Time-averaged concentration calculations in pulse electrochemical machining, spectral approach

Simulation of the species concentrations during the pulse electrochemical machining (PECM) process can provide information on system design and guidelines for practical use. In detailed numerical calculations, the concentrations will be calculated simultaneously with the temperature due to mutual dependencies. The pulses that are applied to the PECM system have to be described on a timescale that can be orders of magnitude smaller than the physical timescales in the system. If the full detail of the applied pulses has to be taken into account, the time accurate calculation of the variable distributions' evolutions in PECM can become a computationally very expensive procedure. A different approach is used by time averaging the pulses applied to the system. Performing this, the timesteps used during the calculations are no longer dictated by the pulse characteristics. Using this approach is computationally very cheap, yet satisfying results can be obtained. In the previous study of the authors (Smets et al., J Appl Electrochem 37(11):1345–1355, 2007 [8]), the hybrid calculation and the quasi-steady-state shortcut (QSSSC) were introduced. These methods introduce errors, however, which were quantified using analytical solutions and found to be acceptable. The results applied only to rectangular pulses. In this study, the more general case of arbitrary pulse forms is considered using a spectral approach. The concentration and the temperature calculation have different requirements for optimal approximated calculations, and a compromise has to be found between them. An analysis is performed on a simplified model, which provides useful guidelines during simulations.