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ScienceDirect Procedia CIRP 58 (2017) 257 – 262

16th CIRP Conference on Modelling of Machining Operations

Multiscale multiphysics simulation of a pulsed electrochemical machining process with oscillating cathode for microstructuring of impact extrusion punches Ingo Schaarschmidta*, Mike Zineckera, Matthias Hackert-Oschätzchena, Gunnar Meichsnerb, Andreas Schuberta,b a

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

* Corresponding author. Tel.: +49 371 531 35459 fax: +49 371 531 835459. E-mail address: [email protected]

Abstract The pulsed electrochemical machining (PECM) with oscillating cathode is a manufacturing technology which is used for shaping and surface structuring of different workpieces, e.g. impact extrusion punches. The principle behind the ECM-process is the controlled anodic dissolution of the workpiece material without any thermal or mechanical impact and independent from workpiece material hardness. In this study, a new multi-scale approach for the modelling of PECM with oscillating cathode was created integrating the short and long time scale physical phenomena. In the short time scale simulation step (t < 0.02 s) the physical processes (current density distribution, motion of cathode, heat and hydrogen generation) during one single oscillation were analyzed. An averaged dissolution speed at the anode boundary over the small time range was calculated. The averaged values were imported as initial and boundary conditions into the long times scale simulation step (t > 10 s). Within this simulation step, the anodic dissolution was simulated by deforming the geometry. This approach allows simulat ions for long overall time ranges (t > 1000 s) while considering the short times scale processes in combination with a relatively small computational effort. This multiscale and multiphysics model helps to analyze the differences between front and lateral working gap and supports the process design for the pulsed electrochemical machining with oscillating cathode. © 2017 The Authors. Published by Elsevier B.V. © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations, in the (http://creativecommons.org/licenses/by-nc-nd/4.0/). Poulachon. person of the Conference Chairs J.C. Outeiro and Prof. Peer-review under responsibility of theProf. scientifi c committee of The 16thG. CIRP Conference on Modelling of Machining Operations Keywords: Electro chemical machining (ECM), Material removal, Multiscale-multiphysics-modelling

1. Introduction Impact extrusion is a mass production technology for manufacturing precise, highly loaded components with a complex geometrical shape [1]. During the process, a lot of mechanical stress is induced into the tools, especially the die and punch. To reduce the wear and increase the lifetime, wear resistant materials like powder metallurgy steels (PM-steels) are needed. These materials are characterized by high hardness and high ductility [2]. Because of those mechanical properties, the high precision machining of tools like impact extrusion punches with conventional manufacturing methods is not trivial. An alternative manufacturing method of shaping such

geometries is the pulsed electrochemical machining (PECM) with oscillating cathode, which is a further development of the conventional electrochemical machining (ECM). In general the ECM works independent from the workpiece (anode) hardness [3]. Figure 1 shows the principle and phases of the pulsed electrochemical machining with oscillating cathode. In the first step, the cathode and anode are aligned to each other and the electrolyte flow is started. In the second step the cathode moves along the feed rate direction towards the anode (workpiece) and a short current pulse is initiated at the bottom dead center of the cathode oscillation. At this point, the material dissolution begins and reaction products like hydrogen, dissolved material, and process heat influences the electric conductivity of the

2212-8271 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations doi:10.1016/j.procir.2017.04.005

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electrolyte inside the working gap. After this, the electric current is paused and the cathode moves back to the top dead center of the cathode oscillation in the third step. The working gap increases and is flushed with sufficiently conductive electrolyte before a new electric pulse is triggered again at the new bottom dead center of the oscillation [4].

Fig. 1. Principle of a pulsed ECM-process with oscillating cathode [4]

In praxis, the designing of the machining parameters and tool design is a very time-consuming and cost intensive empirical procedure. This study presents an investigation of a multiscale multiphysics model for the PECM with oscillating cathode. The model addresses the influence of the heat generation and hydrogen production on the electric conductivity of the electrolyte as well as the influence of the resulting shape of workpiece. 2. Model Description

5 mm. The inner side of the cathode has a chamfer with an angle of 45° and length of 4 mm. The whole concept is nearly axisymmetric. Figure 3 represents the model geometry derived from the design concept containing the numbering of domains and boundaries.

Fig. 3. 2D-axisymmetric geometry of the model containing the numbering of domains and boundaries at initial time t = 0 s

Domain I (blue) represents the electrolyte with a mass fraction of 8% sodium nitrate (NaNO3) and is defined as a fluid. Domain II (grey) is the anode, or workpiece and defined as a solid. The material is a powder-metallurgical steel, named CPM REX T15. The yellow marked domain III is defined as the cathode. The cathode is made from copper alloy (MS58) and describes the tool. The green domain IV is the insulation in this geometry and is made from Polyoxymethylen (POM). Table 1 summarizes further information of the defined material parameters, including the density ρ, the electric conductivity σ, the thermal conductivity λ and the heat capacity cP .

2.1. Geometry and Materials

Table 1. Allocation of material parameters .

For the pulsed electrochemical machining with oscillating cathode of external geometries a design concept was developed. Figure 2 shows a 3D cad model with the relevant elements of the concept. The concept consists of the workpiece (gray), the cathode (yellow), the insulation (green) and clamping components of the cathode (purple).

Domain

Materials

ρ

σ

λ

cP

[kg/m3]

[S/m]

[W/(m·K)]

[J/(kg·K)]

I

Electrolyte

1025.5

σeff(ϕEl,T)

0.599

3877

II

REX T15

8190

ͳ ή ͳͲ଺

24,2

4700

III

MS58

8470

ͳͷ ή ͳͲ଺

123

3770

IV

POM

1410

10-10

0.31

1500

The effective electric conductivity of the electrolyte σeff is influence massively by the generated hydrogen bubbles and temperature. Both effects considered in the definition of σeff by equation (1). Here ߶୉୪ is the electrolyte volume concentration, which decreases with the increasing hydrogen volume concentration ߶ுమ [5]. య

య

ߪ௘௙௙ ሺܶǡ߶ா௟ ሻ ൌ ߪா௟ ሺܶሻ ή ߶ா௟ మ ൌ ߪா௟ ሺܶሻ ή ሺͳ െ ߶ுమ ሻమ

Fig. 2. Design concept for machining external precision geometries with pulsed electrochemical machining and oscillating cathode

The workpiece has an outer diameter of 20 mm and the cathode has an inner diameter of 16.4 mm with a thickness of

(1)

Further represents ߪா௟ ሺܶሻ the experimentally determined conductivity of the pure electrolyte with a mass fraction of 8% NaNO3 as a function of the temperature and is described by equation (2). ߪா௟ ሺܶሻ ൌ ͳǤ͸Ͷ͸

݉ܵ ௖௠

ሺܶ െ ʹ͹͵Ǥͳͷሻ ൅ ͵ͻǤ͹ͻ͸

௠ௌ ௖௠

(2)

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2.2. Physics The displacement of the cathode is defined as a superimposed motion of constant feed and oscillation along the z-direction and is set on boundaries 7, 12, 13 and 14. Equation (3) describes the superimposed motion of the cathode. The motion of the cathode leads to a massively change in geometry in a relatively short time range and in consequence in change of the boundaries of the other physics (coupling between motion and other physics). ߨ ‫ݏ‬௭ ൌ ‫ݏ‬Ƹ ή ܿ‫ ݏ݋‬ቀʹߨ ή ݂ ή ‫ ݐ‬൅ ቁ െ ‫ݒ‬௭ ʹ

(3)

Here ‫ݏ‬Ƹ is the amplitude with 200 µm and ݂ the frequency of the oscillation with 50 Hz. Further on is ‫ݒ‬௭ the constant feed velocity with 0.1 mm/min and ‫ ݐ‬the ongoing processing time. The cycle duration TOsc is 0.02 s. The blue line in figure 4 shows the displacement-time relationship for two cycle durations.

Fig. 5. Material-specific removal velocity va as a function of the normal current density Jn

The generation of hydrogen trough the conversion of electrical energy (electric current) to chemical energy (hydrogen) and is defined as equation (7) on boundary 12. ߔுమǡ௡ ൌ െ

Fig. 4. Displacement-time function (blue) and electric potential-time function (green) for two cycle durations

The electrodynamics interface is solved for every domain. The pulsed electric potential is defined on boundary 10 and changes with time. The maximum value of the electric potential ෝ is 8 V at the bottom dead center of the oscillation. The pulse߮ on time ton is set to 4 ms and the cycle duration is equal to the cycle duration of the oscillation. The green line in figure 4 represents the electric potential-time function. Boundary 5 is set as the electric ground. The boundary condition electric insulation is used on boundaries 3, 4 and 6 – 9. The electric current density at the anode surface leads to the material dissolution that is modelled as a moving mesh on boundary 11. The calculation of the moving mesh velocity based on an experimental material-specific removal velocity function shown in figure 5 [6]. For the electric current density range from 17 A/cm2 to 33 A/cm2 a material specific removal velocity function va,I is defined as equation (4). From 33 A/cm2 to 36 A/cm2 va,II is defined as equation (5) and from 36 A/cm2 to 110 A/cm2 as equation (6). ‫ݒ‬௔ǡூ ൌ ͲǡͲͲͲͺͷ ή ‫ܬ‬௡ െ ͲǤͲͳͷ ‫ݒ‬௔ǡூூ ൌ ͲǡͲͳ͵ͷ ή ‫ܬ‬௡ െ ͲǤͶ͵

݉݉ ݉݅݊

݉݉ ݉݅݊

‫ݒ‬௔ǡூூூ ൌ ͲǡͲͲ͵͵ ή ‫ܬ‬௡ െ ͲǤͲͷ͵

݉݉ ݉݅݊

(4) (5) (6)

‫ܯ‬ுమ ‫ܬ‬መ ʹ‫ ܨ‬௡

(7)

Here the normal electric current density Jn influences directly the normal hydrogen mass flow densityߔୌమǡ୬. The parameter F is the Faraday constant and ‫ܯ‬ୌమ the molar mass of hydrogen. The generation of hydrogen is the electrofluidynamics coupling. The thermodynamics interface is solved for every domain. This model focuses the joule heating (electro-and thermodynamics coupling) on every domain. The heating in the electrochemical double layer is defined as a line heat source at boundary 11 and 12 adapted from [7]. The transport of heat and hydrogen through the electrolyte (thermoand fluid dynamics-coupling) is modelled by a modified potential two phase flow adapted from [8]. The potential twophase flow is defined as the gradient of the velocity potential ϕ with an inflow described by equation (8). ߘ߶ ή݊ሬԦൌ

ܸሶா௟ ‫ܣ‬ூ௡

(8)

The inflow is set on boundary 9. The outlet is set on boundary 3 with ߶ ൌ Ͳ m2/s. Here ܸሶ୉୪ is the electrolyte flow rate and AIn the cross-sectional area of the inflow zone. Variable ݊ሬԦ represents the boundary normal vector. Table 2 summarizes the simulation parameter of the interfaces. Table 2. Summary of simulation parameter for the multiphysics model Symbol

Definition

Value

f

Frequency of oscillation

50

Unit Hz

p Out

Outlet absolute pressure

7

bar

߮ො

Electric Potential

8

V

‫ݏ‬Ƹ

Amplitude of oscillation

200

µm

ton

Pulse on time

4

ms

ሶ ܸ୉୪

Electrolyte flow rate

6

l/min

vz

Feed velocity

0.1

mm/min

TU

Ambient Temperature

20

°C

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2.3. Multiscale approach The time scales of the physical phenomena involved in this model are very different [9]. It is practically not possible to simulate the material removal over a long time range (t > 1000 s) considering every single electric pulse and the resulting influence of the process. The computational time is unacceptably long. Therefore, an alternative approach is necessary. The multiscale approach in this simulation model is to group phenomena and process influences with similar time scales together and calculate them in individual simulation steps. Between those simulation steps coupling functions were defined. This approach allows larger time steps for the simulation step with the long time scales that are independent of the short time scale phenomena and process influences. To group the phenomena and process influences, assumptions of the different time scales were made. Table 3 summarizes the time scales of the different phenomena and process influences. Table 3. Time scales of the different phenomena and process influences phenome

assumption

Time scale [s]

Convective heat transfer

‫ݑ‬Ȁ݈

10-4

Current pulse

–‘

10-3

Constant feed rate of cathode

vz/sz

102

Fluid dynamics

‫ݑ‬Ȁ݈

10-4

Heat generation

–‘

10-3

Hydrogen generation

–‘

10-3

Hydrogen transport

‫ݑ‬Ȁ݈

10-4

Material removal

tsim

103

Oscillation of cathode

TOsc

10-2

The current pulse time scale corresponds roughly to the pulse on time ton. The electric current leads to heat generation and hydrogen production. Thus, the time scales for heat generation and hydrogen production are equal to the time scale of the electric current pulse. The assumption of the time scale of the fluid dynamics is based on the flow time of the fluid through the working gap with a flow length l ≈ 10 -3 m (≈ length of working gap) and a flow velocity ‫ ݑ‬ൌ ͳͲଵ Ȁ•. The value of the flow velocity is based on typical empirical values from experiments. The time scale of the material removal complies with the considered simulation or process time tsim > 1000 s. The assumption for the time scale of the constant feed of cathode is based on the ratio of the feed rate velocity vz and the feed rate displacement sz of the cathode. The time scale of the oscillation of the cathode is equal to the periodic time of the displacement-time function TOsc or 1/f. All phenomena and process influences with a time scale less than 10 -2 s grouped together in simulation step A and bigger than 10 -2 s in simulation step B. Figure 6 shows the multiscale approach for one complete iteration step. The target variable of simulation step A is the actual removal velocity va,i (Jn) at boundary 11. Furthermore the actual removal velocity va,i (Jn) is the input variable for the coupling function between simulation step A and simulation step B.

Fig. 6. Multiscale approach for one iteration step including both simulations steps and coupling functions.

The coupling A-B is defined as equation (7) and is set on boundary 11 as an additional differential equation. ௧ା௧ೌ

ͳ ‫ݒ‬ҧ௔ ൌ ή න ‫ݒ‬௔ǡ௜ ሺ‫ܬ‬௡ ሻ ݀‫ݐ‬ ‫ݐ‬௔

(9)

௧

Equation (9) calculates the average removal velocity ‫ݒ‬ҧୟ at the anode surface over a specific time. Here t is the process time. Variable ta is the time for the simulation step A and defined as multiple times the periodic time ܶ୓ୱୡ  of the oscillation of cathode (equation (10)). Overall ‫ݒ‬ҧୟ represents the changing input variable for every iteration for simulation step B. ‫ݐ‬௔ ൌ ݊ ή ܶை௦௖ ൌ ݊ ή

ͳ ݂

(10)

The coupling function from simulation step B to simulation step A is the updated geometry after the relatively long material removal time tb. The parameter tb is the time for 50 µm feed rate displacement of the cathode. For a feed rate velocity vz = 0.1 mm/min the time for simulation step B tb is 30 s. 3. Simulation Results 3.1. Short time-scale time step results In figure 7 the result of the electric current density at the bottom dead center of the cathode oscillation is shown. The electric current density in the free area of the electrolyte is about 10 A/cm². It increases with reaching the working gap up to 50 A/cm². Within the front working gap, the electric current density is almost constant. With reaching the side working gap, the electric current density decreases. At the exit of the side working gap, the electric current density is about 25 A/cm². As a consequence of the electric current inside this system, heat is generated and hydrogen is produced which is shown in

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figure 8. The initial temperature is 20 °C. It is obvious that the temperature increases along the workings gap. The heat generation within the anodic double layer is much bigger than the cathodic double layer. Insulation

Anode

Cathode

Both the change in temperature and hydrogen production influences the electric conductivity of the electrolyte. Figure 10 shows the resultant effective electric conductivity of the electrolyte as a false color rendering. The initial effective electric conductivity at 20 °C is 7.27 S/m. Because of the higher temperatures near the anode surface, the effective electric conductivity increases progressively up to the maximum value of 8.52 S/m. The production of hydrogen leads to a decreasing value of the effective electric conductivity of electrolyte near the cathode surface due to the decreased volume concentration of electrolyte. The minimum value of the effective conductivity of 5.40 S/m occurs in the corner between the cathode and insulation. Insulation

Fig. 7. False color rendering of the electric current density at the bottom dead center of the cathode oscillation after 1202.005 s

The temperature raises up to a local maximum of about 27 °C in the curve of the anode surface. Furthermore, a small increase of the temperature of the cathode is observed in the area of the front working gap. The local maximum within the cathode domain is about 22 °C. The increase of temperature within the anode is about 25 °C. The generated heat is flushed away by the convective heat transfer and the fluid flow along the positive z-direction. Insulation

Anode

Cathode

Fig. 8. False color rendering of the resulting temperature at the bottom dead center of the cathode oscillation after 1202.005 s

Figure 9 shows the hydrogen production as a false color view of the electrolyte volume concentration߶୉୪. Within the working gap, the electrolyte volume concentration decreases from initially 100% to a minimum value of about 85% in the corner between the cathode and the insulation. The hydrogen production only occurs at the cathode surface. This produced hydrogen is transported by the fluid flow towards the outflow along the positive z-direction.

Anode

Cathode

Fig. 10. False color rendering of the effective electric electrolyte conductivity at the bottom dead center of the cathode oscillation after 1200.005 s

To calculate the actual material removal velocity, the resultant normal current density along the anode surface (boundary 11) is the relevant variable. Figure 11 shows the normal current density and the actual material removal velocity as a function of the arc length L of the anode surface at the bottom dead center of the cathode oscillation after a processing time of 1200.005 s. At the area of the curvature at L ≈ 8 mm, the normal current density starts to increase. After reaching a value of Jn = 17 A/cm2 at an arc length of L ≈ 9 mm the passivation barrier passed and the material dissolution takes place. This results in an increase of the actual material removal velocity up to a maximum value of 0.57 mm/min at L ≈ 10 mm.

Insulation

Anode

Cathode

Fig. 9. False color rendering of the resulting hydrogen production at the bottom dead center of the cathode oscillation after 1202.005 s

Fig. 11. Correlation between normal electric current density and actual material removal velocity as a function of the arc length L at the bottom dead center of the cathode oscillation after 1200.005 s

After passing the front working gap at an arc length of around 12 mm, the normal current density decreases strongly and exceeds at L ≈ 12.8 mm the passivation barrier again. From here, there is no material dissolution and the actual material removal is equal zero.

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3.2. A-B-Coupling

4. Summary

The actual removal velocity va at the anode surface represents the target variable of the short time scale simulation step A. At the same time, it is the input variable for the coupling function between simulation step A and simulation step B calculated by equation 9. The output variable of the coupling function is the averaged removal velocity at the anode surface. To understand the coupling function A-B, the correlation between the maximum value of the actual removal velocity at the anode surface and the maximum value of the averaged removal velocity during a complete short time scale simulation step is shown in figure 12 as a function of the process time.

In this study multiscale multiphysics simulations of the pulsed electrochemical machining process with oscillating cathode were performed. The fully coupled model considers the electrodynamics, thermodynamics, fluid dynamics and the superimposed motion of the cathode to calculate the shape of a 2D-axisymmetric external geometry over a long machining time. The multiscale approach contains the principle to group all relevant physical phenomena and process influences with a similar time scale together and perform them in a separate simulation step. Between those separate simulation steps a specific coupling function was defined. The averaged material velocity for the material removal modelling based on the resulting normal electric current density, which considers all influences due the heat generation and hydrogen production to the electric conductivity of the electrolyte. This multiscale approach allows detailed analyses of the short times scale PECM-process parameter within one oscillation period. At the same time the resulting shape after a long time range can be determine with a reasonable amount if computational effort. This can reduce the amount of required costly and timeconsuming experiments. The next step is to determine the influence of specific process parameter to the resulting shape.

Fig. 12. Correlation between the actual removal velocity ‫ ܽݒ‬ǡ݅ and the averaged material removal velocity ‫ ݒ‬௔ as a function of the process time

It can be seen, that the maximum value of the actual material removal velocity along the anode surface increases up to the known value of 0.57 mm/min at a process time of 1200.005 s. The averaged material removal velocity raises up to 0.08 mm/min and is constant up to the end of simulation step A at t = ta =1202.02 s.

Acknowledgements This project is funded by the Federal Ministry of Economics and Technology, following a decision of the German Bundestag. References

3.3. Long time-scale simulation step results [1]

The result for the long time scale simulation step is shown over a time of 5 complete iterations of simulation step A and simulation step B in figure 13 to represent the material dissolution over a long time range from 1200 s to 1350 s. This figure shows a detailed view of the corner area of the anode. It can been seen that the anode surface displacement at the area of the front working gap is about 0.28 mm every iteration. The shaping due the side working gap is far less. The final result of the simulation is a deformed geometry after an overall process time of 1350 s with a resulting radius of 7.973 mm.

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Electrochemical Machining of In- ternal Precision Geometries,” Pulsed Electrochemical Micro- Machining,” Procedia CIRP Fig. 13. Resulting geometrical shape after 5 iterations of simulation step A and simulation step B for a process time from 1200 s to 1350 s