Modeling moving boundary value problems in electrochemical machining

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.

Consideration of chemically‐induced damage in a thermo‐electrically coupled system

“…In the following, we refer to the material description introduced by [1] and [2]. As a result of the chemical effect of the anodic dissolution, the material vanishes and is replaced by the electrolyte.…”

Modeling the moving boundary value problem of electrochemical machining

“…In this section, we briefly summarize the main aspects of the cathode modeling procedure proposed in [7]. The surface of the cathode is defined by a zero electric potential v ca = 0 V. Thus, all nodes that are located inside the cathode are assigned the corresponding Dirichlet boundary condition.…”

“…In [6], we presented a new approach to circumvent the issue of remeshing, which is introduced in Section 3. Recently, the methodology has been extended in [7] to account for the cathode modeling without remeshing, which is explained in Section 4 and denoted as modeling of moving boundary value problems (MBVP).…”

“…On the tool side, an efficient methodology to incorporate the movement of the cathode into the simulation without remeshing had been lacking so far. Thus, we proposed to extend the modeling approach of [6] to model the cathode also based on effective material parameters whilst using a constant finite element mesh (see [7]). The procedure allows for the consideration of arbitrarily complex geometries that additionally may possess differently oriented feed vectors.…”