Modeling the moving boundary value problem of electrochemical machining

Abstract

AbstractTwo evolving surfaces define the moving boundary value problem in electrochemical machining. On the side of the work piece, the anodic dissolution yields the evolution of the machined surface. A novel approach for modeling the dissolution process of the anode has recently been proposed by [6], which is based on internal variables and effective material parameters that are inserted into the balance equation of electric charge. Thereby, the resulting distributions of the electric current densities ‐ the driving forces of the dissolution process ‐ are accurately captured without the necessity to adapt the finite element mesh in each time step. 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. In this paper, a new anisotropic rule of mixture is put forward. The presented example is restricted to a stationary cathode, but focuses on a detailed investigation of the new methodology and a comparison with existing rules of mixture, which are a key component of the methodology and equivalently applicable to moving boundary value problems.