<p>Classical thermal models for die-sinking electrical discharge machining (EDM) assume constant thermophysical properties evaluated at room temperature. However, during discharge, the workpiece surface may reach temperatures of several thousand Kelvin, at which the thermal conductivity, specific heat, and density of metals change substantially. This paper quantifies the error introduced by the constant-property assumption through a controlled benchmark study comparing three models under identical conditions: the analytical solution of Jilani and Pandey (Precis Eng 4(4):215–221, <CitationRef CitationID="CR5">1982</CitationRef>), the energy balance model of Gulbinowicz et al. (Arch Mech Technol Mater 40:23–30, <CitationRef CitationID="CR6">2020</CitationRef>), and a finite difference solver developed by the authors with temperature-dependent properties from primary metrological sources. The central comparison uses two runs of the same solver, one with constant and one with temperature-dependent properties, so that the common numerical bias does not govern the relative metric. For low-carbon steel, the error in maximum temperature ranges from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(-4\%\)</EquationSource> </InlineEquation> (short pulses, where the increase in specific heat dominates) to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(+26\%\)</EquationSource> </InlineEquation> (long pulses, where the decrease in thermal conductivity dominates), with a crossover at approximately 50&#xa0;<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mu\)</EquationSource> </InlineEquation>s. For copper, the error is smaller, ranging from <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(+5\%\)</EquationSource> </InlineEquation> to <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(+19\%\)</EquationSource> </InlineEquation>, consistent with its lower property variation. A property decomposition reveals that thermal conductivity and specific heat act in opposing directions on the peak temperature; to the best of the authors’ knowledge, this competing mechanism has not been quantitatively documented in EDM thermal modeling. The finite difference solver is further validated against single-discharge crater volume measurements on AISI D3 tool steel reported by Lira et al. (Int J Adv Manuf Technol 136:4545–4568, <CitationRef CitationID="CR15">2025</CitationRef>); after applying a literature-consistent ejection efficiency of 0.15, the temperature-dependent prediction lies within the experimental range and close to the experimental mean, while the constant-property prediction exceeds the experimental maximum by approximately 16&#xa0;percent, providing a direct experimental indication that the constant-property assumption overestimates the cavity volume. A practical error map identifies the conditions under which constant-property models remain acceptable (source radius above 75&#xa0;<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mu\)</EquationSource> </InlineEquation>m) and those that require numerical simulation using temperature-dependent data (source radius below 50&#xa0;<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\mu\)</EquationSource> </InlineEquation>m). The complete source code is implemented in Python and openly available.</p>

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Quantifying the error of constant thermophysical properties in classical thermal models for die-sinking EDM

  • Valdemir Martins Lira,
  • Romulo Gonçalves Lins

摘要

Classical thermal models for die-sinking electrical discharge machining (EDM) assume constant thermophysical properties evaluated at room temperature. However, during discharge, the workpiece surface may reach temperatures of several thousand Kelvin, at which the thermal conductivity, specific heat, and density of metals change substantially. This paper quantifies the error introduced by the constant-property assumption through a controlled benchmark study comparing three models under identical conditions: the analytical solution of Jilani and Pandey (Precis Eng 4(4):215–221, 1982), the energy balance model of Gulbinowicz et al. (Arch Mech Technol Mater 40:23–30, 2020), and a finite difference solver developed by the authors with temperature-dependent properties from primary metrological sources. The central comparison uses two runs of the same solver, one with constant and one with temperature-dependent properties, so that the common numerical bias does not govern the relative metric. For low-carbon steel, the error in maximum temperature ranges from \(-4\%\) (short pulses, where the increase in specific heat dominates) to \(+26\%\) (long pulses, where the decrease in thermal conductivity dominates), with a crossover at approximately 50  \(\mu\) s. For copper, the error is smaller, ranging from \(+5\%\) to \(+19\%\) , consistent with its lower property variation. A property decomposition reveals that thermal conductivity and specific heat act in opposing directions on the peak temperature; to the best of the authors’ knowledge, this competing mechanism has not been quantitatively documented in EDM thermal modeling. The finite difference solver is further validated against single-discharge crater volume measurements on AISI D3 tool steel reported by Lira et al. (Int J Adv Manuf Technol 136:4545–4568, 2025); after applying a literature-consistent ejection efficiency of 0.15, the temperature-dependent prediction lies within the experimental range and close to the experimental mean, while the constant-property prediction exceeds the experimental maximum by approximately 16 percent, providing a direct experimental indication that the constant-property assumption overestimates the cavity volume. A practical error map identifies the conditions under which constant-property models remain acceptable (source radius above 75  \(\mu\) m) and those that require numerical simulation using temperature-dependent data (source radius below 50  \(\mu\) m). The complete source code is implemented in Python and openly available.