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Computational Modelling of Electrical Discharge Machining (EDM) for Tuning Surface Roughness and Curvature

Abstract

Electrical Discharge Machining (EDM) is a processing method to create rough surfaces on metallic substrates. The surface is modified by recurring current discharges between an electrode and a substrate separated by a dielectric. The extent of roughness is dependent on the applied current and the distance between electrode and substrate. The process of EDM provides a stochastic method for creating a randomly generated surface. In order to phenomelogically understand how such certain topographies are generated and what surface parameters may change, a predictive model was created for further understanding. The model assumes that impacts on an arbitrarily sized surface are stochastic and independent of previous impacts. The underlying shape change during the process was deemed most crucial, thus heat transfer and surface charge were not taken into account. A number of input parameters such as number of impacts, size of impact, depth of impact, volume fraction were chosen. Subsequently, Abbott-Firestone curves were used to evaluate both surface roughness and surface curvature. In addition, equilibria for a given set of parameters were determined – i.e. a surface reaches its final form and undergoes no further significant topographical change. For each iteration a point was randomly chosen as the point of impact. Subsequently the surface was deformed according to an ellipsoid-torus model for crater formation, which was based on a previously reported model of Micro Wire Electrical Discharge Machining (Micro-WEDM). A fraction of the removed volume was used to form the torus ridge surrounding the crater. This process is then repeated for the given number of impacts. The script for the modelling was written in Python 3.7 with packages NumPy for algebraic calculations and CUDA libraries for parallelization were used for faster computation. The application of such a computational model may be useful in predicting how a surface is deformed, and what input parameters to use to create a surface with certain desired surface function. Future improvements of the model may include volumetric changes, surface charge and heat transfer.
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