Study on the dynamic generation of the jet shape in Jet Electrochemical Machining

Accepted Manuscript Title: Study on the Dynamic Generation of the Jet Shape in JetElectrochemical Machining Author: Matthias Hackert-Osch¨atzchen Raphael Paul Andr´e Martin Gunnar Meichsner Norbert Lehnert Andreas Schubert PII: DOI: Reference:

S0924-0136(15)00152-1 http://dx.doi.org/doi:10.1016/j.jmatprotec.2015.03.049 PROTEC 14366

To appear in:

Journal of Materials Processing Technology

Received date: Revised date: Accepted date:

20-5-2014 26-3-2015 27-3-2015

Please cite this article as: Matthias Hackert-Osch¨atzchen, Raphael Paul, Andr´e Martin, Gunnar Meichsner, Norbert Lehnert, Andreas Schubert, Study on the Dynamic Generation of the Jet Shape in JetElectrochemical Machining, Journal of Materials Processing Tech. (2015), http://dx.doi.org/10.1016/j.jmatprotec.2015.03.049 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

*Manuscript

ip t

Study on the Dynamic Generation of the Jet Shape in Jet Electrochemical Machining Matthias Hackert-Osch¨ atzchena,∗, Raphael Paula , Andr´e Martina , Gunnar b Meichsner , Norbert Lehnerta , Andreas Schuberta,b a Professorship

us

cr

Micromanufacturing Technology, Faculty of Mechanical Engineering, Technische Universit¨ at Chemnitz, D-09107 Chemnitz, Germany b Fraunhofer Institute for Machine Tools and Forming Technology IWU, Reichenhainer Strasse 88, D-09126 Chemnitz, Germany

an

Abstract

Jet Electrochemical Machining (Jet-ECM) is a technology for fast creating micro

M

structures into metallic parts without any thermal or mechanical impact and independent from the material’s hardness. The processed surface is very smooth and no tool wear occurs. The Jet-ECM process depends strongly on the shape

d

of the jet which is hardly predictable. In a previous study Hackert (2010) built a numerical model with COMSOL Multiphysics based on a predefined jet shape.

te

In the present study a new model was created integrating fluid dynamics using the level set method for two-phase flow. According to the Jet-ECM process the

Ac ce p

simulation was divided into two steps. In the first step the jet is formed. In the second step the anodic dissolution is simulated by deforming the geometry. The dynamic behavior of the electrolyte jet could be simulated during the dissolution process. So effects became visible which affect the machining results. The results of the present study lead to a better understanding of electrochemical machining via electrolytic free jet. Especially a secondary electric contacting of the nozzle by electrolyte reflected from the work piece could be proven. Keywords: Jet Electrochemical Machining, localized anodic dissolution, closed electrolytic free jet, Multiphysics Simulation

∗ Corresponding

author. Tel.: +49 371 531 35131; fax: +49 371 531 835131. Email address: [email protected] (Matthias Hackert-Osch¨ atzchen)

Preprint submitted to Journal of Materials Processing Technology

March 26, 2015

Page 1 of 35

1. Introduction

ip t

Jet Electrochemical Machining is a manufacturing technology which is based upon anodic dissolution. Hackert-Osch¨atzchen et al. (2012) showed that the

manufacturing method enables a fast production of complex micro geometries. Defined volumes of material can be removed from metallic work pieces by con-

cr

5

centrating an electric direct current in an electrolyte jet, ejected from a small

us

nozzle. Working gaps down to 25% of the nozzle diameter between work piece and nozzle can be used. The removal depends on the local current density which, as Schubert et al. (2011) found, amounts up to 2100 A/cm2 . This high current density is locally restricted by the shape of the jet. Hackert-Osch¨atzchen et al.

an

10

(2013) revealed that Jet-ECM is qualified to machine carbide metals. Hommel

M

et al. (2013) and Hackert et al. (2010b) showed the technology’s flexibility applying inverse Jet-ECM as well as Jet-EC Turning. The major benefits of Jet Electrochemical Machining are the high localization of the machined area and the high achievable surface quality. During machining no tool wear occurs.

d

15

One important parameter of the process which strongly influences the re-

te

sults is the shape of the jet. However, it is hardly predictable. Yoneda and Kuneida (1995) showed an axially symmetric stationary model of Jet-ECM for

Ac ce p

a plane surface at machining time zero, which has been proven by Natsu et al.

20

(2006). Based on this Hackert (2010) created a numerical model with COMSOL Multiphysics to describe the process of material dissolution. The jet shape was predefined as a domain with a flexible mesh. The simulated dissolution results progressively differ from experimental results with increasing processing time. This difference is based on the fact that this model does not consider dynamic

25

interaction of the fluids with the calculated geometry. Hackert et al. (2010a) made an improvement of the simulation by using a dynamic jet shape. In the present study the jet shape is simulated considering fluid dynamics to gain a more realistic model. The dynamic generation of the jet shape could be investigated and a secondary contact between work piece and nozzle by reflected

30

electrolyte could be shown.

2

Page 2 of 35

2. Model Description

ip t

The developed model consits of couplings of the physical phenomena electrodynamics, fluid dynamics and deformation of the geometry. Beginning with

the initial geometry given by the used nozzle fluid dynamics is solved and the jet shape is calculated. Electrodynamics is calculated based on the simulated

cr

35

jet shape. The material removal is implemented by deforming the geometry

us

using Faraday’s law and the calculated electric current density. The deformed geometry interacts with the jet shape and thus with electrodynamics. These three couplings are determined in every time step.

Figure 1 shows a scheme of the developed model.

an

40

The model encompasses a small zone in adjacencies of the free jet. It is

M

assumed that electrolyte exiting this zone through the model boundary is immediately removed by the airflow. This entails that the model neglects a possible secondary contacting of reflected electrolyte and the nozzle. Furthermore the flow of the electrolyte is assumed to be symmetric and stable. Therefore a 2D

d

45

axially symmetric model is used. Moreover the model is built up parametrically

te

to be able to modify the geometry easily. The following sections contain several terms which are assigned to COMSOL

Ac ce p

Multiphysics. These terms are highlighted by quotation marks, e.g. ”Fluid

50

Properties”.

2.1. Geometry

The chosen parameter values of the geometry refer to the experimental stud-

ies, which were described in Hackert-Osch¨atzchen et al. (2011, 2014, 2012). The 2D axially symmetric model geometry is shown in figure 2 with the parameter

55

values a = d = 100 µm. Parameter a is the working distance and d is the diameter of the nozzle. The chosen values correspond to the ones of available experimental data. The axis of symmetry is r = 0 µm. Domain I is the nozzle and domains II to V are the zones of the fluids. Boundaries 3 to 6 are the axis of symmetry and boundary 7 is the work piece surface.

3

Page 3 of 35

60

Boundaries 8 to 12 are the model boundary which is permeable for fluids. The zone of the fluids is separated into 4 domains to be able to handle each part on

ip t

its own and to define the mesh parameters individually. Although domain II

is part of the fluid zones, in COMSOL it is defined as a solid domain with the

65

cr

electrodynamic properties of the electrolyte. This has no significant impact on

the solution of electrodynamics and material dissolution. However, it reduces

us

the calculation effort since fluid dynamics needs to be calculated for domains III to V only. 2.2. Mesh

70

an

All application modes use the same mesh. So it must be suitable for fluid dynamics, electrodynamics and geometry deformation. Figure 3 shows the gen-

M

erated mesh. In table 1 the definition of the mesh is shown. Because shape and size of the mesh elements has a significant influence on the accuracy, the mesh was varied in dependence of the mesh parameter h.

75

d

Referred to Laurien and Oertel (2011), a higher resolution of the mesh reduces the discretization error and leads to a more accurate solution. If the solution

te

only changes slightly with further refinement of the mesh, the simulation result can be considered as a good approximation to the exact solution. To verify the

Ac ce p

accuracy of the solution the calculated values were compared with experiments of Hackert (2010). A value of h = 2 µm was identified as well suited for a high

80

accuracy on the one hand and a moderate calculation effort on the other hand. The used mesh with h = 2 µm consists of 9539 triangular elements. Because of the small expected gradients domains I to IV have a coarser mesh. The greatest gradients are expected for domain V with the stagnation flow, the interface of electrolyte and air and the boundary of the material removal. Therefore it has a

85

finer mesh. Additionally the mesh is refined at boundary 7 as well as at point A, which is the edge of the nozzle. 2.3. Fluid Dynamics The electrolyte interacts with the surrounding air as a two-phase flow. In COMSOL Multiphysics this interaction is implemented using the ”Laminar 4

Page 4 of 35

90

Flow, Two-Phase, Level Set” mode with the time-dependent, laminar and incompressible form of the Navier-Stokes equations. The level set function (1) is a

ip t

continuous function that describes the type of phase using the level set variable φ where φ = 0 means fluid 1 (electrolyte) and φ = 1 means fluid 2 (air). φ = 0.5

cr

can be interpreted as the interface.

(1)

us

  ∂φ ∇φ + ~u · ∇φ = γ∇ · ∇φ − φ(1 − φ) ∂t |∇φ|

Here ~u is the fluid velocity and γ as well as  are model-specific parameters.

95

Table 2 shows the material properties of the two fluids. Figure 4 shows the

an

model definitions for fluid dynamics. Fluid dynamics is calculated in the blue marked domains only. To simplify the simulation domain II is defined as solid. Table 3 shows the domain and boundary conditions of fluid dynamics. The parameter  in the ”Fluid Properties” domain condition defines the thickness

M

100

of the interface, which is for numerical reasons finitely small. Here the value  = 2 µm means that φ will rise from 0 to 1 by the interface-normal distance of

d

approximately 2 ·  = 4 µm.

105

te

As table 3 shows, at the simulation time t = 0 s electrolyte is solely located in domain III. In domains IV and V the initial phase is air. The initial interface

Ac ce p

lies on boundaries 18 and 24. That means that at the initial state the jet is not formed. Before simulating the material dissolution the quasi-stationary form of the electrolyte jet is initialized in a previous simulation step with the duration of tinit . In the ”Wetted Wall” boundary condition θ is the contact angle and

110

β the slip length, which is a model-specific parameter. Here it is defined as equal to the local mesh element size hlocal . In the ”Inlet Electrolyte” boundary condition Lentr defines the length of a virtual inlet channel, in which the laminar flow profile is formed before entering the model. In the ”Outlet” boundary condition the relative pressure is defined depending on time and location as

115

prel = prel (t, r). During the first simulation step, which initializes the electrolyte jet, pint (t ≤ 0.7 · tinit ) = 1,

(2)

5

Page 5 of 35

afterwards it linearly decreases and is pint (t ≥ 0.9 · tinit ) = 0

ip t

(3)

for the remaining simulation time. The pressure dependence on the radius r is

120

cr

scaled by pint (t). This definition was necessary due to a better convergence. During the dissolution process prel (t ≥ tinit ) = 0.

us

As the outlet condition is defined via pressure, depending on the pressure field it is possible that fluid flows from outside the model through the model boundary into the model domains. In the ”Outlet” boundary condition of

125

an

COMSOL there is no option available that defines φ for an incoming flow. So the type of fluid that flows through this boundary into the model domain is not distinguished as air or electrolyte. Hence here a ”Weak Contribution” on the

M

model boundary adds an additional term to the level set function according to equation 4.

(4)

te

d

  ∂φ ∇φ + ~u · ∇φ = γ∇ · ∇φ − φ(1 − φ) + (1 − φ) · |un | · (un < 0) ∂t |∇φ|

The term (un < 0) is a Boolean operator which returns 0 or 1. By the additional summand the incoming flow (un < 0) = 1 is forced to φ = 1 (air).

Ac ce p

130

2.4. Electrodynamics

Since changes in fluid dynamics as well as geometry deformation take place

in a much slower time scale than in electrodynamics, for electrodynamics the stationary form of the equations of the ”Electric Currents” mode is used. Table 4

135

shows the material definition. The values correspond to Hackert (2010) for achieving comparable results. In domains IV and V, where fluid dynamics is solved, the electric conductivity σ is defined depending on the level set variable φ. The electric conductivity of air is defined as σA = σE · 10−3 , which is greater than zero, to ensure numerical stability.

140

Table 5 shows the domain and boundary conditions of electrodynamics, which are illustrated in Figure 5. 6

Page 6 of 35

By the condition ”Electric Potential” the electric potential ϕ is defined as a time-dependent function. During the jet initialization simulation step ϕ = 0 V

145

ip t

is applied. During the second simulation step, considering material dissolution, ϕ = 56 V is applied. Due to numerical stability, the function ϕint (t) is defined

cr

as a cubic spline. 2.5. Geometry Deformation

us

The anodic dissolution is implemented in COMSOL Multiphysics using the ”Deformed Geometry” mode in domains IV and V. Hackert (2010) quantified the deformation by equation 5 which results from Faraday’s law.

~vn = η ·

an

150

M · ~n · Jn zA · ρ · F

(5)

M

Where η is the current efficiency, M the molar mass, zA the valency and ρ the density of the dissolved material. ~n is the normal unit vector and Jn is the normal electric current density. The fraction in equation 5 is equal to the

d

specific dissolved volume Vsp .

M zA · ρ · F

(6)

Here a value of Vsp = 2.1402 cm3 /C results for the stainless steel 1.4541,

Ac ce p

155

te

Vsp =

which is considered in the present study. Beside simulating the material dissolution, the application mode is used to keep domain V as small as possible, since this is the domain with the finest mesh. Figure 6 shows the conditions of domains, boundaries and points of geometry

160

deformation, which are listed in table 6. In the first ”Prescribed Mesh Velocity” boundary condition ηint (Jn ), the

current efficiency, is defined as a cubic spline. It returns 0% for Jn ≤ 3 A/cm2 and 100% for Jn ≥ 20 A/cm2 . vint (t) is a time-dependent function, which increases linearly from 0 to 1 over the period t = tinit ± 1 µs. It returns 0

165

during the jet initialization simulation step and 1 during the material dissolution simulation step. In the second ”Prescribed Mesh Velocity” boundary condition vz (Pt. B) is the z component of the velocity of point B. This condition has the 7

Page 7 of 35

effect that domain IV enlarges in z direction with 3/4 of the velocity of that

170

ip t

point. 2.6. Simulation Procedure

cr

As described above, according to the real Jet-ECM process, the simulation

is divided into two simulation steps. In the first simulation step the electrolyte jet is formed. This step lasts until t = tinit = 1·10−4 s. In the second simulation

175

us

step, which lasts until tECM = 2 s (with the processing time tECM = t−tinit ) the material dissolution takes place. So the simulation is terminated at t = 2.0001 s.

an

The solver uses a maximum time step of 1 · 10−3 s. Since the mesh is partially intensely deformed, automatic remeshing is used in order to avoid a bad mesh quality. Thus the deformed geometry is remeshed if a definable criterion is

3. Results and Evaluation 3.1. Fluid Dynamics

d

180

M

fulfilled. Here the minimum mesh quality is set to 0.65.

te

Fluid dynamics is important to the Jet-ECM process, since it is directly or indirectly coupled with all other significant physical phenomena. In this section

Ac ce p

the simulated dynamic jet shape is shown during the complete Jet-ECM process

185

in comparison to the simulation results with static jet shape of Hackert (2010). Figure 7 shows a comparison of the simulated jet shape at the processing

time tECM = 0 s and the predefined static jet shape, used by Hackert (2010). The result of the present study is the red line, which is the interface between

electrolyte and air. The blue line represents the predefined jet shape used by

190

Hackert (2010). The greatest differences between the simulated (red) and static (blue) jet shape occur in the stagnation zone of the jet. While the geometry used by Hackert (2010) has a sharp edge, the simulated jet has a smooth shape. Figures 8 shows the velocity field at tECM = 0 s. The arrows show the velocity field ~u and the white isoline φ = 0.5 represents the interface. Inside

195

the nozzle as well as directly beneath the nozzle, there is a laminar flow profile.

8

Page 8 of 35

Near the stagnation point the velocity decreases and the flow aligns to the

minimum. The boundary layer thickness grows with the radius.

ip t

radial direction. In the stagnation point (coordinate origin) there is a velocity

The variation of the jet shape during the machining process is shown in

figures 9 to 12. Here subfigures (a) in all figures show the level set variable and

cr

200

subfigures (b) a rotated pseudo 3D view. The isosurface φ = 0.5 is light blue,

us

the electrolyte φ < 0.5 is dark blue and the air φ > 0.5 is blanked out.

Figure 9 shows the jet shape at tECM = 0 s. The work piece surface is plain. After 0.5 s (figure 10) a calotte with a depth of about 40 µm can be seen. The wall jet adapts the work piece surface. With growing processing time this flow

an

205

condition becomes increasingly instable. At the processing time tECM ≈ 0.8 s the wall jet detaches from the work piece surface. This can be traced back to

M

a pressure minimum at the edge of the calotte, which comes along with the progressively concave flow. It should be pointed out here that the developed 2D 210

axially symmetric model cannot completely describe this detachment process,

d

which in reality is very probably three-dimensional. In the 2D simulation the

te

air, that fills the space between the electrolyte jet and the work piece surface, originates from the outlet boundary of the model, since the outlet is defined via

Ac ce p

pressure (table 3). The simulated detachment process proceeds in a very short 215

period of time.

At the time tECM = 1.0 s (figure 11) the electrolyte jet flows off detached

from the work piece surface. There are no significant changes in the jet shape after the detachment. However the flow-off angle increases. Figure 12 shows the jet shape at tECM = 2.0 s. The flow profile indicates

220

that reflected electrolyte contacts the nozzle. This effect is not depicted by the developed model, due to the positioning of the model boundary. However it is observed in experiments. Figur 13 shows photos of the Jet-ECM process. At tECM ≈ 0.5 s the flow-off angle is low. There is no secondary contact

225

between electrolyte and nozzle. At tECM ≈ 2 s the high flow-off angle and the resulting contacting are visible. In the experiments this secondary contact leads 9

Page 9 of 35

to a secondary anodic dissolution at the edge of the calotte, which is further

ip t

discussed in section 3.3. 3.2. Electrodynamics

Figure 14 shows the electric potential and figure 15 the magnitude of the

cr

230

electric current density at the beginning of the ECM process tECM = 0 s. In ~ the figures of this section the arrows denote the electric current density J.

us

In figure 14 the pseudocolor represents the value of the electric potential. According to the electrical boundary conditions ϕ = 0 V at the nozzle and ϕ = 56 V at the work piece. In between a smooth transition takes place.

an

235

In figure 15 the pseudocolor represents the magnitude of the electric current density J~ between 0 A/cm2 and 1000 A/cm2 . In the free jet the highest current

M

densities occur at large radii r, near the interface. Near the work piece surface the current density decreases with the radius r. 240

Figure 16 shows the normal electric current density on the work piece surface

d

plotted against the radius r.

te

The red curve shows the result of the present study and the blue curve represents the result of Hackert (2010) using the static jet shape. The orange dashed line illustrates the nozzle. In both cases there is a maximum at r = 0 µm. At r = 100 µm the values become approximately zero. However the curves differ

Ac ce p 245

in the localization of the electric current. The simulation with fluid dynamics of the present study gives lower normal current densities for r < 40 µm. For r > 40 µm the values are higher than with the simulation without fluid dynamics of Hackert (2010). This can be traced back to the shape of the electrolyte jets.

250

Since the predefined jet shape used in the previous study has a sharp edge at the stagnation zone, there the jet diameter is smaller than the one of the simulated electrolyte jet of the present study. Consequently, in the simulation with fluid dynamics the current localization is lower. Figure 17 shows the electric potential and figure 18 shows the electric current

255

density at selected time steps of the anodic dissolution process. The jet shape is represented by the white isoline φ = 0.5. 10

Page 10 of 35

Because of the growing distance between nozzle and work piece the gradient of the electric potential decreases with time. Therefore the current density gets

260

ip t

smaller as well. However current localization remains high, since the surrounding air is electrical insulating.

cr

Figure 19 shows the simulated averaged electric current density Jm as well as

the electric current I plotted against time tECM compared with simulation and

us

experiments of Hackert (2010).

It can be seen that the simulated values of the present study are higher at 265

the beginning than the simulated values of Hackert (2010) and also higher than

an

the measured values. The simulated values of the present study systematically overestimate the experimental values and decrease faster. At tECM ≈ 0.3 s the two simulated curves intersect. After that the curve simulated in the present

270

M

study describes the values of the experiments much better. The higher values in the experiments after tECM > 1.5 s are probably caused by reflected electrolyte,

the following section.

d

which contacts the nozzle. The shape of the generated calottes is discussed in

te

3.3. Geometry Deformation

Figure 20 shows the depth of the calottes plotted against time. The black curve represents experimental results, the blue curve the simulation without

Ac ce p 275

fluid dynamics of Hackert (2010) and the red curve the simulation with fluid dynamics of the present study. All curves rise degressively. The results of previous studies have a high accu-

racy over the complete processing time compared with the experimental results.

280

The simulation of the present study gives depths which are systematically too high and overestimate the experiments by up to 20%. Hackert et al. (2010a) observed a similar behavior in investigations with a dynamic jet shape, which was simulated without fluid dynamics. Figure 21 shows the diameter of the calottes plotted against time. Here

285

again, the black curve represents experimental results, the blue curve the results of the simulation without fluid dynamics of Hackert (2010) and the red curve 11

Page 11 of 35

the results of the simulation with fluid dynamics of the present study. All three curves rise degressively. Compared to the experimental results,

290

ip t

in contrast to the depth, the diameter is computed much more accurately by

the simulation of the present study than by the one with static jet shape. The

cr

reduction of the gradient at a processing time of 0.3 s is described by the simulation with fluid dynamics. Until tECM ≈ 1 s the values of simulation and

us

experiments differ minimally. At a processing time of tECM = 2 s the simulation result is circa 14% lower than the experimental result. The result of the 295

simulation without fluid dynamics is systematically too high.

an

Figure 22 shows cross-sectional profiles of calottes Hackert (2010) generated by Jet-ECM compared to the simulated calottes of Hackert (2010) (figure 22(a)) and the present study (figure 22(b)).

300

M

It can be recognized that the experimental depths of the calottes agree better with the simulation without fluid dynamics. In contrast the diameters agree better with the simulation with fluid dynamics.

te

different processing times.

d

Figures 23 to 25 show SEM images of calottes generated with Jet-ECM of

At tECM = 1.0 s the edge of the calotte is nearly rounded. At tECM = 1.5 s and tECM = 2.0 s the calottes feature a chamfer. This chamfer is caused by a

Ac ce p

305

secondary material dissolution in consequence of the reflected electrolyte and its secondary contact with the nozzle. The widening of the diameter in the experiments for processing times tECM ≥ 1.5 s is attributable to this.

4. Conclusion

310

In this study a multiphysical model for the simulation of the Jet-ECM pro-

cess was created with COMSOL Multiphysics. In contrast to previous studies fluid dynamics is considered in this model in addition to electrodynamics and material dissolution. This was implemented using the level set method for describing the two-phase flow. The simulation leads to a better understanding

315

of electrochemical machining via electrolytic free jet. The variation of the jet

12

Page 12 of 35

shape during the machining process could be simulated. This shows effects like the reflection of the electrolyte jet, which was also observed in experiments.

ip t

The simulation results were compared and validated with simulative and experimental results of Hackert (2010). The depth of the calottes is systematically

overestimated by the simulation. This can be traced back to an overestimation

cr

320

of the electric current, since the model does not consider electric boundary re-

us

sistances.

For processing times tECM > 1.5 s a widening of the diameter is observed in experiments, which is not described by the simulation. Caused by a secondary contacting, induced by reflected electrolyte, in experiments a chamfer occurs at

an

325

the edge of the calottes. This is not considered in the model. In the future the model can be improved by integrating the electric boundary

M

resistance of the interface between electrolyte and work piece, like applied by Weber et al. (2013). This would allow considering the voltage drop on interfaces. 330

Another improvement can be done by taking into account that the reflected elec-

te

d

trolyte contacts the nozzle and causes a secondary material dissolution.

5. Acknowledgement

Ac ce p

The authors thank the German Research Foundation (DFG - Deutsche

Forschungsgemeinschaft) for supporting these investigations.

335

References

VDI-W¨ armeatlas. delberg, 2006.

VDI Buch. Berlin, Heidelberg:

Springer Berlin Hei-

URL: http://www.springerlink.com/index/10.1007/

978-3-540-32218-4. doi:10.1007/978-3-540-32218-4; ISBN: 978-3-540-

25504-8. 340

Hackert M. Entwicklung und Simulation eines Verfahrens zum elektrochemischen Abtragen von Mikrogeometrien mit geschlossenem elektrolytischen Freistrahl (PhD Thesis). In: Andreas Schubert, editor. Scripts precision and

13

Page 13 of 35

microproduction engineering, Band 2. Auerbach, Germany: Verlag Wis-

345

Hackert M, Meichsner G, Jahn S, Schubert A.

ip t

senschaftliche Scripten, 2010. ISBN: 978-3-937524-95-5. Investigating the Influ-

ence of Dynamic Jet Shapes on the Jet Electrochemical Machining ProIn:

Proceedings of the European COMSOL Conference. 2010a.

cr

cess.

URL: http://www.comsol.com/cd/direct/conf/mechspotlight/papers/

350

us

8002/5703_hackert_paper.pdf.

Hackert M, Meichsner G, Zinecker M, Schubert A. In:

Proceedings of 6th Interna-

an

with Closed Electrolytic Free Jet.

Micro Turning

tional Symposium on Electrochemical Machining Technology. 2010b. p. 97 – 103.

URL: http://publica.fraunhofer.de/eprints/urn:nbn:de:

355

M

0011-n-1456670.pdf; ISBN: 978-90-5487-818-6.

Hackert-Osch¨ atzchen M, G. M, Zeidler H, Zinecker M, Schubert A. Micro Ma-

d

chining of Different Steels with Closed Electrolytic Free Jet. In: AIP Conference Proceedings. 2011. p. 1337 –43. URL: http://publica.fraunhofer.

te

de/eprints/urn:nbn:de:0011-n-1748836.pdf. Hackert-Osch¨ atzchen M, Martin A, Meichsner G, Schubert A. Evaluation of Gap Control Strategies in Jet Electrochemical Machining on Defined Shape

Ac ce p 360

Deviations. In: Proceedings of the 10th International Symposium on Electrochemical Machining Technology. 2014. p. 23 – 36.

Hackert-Osch¨ atzchen M, Martin A, Meichsner G, Zinecker M, Schubert A.

365

Microstructuring of Carbide Metals Applying Jet Electrochemi-

cal Machining.

Precision Engineering 2013;37(3):621–34.

URL: http:

//www.sciencedirect.com/science/article/pii/S0141635913000123. doi:10.1016/j.precisioneng.2013.01.007.

Hackert-Osch¨ atzchen M, Meichsner G, Zinecker M, Martin A, Schubert 370

Jet.

A.

Micro

Machining

with

Continuous

Precision Engineering 2012;36(4):612–9.

Electrolytic

Free

URL: http://www.

14

Page 14 of 35

sciencedirect.com/science/article/pii/S0141635912000918.

ip t

doi:10.1016/j.precisioneng.2012.05.003. Hommel B, J¨ ahn F, Scharrnbeck M, Garn R, Lenk A, Hackert-Osch¨atzchen M,

Schubert A. Edge Rounding of Micro Bores by Inverse Jet Electrochemical

Machining. In: Proceedings of the 9th International Symposium on Electro-

cr

375

chemical Machining Technology. 2013. p. 33 – 44. ISBN: 978-3-942267-95-3. Density, viscosity, and electrolytic conductivity of concentrated

us

Isono T.

aqueous electrolyte solutions at several temperatures. Alkaline-earth chlo-

380

an

rides, lanthanum chloride, sodium chloride, sodium nitrate, sodium bromide, potassium nitrate, potassium bromide, a. Journal of Chemical & Engineering Data 1984;29(1):45–52. URL: http://pubs.acs.org/doi/abs/10.1021/

M

je00035a016. doi:10.1021/je00035a016.

Laurien E, Oertel H. Numerische Str¨omungsmechanik. Iv ed. Wiesbaden:

Natsu W, Ikeda T, Kunieda M. Study on Characteristics of High Speed Elec-

te

385

d

Vieweg+Teubner Verlag, 2011.

trolyte Jet Machining. Proceedings of 7th International Conference of Design

Ac ce p

and Manufacturing 2006;:333–8. Norton J, Pederson L. Ammonia in simulated Hanford double-shell tank wastes: Solubility and effects on surface tension. Technical Report; Pacific North-

390

west National Laboratory (PNNL); Richland, WA; 1994. URL: http://www.

osti.gov/servlets/purl/10192447-YXSaOb/webviewable/. doi:10.2172/ 10192447.

Schubert A, Hackert-Osch¨ atzchen M, Meichsner G, Zinecker M, Martin A. Evaluation of the influence of the electric potential in jet electrochemical machin-

395

ing. In: Proceedings of the 7th International Symposium on Electrochemical Machining Technology. 2011. p. 47 – 54. URL: http://publica.fraunhofer. de/eprints/urn:nbn:de:0011-n-1862722.pdf; ISBN: 978-3-00-036247-7.

15

Page 15 of 35

Weber O, Rebschl¨ ager A, Steuer P, B¨ahre D.

Modeling of the Mate-

rial/Electrolyte Interface and the Electrical Current Generated during the Pulse Electrochemical Machining of Grey Cast Iron. In: Proceeding of the Eu-

ip t

400

ropean COMSOL Conference. 2013. URL: http://www.comsol.com/paper/

cr

download/182317/weber_paper.pdf.

Yoneda K, Kuneida M. Numerical Analysis of Cross Sectional Shape of Micro-

405

us

Indents Formed by the Electrochemical Jet Machining (ECJM). Journal of The Japan Society of Electrical Machining Engineers 1995;29(62):1–8. doi:10.

Ac ce p

te

d

M

an

2526/jseme.29.62_1.

16

Page 16 of 35

ip t cr us an

Ac ce p

te

d

M

Figure 1: Scheme of the developed model

(a) Dimensions with parameters a and d

(b) Definition of domains, boundaries and points

µ

Figure 2: Parametrical model geometry with a = d = 100 m

17

Page 17 of 35

ip t cr us an

(a) Complete mesh

(b) Detail

Ac ce p

te

d

M

Figure 3: Generated Mesh

Figure 4: Conditions of fluid dynamics

18

Page 18 of 35

ip t cr us an M

Ac ce p

te

d

Figure 5: Conditions of electrodynamics

Figure 6: Conditions of geometry deformation

19

Page 19 of 35

ip t cr us an

Ac ce p

te

d

M

Figure 7: Simulated (red) and static (blue) jet shape of Hackert (2010) at tECM = 0 s

Figure 8: Velocity field at tECM = 0 s, arrows represent the direction of the velocity field

20

Page 20 of 35

ip t cr us an

(b) Rotated pseudo 3D view

M

(a) Level set variable

Ac ce p

te

d

Figure 9: Simulated jet shape at tECM = 0 s

(a) Level set variable

(b) Rotated pseudo 3D view

Figure 10: Simulated jet shape at tECM = 0.5 s

21

Page 21 of 35

ip t cr us an M

(a) Level set variable

(b) Rotated pseudo 3D view

Ac ce p

te

d

Figure 11: Simulated jet shape at tECM = 1.0 s

(a) Level set variable

(b) Rotated pseudo 3D view

Figure 12: Simulated jet shape at tECM = 2.0 s

22

Page 22 of 35

ip t cr us an

Ac ce p

te

d

M

Figure 13: Photos of the Jet-ECM process at different processing times

Figure 14: Electric potential at tECM = 0 s, arrows represent the electric current density

23

Page 23 of 35

ip t cr us an M

Figure 15: Magnitude of the electric current density at tECM = 0 s, arrows represent the

Ac ce p

te

d

electric current density

Figure 16: Electric current density on the work piece surface at tECM = 0 s

24

Page 24 of 35

ip t cr us an M

Figure 17: Electric potential at selected time steps, arrows represent the electric current

Ac ce p

te

d

density

Figure 18: Magnitude of the electric current density at selected time steps, arrows represent the electric current density

25

Page 25 of 35

ip t cr us an M d te Ac ce p

Figure 19: Simulated averaged electric current density Jm and electric current I plotted

against tECM compared with simulation and experiments of Hackert (2010)

26

Page 26 of 35

ip t cr us an M d te Ac ce p

Figure 20: Comparison of simulated and experimental depth of calottes as function of time without and with fluid dynamics

27

Page 27 of 35

ip t cr us an M d te Ac ce p

Figure 21: Comparison of experimental and simulated diameters of calottes as function of time without and with fluid dynamics

28

Page 28 of 35

ip t cr us an M

Ac ce p

te

d

(a) Static jet shape

(b) Dynamic jet shape with fluid dynamics

Figure 22: Comparison of experimental and simulated calotte profiles

29

Page 29 of 35

ip t cr us an

M

Figure 23: SEM image of a calotte at tECM = 1.0 s, with the same parameters as in the

Ac ce p

te

d

simulation

Figure 24: SEM image of a calotte at tECM = 1.5 s, with the same parameters as in the simulation

30

Page 30 of 35

ip t cr us an M d te Ac ce p

Figure 25: SEM image of a calotte at tECM = 2.0 s, with the same parameters as in the

simulation

31

Page 31 of 35

ip t

Table 1: Definition of the mesh

Geometry Reference

Value

Domains I - IV

4 µm

Domain V Maximum Element Size

h

h/2

us

Boundary 7

cr

Parameter

h/2

all

h/5

an

Minimum Element Size

Point A

Maximum Element Growth Rate Curvature Factor

1.13

All

0.3

all

1

te

d

M

Resolution of Narrow Regions

all

Ac ce p

Table 2: Properties of the electrolyte and air at 1 bar and 20

‰ following VDI (2006); Isono

(1984); Norton and Pederson (1994)

Propertys electrolyte

Symbol

Value

Mass fraction of NaNO3

ω

30%

Density

ρE

1221.51 kg/m3

Dynamic viscosity

µE

1.607 mPas

Surface tension

σE/A

79.5 mN/m

Propertys air

Symbol

Value

Density

ρL

1.1885 kg/m3

Dynamic viscosity

µL

18.205 mPas

32

Page 32 of 35

Domain Condition

Domain

Property

ip t

Table 3: Domain and boundary conditions fluid dynamics

Fluid 1: Electrolyte; ρ1 = ρE ; µ1 = µE Fluid 2: Air; ρ2 = ρL ; µ2 = µL III-V

σ = σE/A

cr

Fluid Properties

γ = (2 − /2 µm) · 1 m/s

us

 = 2 µm ~u = 0

Initial Values

prel = 0 Pa

an

III

Electrolyte

Fluid initially in domain: Fluid 1 ~u = 0

Initial Values IV, V

prel = 0 Pa

M

Air

Fluid initially in domain: Fluid 2

III - V

gr = 0; gz = −g

Boundary Condition

Boundary

Property

3-6

-

Ac ce p

Wall

te

Axial Symmetry

d

Gravity

Wall

Initial Interface

Inlet Electrolyte

25

No slip (~u = 0) Wetted wall (~u ≈ 0)

7, 22, 23

θ = π/2 β = hlocal

18, 24

Laminar inflow φ=0

17 u ¯ = 20 m/s Lentr = 0.8 mm Pressure, no viscous stress

Outlet

prel = −(r − 57.5 µm)/(93.5 µm)

8 - 12

·1000 Pa ·pint (t) Weak Contribution

-test(φ) · (1 − φ) · |un | · (un < 0)

8 - 12

33

Page 33 of 35

ip t

Table 4: Material definition electrodynamics

Material

Parameter

I

Steel

σ = 4.032 · 106 S/m

II

Electrolyte

σ = 16 S/m

III - V

Electrolyte/Air

us

cr

Domain

σ = σE + (σA − σE )φ

te

d

M

an

σE = 16 S/m, σA = σE · 10−3

Table 5: Domain and boundary conditions electrodynamics

Domain

Property

Current Conservation

all

σ from material (table 4)

Initial Values

all

ϕ = 0V

Boundary Condition

Boundary

Property

Axial Symmetry

3-6

-

Electric Insulation

8 - 15

-

Ground

1, 2

ϕ = 0V

Electric Potential

7

Ac ce p

Domain Condition

ϕ = ϕint (t) · U U = 56 V

34

Page 34 of 35

ip t cr us

Table 6: Domain and boundary conditions geometry deformation

Domain

Fixed Mesh

I - III

Free Deformation

IV, V

Boundary Condition

Boundary

Property

Prescribed Mesh

9 - 13, 18,

Global coordinate system (r, z)

Displacement

22 - 24

dr = 0; dz = 0

M

Ac ce p

7

Global coordinate system (r, z) dr = 0

vt = 0 vn = Vsp · ηint (Jn ) · Jn · vint (t) Global coordinate system (r, z)

Prescribed Mesh Velocity

dr0 = 0; dz0 = 0

Boundary system (t, n)

Prescribed Mesh Velocity

-

5, 6, 8, 21

te

Displacement

d

Prescribed Mesh

Property

an

Domain Condition

19, 20

vr = 0 vz = 0.75 · vz (Pt. B)

35

Page 35 of 35