Multiphysics Modeling of Surface Finishing Performance in Pulsed-Waveform Electrochemical Machining
Authors: Skinn Brian , Hall Timothy D , Snyder Stephen , Taylor E. J. 
Published: February 2020

Electrochemical machining (ECM) is a manufacturing technology that allows metal to be precisely removed by electrochemical oxidation and dissolution into an electrolyte solution. ECM is suited for machining parts fabricated from “difficult to cut” materials and/or parts with complicated and intricate geometries. In ECM, the workpiece is the anode and the tool is the cathode in an electrochemical cell; by relative movement of the shaped tool into the workpiece, the mirror image of the tool is “copied” or machined into the workpiece. One notable difficulty with ECM is an inability to predict a priori the tool and process parameters required in order to satisfy the final specifications of the fabricated part [[1]]. Accordingly, there is potential value in development of a physical phenomenon-based design platform to predict optimal ECM tool shape. Such a capability is anticipated to dramatically shorten the process/tooling development cycle.
A further goal of ECM is to simultaneously achieve a target surface finish on the machined part. It is thus of interest to develop the capability also to predict the distribution of local surface finish resulting from ECM processing. Modeling of the changes in local surface finish intrinsically operates on a different length scale from that of bulk material removal (μm, versus mm or cm), and thus is most easily treated separately. The physicochemical phenomena involved in the evolution of surface finish during ECM processing are strongly coupled, and include the electric field itself (primary current distribution), surface polarization and electrochemical kinetics (secondary current distribution), and fluid flow and mass transfer (tertiary current distribution). Of particular interest is modeling of pulsed-waveform ECM, for which significant practical advantages have been demonstrated [[2],[3],[4]]. While an extensive body of literature exists analyzing pulsed electrodeposition [[5],[6]], comparatively little work has been published to date on pulsed ECM [[7],[8]].
This talk will discuss recent modeling work seeking to develop a solid foundation for a predictive understanding of the surface finishing aspects of ECM processes. The work described herein encompasses time-dependent modeling of concentration profiles and other relevant physical quantities under the application of pulse(-reverse) current ECM waveforms, starting from simulations assuming a locally flat surface and working toward quantitative descriptions of the transient and steady-periodic behavior on structured substrates. Prior work (see, e.g., Ref. 3) has demonstrated the value in differential pulsed-ECM processing of surfaces with features of size comparable to or larger than the hydrodynamic boundary layer thickness (“macroprofiles”) versus surfaces with features much smaller than the boundary layer thickness (“microprofiles”). Figure 1 (left) plots a schematic of the pulsating concentration profiles at the end of the pulse on-time in forward-only pulsed ECM, assuming 100% current efficiency. Here, the pulse period (ton + toff) and the peak applied current density (jpeak) are assumed constant, with the curves corresponding to different values of ton. The saturation concentration of the dissolved metal is Cs, and the bulk metal concentration Cb equals zero. The quantity τ is the “transition time,” which is the value for ton for which the metal concentration at the surface rises exactly to Cs at the end of the forward pulse. As can be seen, for ton < τ, metal dissolution is not mass transfer limited, but for any ton > τ the rate of dissolution is constrained by the diffusion of the dissolved material, approaching the DC mass transfer rate for sufficiently high ton. Figure 1 (right) illustrates that preliminary simulations performed with COMSOL Multiphysics® exhibit behavior consistent with this qualitative concept.

References

[1]. Rajurkar, K.P. et al. Annals of the CIRP 82(2), 1999.
[2]. Taylor, E.J. et al. “Breaking the Chemical Paradigm in Electrochemical Engineering: Case Studies and Lessons Learned from Plating to Polishing,” in Advances in Electrochemical Science & Engineering: The Path from Discovery to Product, x, y Eds. In press.
[3]. Taylor, E.J. and M. Inman. “Electrochemical Surface Finishing.” ECS Interface, Fall 2014: 57-61.
[4]. Taylor, E.J. et al. U.S. Patent 9,006,147, 14 Apr 2015.
[5]. Puippe, J.C. and F. Leaman, eds. “Theory and Practice of Pulse Plating.” Orlando, FL: AESF, 1986.
[6]. Hansel, W.E.G. and S. Roy. “Pulse Plating.” Bad Saulgau, Germany: Leuze Verlag KG, 2012.
[7]. Sautebin, R. et al. J Electrochem Soc 127(5): 1096, 1980.
[8]. Sautebin, R. and D. Landolt. J Electrochem Soc 129(5): 946, 1982.

Figure 1