Статья
2017

Pseudotransient method for modeling of electrochemical machining

V. M. Volgin V. M. Volgin , A. D. Davydov A. D. Davydov
Российский электрохимический журнал
https://doi.org/10.1134/S1023193517100147
Abstract / Full Text
Volgin, V.M., Davydov, A.D. Pseudotransient method for modeling of electrochemical machining. Russ J Electrochem 53, 1109–1121 (2017). https://doi.org/10.1134/S1023193517100147

The electrochemical machining is aimed at the fabrication of parts of prescribed shape and dimensions by the anodic metal dissolution using tool-electrodes of various types. The task of the theory of electrochemical machining is to calculate the shape and dimensions of the workpiece depending on the shape of tool-electrode and operation conditions. In this work, a pseudotransient method of modeling, which is new for the steady-state electrochemical machining, is developed. In this method, first, the initial approximation of workpiece surface is prescribed; in the course of modeling, it shifts in the normal direction at a rate proportional to the residual of steady-state condition. The proposed method requires substantially lower computational cost than the non-steady-state method and can be used for the tool-electrodes of arbitrary shape.

Author information

  • Tula State University, pr. Lenina 92, Tula, 300012, Russia

    V. M. Volgin

  • Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Leninskii pr. 31, Moscow, 119071, Russia

    A. D. Davydov

References
  1. Rajurkar, K.P., Levy, G., Malshe, A., Sundaram, M.M., McGeough, J., Hu, X., Resnick, R., and DeSilva, A., Micro and nano machining by electro-physical and chemical processes, CIRP Ann.-Manuf. Techn., 2006, vol. 55, no. 2, p. 643.
  2. Datta, M. and Landolt, D., Fundamental aspects and applications of electrochemical microfabrication, Electrochim. Acta, 2000, vol. 45, p. 2535.
  3. Rajurkar, K.P., Sundaram, M.M., and Malshe, A.P., Review of electrochemical and electrodischarge machining, Procedia CIRP, 2013, vol. 6, p. 13.
  4. Datta, M., Fabrication of an array of precision nozzles by through-mask electrochemical micromachining, J. Electrochem. Soc., 1995, vol. 142, no. 11, p. 3801.
  5. Davydov, A.D., Kabanova, T.B., and Volgin, V.M., Modeling of through-mask electrochemical micromachining, Chem. Eng. Trans., 2014, vol. 41, p. 85.
  6. Schonenberger, I. and Roy, S., Microscale pattern transfer without photolithography of substrates, Electrochim. Acta, 2005, vol. 51, no. 5, p. 809.
  7. Forster, R., Schoth, A., and Menz, W., Micro-ECM for production of microsystems with a high aspect ratio, Microsyst. Technol., 2005, vol. 11, nos. 4 and 5, p. 246.
  8. Kim, B.H., Ryu, S.H., Choi, D.K., and Chu, C.N., Micro electrochemical milling, J. Micromech. Microeng., 2005, vol. 5, p. 124.
  9. Spieser, A. and Ivanov, A., Recent developments and research challenges in electrochemical micromachining (µECM), Int. J. Adv. Manuf. Technol., 2013, vol. 69, nos. 1—4, p. 563.
  10. Davydov, A.D., Volgin, V.M., and Lyubimov, V.V. Electrochemical machining of metals: Fundamentals of electrochemical shaping, Russ. J. Electrochem., 2004,vol. 40, p. 1230.
  11. Volgin, V.M., Lyubimov, V.V., Kukhar, V.D., and Davydov, A.D., Modeling of wire electrochemical micromachining, Procedia CIRP, 2015, vol. 37, p. 176.
  12. Volgin, V.M., Lyubimov, V.V., and Davydov, A.D., Modeling and numerical simulation of electrochemical micromachining, Chem. Eng. Sci., 2016, vol. 140, p. 252.
  13. Collett, D.E., Hewson-Browne, R.C., and Windle, D.W., A complex variable approach to electrochemical machining problems, J. Eng. Math., 1970, vol. 4, no. 1, p. 29.
  14. Karimov, A.Kh., Klokov, V.V., and Filatov, E.I., Metody rascheta elektrokhimicheskogo formoobrazovaniya (Methods of Calculation of Electrochemical Shaping), Kazan: Kazan. Univ., 1990.
  15. Zhitnikov, V.P. and Zaitsev, A.N., Impul’snaya elektrokhimicheskaya razmernaya obrabotka (Pulse Electrochemical Machining), Moscow: Mashinostroenie, 2008.
  16. Monakhov, V.N., Kraevye zadachi so svobodnymi granitsami dlya ellipticheskikh sistem uravnenii (Free-Boundary Problems for Elliptic Systems of Equations), Novosibirsk: Nauka, 1977.
  17. Friedman, A., Variational Principles and Free-Boundary Problems, New York: Wiley, 1982.
  18. Crank, J., Free and Moving Boundary Problems, Oxford: Oxford Univ. Press, 1987.
  19. Vabishchevich, P.N., Chislennye metody resheniya zadach so svobodnoi granitsei (Numerical Methods of Solution of Free-Boundary Problems), Moscow: Mosk. Gos. Univ., 1987.
  20. Finlayson, B.A., Numerical Methods for Problems with Moving Fronts, Seattle: Ravenna Park, 1992.
  21. Minazetdinov, N.M., One scheme of electrochemical machining of metals by a curvilinear electrode tool, J. Appl. Mech. Tech. Phys., 2010, vol. 51, no. 2, p. 288.
  22. Minazetdinov, N.M., The two-dimensional problem of the electrochemical machining of metals with a periodic cathode tool, J. Appl. Math. Mech., 2012, vol. 76, no. 4, p. 475.
  23. Zhitnikov, V.P., Oshmarina, E.M., Porechny, S.S., and Fedorova, G.I., Limit model of electrochemical dimensional machining of metals, J. Appl. Mech. Tech. Phy., 2014, vol. 55, no. 4, p. 718.
  24. Kotlyar, L.M. and Minazetdinov, N.M. Modeling of electrochemical machining with the use of a curvilinear electrode and a stepwise dependence of the current efficiency on the current density, J. Appl. Mech. Tech. Phys., 2016, vol. 57, no. 1, p. 127.
  25. Zhitnikov, V.P., Sherykhalina, N.M., and Zaripov, A.A., Modelling of precision steady-state and non-steadystate electrochemical machining by wire electrodetool, J. Mater. Process. Technol., 2016, vol. 235, p. 49.
  26. Zhou, Y. and Derby, J.J., The cathode design problem in electrochemical machining, Chem. Eng. Sci., 1995, vol. 50, no. 17, p. 2679.
  27. Elliott, C.M., A Variational Inequality Formulation of a Steady State Electrochemical Machining Free Boundary Problem, in Free Boundary Problems: Theory and Applications, vol. 2, Boston: Pitman, 1983, p. 505.
  28. Fletcher, C., Computational Techniques for Fluid Dynamics, vol. 1: Fundamental and General Techniques, Berlin: Springer, 1988.
  29. Volgin, V.M., Lyubimov, V.V., Gnidina, I.V., Davydov, A.D., and Kabanova, T.B., Effect of current efficiency on electrochemical micromachining by moving electrode, Procedia CIRP, 2016, vol. 55, p. 65.