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Journal of Applied Electrochemistry

, Volume 40, Issue 7, pp 1395–1405 | Cite as

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

  • N. Smets
  • S. Van Damme
  • D. De Wilde
  • G. Weyns
  • J. Deconinck
Original Paper

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 NaNO3 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 non-linearity 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.

Keywords

Approximate Concentration FEM Non-linear Pulse electrochemical machining (PECM) Temperature Time averaging Transient 

List of symbols

a

Polarization parameter 1 (S m−2);

A

Electrode surface (m2);

b

Polarization parameter 2 (A m−2);

c

Concentration (mol m−3);

Cp

Heat capacity (J kg−1 K−1)

D

Diffusion coefficient (m2s−1)

E0

Equilibrium potential (V)

F

Faraday constant (= 96485 C mol−1)

h

Heat transfer coefficient (W m−2 K−1)

I

Electrical current (A)

J

Current density distribution (A m−2)

k

Thermal conductivity (W m−1 K−1)

Pdl

Heat produced, in the double layer (W m−2)

Pbulk

Heat produced in the bulk (W m−3)

Prt

Turbulent Prandtl number (–)

\(\overline{r}\)

General location vector (m)

Re

Reynolds number (–)

t

Time (s)

T

Pulse period (s)

U

Potential distribution (V)

v

Velocity (m s−1)

w

Water depletion factor (–)

x

Distance (m)

z

Valence (–)

Greek symbols

α

Duty cycle (–)

η

Overpotential (V)

\(\Uptheta\)

Temperature (K)

μ

Dynamic viscosity (kg m−1 s−1)

ρ

Density (kg m−3)

σ

Electrical conductivity (S m−1)

τ

Time constant (s)

\(\Upphi_c\)

Mass flux (mol s−1m−2)

ψ

Pulse delay (s)

ψ*

Optimal pulse delay (s)

Abbreviations

2D

two dimensional

DC

Direct current

DNS

Direct numerical simulation

ECM

Electrochemical machining

FEM

Finite elements method

PAP

Prior averaging pulse

PECM

Pulse electrochemical machining

QSS

Quasi steady state

QSSSC

Quasi steady state shortcut

RANS

Reynolds averaged Navier-stokes

SS

Steady state

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • N. Smets
    • 1
  • S. Van Damme
    • 1
  • D. De Wilde
    • 1
  • G. Weyns
    • 1
  • J. Deconinck
    • 1
  1. 1.IR / ETEC DepartmentVrije Universiteit BrusselBrusselsBelgium

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