A novel numerical strategy for modeling the moving boundary value problem of electrochemical machining

International Journal for Numerical Methods in Engineering, vol. 124, pp. 1856–1882

Abstract

Abstract This work presents a new numerical approach to efficiently model the cathode's moving surface 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 an innovative 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 suggest a new numerical method to model arbitrarily shaped and moving cathodes. Two methodologies are investigated to describe the time varying position of the cathode and compared in terms of implementational effort and numerical efficiency. 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.

Authors 4

1. Tim van der Velden corresponding Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Aachen, Germany

2. Stephan Ritzert Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Aachen, Germany

3. Stefanie Reese Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Aachen, Germany

4. Johanna Waimann Aachen Junior Professorship for Modeling and Simulation Techniques for Systems of Polycrystalline Materials Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Junior Professorship for Modeling and Simulation Techniques for Systems of Polycrystalline Materials, Institute of Applied Mechanics RWTH Aachen University Aachen Germany

   Junior Professorship for Modeling and Simulation Techniques for Systems of Polycrystalline Materials, Institute of Applied Mechanics, RWTH Aachen University, Aachen, Germany