Keywords

1 Introduction

With the rapid development of micro-electromechanical systems (MEMS), fuel cells, biomedical devices, and other fields, the advanced manufacturing technology of micro-parts is becoming urgently needed. Nowadays, a number of non-conventional energy-assisted forming technologies have been studied for manufacturing these micro-parts. Electromagnetic forming (EMF) has attracted wide attention because of its ability to improve the formability and deformation uniformity of difficult-to-form metallic sheets at room temperature and high strain rates.

Langstädtler et al. [1] performed the electromagnetic micro-embossing of a 1050 aluminum alloy thin sheet. Triangular cross-section micro V-grooves with a width of 86.6 µm and structure angle of 30° were achieved. Kamal et al. [2] developed a uniform pressure actuator (UPA) for generating uniform electromagnetic force distribution on such a sheet. The electromagnetic micro-forming of a 5052-H32 aluminum alloy thin sheet with UPA was performed to fabricate a micro-part with optical diffraction grating features. Zhao et al. [3] performed the electromagnetic micro-punching experiments of a 20-μm-thick T2 copper thin sheet with a UPA. Micro holes with a diameter of 0.4 mm were successfully punched. Dong et al. [4] performed the electromagnetic micro-forming (EMMF) of titanium bipolar plates with a UPA. The simulated and experimental results showed that EMMF can significantly improve the thickness uniformity and the uniformity of the channel depth; however, a UPA has the limitations of coil winding intervals, complex structures, and electrical contacts. Long et al. [5] carried out the electromagnetic micro-forming of a 0.2-mm-thick 1060 aluminum alloy thin sheet with a plane runway coil. An eddy current must be induced in order to generate electromagnetic forces.

Shang et al. [6] proposed the EMF process with a compliant layer for fabricating bipolar plates; a non-uniform electromagnetic force was transmitted by the compliant layer to deform the sheet. Zhu et al. [7] developed a hybrid forming process that combined EMF and stamping. The dimensional precision and thickness uniformity of the micro-channel were significantly higher under this hybrid process than that of single EMF or stamping. Yan et al. [8] experimentally and numerically investigated the electromagnetic hydraulic forming process of an AA5052 aluminum alloy sheet. This not only obtained good fittability with the die but also improved the formability of the materials. Thus, electromagnetic hybrid micro-forming processes exhibit enormous potential for the fabrication of micro-parts.

Herein, electromagnetic-impacted micro-forming (EMIMF) processes were adopted to solve the problem of coil-winding intervals and non-uniform electromagnetic forces. Numerical simulations of electromagnetic-impacted rubber micro-forming (EMIRMF), electromagnetic-impacted micro-hydroforming (EMIMHF), and electromagnetic-impacted pneumatic micro-forming (EMIPMF) were performed in order to compare the influences of a flexible medium. By comparing these with the experimental results, the numerical simulations were validated.

2 Numerical Simulation

2.1 Numerical Model

The numerical simulations of the EMIMF processes were fulfilled by using LS-DYNA software. Figure 1a shows half of a numerical model of an EMIRMF simulation, which consisted of a coil, drive plate, piston, rubber, pressure chamber, aluminum alloy thin sheet, and die. The electromagnetic fields of the coil and drive plate were calculated by using the finite element method (FEM), while their surrounding air field was analyzed by the boundary element method (BEM). The coil, drive plate, and piston were defined to be rigid bodies, those numerical models were divided into hexahedral entity elements. The electromagnetic and mechanical fields were sequentially coupled. The time steps of the electromagnetic and structural fields were both set to be 2 μs. The mechanical fields of the other components were simulated by the Lagrange algorithm. The nonlinear hyper-elastic behavior of the rubber was described by the Mooney-Rivlin model [9]. AA5052-O aluminum alloy thin sheets with a thickness of 0.1 mm were used. The sheet was discretized with shell elements, and the effect of the high strain rate on the mechanical behavior of the sheet was described by the Johnson–Cook model (\(\upsigma =\left(35.4{\text{MPa}}+114.1{\text{MPa}}{\varepsilon }_{p}^{0.3246}\right)\left(1+0.0028{\text{ln}}\dot{\overline{\varepsilon }}/{\dot{\overline{\varepsilon }}}_{0}\right)\)). A surface-to-surface contact with a friction coefficient of 0.2 was considered for the sheet and the tools. The cross-section sizes of the die are detailed in Fig. 1a. The meshes for the deformation zone of the sheet and its surrounding die zone were locally refined to reduce the computational cost. The longitudinal direction (LD) and transverse direction (TD) sections of the micro-channel were inspected.

Fig. 1
figure 1

Numerical model: a EMIRMF; b EMIMHF/EMIPMF

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Half of a numerical model of the EMIMHF/EMIPMF simulation was established (as shown in Fig. 1b). Instead of rubber for EMIRMF, the flexible mediums of EMIMHF and EMIPMF were substituted by liquid and forming gas, respectively. The fluid–structure interaction (FSI) of the aluminum alloy thin sheet and fluid (water, forming gas, and air) was simulated by the arbitrary Lagrangian–Eulerian (ALE) algorithm in order to avoid the problem of mesh distortion due to the massive deformation of the fluid. The state equation of the air was defined by the linear polynomial equation, and the state equations of the water and forming gas were described by the Gruneisen equation [10].

2.2 Simulated Results

To study the effects of the discharge voltages on the deformation profile and thickness distribution of the micro-channel, numerical simulations of EMIRMF were performed at different discharge voltage values (1.4, 1.6, 1.8, 2.0, and 2.2 kV). For EMIMHF, these voltages were 0.8, 1.0, 1.2, 1.4, and 1.6 kV, while for EMIPMF, they were 1.6, 1.7, 1.8, 1.9, and 2.0 kV.

With increase in the discharge voltage, the forming accuracy and thickness distribution of the micro-channel were gradually improved and decreased, respectively (as shown in Figs. 2, 3, and 4). As the discharge voltage further increased to the maximum value of each process, the minimum thickness of the micro-channel was greatly reduced, and the local thinning became serious. Thus, the optimum discharge voltages of the EMIRMF, EMIMHF, and EMIPMF processes for fabricating the micro-channel were chosen to be 2.0, 1.4, and 1.9 kV, respectively.

Fig. 2
figure 2

Effects of discharge voltage on simulated results of micro-channel during EMIRMF: a profile along LD; b profile along TD; c thickness along LD; d thickness along TD

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Fig. 3
figure 3

Effects of discharge voltage on simulated results of micro-channel during EMIMHF: a profile along LD; b profile along TD; c thickness along LD; d thickness along TD

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Fig. 4
figure 4

Effects of discharge voltage on simulated results of micro-channel during EMIPMF: a profile along LD; b profile along TD; c thickness along LD; d thickness along TD

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The thinning rate was used to analyze the formability (which is defined as the change of the sheet thickness divided by the sheet’s initial thickness). Figure 5 shows the thinning-rate contours of the micro-channel at the optimum discharge voltages for each process. The maximum thinning-rate values of the micro-channel for the EMIRMF, EMIMHF, and EMIPMF processes were 28.6, 25.4, and 26.2%, respectively.

Fig. 5
figure 5

Thinning rate contours of micro-channel

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3 Experimental Validation

The experimental setup of the EMIMF processes is shown in Fig. 6a. The forming coil was selected as a flat spiral coil. The coil and drive plate were made of copper due to the property of high electrical conductivity. When the electrical current flowed along the coil, a transient magnetic field was created. Subsequently, an eddy current was evoked between the drive plate, and non-uniform Lorentz forces were stimulated between the coil and the drive plate (as shown in Fig. 6b). When the drive plate impacted the piston, the flexible medium made the aluminum alloy thin sheet fit with the die. Seal rings were installed in the pressure chamber to prevent fluid leakage. The specimens were obtained by performing the EMIMF processes at the optimum discharge voltages for each process (as shown in Fig. 7). These specimens were cut along the LD and TD used wire cut electrical discharge machining. An optical microscope with a micron resolution was used to measure the deformation profiles and thickness distributions of the specimens. The relative error of measurement was less than 1.5%.

Fig. 6
figure 6

EMIMF processes: a experimental setup; b schematic diagram

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Fig. 7
figure 7

Specimens via different processes

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Figure 8 compares the simulated and experimental deformation profiles of the specimens for each process. The simulated and experimental deformation profiles agreed well. Figure 9 compares the simulated and experimental thicknesses of the specimens. Similarly, the simulated thickness values nearly matched those of the experimental ones; thus, the numerical simulations of the EMIMF processes were validated. The experimental maximum thickness reduction ηmax is also compared in Fig. 9. The specimen that was obtained by the EMIMHF process exhibited more thickness uniformity due to the smaller maximum thinning rate. To directly assess the forming accuracy of the specimen, the experimental filling rate values of the specimens by each process were compared (as shown in Fig. 10). The filling rate values of the specimen that was obtained by the EMIMHF process were the greatest; therefore, the forming accuracy and thickness uniformity of the micro-channel were the best via the EMIMHF process.

Fig. 8
figure 8

Comparisons of simulated and experimental deformation profiles: a LD; b TD

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Fig. 9
figure 9

Comparisons of simulated and experimental thicknesses: a LD; b TD

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Fig. 10
figure 10

Comparisons of filling rates of different processes

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4 Conclusion

The EMIMF processes that used flexible mediums were adopted in order to avoid the problem of the coil-winding interval and non-uniform electromagnetic forces. The EMIRMF, EMIMHF, and EMIPMF processes were applied to fabrications of micro-channels in order to compare the influences of a flexible medium. The numerical simulations of the EMIMF processes were performed with the sequential coupling method of the electromagnetic and mechanical fields. The discharge voltage could significantly affect the deformation profile and thickness distribution of the micro-channel of an AA5052-O aluminum alloy thin sheet. By comparing the simulated and experiment deformation profiles and thicknesses, the numerical simulations of the EMIMF processes were deemed to be accurate. The forming accuracy and thickness uniformity of the micro-channel were the best via the EMIMHF process.