Time averaged temperature calculations in pulse electrochemical machining, part II: numerical simulation

Smets, Nico; Damme, S. Van; Wilde, D. De; Weyns, G.; Deconinck, Johan

doi:10.1007/s10800-007-9472-4

Cited by 29 publications

(13 citation statements)

References 14 publications

(33 reference statements)

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“…The ion distributions are calculated using convective-diffusion equations with mass fluxes on the boundaries [23]. The temperature distribution [19] in the system is calculated using a convective-diffusion equation with heat sources. Joule heating in the bulk of both the electrolyte and the electrodes is considered.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Analytical formulae for optimal values of w were presented in the work. The hybrid method and the derived QSSSC have also been used in other work of the authors [18][19][20][21].…”

mentioning

confidence: 99%

“…In [19] the averaged heat was estimated based on the polarization parameters and pulse characteristics only. This method will no longer be adequate with the changing polarization.…”

mentioning

confidence: 99%

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

et al. 2010

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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 )

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Section: Mathematical Modelmentioning

confidence: 99%

“…Analytical formulae for optimal values of w were presented in the work. The hybrid method and the derived QSSSC have also been used in other work of the authors [18][19][20][21].…”

mentioning

confidence: 99%

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

et al. 2010

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“…Significant efforts have been made to tackle such issues, yielding shortcut techniques such as the so-called Time Averaging Method. For instance, Smets [27][28][29] used the time averaging to perform temperature calculations in the context of PECM.…”

Section: Introductionmentioning

confidence: 99%

A novel pulse shortcut strategy for simulating nano-second pulse electrochemical micro-machining

Hotoiu

Deconinck

2014

J Appl Electrochem

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Nano-second pulse electrochemical micromachining is essentially employed in high precision metal processing applications. Simulation wise, such a process involves heavy time-accurate calculations necessary to obtain the confined anodic current density distribution, crucial for the machining copy accuracy. A new alternative simulation method is presented, entitled the Pulse Shortcut Strategy (PSS), that avoids the entire time-accurate procedure and significantly reduces the computational effort and runtime. The PSS relies on calculating a current density Correction Factor (CF) that is based on the local electrolyte resistance, the interface polarization and double layer (DL) properties in combination with the nano-second pulse characteristics. The same confining effect is achieved by simulating a computationally cheap stationary current density distribution and altering it locally through the space-dependent CF. When the system has constant electrolyte resistivity, constant DL capacitance and linear polarization, the CF calculation reacts in full agreement with the time-accurate simulation results for any pulse ontime/off-time combination. The PSS accuracy is compared with full time-accurate simulations and represents a mutual validation method between the two. These results offer promising perspectives for the simulation of nano-second pulse electrochemical micro-machining, making it more attractive from a practical point of view once the general interest in the technology emerges. The approach can be generalized to other pulsating electrochemical systems.

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“…To avoid these unnecessary calculations, the knowledge obtained in this paper is very useful. Numerical calculations using the hybrid technique were performed in [12] for rectangular pulses.…”

Section: Introductionmentioning

confidence: 99%

Time averaged temperature calculations in pulse electrochemical machining, spectral approach

et al. 2008

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Simulation of the temperature distribution during the Pulse Electrochemical Machining (PECM) process provides 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 time scale on which the thermal effects evolve. If the full detail of the applied pulses has to be taken into account, the time accurate calculation of the temperature distribution in PECM can become a computationally very expensive procedure. A different approach is used by time averaging the heat sources of the system. Performing this, the time steps used during the calculations are no longer dictated by the pulse characteristics. Using this approach, computationally very cheap, yet satisfying results can be obtained. In previous work of the authors, the hybrid calculation and the Quasi Steady State ShortCut (QSSSC) were introduced. This method allows to perform simplified calculations while getting satisfactory results. The method introduces errors however, which were quantified using analytical solutions and found to be acceptable. The results applied only to rectangular pulses. In this work, the more general case of arbitrary pulse forms is considered using a spectral approach.

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Time averaged temperature calculations in pulse electrochemical machining, part II: numerical simulation

Cited by 29 publications

References 14 publications

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

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

A novel pulse shortcut strategy for simulating nano-second pulse electrochemical micro-machining

Time averaged temperature calculations in pulse electrochemical machining, spectral approach

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