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

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.

Modeling electrochemical machining based on effective parameters

“…1. Concept of the dissolution process with iron-based dissolution, see also [6,7]: dissolution variable 𝒅𝒅 varying between 𝒅𝒅 = 𝟎𝟎 in the metal and 𝒅𝒅 = 𝟏𝟏 in the electrolyte.…”

“…The original paper [6] additionally considers a thermally coupled system. There also a more detailed description of the effective parameter approach can be found, which is also later used for the consideration of a relocatable cathode in terms of a moving boundary value problem [7]. Due to simplicity, the additional thermal problem is skipped, here.…”

“…The temporal amount of the dissolution by this reaction can be described by Faraday's law of electrolysis. Motivated by [9] and introduced in [6,7], one can formulate the evolution equation of the inner variable 𝑑𝑑. The dissolution level of an incremental reference volume d𝑉𝑉 𝑟𝑟𝑟𝑟𝑟𝑟 reads…”

An anisotropic damage model for finite strains with full and reduced regularization of the damage tensor

“…Here, the presented model utilizes a second order damage tensor and a finite strain formulation and is applied to purely mechanical problems. In future, the anisotropic damage modeling can be incorporated into multiphysical process simulations (e.g., [12,13]) and medical applications (e.g., [14]).…”

Optimization and experimental study on cathode structure of electrochemical machining Titanium alloy inner helix

“…Thus, scholars at home and abroad have carried out a lot of scienti c research. Velden used numerical simulation method to simulate and analyze the cathode pro le, which shortened the cathode development cycle [15]. Mishra Technology studied the cathode structure based on the ow eld simulation model of transverse groove ECM, and concluded that symmetrical and uniform placement of cathode holes can improve the gap ow eld homogeneity [17].…”