电解加工中的动边值问题建模
Modeling moving boundary value problems in electrochemical machining
摘要：
本文提出了一种新的方法来有效地模拟电解加工中的移动边值问题的阴极。直到最近，用有限元进行的工艺模拟还存在因表面几何形状的变化而需要重新划分网格的缺点。这一缺点是克服了一种新的模型配方的阳极溶解，利用有效的材料参数以及作为内部变量的溶解水平，从而不需要重新划分网格。现在，我们将这个概念扩展到任意形状和移动的阴极模型。研究了两种方法来描述阴极随时间变化的位置。在第一种方法中，我们改变阴极内元素的电导率，在第二种方法中，我们在相应元素的节点上应用Dirichlet边界条件。对于这两种方法，阴极表面上的元素被处理与有效的材料参数。该过程允许有效模拟工业相关的复杂几何形状，而无需网格自适应。该模型的性能进行了验证，从文献的分析，数值和实验结果。较短的计算时间使该方法对于工业应用很有趣。
英文摘要：
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.
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