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Interelectrode gas–liquid-solid three-phase flow analysis and simulation for drilling holes with high aspect ratio by micro-EDM

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Abstract

In micro-electrical discharge machining (micro-EDM) using the non-hollow circular cross-section tool electrode with the side flushing technique, when the aspect ratio of machined micro-hole is expected to be further increased, the discharge debris expelling speed and the working fluid renewal efficiency are weakened, which hinders the improvement of machining efficiency and accuracy with increased machining depth. In order to reveal the flow behavior of the working fluid in the micro-EDM gap, so as to realize the high-precision and high-efficiency machining of micro-hole with high aspect ratio, a three-phase flow simulation model of fluid, bubble, and debris is established in Fluent under the ideal assumption that the spark discharges occur continuously to generate high-pressure bubbles. The simulation results show that when the boundary condition of the flushing pressure at the side gap entrance is set to 0, the pressure wave emitted when the high-pressure bubble expands, which is formed by the instantaneous gasification of the working fluid between electrodes under high temperature, is the source of pneumatic force that drives the working fluid flow at the micron scale. Affected by the gap flow channel structure and the viscous resistance from inner wall, the flow velocity direction of the fluid dragging the discharge debris to rise up and expel will change, forming a dynamic alternation process of flowing into and out of the side machining gap entry. As the machining depth increases, due to the energy attenuation of the pressure wave propagating from the bottom gap to the side gap entrance, the expelling speed of the discharge debris decreases exponentially at the side gap entrance, resulting in the reduced machining efficiency and accuracy. However, when the simulated bubble generation frequency is increased to the megahertz level, the expelling efficiency of debris has a step-like improvement. The continuous and high-frequency generation of high-pressure bubbles can maintain a high pressure gradient in the bottom gap, and the discharge debris is able to continuously move upward without falling back to accumulate in the bottom gap, which is beneficial to the stable and smooth machining process, realizing the high-precision and high-efficiency machining of micro-hole with high aspect ratio.

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Abbreviations

A 0 :

Initial amplitude of pressure wave, m

A l :

Amplitude of pressure wave after propagation distance l, m

A S :

Flow area of side machining gap cross-section, μm2

c :

Constant

c 1 :

Sound velocity of liquid phase, m/s

c wave :

Transmission velocity of pressure wave in liquid, m/s

d 1 :

Diameter of tool electrode, μm

d 2 :

Diameter of machined micro-hole, μm

dp:

Change of fluid pressure, Pa

dT:

Change of fluid temperature, K

dv:

Change of fluid velocity, m/s

dV:

Symbol of volume integral

dρ:

Change of fluid density, kg/m3

d p :

Diameter of debris, μm

d e :

Equivalent diameter of side machining gap cross-section, μm

E e :

Energy in the energy equation, J

E wave :

Energy of pressure waves, J

F buoy :

Buoyancy on bubbles, N

F disjoin :

Disjoining pressure between bubble and contact wall, N

F drag :

Drag force exerted on debris by surrounding fluid, N

F pressure :

Pressure gradient force exerted on debris by surrounding fluid, N

F saffman :

Saffman lift force exerted on debris by surrounding fluid, N

F σ :

Surface tension of the fluid, N

g :

Gravitational acceleration, m/s2

h v :

Heat of vaporization, kJ/kg

I(t):

Discharge current, A

K qp :

Factor of phase transition intensity

K eff :

Effective thermal conductivity coefficient in energy equation

k G :

Gaussian heat coefficient

L e :

Latent heat of vaporization, kJ/kg

l :

Distance between any two points in machining gap, μm

l c :

Capillary length of the dielectric fluid, m

l d :

Machining depth of micro-holes, mm

l f :

Liquid film thickness between bubbles and contact wall, nm

l g :

Machining gap width, μm

m p :

Mass of debris, kg

\({\dot{\mathrm{m}}}_{\mathrm{pq}}\) :

Mass transfer velocity from liquid phase to gas phase, kg/s

\({\dot{\mathrm{m}}}_{\mathrm{qp}}\) :

Mass transfer velocity from gas phase to liquid phase, kg/s

N :

Number of initial generated bubbles

n :

Number of particles released at one time

n v :

Unit normal vector of fluid interface

p :

Shared pressure of fluid phase, Pa

p 0 :

Atmospheric pressure, Pa

p flush :

Lateral flushing pressure, Pa

p q :

Pressure of gas phase, Pa

p sat :

Saturated vapor pressure, Pa

q(r,t):

Gaussian heat, J

Reb :

Fluid Reynolds number in bottom machining gap

Res :

Fluid Reynolds number in side machining gap

R(t):

Discharge channel radius, μm

r :

Distance from discharge center, μm

r b :

Bubble radius, μm

r bi :

Initial bubble radius, μm

\({\mathrm{S}}_{{\mathrm{a}}_{\mathrm{q}}}\) :

Source term in Continuity Equation, kg/m3-s

S h :

Source term in Energy Equation, W/m3

T e :

Temperature in Energy Equation, K

T nuc :

Nucleation temperature, K

T sat :

Saturated temperature, K

t c :

Time of bubble collapse, μs

t on :

Pulse width of the pulsed power supply, μs

t total :

Total time of micro-hole machining, s

U(t):

Discharge voltage, V

V c :

Volume of single grid cell, μm3

V crater :

Volume of single discharge crater, μm3

V debris :

Volume of single debris, μm3

\({\mathrm{V}}_{\mathrm{f}}^{\mathrm{n+1}}\) :

Volumetric flux on surface through normal velocity vector at n + 1 time step, m3/s

V total :

Total volume of removed workpiece material, m3

v :

Shared velocity of fluid phase, m/s

v b :

Initial expansion velocity of bubbles, m/s

v f :

Lateral flushing speed, m/s

v p :

Movement velocity of debris, m/s

v q :

Movement velocity of gas interface, m/s

v s :

Fluid flow speed in side machining gap, m/s

v up :

Rising speed of bubbles in narrow gap, nm/s

α q :

Volume fraction of gas phase

\({\alpha }_{\mathrm{q}}^{\mathrm{n}}\) :

Volume fraction of gas phase at n time step

\({\alpha }_{\mathrm{q}}^{\mathrm{n+1}}\) :

Volume fraction of gas phase at n + 1 time step

ΔP :

Pressure loss along the side gap channel, Pa

Δt :

Unit of time, s

ΔV :

Material removal volume per unit time, m3

η :

Pressure wave energy attenuation coefficient

η G :

Gaussian heat transfer coefficient

κ :

Surface curvature, m−1

λ :

Pressure loss coefficient along the side gap channel

μ :

Dynamic viscosity of fluid, Pa·s

ρ :

Shared density of fluid phase, kg/m3

ρ p :

Density of debris, kg/m3

ρ q :

Density of gas phase, kg/m3

\({\rho }_{\mathrm{q}}^{\mathrm{n}}\) :

Gas-phase density at n time step, kg/m3

\({\rho }_{\mathrm{q}}^{\mathrm{n+1}}\) :

Gas-phase density at n + 1 time step, kg/m3

σ :

Surface tension coefficient of fluid, N/m

τ :

Tangential stress, Pa

υ :

Kinematic viscosity of fluid, m2/s

χ :

Wet perimeter of side machining gap, μm

References

  1. Chen Y, Chen, MY (2020) Fabrication of vertical through-holes to realize high throughput cell counting. IEEE Electron Packag Technol Conf, EPTC 189–193. https://doi.org/10.1109/EPTC50525.2020.9315101

  2. Adrija B, Shibendu SR (2021) A review on multi nozzle electrohydrodynamic inkjet printing system for MEMS applications. IOP Conf Ser: Mater Sci Eng 1136:012015. https://doi.org/10.1088/1757-899X/1136/1/012015

    Article  Google Scholar 

  3. Kumar R, Singh I (2021) Blind hole fabrication in aerospace material Ti6Al4V using electric discharge drilling: a tool design approach. J Mater Eng Perform 30:8677–8685. https://doi.org/10.1007/s11665-021-06052-0

    Article  Google Scholar 

  4. Tong H, Li Y, Zhang L, Li BQ (2013) Mechanism design and process control of micro EDM for drilling spray holes of diesel injector nozzles. Precis Eng 37:213–221. https://doi.org/10.1016/j.precisioneng.2012.09.004

    Article  Google Scholar 

  5. Feng GL, Yang XD, Chi GX (2019) Experimental and simulation study on micro hole machining in EDM with high-speed tool electrode rotation. Int J Adv Manuf Technol 101:367–375. https://doi.org/10.1007/s00170-018-2917-6

    Article  Google Scholar 

  6. Li ZK, Bai JC (2018) Influence of alternating side gap on micro-hole machining performances in micro-EDM. Int J Adv Manuf Technol 94:979–989. https://doi.org/10.1007/s00170-017-0959-9

    Article  Google Scholar 

  7. Tong H, Li Y, Wang Y (2008) Experimental research on vibration assisted EDM of micro-structures with non-circular cross-section. J Mater Process Technol 208:289–298. https://doi.org/10.1016/j.jmatprotec.2007.12.126

    Article  Google Scholar 

  8. Li GD, Natsu W (2020) Realization of micro EDM drilling with high machining speed and accuracy by using mist deionized water jet. Precis Eng 61:136–146. https://doi.org/10.1016/j.precisioneng.2019.09.016

    Article  Google Scholar 

  9. Liao Y, Liang HW (2016) Study of vibration assisted inclined feed micro-EDM drilling. Proc CIRP 42:552–556. https://doi.org/10.1016/j.procir.2016.02.250

    Article  Google Scholar 

  10. Li Y, Hu RQ (2013) Size and profile measurement of micro holes by mold extraction and image processing. Nano Technol Precis Eng 11(4):341–347. https://doi.org/10.13494/j.npe.2013.057. ([in Chinese])

    Article  Google Scholar 

  11. Li GD, Natsua W, Yu ZY (2019) Study on quantitative estimation of bubble behavior in micro hole drilling with EDM. Int J Mach Tool Manuf 146:103437. https://doi.org/10.1016/j.ijmachtools.2019.103437

    Article  Google Scholar 

  12. Yin QF, Wu PY, Qian ZQ, Zhou L, Shi W, Zhong L (2020) Electrical discharge drilling assisted with bubbles produced by electrochemical reaction. Int J Adv Manuf Technol 109:919–928. https://doi.org/10.1007/s00170-020-05709-9

    Article  Google Scholar 

  13. Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39(1):201–225. https://doi.org/10.1016/0021-9991(81)90145-5

    Article  MATH  Google Scholar 

  14. Shaw SJ, Spelt PDM (2010) Shock emission from collapsing gas bubbles. J Fluid Mech 646:363–373. https://doi.org/10.1017/S0022112009993338

    Article  MATH  Google Scholar 

  15. Ikeda M (1972) The movement of a bubble in the gap depending on the single electrical discharge I. J Jpn Soc Electr Mach Eng 6(11):12–26. https://doi.org/10.2526/jseme.6.12

    Article  Google Scholar 

  16. Shao B, Rajurkar KP (2015) Modelling of the crater formation in micro-EDM. Proc CIRP 33:376–381. https://doi.org/10.1016/j.procir.2015.06.085

    Article  Google Scholar 

  17. Irvine TF, Harnett JP (1978) Advances in heat transfer. Stony Brook, New York.https://doi.org/10.1016/B978-0-12-020051-1.50001-2

  18. Shervani TMT, Abdullah A, Shabgard MR (2006) Numerical study on the dynamics of an electrical discharge generated bubble in EDM. Eng Anal Bound Elem 30:503–514. https://doi.org/10.1016/j.enganabound.2006.01.014

    Article  MATH  Google Scholar 

  19. Kojima A, Natsu W, Kunieda M (2008) Spectroscopic measurement of arc plasma diameter in EDM. CIRP Ann-Manuf Techn 57(1):203–207. https://doi.org/10.1016/j.cirp.2008.03.097

    Article  Google Scholar 

  20. Mastud SA, Kothari NS, Singh RK, Joshi SS (2015) Modeling debris motion in vibration assisted reverse micro electrical discharge machining process (R-MEDM). J Microelectromech Syst 24(3):661–676. https://doi.org/10.1109/JMEMS.2014.2343227

    Article  Google Scholar 

  21. Loth E, Dorgan AJ (2009) An equation of motion for particles of finite Reynolds number and size. Environ Fluid Mech 9:187–206. https://doi.org/10.1007/s10652-009-9123-x

    Article  Google Scholar 

  22. Peng ZB, Ge LH, Moreno-Atanasio R, Evans G, Moghtaderi B, Doroodchi E (2020) VOF-DEM study of solid distribution characteristics in slurry Taylor flow-based multiphase microreactors. Chem Eng J 396:124738. https://doi.org/10.1016/j.cej.2020.124738

    Article  Google Scholar 

  23. Massey BS (1989) Mechanics of Fluids. Van Nostrand Reinhold, New York

    Book  Google Scholar 

  24. Tiwari A, Pantano C, Freund JB (2015) Growth-and-collapse dynamics of small bubble clusters near a wall. J Fluid Mech 775:1–23. https://doi.org/10.1017/jfm.2015.287

    Article  MathSciNet  MATH  Google Scholar 

  25. Bretherton F (1961) The motion of long bubbles in tubes. J Fluid Mech 10(2):166–188. https://doi.org/10.1017/S0022112061000160

    Article  MathSciNet  MATH  Google Scholar 

  26. Dhaouadi W, Kolinski JM (2019) Bretherton’s buoyant bubble. Phys Rev Fluids 4(12). https://doi.org/10.1103/PhysRevFluids.4.123601

  27. Wang J, Han FZ (2014) Simulation model of debris and bubble movement in consecutive-pulse discharge of electrical discharge machining. Int J Mach Tool Manuf 77:56–65. https://doi.org/10.1016/j.ijmachtools.2013.10.007

    Article  Google Scholar 

  28. Lauterborn W, Kurz T (2010) Physics of bubble oscillations. Rep Prog Phys 73(10). https://doi.org/10.1088/0034-4885/73/10/106501

  29. Rayleigh L (1917) On the pressure developed in a liquid during the collapse of a spherical cavity. Phil Mag 34:94–98. https://doi.org/10.1080/14786440808635681

    Article  MATH  Google Scholar 

  30. Plesset MS (1949) The dynamics of cavitation bubbles. ASME J Appl Mech 16:277–282

    Article  Google Scholar 

  31. Huang F, Bai BF, Guo LJ (2004) A mathematical model and numerical simulation of pressure wave in horizontal gas-liquid bubbly flow. Prog Nat Sci 14:344–349. https://doi.org/10.1080/10020070412331343591

    Article  MATH  Google Scholar 

  32. Fortes-Patella R, Challier G, Reboud JL, Archer A (2013) Energy balance in cavitation erosion: from bubble collapse to indentation of material surface. ASME J Fluids Eng 135(1):011303. https://doi.org/10.1115/1.4023076

    Article  Google Scholar 

  33. Cao PY, Tong H, Li Y (2022) Pulsed power supply superposed with radio frequency oscillating wave for the improvement of micro-electrical discharge machining process. ASME J Micro Nano-Manuf 10(1):011004. https://doi.org/10.1115/1.4054974

    Article  Google Scholar 

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Funding

This research was supported by the National Natural Science Foundation of China (grant No. 92060108) and Independent Research Project of State Key Laboratory of Tribology of China (grant No. SKLT2022B08).

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Authors and Affiliations

  1. State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China

    Peiyao Cao, Hao Tong, Yong Li & Jialong Chen

  2. Beijing Key Lab of Precision/Ultra-Precision Manufacturing Equipment and Control, Tsinghua University, Beijing, 100084, China

    Peiyao Cao, Hao Tong, Yong Li & Jialong Chen

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  1. Peiyao Cao
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Correspondence to Yong Li.

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Cao, P., Tong, H., Li, Y. et al. Interelectrode gas–liquid-solid three-phase flow analysis and simulation for drilling holes with high aspect ratio by micro-EDM. Int J Adv Manuf Technol 128, 5261–5276 (2023). https://doi.org/10.1007/s00170-023-12220-4

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