Modeling of Thermal Processes During Electrical Discharge Machining in Order to Determine Rational Processing Conditions
| Authors: Stavitskiy I.B. | Published: 13.04.2026 |
| Published in issue: #1(156)/2026 | |
| Category: Mechanical Engineering and Machine Science | Chapter: Technology and Equipment of Mechanical and Physical Processing | |
| Keywords: electrical discharge machining, EDM pulse parameters, heat flux density, duration of electrical impulses, modeling of the EDM process, Stefan’s problem | |
Abstract
The article presents a method for determining the rational modes of electrical discharge machining (EDM). The method is based on solving the thermal problem of moving the boundary of the material phase transformation (Stefan's problem) and calculating the depth of the holes formed on the surface of the workpiece from electrical discharges. In this case, the depth of the hole is equal to the depth of penetration of the material, and the molten material is completely removed from the workpiece. The density of the heat flux coming to the workpiece depends on the pulse energy of the generator, which is distributed between the anode, cathode, interelectrode gap, and is also spent on radiation and other losses. In this regard, it is important to determine the pulse energy coming directly to the workpiece. Currently, no exact correlation has been established between the pulse energy set by the generator and the heat flow acting on the workpiece. It is possible to determine the density of the heat flux coming on the workpiece by solving the inverse thermal problem: according to a known or specified melting depth of the material and the duration of the heat source. Thus, knowing the pulse energy of the generator, as a result of which the hole was formed, and the melting depth of the hole, it is possible to calculate the fraction of the pulse energy that falls directly on the workpiece. The article defines the proportion of generator pulse energy supplied to the workpiece, the achievable performance of the EDM process, the temperature distribution over the depth of the workpiece and the thickness of the thermally modified layer. Using the direct thermal problem, the melting depth of the material is determined depending on the energy and pulse duration, and the surface roughness is predicted
Please cite this article in English as:
Stavitskiy I.B. Modeling of thermal processes during electrical discharge machining in order to determine rational processing conditions. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2026, no. 1 (156), pp. 57--73 (in Russ.). EDN: BXSWFG
References
[1] Swiercz R., Oniszczuk-Swiercz D. Influence of EDM parameters on the functional properties of the steel with a high thermal conductivity. Mechanik, 2015, vol. 53, pp. 29--34. DOI: http://doi.org/10.17814/mechanik.y2015.iss1.art15
[2] Singh V., Bhandari R., Yadav V.K. An experimental investigation on machining parameters of AISI D2 steel using WEDM. Int. J. Adv. Manuf. Technol., 2017, vol. 93, no. 1-4, pp. 203--214. DOI: http://doi.org/10.1007/s00170-016-8681-6
[3] Yusoff A.R., Ghazalli Z., Hussain H.C. Determining optimum EDM parameters in drilling a small hole by Taguchi method. Int. J. Manuf. Technol. Manag., 2009, vol. 17, no. 4, pp. 345--352. DOI: http://doi.org/10.1504/ijmtm.2009.023952
[4] Kumar M., Rana J., Sharma A. Multi-objective optimization of electro-discharge machining (EDM) parameter for sustainable machining. Mater. Today: Proc., 2017, vol. 4, no. 8, pp. 9147--9157. DOI: http://doi.org/10.1016/j.matpr.2017.07.271
[5] Parthasarathi S. Optimization of wire-EDM parameters to calculate MRR and measure surface finish on SS410. Int. J. Innov. Sc. Res. Technol., 2017, vol. 2, no. 3, pp. 20--45. DOI: http://doi.org/10.13140/RG.2.2.36343.68003
[6] Yerui F., Yongfeng G., Zongfeng L. Experimental investigation of EDM parameters for TiC/Ni cermet machining. Procedia CIRP, 2016, vol. 42, pp. 18--22. DOI: http://doi.org/10.1016/j.procir.2016.02.177
[7] Stavitskiy I.B., Shevchenko A.S. Definition of titanium EDM pulse parameters based on solution of the Stefan heat problem. Inzhenernyy zhurnal: nauka i innovatsii [Engineering Journal: Science and Innovation], 2017, no. 3 (in Russ.). DOI: http://doi.org/10.18698/2308-6033-2017-3-1599
[8] Jonsson T. On the one dimensional Stefan problem: with some numerical analysis. Umea, Umea University, 2013. URL: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80215 (дата обращения: 15.01.2026).
[9] Patel M.R., Barrufet M.A., Eubank P.T., et al. Theoretical models of the electrical discharge machining process. II. The anode erosion model. J. Appl. Phys., 1989, vol. 66, no. 9, pp. 4104--4111. DOI: http://doi.org/10.1063/1.343995
[10] Dibitonto D.D., Eubank P.T., Patel M.R., et al. Theoretical models of the electrical discharge machining process. I. A simple cathode erosion model. J. Appl. Phys., 1989, vol. 66, no. 9, pp. 4095--4103. DOI: http://doi.org/10.1063/1.343994
[11] Osswald K., Schneider S., Hensgen L., et al. Experimental investigation of energy distribution in continuous sinking EDM. CIRP J. Manuf. Sc. Technol., 2017, vol. 19, pp. 36--43. DOI: http://doi.org/10.1016/j.cirpj.2017.04.006
[12] Xia H., Hashimoto H., Kunieda M., et al. Measurement of energy distribution in continuous EDM process. J. Jpn. Soc. Precis. Eng., 1996, vol. 62, no. 8, pp. 1141--1145. DOI: http://doi.org/10.2493/jjspe.62.1141
[13] Zahiruddin M., Kunieda M. Energy distribution ratio into micro EDM electrodes. J. Adv. Mech. Des. Syst. Manuf., 2010, vol. 4, no. 6, pp. 1095--1106. DOI: http://doi.org/10.1299/jamdsm.4.1095
[14] Xia H., Kunieda M., Nishiwakp N., et al. Measurement of energy distribution into electrodes in EDM processes. In: Advancement of intelligent production. Elsevier, 1994, pp. 601--606. DOI: http://doi.org/10.1016/b978-0-444-81901-7.50114-6
[15] Shankar P., Jain V.K., Sundararajan T. Analysis of spark profiles during EDM process. Mach. Sc. Technol., 1997, vol. 1, no. 2, pp. 195--217. DOI: http://doi.org/10.1080/10940349708945647
[16] Zolotykh B.N. Fizicheskie osnovy elektroiskrovoy obrabotki metallov [Physical fundamentals of electrospark processing of metals]. Moscow, GOSTEKHIZDAT Publ., 1953.
[17] Singh H. Experimental study of distribution of energy during EDM process for utilization in thermal models. Int. J. Heat Mass Transf., 2012, vol. 55, no. 19-20, pp. 5053--5064. DOI: http://doi.org/10.1016/j.ijheatmasstransfer.2012.05.004
[18] Budak B.M., Solovyeva E.N., Uspenskiy A.B. A difference method with coefficient smoothing for the solution of Stefan problems. U.S.S.R. Comput. Math. Math. Phys., 1965, vol. 5, no. 5, pp. 59--76. DOI: https://doi.org/10.1016/0041-5553(65)90005-4
[19] Meyer G.H. The numerical solution of Stefan problems with front-tracking and smoothing methods. Appl. Math. Comput., 1978, vol. 4, no. 4, pp. 283--306. DOI: http://doi.org/10.1016/0096-3003(78)90001-2
[20] Crowley A.B. Numerical solution of Stefan problems. Int. J. Heat Mass Transf., 1978, vol. 21, no. 2, pp. 215--219. DOI: http://doi.org/10.1016/0017-9310(78)90225-9
[21] Caldwell J., Kwan Y.Y. Numerical methods for one-dimensional Stefan problems. Commun. Numer. Methods Eng., 2004, vol. 20, no. 7, pp. 535--545. DOI: http://doi.org/10.1002/cnm.691
[22] Samarskiy A.A., Moiseenko B.D. An economic continuous calculation scheme for the Stefan multidimensional problem. U.S.S.R. Comput. Math. Math. Phys., 1965, vol. 5, no. 5, pp. 43--58. DOI: https://doi.org/10.1016/0041-5553(65)90004-2
[23] Zhang Y., Cohen J., Davidson A.A., et al. A hybrid method for solving tridiagonal systems on the GPU. In: GPU computing gems. Waltham, Morgan Kaufmann, 2012, pp. 117--132. DOI: http://doi.org/10.1016/b978-0-12-385963-1.00011-3
[24] Backemo J., Heuchel M., Reinthaler M., et al. A. Predictive topography impact model for Electrical Discharge Machining (EDM) of metal surfaces. MRS Advances, 2020, vol. 5, no. 12-13, pp. 621--632. DOI: http://doi.org/10.1557/adv.2019.433
[25] Tan P.C., Yeo S.H. Modelling of overlapping craters in micro-electrical discharge machining. J. Phys. D: Appl. Phys., 2008, vol. 41, no. 20, art. 205302. DOI: http://doi.org/10.1088/0022-3727/41/20/205302
