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Numerical Treatment of Free Boundary Value Problems / Numerische Behandlung freier Randwertaufgaben pp 187–201Cite as

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Some Moving Boundary Problems in Electrochemical Machining

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Abstract

Solutions to the potential equation with moving boundary conditions, applicable to the electrochemical machining process, are presented. A model is proposed for the removal by electrochemical machining of irregularities on the surface of the anode. These irregularities are described by Fourier series with time-dependent coefficients. Differential equations are derived for these coefficients in order that the variation in time of the height of the irregularities and also the shape of the anode surface can be described. Attention is drawn to the usefulness of the model for investigating practical cases such as the loss of parent metal from the anode in deburring by electrochemical machining, and other problems like the electrochemical removal of cusps caused by numerically controlled milling. The model is extended to cover the electrochemical smoothing of a rough cylinder.

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References

  1. McGeough, J. A.: ‘Principles of Electrochemical Machining’, London Chapman and Hall (Publishers) Ltd., 1974, 1–10.

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  2. Stronach, A. F., McGeough, J. A. and Clark, W. G.: ‘Experimental and Numerical Analyses of the Pressure Distribution in Electrochemical Machining’, Int. J. Mechanical Science 18 (1976), 261–268.

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  3. Fitzgerald, J. M. and McGeough, J. A.: ‘Mathematical Theory of Electrochemical Machining’, J. Inst. Maths. Applics., 5, (1969), 387–408.

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  4. McGeough, J. A. and Rasmussen, H.: ‘On the Derivation of the Quasi-steady Model in Electrochemical Machining’, J. Inst. Maths. Applics., 13, (1974), 13–21.

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  5. McGeough, J. A.: ‘Method of and Apparatus for Treating Workpieces’, British Patent No. 11939/75, 1975.

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  6. Fitzgerald, J.M. and McGeough, J. A.: ’Mathematical Theory of Electrochemical Machining 3, J. Inst. Maths. Applics., 6, (1970), 102–110.

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Author information

Authors and Affiliations

  1. Department of Engineering, Marischal College, University of Aberdeen, Aberdeen, AB9 1AS, UK

    J. A. McGeough

Authors
  1. J. A. McGeough
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Technische Universität Clausthal, D-3392, Clausthal-Zellerfeld, Germany

    J. Albrecht

  2. Institut für Angewandte Mathematik, Universität Hamburg, Bundesstrasse 55, D-2 Hamburg 13, Germany

    L. Collatz

  3. Institut für Mathematik III, Freie Universität Berlin, Arnimallee 2-6, D-1 Berlin 33, Germany

    K.-H. Hoffmann

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© 1982 Springer Basel AG

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McGeough, J.A. (1982). Some Moving Boundary Problems in Electrochemical Machining. In: Albrecht, J., Collatz, L., Hoffmann, KH. (eds) Numerical Treatment of Free Boundary Value Problems / Numerische Behandlung freier Randwertaufgaben. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 58. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6563-0_14

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  • DOI: https://doi.org/10.1007/978-3-0348-6563-0_14

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-6565-4

  • Online ISBN: 978-3-0348-6563-0

  • eBook Packages: Springer Book Archive

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