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Multi-spark model for predicting surface roughness of electrical discharge textured surfaces

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Abstract

Several models in the literature predict the average surface roughness (Ra) of electrical discharge textured surfaces using either a single-spark simulation for roughness estimation, or a multi-spark simulation with a uniform or a symmetric distribution of sparks. This paper presents an improved approach for surface roughness prediction, by generating surface profiles with the stochastic distribution of sparks with respect to the following: (i) location, (ii) energy level, and (iii) time. In addition, the formulation for single-spark adopts better assumptions, such as a Gaussian heat flux distribution for sparks, temperature dependency of material properties, and the operating parameter-dependent variation of factors, such as spark radius, cathode energy fraction, and plasma flushing efficiency. Surface profiles are simulated by the multi-spark model, considering the stochastic distribution of crater profiles, which are evaluated by the single-spark model. Unique profiles are obtained for each run of the multi-spark model, for a particular parameter combination. They vary in location, size, and shape of individual peaks and valleys, among each other due to this stochastic distribution of sparks. This variation among profiles agrees well with the variable distribution of peaks and valleys in actual EDTed surface profiles. It is observed that an increase in discharge current and pulse on-time leads to a lesser number of peaks and valleys, and a higher peak-to-valley height on the surface profile, due to increase in individual crater dimensions. The adoption of the more realistic assumptions in current model reduces the average Ra prediction error to 11.5%.

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Abbreviations

T :

(Temperature)

T 0 :

Ambient temperature

r :

Radial coordinate

z :

Axial coordinate

t :

(Time)

ρ :

Density of work material

C p :

Specific heat of work material

K T :

Thermal conductivity of work material

α :

Thermal diffusivity of work material

q(r):

Gaussian heat flux distribution

q 0 :

Heat flux intensity at the center of spark

F c :

Cathode energy fraction

U :

Gap voltage

I :

Discharge current

r g :

Spark radius

t on :

Discharge duration

E :

Spark energy

J 0 :

Bessel function of zeroth order

J 1 :

Bessel function of first order

λ :

Dummy variable

χ :

Variable defined in Eq. (14)

erfc :

Error function

D C ∣ a :

Adjusted crater depth

R C ∣ a :

Adjusted crater radius

D C ∣ t :

Theoretical crater depth

R C ∣ t :

Theoretical crater radius

PFE :

Plasma flushing efficiency

L :

Work surface

P :

Set of points on work surface L

r1, r2, ⋯, rn :

Randomly selected points from P

μ :

(Mean)

σ :

(Standard deviation)

Z(x):

Profile height function

Z :

Set of z-coordinate values of points on surface profile

R a :

Average surface roughness or arithmetic mean deviation

R max :

Maximum peak-to-valley height

P c :

Peak density

l :

Sampling length

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, 400 076, India

    S. Jithin, Upendra V. Bhandarkar & Suhas S. Joshi

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  1. S. Jithin
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Jithin, S., Bhandarkar, U.V. & Joshi, S.S. Multi-spark model for predicting surface roughness of electrical discharge textured surfaces. Int J Adv Manuf Technol 106, 3741–3758 (2020). https://doi.org/10.1007/s00170-019-04841-5

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