Modeling moving boundary value problems in electrochemical machining

TL;DR

This paper introduces a novel, remesh-free modeling approach for moving cathodes in electrochemical machining, enabling efficient simulation of complex geometries with validated accuracy and reduced computational effort.

Contribution

It extends a previous model to simulate arbitrarily shaped, moving cathodes without remeshing, using effective parameters and boundary conditions for industrially relevant applications.

Findings

Model accurately predicts cathode movement and dissolution.

Approaches reduce computational time significantly.

Validated against analytical, numerical, and experimental data.

Abstract

This work presents a new approach to efficiently model the cathode in the moving boundary value problem of electrochemical machining. Until recently, the process simulation with finite elements had the drawback of remeshing required by the changing surface geometries. This disadvantage was overcome by a novel model formulation for the anodic dissolution that utilizes effective material parameters as well as the dissolution level as an internal variable and, thereby, does not require remeshing. Now, we extend this concept to model arbitrarily shaped and moving cathodes. Two methodologies are investigated to describe the time varying position of the cathode. In the first approach, we change the electric conductivity of elements within the cathode and, in a second approach, we apply Dirichlet boundary conditions on the nodes of corresponding elements. For both methods, elements on the cathode's surface are treated with effective material parameters. This procedure allows for the efficient simulation of industrially relevant, complex geometries without mesh adaptation. The model's performance is validated by means of analytical, numerical and experimental results from the literature. The short computation times make the approach interesting for industrial applications.