<p>The electroplating process is widely employed across various industries to enhance the surface quality of industrial products, providing improved resistance to abrasion and corrosion, as well as aesthetic benefits. Achieving uniform deposition thickness is crucial for ensuring the desirable surface properties. However, the deposition thickness varies depending on the geometry of the workpiece and the arrangement and shape of cathodes and anodes, making it difficult or challenging to determine the appropriate arrangement and shape using a trial-and-error approach. This paper proposes a topology optimization method for the design of shielding structures in the electroplating process using tertiary current distribution. It accounts for ion transport in the electrolyte, driven by diffusion, migration, and convection, using the Nernst–Planck equation. The charge transfer reaction at the electrode is described by the Butler–Volmer equation, while fluid flow within electrolyte cells is described by the Navier–Stokes equation. The optimization aims to find the optimal layout of shielding structures that enhance the uniformity of electroplating thickness on the target workpiece. The Navier–Stokes equation is weakly coupled with the Nernst–Planck equation to evaluate the current density distribution at the surface of the workpiece, considering concentration variation and ion transport in electrolyte solution. The uniformity of the current density distribution on the target surface is set as the objective functional, while its magnitude is imposed as a constraint. The sensitivties are obtained by solving two sets of adjoint problems—the adjoint flow problem and adjoint electrochemical problem which are weakly coupled. The numerical examples are provided to confirm the validity and utility of the proposed method. The results demonstrate its ability to obtain shielding structures that improve the uniformity of deposition thickness.</p>

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Topology optimization of shielding structures in electroplating using tertiary current distribution

  • Masaki Otomori,
  • Hao Li,
  • Naoyuki Ishida,
  • Kazuhiro Izui,
  • Shinji Nishiwaki

摘要

The electroplating process is widely employed across various industries to enhance the surface quality of industrial products, providing improved resistance to abrasion and corrosion, as well as aesthetic benefits. Achieving uniform deposition thickness is crucial for ensuring the desirable surface properties. However, the deposition thickness varies depending on the geometry of the workpiece and the arrangement and shape of cathodes and anodes, making it difficult or challenging to determine the appropriate arrangement and shape using a trial-and-error approach. This paper proposes a topology optimization method for the design of shielding structures in the electroplating process using tertiary current distribution. It accounts for ion transport in the electrolyte, driven by diffusion, migration, and convection, using the Nernst–Planck equation. The charge transfer reaction at the electrode is described by the Butler–Volmer equation, while fluid flow within electrolyte cells is described by the Navier–Stokes equation. The optimization aims to find the optimal layout of shielding structures that enhance the uniformity of electroplating thickness on the target workpiece. The Navier–Stokes equation is weakly coupled with the Nernst–Planck equation to evaluate the current density distribution at the surface of the workpiece, considering concentration variation and ion transport in electrolyte solution. The uniformity of the current density distribution on the target surface is set as the objective functional, while its magnitude is imposed as a constraint. The sensitivties are obtained by solving two sets of adjoint problems—the adjoint flow problem and adjoint electrochemical problem which are weakly coupled. The numerical examples are provided to confirm the validity and utility of the proposed method. The results demonstrate its ability to obtain shielding structures that improve the uniformity of deposition thickness.