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Time averaged temperature calculations in pulse electrochemical machining, spectral approach

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Abstract

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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Abbreviations

1D:

One dimensional

ECM:

Electrochemical machining

PECM:

Pulse electrochemical machining

QSS:

Quasi steady state

QSSSC:

Quasi steady state shortcut

SS:

Steady state

A :

Pulse scale factor (K)

Bi :

Biot number \((=\frac{hH}{k}) (-)\)

C p :

Heat capacity (J kg−1 K−1)

Fo :

Fourier number \((=\frac{\alpha^{\prime}t}{H^2}) (-)\)

h :

Heat transfer coefficient (W m−2 K−1)

H :

Characteristic size electrode (m)

J :

Current density (A m−2)

k :

Thermal conductivity (W m−1 K−1)

n :

Spectral component index (–)

P dl :

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

P bulk :

Heat density produced in the bulk (W m−3)

t :

Time (s)

t′:

Time (s)

T :

Pulse period (s)

T′:

Dimensionless pulse period (–)

v :

Scalar velocity (m s−1)

\(\overline{v}\) :

Velocity vector (m s−1)

x :

Distance (m)

x′:

Dimensionless distance (–)

α:

Duty cycle (–)

α′:

Thermal diffusivity (m2 s−1)

η:

Overpotential (V)

θ:

Relative temperature (K)

\(\overline{\theta}\) :

Averaged temperature (K)

\(\tilde{\theta}\) :

Temperature ripple (K)

θ decay :

Decaying temperature (K)

Θ:

Temperature (K)

Θ∞ :

Reference temperature (K)

Θ*:

Electrolyte temperature (K)

\(\hat{\lambda}_{n}\) :

Transcendental coefficients (–)

ρ:

Density (kg m−3)

σ:

Electrical conductivity (S m−1)

τ:

Time constant (s)

ω:

Angular frequency (s−1)

ψ:

Pulse delay (s)

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Authors and Affiliations

  1. IR/ETEC Department, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium

    N. Smets, S. Van Damme, D. De Wilde, G. Weyns & J. Deconinck

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  1. N. Smets
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  2. S. Van Damme
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  3. D. De Wilde
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  4. G. Weyns
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  5. J. Deconinck
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Correspondence to N. Smets.

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Smets, N., Van Damme, S., De Wilde, D. et al. Time averaged temperature calculations in pulse electrochemical machining, spectral approach. J Appl Electrochem 39, 791–798 (2009). https://doi.org/10.1007/s10800-008-9723-z

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  • DOI: https://doi.org/10.1007/s10800-008-9723-z

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