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Application of edge-based smoothed finite element method to electrodeposition simulation aiming for super-linear mesh convergence in film thickness accuracy
Last modified: 2023-05-11
Abstract
Electrodeposition (ED) is widely used as an anti-corrosion base-coating method for various metal products such as automobile carbodies.
In the cationic ED coating, the coating objects (cathodes) are dipped in a paint pool with electrodes (anodes), and direct current is applied from the anodes to the cathodes.
Therefore, the governing equation in the space of the ED simulation is a simple Laplace equation.
By calculating the time history of electric current density all over the carbody surface, the distribution of deposited film thickness at the end of the ED process can be predicted.
In order to guarantee a certain thickness of coating film over the entire surface, ED simulation has become an indispensable technology in automobile manufacturing.
In contrast to the computational fluid dynamics (CFD) simulation of carbodies, an ED simulation requires a mesh for complex narrow spaces in the carbody, such as side-sill with many small holes (ED holes).
To discretize the volume with complex shapes, tetrahedral meshing is preferred rather than hexahedral meshing.
The 10-node tetrahedral (T10) element has a super-linear mesh convergence rate;
however, a T10 mesh without kinks at mid-nodes around small holes requires a large number of nodes compared to a 4-node tetrahedral (T4) mesh.
Therefore, T4 meshing has been usually adopted for ED simulation, although the standard T4 element has a poor (linear) mesh convergence rate.
Meanwhile, the smoothed finite element method (S-FEM) has been widely used as a next-generation FEM in recent years.
The edge-based S-FEM with T4 mesh (ES-FEM-T4) is known as an especially beneficial FE formulation due to its super-linear mesh convergence rate even with T4 mesh.
Hence, ES-FEM-T4 perfectly suits the requirements of accurate ED simulation.
In this study, an ED simulator introducing ES-FEM-T4 is developed for actual automotive ED line simulation.
The simulator aims for super-linear mesh convergence in film thickness accuracy with the aid of S-FEM.
In addition, the MPI/OpenMP hybrid parallelization, moving boundary feature, stabilized Newton's iteration, and so on are also introduced for large-scale practical simulation.
Some benchmark tests reveal that the simulator using ES-FEM-T4 presents much more accurate results than the standard FEM-T4 with the same CPU time.
In the cationic ED coating, the coating objects (cathodes) are dipped in a paint pool with electrodes (anodes), and direct current is applied from the anodes to the cathodes.
Therefore, the governing equation in the space of the ED simulation is a simple Laplace equation.
By calculating the time history of electric current density all over the carbody surface, the distribution of deposited film thickness at the end of the ED process can be predicted.
In order to guarantee a certain thickness of coating film over the entire surface, ED simulation has become an indispensable technology in automobile manufacturing.
In contrast to the computational fluid dynamics (CFD) simulation of carbodies, an ED simulation requires a mesh for complex narrow spaces in the carbody, such as side-sill with many small holes (ED holes).
To discretize the volume with complex shapes, tetrahedral meshing is preferred rather than hexahedral meshing.
The 10-node tetrahedral (T10) element has a super-linear mesh convergence rate;
however, a T10 mesh without kinks at mid-nodes around small holes requires a large number of nodes compared to a 4-node tetrahedral (T4) mesh.
Therefore, T4 meshing has been usually adopted for ED simulation, although the standard T4 element has a poor (linear) mesh convergence rate.
Meanwhile, the smoothed finite element method (S-FEM) has been widely used as a next-generation FEM in recent years.
The edge-based S-FEM with T4 mesh (ES-FEM-T4) is known as an especially beneficial FE formulation due to its super-linear mesh convergence rate even with T4 mesh.
Hence, ES-FEM-T4 perfectly suits the requirements of accurate ED simulation.
In this study, an ED simulator introducing ES-FEM-T4 is developed for actual automotive ED line simulation.
The simulator aims for super-linear mesh convergence in film thickness accuracy with the aid of S-FEM.
In addition, the MPI/OpenMP hybrid parallelization, moving boundary feature, stabilized Newton's iteration, and so on are also introduced for large-scale practical simulation.
Some benchmark tests reveal that the simulator using ES-FEM-T4 presents much more accurate results than the standard FEM-T4 with the same CPU time.
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