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Analysis, simulation and experimental study of electromagnetic forming of titanium bipolar plate with arc-shaped uniform pressure coil

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Abstract

In the electromagnetic forming (EMF) titanium bipolar plates (BPPs), a reasonable coil structure can provide higher forming efficiency and repeatability. An arc-shaped uniform pressure coil (UPC) is proposed, and an efficient and reliable multiphysics sequentially coupled analytical model is established. Through the LS-DYNA numerical model and the fitted current curve obtained from experiments, the predictive capabilities of equivalent circuit parameters and dynamic phenomena are verified, and the rationality of the magnetic shielding assumption and magnetic flux uniform distribution are evaluated. Starting from the durability and forming efficiency of the coil, the optimal coil geometry in analytical form is constructed. The study found that there is an optimal solution for the height of the primary coil, wire thickness, primary and secondary side gap, which are 18.3 mm, 2.7 mm, and 3.2 mm, respectively. Based on this, under the discharge capacitor of 100 μF, acceleration distance of 2 mm, and driven by 0.3 mm thick Cu110, a TA1 titanium BPP with a channel depth-to-width ratio of 0.53 was successfully manufactured. Its maximum thinning rate is 18.2%, the maximum fluctuation rate does not exceed 2.5%, and the filling rate of the channel above 95%. Overall, this study provides theoretical basis and reference for the design of UPC in EMF for BPPs.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (51965050), Inner Mongolia Natural Science Foundation (2021MS05004) and Inner Mongolia University youth Science and technology talent program (NJYT22087). Thank you for the assistance of professor Haiping Yu in the Electromagnetic Forming Research Group at Harbin Institute of Technology.

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Authors and Affiliations

  1. School of Materials Science and Engineering, Inner Mongolia University of Technology, Hohhot, 010051, China

    Qiangkun Wang, Junrui Xu, Shaobo Wang, Yudong Zhao & Yuanfeng Wang

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  1. Qiangkun Wang
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Contributions

Qiangkun Wang: investigation, methodology, writing, and original draft; Junrui Xu: Supervision, Writing revision; Shaobo Wang: Data curation, Formal analysis; Yudong Zhao: Data curation, Formal analysis; Yuanfeng Wang: Data curation, Formal analysis.

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Appendix A: Ampere's circuital law and gauss's magnetism law

Appendix A: Ampere's circuital law and gauss's magnetism law

The following is the integral form of Ampère's Circuital Law and Gauss's Magnetism Law, which establish the physical foundations for electromagnetic modeling in Section “Prediction of discharge current and applied magnetic pressure”:

$$\oint_{\partial\sum}\text{H}\cdot{\text{d}}_l=\iint_\sum \nolimits\text{J}\cdot{\text{d}}_s$$
(29)
$$\oiint_{\partial\Omega}\text{B}\cdot{\text{d}}_s=0$$
(30)

where H is the magnetic field strength, J is the current density, B is the magnetic induction intensity of the current on a surface S, Σ is the arbitrary fixed surface with closed boundary curve ∂Σ, and Ω is the arbitrary fixed volume with closed boundary surface ∂Ω. And H and B satisfy the following relation:

Here, H represents the magnetic field intensity, J represents the current density, B represents the magnetic induction due to current through the surface S, Σ is an arbitrary fixed surface bounded by the closed curve ∂Σ, and Ω is an arbitrary fixed volume enclosed by the closed surface ∂Ω. Additionally, H and B satisfy the following relationship:

$${\text{B}}={\mu }_{0}H$$
(31)

  • Eq. (29) is called Ampère's Circuital Law, which states that the integral of the magnetic field intensity H around the closed curve ∂Σ is proportional to the total current passing through the surface Σ.

  • Eq. (30) is called Gauss's Magnetism Law, which states that the total magnetic flux passing through the closed surface ∂Ω is zero.

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Wang, Q., Xu, J., Wang, S. et al. Analysis, simulation and experimental study of electromagnetic forming of titanium bipolar plate with arc-shaped uniform pressure coil. Int J Mater Form 17, 23 (2024). https://doi.org/10.1007/s12289-024-01818-y

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