Physics-Guided Predictive Modeling of Tool Wear in Electrical Discharge Machining via Dimensional Analysis: A Buckingham Π Framework with TOPSIS-Based Electrode Selection
Abstract
Abstract Electrical discharge machining (EDM) is a non-contact process used to shape hard, electrically conductive components for aerospace, automotive, and biomedical manufacturing. Electrode wear is a progressive phenomenon characterized by localized temperatures of 8,000–12,000°C that gradually deteriorate dimensional accuracy and increase production costs; however, quantitative, physics-based models of the tool wear rate (TWR) are not yet available. In the present work, the Buckingham Π theorem is applied to die-sinking EDM, reducing eight governing variables and five fundamental dimensions to three independent dimensionless groups and deriving a closed-form, physically interpretable power-law model for TWR. Log-linear ordinary least-squares regression calibration of a nine-run Taguchi L9 dataset (copper electrode on mild steel; I = 2–6 A, V = 40–80 V, ton = 50–200 µs) yields R² = 0.969 and a mean absolute percentage error (MAPE) of 10.1%. The fitted thermal group exponent β = −0.990 agrees with EDM erosion theory. Higher electrode thermal conductivity and melting point together increase the specific energy needed to reach the ablation threshold. This, in turn, reduces TWR. Independent validation against nine experiments reported by (Bose & Mahapatra, 2015) (copper electrode, AISI H-13 tool steel; I = 7–11 A) shows a validation MAPE of 18.5%. All four outliers occur under operating conditions outside the calibration range, highlighting the known limitations of…
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