming are fundamentally identical to those for conventional electromagnetic repulsive forming. The only distinction lies in the direction of the resulting electromagnetic force, which is naturally captured by the same numerical framework without any modification to the modeling approach. Consequently, this review focuses specifically on the experimental achievements and challenges unique to the attractive mode. For an in-depth discussion of numerical models, readers are directed to existing comprehensive reviews on electromagnetic pulse forming [28].

3. Attractive Forming Using a Dual-Frequency Discharge

3.1. Principle for Attractive Force Generation

Furth et al. [35] proposed a method for generating electromagnetic attractive force employing a dual-frequency discharge current, and this method was confirmed by Deng et al. [36] through simulation. In this method, as shown in Figure 3a, a coil current composed of a slow rising and fast falling stage is employed. During the slow rising stage, the coil current generates a magnetic field B₁ in space, inducing an eddy current J₁ within the workpiece. At this point, the electromagnetic force manifests as a repulsive force. Due to the relatively slow rise in current, the induced eddy current J₁ is small, resulting in a correspondingly weaker electromagnetic force, which can be expressed as:

$${\mathbf{F}}_1={\mathbf{J}}_1\times {\mathbf{B}}_1$$

(7)

When the coil current decreases rapidly, the magnetic field B₁ decays swiftly, inducing a counter eddy current J₂ within the workpiece to delay the magnetic field’s decay. Owing to the high rate of current decay, the induced eddy current J₂ is significantly amplified. At this point, the electromagnetic force acting upon the workpiece can be expressed as:

$${\mathbf{F}}_2=-{\mathbf{J}}_2\times {\mathbf{B}}_1$$

(8)

The direction of the magnetic field remains unchanged, while the direction of the eddy current reverses, thereby altering the direction of the electromagnetic force, which transforms into an attractive force. This method works, but generating a slow-rising and fast-falling current waveform in the coil remains challenging. This is because conventional electromagnetic forming techniques predominantly employ discharge circuits equivalent to an RLC circuit, whereby discharge occurs from a capacitor to the coil, as shown in Figure 2c. The resulting current is an uncontrollable, decaying sinusoidal waveform, failing to meet the requirements for the aforementioned specialized waveform. So, how to obtain the dual-frequency discharge current? There are three primary methods to achieve this: (1) using a single-coil and dual-power configuration, (2) using a dual-coil and dual-power configuration and (3) using a novel discharge circuit.

3.2. Dual-Frequency Current Generation by a Single-Coil and Dual-Power Configuration

To generate the target waveform in the coil, Cao et al. [37] proposed a sequential dual-capacitor discharge solution, employing two power supplies with differing capacitance values to discharge the same coil, as illustrated in Figure 3b. This approach first discharges the coil using a large capacitor C_s, generating a long-pulse-width current. When this current approaches its peak, a second discharge is initiated using a smaller capacitor C_f in the opposite direction, producing a short-pulse-width reverse current. The superposition of these two currents yields a composite waveform in the coil that approximates a slow rise and fast fall characteristic.

Success hinges upon fulfilling two conditions: (1) the amplitude of i_f must be smaller than i_s to maintain the magnetic field direction; (2) by substantially shortening the rise time of i_f, its rate of change becomes significantly greater than that of i_s, thereby inducing dominant reverse eddy currents within the workpiece. Experimental results indicate that when the large capacitor has a capacitance of 3200 μF and a voltage of 8 kV, and the small capacitor has a capacitance of 160 μF and a voltage of 3.2 kV, a 1 mm thick AA1060-H28 aluminum alloy sheet can deform approximately 4.7 mm towards the coil. This marks the first experimental verification of the feasibility of generating an electromagnetic attractive force through a dual-frequency discharge.

Beyond sheet metal forming applications, Xiong et al. [38,39] extended this method to the forming of small-diameter tube components, as shown in Figure 3b. The employed AA1060-O aluminum alloy tube has an internal diameter of merely 28 mm and a wall thickness of 1 mm. Such small-diameter tubes typically prove challenging to form directly using conventional electromagnetic repulsive forming. In the experiment, the coil was positioned externally around the tube and connected to two power supplies with differing capacitance values. Results demonstrated that when the larger capacitor was set to 3200 μF at 9 kV and the smaller capacitor to 160 μF at 11 kV, the aluminum alloy tube exhibited an expansion deformation of approximately 1.67 mm towards the coil. Furthermore, this method is also employed in the flanging of a small-diameter tube by Xiong et al. [40].

3.3. Dual-Frequency Current Generation by a Dual-Coil and Dual-Power Configuration

Ouyang et al. [41] proposed an electromagnetic attractive force generation method based on a dual-coil and dual-power configuration, applying it to the attractive forming of AA6061-O aluminum alloy tubes. The schematic diagram is shown in Figure 3c, with the tube, inner coil, and outer coil arranged from inside to outside. This method is similar to that described earlier [37,38,39,40], with the difference that long-pulse-width current and short-pulse-width current are now fed into different coils. Specifically, the long-pulse-width current is applied to the outer coil to control the magnetic field, while the short-pulse-width current is applied to the inner coil to control the eddy current. Compared to the single-coil configuration, where both the long-pulse-width current and the short-pulse-width current flow through the same coil, the separation of currents effectively distributes the thermal load, reducing the peak temperature experienced by each individual coil and thereby mitigating overall heating. Consequently, the dual-coil configuration offers improved thermal management, which is beneficial for extending coil lifespan and maintaining process stability under repeated discharges. Figure 4b shows the discharge currents, where the larger capacitor was set to 3200 μF at 9 kV for the outer coil, while the smaller capacitor was set to 160 μF at 9 kV for the inner coil. The AA6061-O aluminum alloy tube, with an external diameter of 35 mm and a thickness of 1 mm, exhibited an expansion deformation of approximately 4.75 mm towards the coil.

3.4. Dual-Frequency Current Generation by a Novel Discharge Circuit

Although the aforementioned methods have been successfully applied to the forming of sheet metal and tube components, their scope of application remains relatively limited. The primary reason lies in the requirement for two independent power supplies and a sophisticated sequential discharge control system, resulting in complex equipment structures and elevated costs that constrain its widespread adoption. Consequently, generating the requisite dual-frequency current within the coil using only a single power supply has emerged as a significant research focus in this field.

To address this issue, Ouyang et al. [42] proposed a novel discharge circuit configuration. This design incorporates an additional inductive load within the conventional circuit, with a diode connected in parallel across its terminals, as shown in Figure 3d. When the capacitor begins discharging, current flows through both the coil and the inductive load. Due to the high inductance value of the load, the current exhibits a gradual rise. Upon entering the current decay phase, the diodes conduct, short-circuiting the inductive load and causing the current to decay rapidly. Once the coil current crosses zero, the thyristor switch deactivates. This mechanism ultimately generates the desired slow rise-rapid fall current waveform within the coil. According to circuit theory, the rise time of the current t_rise is:

$$t_{\mathrm{rise}}={\displaystyle \frac{\arccos \left[\frac{{\alpha }_1}{\sqrt{\left({{\alpha }_1}^2+{\omega }_{\mathrm{d}1}^2\right)}}\right]}{{\omega }_{\mathrm{d}1}}}$$

(9)

$${\alpha }_1={\displaystyle \frac{R_{\mathrm{eq}}}{2(L_{\mathrm{eq}}+L_0)}}$$

(10)

$${\omega }_{\mathrm{d}1}=\sqrt{{\displaystyle \frac{1}{(L_{\mathrm{eq}}+L_0)C}}-{({\displaystyle \frac{R_{\mathrm{eq}}}{2(L_{\mathrm{eq}}+L_0)}})}^2}$$

(11)

At the same time, the fall time of the current t_fall is:

$$t_{\mathrm{fall}}={\displaystyle \frac{2L_{\mathrm{eq}}\arccos \left[-\frac{1}{2}{R}_{\mathrm{eq}}\sqrt{\frac{C}{L_{\mathrm{eq}}}}\right]}{\sqrt{-{R_{\mathrm{eq}}}^2+\frac{4L_{\mathrm{eq}}}{C}}}}$$

(12)

where α₁ and ω_d1 denote the attenuation coefficient and oscillation angular frequency during the current rise phase, respectively. From Equations (9) and (12), it can be seen that the rise time of the coil current is related to the capacitance, coil parameters, and inductive load parameters, while the fall time depends solely on the capacitance and coil parameters. Therefore, increasing L₀ can prolong the current rise time while maintaining the fall time unchanged, thereby achieving a slow-rise and fast-fall current waveform. Experimental verification indicates that under discharge conditions of 640 μF capacitance and 17 kV voltage, the current rise time is 1.9 ms, with a fall time of merely 0.5 ms, exhibiting the characteristic of a slow rise and rapid fall. Under this discharge, an AA6061 aluminum alloy tube with an inner diameter of 33 mm and a wall thickness of 0.9 mm exhibits approximately 2 mm of expansion deformation towards the coil. However, this method also exhibits significant shortcomings. The introduction of large inductive load severely reduces the current amplitude, resulting in low energy utilization efficiency.

Based on this, Ouyang et al. [42] further extended the application of this method to the non-destructive separation of tube components. Experiments demonstrate that during the discharge process, the electromagnetic attractive force enables the smooth separation of tightly connected tubes, achieving disassembly without mechanical damage. This outcome not only validates the technology’s feasibility for tube separation but also provides a rapid, non-destructive disassembly solution for scenarios such as high-end equipment maintenance and component replacement. This approach effectively avoids potential damage associated with traditional mechanical methods, significantly enhancing remanufacturing efficiency and cost-effectiveness.

3.5. Application for Strengthening Fatigue Performance of Hole Fastener

Electromagnetic attractive forming is not only suitable for the processing of sheets and tubes but also holds significant application prospects in strengthening hole fasteners. The hole fasteners serve as critical connecting components in the aerospace area, and their fatigue life directly influences the extension of aircraft service life and the assurance of flight safety. Generally, the cold expansion process is employed to enhance the fatigue life of hole fasteners.

The cold expansion process involves forcibly passing a mandrel, slightly larger in diameter than the hole, through the hole component via an interference fit, as shown in Figure 4a. This causes plastic expansion deformation of the hole wall while inducing elastic deformation in the surrounding area. Following mandrel passage, the externally elastically deformed zone springs back, exerting compressive forces upon the plastically deformed inner material [43,44]. This establishes a beneficial residual compressive stress field around the bore, effectively counteracting external alternating loads and significantly extending the fastener’s fatigue life [45,46].

However, conventional cold expansion suffers from inherent limitations such as surface damage caused by direct contact between the mandrel and hole wall, uneven residual stress distribution [47], and potential local warping [48]. To address these issues, researchers have proposed a novel electromagnetic cold expansion process (EMCE), which employs electromagnetic force to replace mandrels. This electromagnetic cold expansion process essentially involves inducing minute plastic expansion of the hole through electromagnetic force and, therefore, is also categorized as electromagnetic forming.

To achieve hole expansion, Dalle et al. [49] proposed an approach involving the placement of a coil within the hole, as illustrated in Figure 4b. This approach directly applies the radial electromagnetic expansion force to the hole wall, representing the most direct method for hole expansion. However, the confined internal space (typically less than 10 mm) poses significant challenges in accommodating the coil, limiting the practical applicability of this method in engineering practice. This constraint mirrors the challenges encountered with small-diameter tube components. Consequently, the coil has to be positioned externally around the hole. Under this configuration, however, the electromagnetic force induced within the hole primarily manifests as a hole-shrinking force (or repulsive force), as depicted in Figure 4c. This force tends to constrict the hole diameter, which runs counter to what we would expect.

To overcome this issue, Zhou et al. [50] employed a dual-coil and dual-power configuration, as shown in Figure 4d, successfully reversing the direction of electromagnetic force acting on the hole wall. This generated an expanding force (or attractive force) on the hole wall. Experimental results indicate that when the large capacitor is set to 3200 μF and voltage to 6 kV, and a small capacitor of 160 μF at 7.7 kV, the fatigue life of the AA2A12-T4 aluminum alloy hole components increased by 5.9, 8.3, and 12.7 times, respectively, compared to non-strengthened specimens under external loads of 180 MPa, 160 MPa, and 130 MPa.

Building upon these findings, Xu et al. [51,52] and Geng et al. [53] conducted further investigations into the fatigue behavior of AA2A12-T4 aluminum alloy and AZ31 magnesium alloy hole fasteners. Results demonstrated that electromagnetic cold expansion produced a more uniform residual stress distribution around the hole, with no significant warping observed around the hole periphery. These indicate that, compared to conventional mandrel cold expansion, electromagnetic cold expansion offers significant advantages in improving residual stress distribution and maintaining geometric integrity.

Furthermore, Geng et al. [54] and Xu et al. [55] employed a single-coil and dual-power configuration to achieve expansion force on the hall wall, as shown in Figure 4e, thereby enhancing fatigue performance of AA2A12-T4 aluminum alloy single-hole fasteners and adjacent-hole fasteners, respectively. Similarly, Ouyang et al. [56] employed the circuit configuration depicted in Figure 4f to achieve fatigue strengthening of the AA6063-T6 aluminum alloy hole fasteners using a single power source. These indicate that the electromagnetic cold expansion process and electromagnetic attractive forming share fundamentally identical physical mechanisms.

4. Attractive Forming Using a Low-Frequency Discharge

Traditional electromagnetic forming commonly employs high-frequency, high-current pulse discharge due to its high energy transfer efficiency, which rapidly induces strong eddy currents in the workpiece, thereby enabling rapid forming of high-conductivity materials through electromagnetic repulsive force. Recent studies have found that appropriately reducing the discharge frequency can alter the mechanism and direction of electromagnetic force, causing the originally dominant repulsive force to weaken or even transform into an attractive force. Based on this, researchers have developed three electromagnetic attractive forming techniques based on a low-frequency discharge, as shown in Figure 5, providing new potential pathways for expanding the electromagnetic attractive forming.

4.1. Attractive Forming for Ferromagnetic Materials Based on Ferromagnetic Effect

The electromagnetic forming process is usually employed to form non-ferromagnetic materials such as aluminum alloys and magnesium alloys. However, Batygin et al. [57,58] employed a conventional electromagnetic forming system to investigate the electromagnetic force distribution on ferromagnetic materials during the electromagnetic forming process, as shown in Figure 5a. Results show that when processing ferromagnetic materials, the electromagnetic force acting upon the workpiece can be decomposed into two components: the first is the electromagnetic force originating from induced eddy current, driving the workpiece away from the coil (manifesting as repulsive force); the second being the ferromagnetic force arising from the material’s ferromagnetism, which attracts the workpiece towards the coil (manifesting as attractive force). This ferromagnetic force stems from the interaction between the magnetic field and the ferromagnetic material. Its magnitude is independent of the excitation frequency but is typically one to two orders of magnitude smaller than the repulsive force. Although the ferromagnetic force’s magnitude does not vary with frequency, the overall electromagnetic force remains closely related to frequency.

When the current frequency is high, the electromagnetic force acting upon the workpiece predominantly manifests as a repulsive force. Conversely, when the current frequency is low, the ferromagnetic force becomes dominant, enabling attractive forming. Under low-frequency discharge conditions at 1.9 kHz, they successfully achieved direct electromagnetic attractive forming of low-carbon steel plates. Experimental results indicate that 0.8 mm thick Deep Drawing Quality (DDQ) steel samples exhibited a bulging deformation of 1.5 mm following a single discharge. Then, the sheet was flipped over, and the electromagnetic attractive process was employed to pull back the dent area, successfully simulating the dent repair process with notable effectiveness.

4.2. Attractive Forming for Non-Ferromagnetic Materials Based on Attractive Screen

The aforementioned method relies on the ferromagnetic properties of materials and is therefore unsuitable for non-ferromagnetic materials such as stainless steel and aluminum alloys. To address this, Batygin et al. [59] proposed a pulsed electromagnetic attractive forming process by introducing an additional attractive screen. As illustrated in Figure 5b, this method incorporates an additional conductive attractive screen around the exterior of a conventional single-turn coil. When a low-frequency discharge current is applied to the coil, eddy currents of identical orientation are induced in both the attractive screen and the sheet metal. According to Ampère’s law, currents of the same direction exert mutual attraction, thereby driving the workpiece towards the attractive screen.

Results indicate an uneven distribution of attractive force, with maximum values concentrated near the edge of the coil. In a verification experiment using a 1 mm thick stainless-steel plate, after eight pulse discharges, a regular dent with a diameter of approximately 80 mm and a depth of about 1 mm was successfully formed on the workpiece surface, which sufficiently demonstrated the feasibility of this method for attractive forming of non-ferromagnetic sheet materials. Moreover, they have successfully applied this technology to dent repair in motor vehicles [60].

4.3. Attractive Forming for Non-Ferromagnetic Materials Based on Current Phase Difference

It is found that during electromagnetic forming of aluminum alloys, an attractive force can be observed on the falling edge of the current when the current frequency is low. This phenomenon arises from the phase difference between the coil current and the eddy currents in the workpiece. At high current frequency, the phase difference between the coil current and the workpiece eddy currents is approximately 180 degrees, with the two currents consistently opposing each other in direction. According to Ampère’s law, the electromagnetic force at this point manifests solely as a repulsive force. However, when the current frequency decreases, the phase difference between the coil current and the eddy currents in the workpiece diminishes. During the rising edge of the current, the coil current and eddy currents oppose each other, resulting in a repulsive electromagnetic force. Conversely, during the falling edge, the coil current and workpiece eddy currents align, manifesting as an attractive electromagnetic force.

Ouyang et al. [61] explained this phenomenon through sinusoidal circuit theory, as illustrated in Figure 2b, yielding the following circuit equation:

$$\left\{\begin{array}{l}\left(R_{\mathrm{c}}+j\omega L_{\mathrm{c}}\right){\mathbf{I}}_1+j\omega M{\mathbf{I}}_2={\mathbf{U}}_1\\ j\omega M{\mathbf{I}}_1+\left(R_{\mathrm{w}}+j\omega L_{\mathrm{w}}\right){\mathbf{I}}_2=0\end{array}\right.$$

(13)

By solving Equation (13), the coil current I_c and eddy current of workpiece I_w can be obtained:

$$\left\{\begin{array}{l}{\mathbf{I}}_1={\displaystyle \frac{\left(R_{\mathrm{w}}+j\omega L_{\mathrm{w}}\right){\mathbf{U}}_1}{\left(R_{\mathrm{c}}+j\omega L_{\mathrm{c}}\right)\left(R_{\mathrm{w}}+j\omega L_{\mathrm{w}}\right)+{(\omega M)}^2}}\\ {\mathbf{I}}_2={\displaystyle \frac{-j\omega M{\mathbf{U}}_1}{\left(R_{\mathrm{c}}+j\omega L_{\mathrm{c}}\right)\left(R_{\mathrm{w}}+j\omega L_{\mathrm{w}}\right)+{(\omega M)}^2}}\end{array}\right.$$

(14)

According to Equation (14), the phase of coil current I_c leads that of induced eddy current I_w by an angle (θ + π/2), where $\theta =\arctan (\omega L_2/R_2)$. Since ω exhibits a linear relationship with discharge frequency, when the discharge frequency is sufficiently high, ωL₂ may become substantially greater than R₂, causing angle θ to approach π/2. At this point, the phase of coil current I_c leads that of induced eddy current I_w by π, meaning the direction of the coil current is essentially opposite to that of the eddy current during discharge. Consequently, the electromagnetic force primarily manifests as a repulsive force, as illustrated. When the discharge frequency is sufficiently low, the phase of coil current I_c leads that of induced eddy current I_w by π/2. This implies that during the rising edge of the current, the current flows in opposition to the eddy currents, whereas during the falling edge, the current flows in the same direction as the eddy currents. This also results in the falling edge being capable of generating an attractive force.

Based on this, Ouyang et al. [61,62] achieved attractive forming of aluminum alloy sheet metal by employing the circuit configuration shown in Figure 5c, where a crowbar circuit composed of a diode and a crowbar resistance R_d is connected in parallel across the capacitor. Under a discharge capacitance of 3200 μF and a voltage of 4 kV, a 1 mm thick AA1060-H24 aluminum alloy sheet was deformed by 8 mm towards the coil direction. It should be noted that the attractive force generated by this method is significantly smaller than the repulsive force. As reported by Ouyang et al. [62], the amplitude of the attractive force is only 40% that of the repulsive force. Successful attractive forming relies on two key factors: (1) the characteristics of the discharge current waveform, the decay rate of the current’s falling edge directly influences the magnitude of the attractive force. When the discharge resistance R_d is excessively low, the current decays slowly, resulting in insufficient attractive force. Conversely, if R_d is excessively high, the current decays too rapidly and oscillates, causing alternating attractive and repulsive forces that similarly hinder stable attractive forming. (2) The multi-stage deformation process of the sheet metal: the sheet metal undergoes concave pre-deformation during the initial repulsive stage. Subsequently, it undergoes snap-through buckling deformation toward the coil, ultimately achieving attraction forming. As a result, the energy required for its reverse deformation (toward the coil) is substantially reduced due to the pre-deformation, enabling noticeable attractive displacement even under a relatively small attractive force.

5. Discussion on Technical Limitations

Although electromagnetic attractive forming exhibits unique advantages in specific scenarios, each of the existing methods still suffers from notable technical limitations:

1.

Dual-Frequency Discharge Method

The dual-frequency discharge method is currently the predominant technical approach in electromagnetic attractive forming research and can be classified into three categories based on implementation:

(1)

Single-coil dual-power configuration: The main limitation lies in high equipment complexity—requiring two independent pulse power supplies and a precise synchronous control system, which increases system cost and implementation difficulty. Additionally, both long- and short-pulse-width currents flow through the same coil, leading to severe Joule heat accumulation and reduced coil lifespan.

(2)

Dual-coil dual-power configuration: Although this configuration reduces the thermal load by distributing the long- and short-pulse-width currents into separate coils, it still requires two power supplies and synchronous control, so the equipment complexity issue persists. Moreover, precise alignment and gap control between the inner and outer coils significantly affect forming results, increasing tooling difficulty.

(3)

Novel single-power-supply circuit: By introducing a large inductive load and a bypass diode, this circuit achieves dual-frequency current output using a single power supply, significantly simplifying the system structure. However, its main limitation is low energy efficiency—the large inductive load substantially attenuates the peak discharge current, resulting in low energy efficiency.

2.

Low-Frequency Discharge Method

To date, the feasibility of low-frequency discharge methods has only been demonstrated in the attractive forming of sheet components, with no reported applications in tube components. The technical maturity and scope of application of this approach remain to be expanded. Furthermore, based on differing mechanisms of action, the three existing technical pathways each exhibit the following limitations:

(1)

Method based on ferromagnetic effect: The primary limitation is that it is only applicable to ferromagnetic materials (such as low-carbon steel) and cannot be directly applied to lightweight materials like aluminum alloys or titanium alloys.

(2)

Method based on attractive screen: Whilst this method is applicable to various metallic materials, it necessitates the addition of a supplementary conductive screen, thereby increasing tooling complexity. Furthermore, the magnetic field distribution proves uneven, with the maximum magnetic force concentrated in the peripheral regions of the coil.

(3)

Method based on current phase difference: The attractive force magnitude is much smaller than that of the repulsive force, requiring the pre-deformation generated during the repulsive force stage to achieve effective attractive forming. Consequently, its application scenarios are considerably limited.

Overall, a common issue across all dual-frequency discharge methods and low-frequency discharge methods is that their energy efficiency is significantly lower than that of conventional repulsive forming.

Table 1. Comparison of energy efficiency.

Method	Material	Thickness	Deformation	Energy	Reference
Dual-frequency discharge	AA1060-H28	1 mm	4.7 mm	103 kJ	[37]
	AA1060-O	1 mm	1.67 mm	140 kJ	[38]
	AA6061-O	1 mm	4.75 mm	46 kJ	[41]
	AA6061-O	1 mm	2 mm	92 kJ	[42]
Low-frequency discharge	AA1060-H24	1 mm	8 mm	25 kJ	[61]
	AA1060-H24	1 mm	10 mm	25 kJ	[62]

summarizes the key process parameters from the aforementioned key literature, including discharge energy, material properties, and the resulting maximum deformation. Although these parameters are not direct indicators of efficiency, they indirectly reflect the energy utilization levels of various electromagnetic attractive forming methods to some extent. It can be observed from the table that this technology is currently mainly applied to lightweight alloy sheets or tubes with small thickness and low yield strength. For instance, in the dual-frequency discharge method, approximately 103 kJ of energy is required to achieve an attractive deformation of about 4.7 mm in a 1 mm thick AA1060-H28 aluminum alloy sheet [37]. In contrast, the low-frequency discharge method requires about 25 kJ of energy to produce an 8 mm deformation in a 1 mm thick AA1060-H24 aluminum alloy sheet [61]. While in traditional repulsive forming, Lai et al. [63] achieved over 8 mm of deformation in an AA1060-H24 aluminum alloy sheet of 1 mm thickness using merely 7.84 kJ of energy. These data clearly indicate that the energy efficiency of current electromagnetic attractive forming remains significantly lower than that of traditional repulsive forming, especially the method using a dual-frequency discharge.

The main reasons for the low efficiency of electromagnetic attractive forming include: in the dual-frequency current method, the short-pulse-width discharge severely weakens the working magnetic field, resulting in a weak energy conversion; in the low-frequency current method, the discharge frequency is much lower than that of traditional repulsive forming, leading to limited electromagnetic force amplitude; furthermore, due to the requirement for sufficient deformation space between the coil and the workpiece in attractive forming, the increased distance between coil and workpiece reduces electromagnetic coupling efficiency.

6. Conclusions and Future Research Directions

Electromagnetic attractive forming (EMAF) offers an innovative solution to address the limitations of traditional electromagnetic forming in specific application scenarios due to its unique capability to deform workpieces towards the coil. This paper systematically reviews the primary technical approaches for achieving electromagnetic attractive forming based on different physical mechanisms. The review findings indicate:

(1)

The dual-frequency discharge method has been successfully implemented through various circuit and coil configurations, including single-coil dual-power-supply sequential discharge, dual-coil dual-power-supply independent discharge, and novel single-power-supply discharge circuits. This approach effectively reverses the direction of electromagnetic force by regulating the temporal relationship between magnetic fields and eddy currents. Its technical feasibility and application versatility have been experimentally validated in applications including sheet metal forming, small-diameter tube expansion, hole fastener strengthening, and even non-destructive tube disassembly.

(2)

The low-frequency discharge method reveals the potential to alter the electromagnetic force by reducing the discharge current frequency. For ferromagnetic materials, their inherent magnetization effect can generate a dominant attractive force at a low frequency. For non-ferromagnetic materials, attractive forming can be achieved at low frequencies by introducing additional attractive screens or utilizing the phase difference between the coil current and the eddy currents in the workpiece. This offers new insights for expanding the material applicability of electromagnetic attractive forming technology.

Whether based on dual-frequency discharge or low-frequency discharge methods, the fundamental principle lies in actively regulating the coil current waveform to alter the direction and distribution characteristics of the electromagnetic force. This reveals a unique and intimate relationship between electromagnetic force and current waveform in electromagnetic forming, an aspect previously underemphasized in research. Although electromagnetic attractive forming has demonstrated potential in specific scenarios, its overall development remains at the stage of technical exploration and principle validation. To advance electromagnetic attractive forming towards deeper and more practical applications, future research should focus on the following key areas:

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Enhance energy efficiency. At present, electromagnetic attractive forming (especially the dual-frequency discharge method) exhibits significantly lower energy efficiency than traditional repulsive forming, coupled with complex equipment, which severely limits its engineering applicability. This issue could be partially addressed by developing new and highly efficient circuit topologies. However, a more fundamental challenge lies in achieving stable, attractive forming under high-frequency discharge without relying on low-frequency excitation or complex waveform modulation. Overcoming this hurdle would greatly enhance the processing efficiency of electromagnetic attractive forming and substantially broaden its industrial application scope.

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Deepening fundamental mechanism research. Currently, the theoretical system of electromagnetic attractive forming remains underdeveloped, with most existing studies focusing primarily on verifying process feasibility and lacking systematic investigation into the forming mechanisms. Future efforts should be undertaken to systematically investigate the microstructural evolution of lightweight alloys under attractive versus repulsive electromagnetic pulses, with a focus on grain refinement, texture development, and defect generation. This will provide a solid scientific foundation for process optimization and engineering applications.

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Expanding application scenarios. Beyond existing sheet and tube forming and hole fastener reinforcement, we should actively explore the unique value of electromagnetic attractive forming in additional fields, such as developing attractive force-based progressive forming or composite forming combining attractive and repulsive forming.

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Engineering reliability and industrialization research. To bridge the gap between laboratory demonstration and industrial application, future efforts must address critical engineering challenges. These include coil durability under repeated high-current discharges, system integration and reliability under high-volume production conditions, and operational safety protocols for high-voltage pulsed power systems.

Through breakthroughs in these directions, electromagnetic attractive forming technology is expected to evolve into an indispensable advanced manufacturing process, thereby expanding the technological boundaries of electromagnetic forming.