Time averaged calculations in pulse electrochemical machining, using a strongly non-linear model

Abstract

Simulation of the Pulse Electrochemical Machining (PECM) process can provide information on system design and guidelines for practical use. The pulses that are applied to the PECM system have to be described on a time scale that can be orders of magnitude smaller than the physical time scales in the system. If the full detail of the applied pulses has to be taken into account, the time accurate calculation of the variable distribution evolutions in PECM can become a computationally very expensive procedure. In previous work of the authors, approximate techniques were introduced: the hybrid calculation and the Quasi Steady State Shortcut (QSSSC). In other previous work of the authors a model for PECM of steel in NaNO 3 was introduced. This model contains a changing polarization behaviour of the double layer as a function of the metal ion surface concentration, which brings a strong non-linearity in the system. In this paper a technique is introduced to integrate the non-linear model into the approximate methods. To achieve this, the strategy of the approximate methods is extended. For the QSSSC, the nonlinearity is handled using an extra convergence level. For the hybrid calculation, live averaging is used to take care of the non-linear effects. Performing this, the timesteps used during the high level calculations are no longer dictated by the pulse characteristics. Using this approach, computationally very cheap, yet satisfying results can be obtained. The technique is very general and very powerful and can be used in any multi-timescale system. List of symbols aPolarization parameter 1 (S m -2 ); A Electrode surface (m 2 ); bPolarization parameter 2 (A m -2 ); c Concentration (mol m -3 );Thermal conductivity (W m -1 K -1 ) P dl Heat produced, in the double layer (W m -2 ) P bulk Heat produced in the bulk (W m -3 ) Pr t Turbulent Prandtl number (-) rGeneral location vector (m) ReReynoldsVelocity (m s -1 ) wWater depletion factor (-) x Distance (m) z Valence (-)Greek symbols a Duty cycle (-) g Overpotential (V) H Temperature (K) lDynamic viscosity (kg m -1 s -1 )

Electrochemical micromachining: Review of factors affecting the process applicability in micro-manufacturing

“…30 Many researchers have investigated the influence of applying pulsed potential during ECM. 5,10,11,14,15,18,19,22,23,[27][28][29][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] Cook et al 31 seem to be the first group to design and apply a pulsed power supply to an ECM system. Their intention was to apply a short negative pulse after a positive pulse to remove the passive layer which was forming on the workpiece, with the aim to improve MRRs and allow machining of difficult-to-machine materials such as tungsten carbide (WC).…”

“…Meijer and Veringa 32 observed that PECM resulted in a better surface finish and tool reproduction than ECM. Van Damme et al 33 and Smets et al 35 created models of the PECM process, investigating the effects Figure 6. Model of the inter-electrode gap.…”

“…Meijer and Veringa 32 observed that PECM resulted in a better surface finish and tool reproduction than ECM. Van Damme et al 33 and Smets et al 35 created models of the PECM process, investigating the effects of local electrolyte concentration variations. They observed an off-time >90 ms, for the system they were studying, allowed the electrolyte in the IEG to be completely refreshed to bulk conditions, meaning each pulse is independent of the last pulse.…”