Transient simulation of electrochemical machining processes for manufacturing of surface structures in high-strength materials

Abstract

Electrochemical machining (ECM) is a method for removing metal by anodic dissolution. At the interface between the workpiece surface and an electrically conductive fluid (electrolyte), the material is dissolved locally without direct physical contact to the cathodic tool. Due to the force-free nature of the process, ECM is used for machining high-strength or hard materials, such as titanium aluminides, Inconel, Waspaloy, and high nickel, cobalt, and rhenium alloys. However, determining suitable process parameters remains challenging due to their interacting effects on working distances during the machining process. Therefore a simulation-based approach to process design substantially reduces resource and time investment to achieve the desired geometry of the finished part. This methodology requires data about the materials electrochemical properties, such as removal velocity and current efficiency, which have to be obtained experimentally. In this study, a methodology for acquiring and processing this data as well as the development of multiphysics simulation models is presented exemplarily for manufacturing a centrifugal impeller with a diameter of 14 mm consisting of the nickel alloy Inconel 713C for use in turbomachinery.

1 INTRODUCTION

Within the collaborative research project AMARETO of Technische Universität Bergakademie Freiberg, Technische Universität Dresden, Chemnitz University of Technology and the Fraunhofer Institute for Machine Tools and Forming Technology, the higher level objective pursued is the development of methods and transfer of solutions for parts of the value chain, focusing on time- and resource-efficiency in product development. One suitable approach is the implementation of the concept of a digital twin, a virtual representation of a physical product.¹ This digital twin contains all available data regarding material, treatment conditions, geometry and surface characteristics along the process chain.² As this digital twin is subjected to simulated process steps, this data must contain relevant input data to be integrated in simulation models via suitable interfaces. While this concept has been mostly applied to machine tools in recent studies,^{3, 4} digital twin development for the workpiece is hardly studied. In particular electrochemical machining processes, which can only be modeled numerically after preceding acquisition of material characteristics, can benefit from consistent use of data obtained during preprocess and postprocess steps.

During electrochemical machining (ECM), electrodynamic, fluid dynamic, and thermodynamic mechanisms as well as reaction kinetics are interacting with each other, influencing local electrolyte conductivity, material transport and resulting workpiece geometry. Consequently, achieving the desired workpiece geometry and surface properties requires multiple iterations for optimizing process configuration and tool design. Multiphysics simulation is an essential tool in order to design ECM processes efficiently.⁵ These process simulation models rely on accurate input of the electrochemical properties of the materials to be machined, such as their normal removal velocity, current efficiency, and overpotentials as functions of the normal current density. These functions are calculated from process data recorded during material characterization experiments and are subsequently integrated into process models in a streamlined data processing chain specifically developed for the simulation-based design of ECM processes.

The specific example presented in the study involves the manufacturing of a centrifugal impeller consisting of Inconel 713C for application in turbomachinery. Inconel 713C is a nickel-based superalloy featuring tensile and yield strengths above 700 MPa at temperatures up to 800°C.⁶ Due to these mechanical properties conventional machining of this alloy is challenging, resulting in high tool wear, long manufacturing times, and need for additional surface finish.⁷ As ECM bypasses these limitations, its implementation for the machining of nickel-based alloys has been studied extensively in the past. Their dissolution characteristics have been described over a wide range of current densities.^{8, 9} This data have been applied for the design of both shaping¹⁰ and finishing¹¹ processes of Inconel parts.

In this study, a pulsed electrochemical machining (PECM) process is applied. In PECM, the cathode is moved into the workpiece utilizing pulsed electric current and dedicated flushing periods during pulse-off times. To further improve the flushing conditions, the linear movement of the tool cathode is superimposed by an oscillation movement. Figure 1 shows the principle of pulsed electrochemical machining with oscillating cathode schematically.

FIGURE 1

Principle of pulsed electrochemical machining (PECM) with oscillating cathode¹²

During PECM with an oscillating cathode, working distances are at their minimum during pulse-on times (phase I and phase III), whereas the electrolyte is reliably renewed during pulse-off times (phase II), hence increasing accuracy and stability of the process.⁹ Current and oscillation frequencies typically range from 50 to 200 Hz with pulse-on times of 1–4 ms.

2 SIMULATION-BASED PROCESS DESIGN

Figure 2 illustrates the developed methodology of simulation-based design of ECM processes utilizing the concept of the digital twin. At the beginning, relevant data regarding material, geometry, or treatment condition of the initial or semifinished part are extracted from the data chain of the digital twin. In combination with the requirements of the part, such as geometric tolerances or surface quality, a removal concept can be outlined. This includes the choice of a suitable manufacturing process and its respective input parameter intervals. In the case that the electrochemical properties of the material are yet unknown, a removal characterization can provide all subsequently necessary information. After integrating these properties in developed models for process simulation, machining parameters can be derived. Finally, geometry and surface properties of the manufactured part can be analyzed and the information returned to the data chain of the digital twin for subsequent manufacturing steps. In this work, removal characterization and process simulation will be discussed more in-depth.

FIGURE 2

Methodology for the simulation-based design of ECM processes. Dark blue and green elements represent theoretical and practical steps, respectively, necessary for designing the ECM process, whereas orange elements depict postprocess steps. Light blue elements are cross-process

2.1 Removal characterization

An essential material property for the development of an ECM process simulation model can be expressed as one of either normal removal velocity v_a, effective dissolution volume V_eff, or current efficiency $\eta$ as a function of the normal current density J, respectively. The following equation describes the relation of these quantities:¹⁰

$$\frac{v_{\mathrm{a}}}{J}=V_{\text{eff}}=\eta V_{\text{sp}}.$$ (1)

V_sp, the specific dissolution volume, can be calculated according to Faraday's law of electrolysis for an alloy of mass density $\rho$ consisting of components indexed i with mass fractions w_i, molar masses M_i and valences z_i:¹³

$$V_{\text{sp}}={\left(\rho F\right)}^{-1}\sum _{\mathrm{i}}\frac{w_{\mathrm{i}}{M}_{\mathrm{i}}}{z_{\mathrm{i}}}.$$ (2)

The composition of the characterized Inconel 713C alloy as well as molar masses and assumed valences of its components are summarized in Table 1. In conjunction with its alloy mass density $\rho =7.91{\text{g cm}}^{-3}$ and the Faraday constant F = 96485.3 C mol⁻¹ a specific dissolution volume of 31.5 × 10⁻³ mm³ C⁻¹ can be determined according to Equation (2).

TABLE 1. Composition of Inconel 713C

i	Ni	Cr	Al	Mo	Nb	Ti	Fe	C	Others
wi (%)	Bal.	13.1	6.3	4.4	2.1	0.9	0.86	0.15	<0.28
$M_i({\text{g mol}}^{-1})$	58.69	52.00	26.98	95.95	92.91	47.87	55.85	12.01	–
zi	2	6	3	6	5	3	3	4	–

In this study, the removal characterization was conducted according to DIN SPEC 91399,¹⁴ which yields the normal removal velocity v_a as a function of normal current density J at the workpiece surface as well as the sum of all overpotentials $U_{\sum }$. The latter describes the voltage drop in the boundary layers between electrodes and bulk electrolyte. $U_{\sum }$ can constitute a significant percentage of the total working voltage U_q, reducing the amount of material removed electrochemically, hence it is another necessary input quantity for ECM process simulation models.

The removal characterization consists of several PECM experiments under variation of working voltage U_q and feed velocity v_f. All experiments were conducted on the manufacturing machine PEMCenter 8000 using a solution of NaNO₃ with a salt content of 8% as electrolyte. Figure 3 displays a basic scheme of the setup. Both the cathodic tool electrode (yellow) and the anodic sample workpiece (gray) were of cylindrical shape with a diameter of 12 mm, aligned coaxially. The voltage U is adjusted automatically by the machine control to compensate the oscillating working distance s(t), resulting in a rectangular current pulse. Therefore, the following equation describes the charge exchange during each pulse-on time:

$$U(t)-U_{\sum }=\frac{s(t)}{{\sigma }_{\text{el}}}J.$$ (3)

FIGURE 3

Scheme of material characterization setup. Feed velocity v_f and average removal velocity $\overline{v_{\mathrm{a}}}$ are of same magnitude and direction

Relevant parameters of the characterization experiments are summarized in Table 2.

TABLE 2. Parameters of the characterization experiments

Parameter	Value
Electrolyte conductivity ${\sigma }_{\text{el}}$	69 mS cm^−1
Electrolyte inlet pressure pin	310 kPa
Feed velocity vf	(0.01 … 0.51) mm min^−1
Oscillation frequency fz	50 Hz
Working voltage Uq	(5.0 … 14.5) V
Pulse frequency fp	50 Hz
Pulse duration tp	4 ms

FIGURE 4

Electrochemical properties of Inconel 713C obtained from material characterization experiments. Normal removal velocities v_a (left) and sums of overpotentials $U_{\sum }$ (right) as functions of normal current density J at the workpiece surface

Within the removal characterization a total of 34 experiments were conducted while recording available process data, such as cathode position and current characteristic over the course each experiment. Calculated removal velocities v_a and sums of overpotentials $U_{\sum }$ as functions of current density J are shown in Figure 4. Inconel 713C displays an active dissolution characteristic as v_a and J are in a linear relation without offset. As this function crosses the origin of coordinates, according to Equation (1) a constant effective dissolution volume V_eff of 43 × 10⁻³ mm³ C⁻¹ at an empirical current efficiency $\eta$ of 1.36 can be determined. As a true current efficiency cannot be greater than unity, it is assumed that the dissolved nickel partly has an atypical valence of one or parts of the multiphase material are not dissolved electrochemically. Sums of overpotentials $U_{\sum }$ ranging from 4 to 12 V were observed. They were obtained by comparing experiments of equal current density but different working distances due to varying working voltages and feed velocities, and extrapolating these working distance to 0  $\mathrm{\mu }$m.

2.2 Data processing and database integration

To perform the calculation of electrochemical properties for each material efficiently from the accumulated process data, an automated data evaluation flow as an interface between characterization experiments, a material database and the simulation environment was developed in the data science tool KNIME Analytics Platform.¹⁵ As outlined in the dataflow in Figure 5, the result of the processed data can be displayed tabularly and graphically. After inspection, all data regarding both machined material and electrolyte properties during the material characterization experiments are reformatted and integrated into a PostgreSQL database structure setup for this purpose. This dataflow also allows accessing all data in a format suitable for integration in multiphysics simulation. As this data are available online, it can also be accessed via web interface.

FIGURE 5

Dataflow developed in KNIME analytics platform for the calculation of electrochemical properties from characterization experiments, interfacing to an online material database. Nodes in yellow boxed contain operations for setting process data location, evaluating and uploading the result and accessing the entire content of the database. The user does not have to interact with the remaining nodes

The structure of the relational database containing relevant parameters and properties is summarized in Figure 6 in the form of a simplified entity-relationship diagram.¹⁶ It contains input parameters, averaged process parameters, and output parameters of all conducted material characterization experiments. Parameters, which vary between experiments are contained in a table labeled Experiment. This includes setting parameters, electrodynamic quantities, and dynamic electrolyte parameters, such as temperature and pH. One or more experiments are now assigned to a series of measurements, which was conducted on a specific device. This table Measurement series is linked to a Material, an Electrolyte and a Cathode, which each possess attributes contained in their respective tables. Unique materials are described by their name and heat treatment condition, unique electrolytes by name and concentration of diluted species and, equally, unique cathodes by their material and geometric parameters. As displayed by means of the cardinalities on the connecting lines between the tables, each measurement series has to contain at least one experiment, while a material, an electrolyte, or a cathode may not be assigned to any measurement series.

FIGURE 6

Structure of the developed database for electrochemically characterized materials

3 MULTIPHYSICS SIMULATION

In this section, the developed process simulation model for the manufacturing of a centrifugal impeller consisting of Inconel 713C via PECM will be presented and selected results will be discussed. A 3D model of the PECM process was developed¹⁷ using the commercial software COMSOL Multiphysics, which utilizes the finite element method (FEM). Removal velocities v_a and sums of overpotentials $U_{\sum }$ determined during the material characterization can be integrated into the models directly from the recorded process data or from the material database.

3.1 Removal concept and process parameters

The impeller is manufactured by moving a cathode sheet with cutouts into a cylindrical rod with a diameter of 14 mm. Utilizing the periodic shape of the impeller, the removal process was modeled only for a single segment. The basic concept is illustrated in Figure 7. Based on the results of the removal characterization, promising process parameters were selected and are summarized in Table 3. In order to improve the geometric reproduction accuracy of the blade profile, the cathode features an isolation on top and a 45° chamfer. For this application, the profile of the cathode was derived from Karpowitz.¹⁸ The electrical contact of the cathode was omitted in the 3D model as its influence of the material removal is negligible.

FIGURE 7

Simulation model of the PECM process for manufacturing centrifugal impellers from a cylindrical workpiece

TABLE 3. Definition of process parameters used in the model of the PECM process

Parameter	Value
Electrolyte conductivity ${\sigma }_{\text{el}}$	69 mS cm^−1
Feed velocity vf	0.5 mm min^−1
Oscillation frequency fz	50 Hz
Working voltage Uq	14.5 V
Pulse frequency fp	50 Hz
Pulse duration tp	4 ms
Initial working distance s0	200  $\mathrm{\mu }$m
Process time tproc	180 s

3.2 Physics and mesh

In this PECM process model, interactions between electrodynamic mechanisms and geometry deformation are fully coupled to model the material removal. Charge transport and resulting current densities in the electrolyte domain are determined by a potential model according to Ohm's law

$$\mathbf{J}=\sigma \mathbf{E}\text{with}\mathbf{E}=-\mathrm{\nabla }\phi ,$$ (4)

and the conservation of electric charge with a charge density $\rho$

$$\frac{\partial \rho }{\partial t}+\mathrm{\nabla }·\mathbf{J}=0.$$ (5)

The geometric deformation at the workpiece surface is calculated according to the experimentally obtained material characteristics shown in Figure 8. In order to reduce the numerical effort, current pulses of the PECM process are simplified as pseudo-direct current under consideration of the selected duty cycle.¹⁹ Fluid dynamics, thermodynamics, and the concentration of reaction products influence the local conductivity in the electrolyte domain, thus also affecting the final workpiece geometry to a minor degree. Unfortunately, the asymmetric electrolyte flushing would require modeling the unreduced geometry of the setup. Considering both stability and solution time of the transient 3D model, these physical mechanisms could not be included.

FIGURE 8

Geometry and boundary conditions in a cut plane at the initial state of the process simulation

Set boundary conditions, which are illustrated by means of a cut plane, are shown in Figure 8. The working voltage U_q of 14.5 V is reduced by the experimentally determined overpotential $U_{\sum }$ of approximately 8 V. Therefore an electric potential of 6.5 V is defined on boundary 3 against a ground potential on boundary 2. Boundaries 2, 4, and 5 are moving in negative z-direction at the feed velocity v_f of 0.5 mm min⁻¹. The workpiece surface, boundary 6, is deformed throughout the machining process according to the material characteristics of Inconel 713C shown in Figure 4. The system is insulated by boundaries 1 and 4 while all inner boundaries allow charge transport. Lateral surfaces, which are not depicted in this representation, are defined as isolating as the lateral current flow is negligible (Table 4).

TABLE 4. Definition of boundary conditions

Boundary	Electrical	Mechanical
1	Insulation	Fixed wall
2	$\phi =0\mathrm{V}$	Feed velocity
3	$\phi =6.5\mathrm{V}$	Fixed wall
4	Insulation	Feed velocity
5	Charge exchange	Feed velocity
6	Charge exchange	Removal velocity

In its initial state, the model consists of approximately 177, 000 mesh elements ranging from 15 to 500  $\mathrm{\mu }$m in size. With the exception of the isolation domain (green), which is built from extruded triangular elements, all domains consist of tetrahedral mesh elements. Due to increasing mesh element distortion, the model was fully remeshed several times over the course of the process simulation. At termination, a maximum of approximately 1, 800, 000 domain elements are used for meshing the model geometry.

FIGURE 9

Removal geometry and normal current density distribution on the workpiece after a machining time of 180 s

FIGURE 10

Superimposed lateral profiles of machined impeller blade (gray) and cathode (orange)

3.3 Results

Figure 9 displays the simulated distribution of normal current density on the workpiece surface after a machining time of 180 s. Figure 11 shows the axial profile of the workpiece through a cut plane (left) and the corresponding current density distribution along this surface path (right). At this point in time, the cathode has fully passed the top of the workpiece resulting in close to zero current density at this part of the workpiece and hence no material removal. For process parameters defined in Table 3, the frontal working distance converges to 46  $\mathrm{\mu }$m at current densities of 96 A cm⁻². At the 45° chamfer of the cathode, the increased working distance of 81  $\mathrm{\mu }$m decreases the current density to 68 A cm⁻². The lateral profile of the simulated impeller blade superimposed with the blade-shaped recess in the cathode is shown in Figure 10. Areas of the impeller blade with concave curvature show a smaller lateral working distance with a minimum of $d_{\min }=74\mathrm{\mu }\mathrm{m}$, whereas areas of convex curvature, experiencing high current densities show distances up to $d_{\max }=108\mathrm{\mu }\mathrm{m}$. These variations have to be accounted for in cathode design in order to obtain the desired impeller blade geometry.

FIGURE 11

Axial workpiece profile (left) and corresponding distribution of normal current density J along the surface path (right) after a machining time of 180 s. Gray markers in left and right image limit the same section of the workpiece profile

4 SUMMARY AND CONCLUSION

In this work a methodology for designing ECM processes based on multiphysics simulation was presented. The data-driven approach utilizes a seamless flow of information on electrochemical material properties. It encompasses recording and processing process data as well as the development of interfaces between experiment, material database, and process simulation model. The methodology was applied exemplarily for the manufacturing process of a centrifugal impeller with a diameter of 14 mm of the nickel-based superalloy Inconel 713C via pulsed electrochemical machining with oscillating cathode. The characteristic material removal velocity and the sum of overpotentials as functions of the normal current density were calculated and effective dissolution volumes derived. Based on requirements for the process simulation, appropriate models using the FEM method were developed. After integrating the material data into the models, transient process simulations were conducted. Having set input parameters, current density distributions on the workpiece surface and resulting removal geometries were characterized. In addition, the reproduction accuracy of the cathode shape used in the PECM process was examined by evaluating lateral distances to the impeller blade.

ACKNOWLEDGMENTS

The authors acknowledge the support of the project “Saxon Alliance for Material- and Resource-Efficient Technologies (AMARETO)” (Project No 100291455) that is funded by the European Union (European Regional Development Fund) and by the Free State of Saxony. Open Access funding enabled and organized by ProjektDEAL

CONFLICT OF INTEREST

The authors declare no potential conflict of interests.

AUTHOR CONTRIBUTIONS

Sascha Loebel equally contributed to the conceptualization, data curation, formal analysis, investigation, validation, visualization, and writing the original draft, review, and editing. Mike Zinecker equally contributed to the methodology, supervision, and writing—review and editing. Philipp Steinert equally contributed to the funding acquisition, methodology, supervision, writing—review and editing. Andreas Schubert equally contributed to the funding acquisition, project administration, supervision, writing—review and editing.

Open Research

PEER REVIEW

The peer review history for this article is available at https://publons.com/publon/10.1002/eng2.12360.

PEER REVIEW INFORMATION

Engineering Reports thanks Ares Argelia Gomez Gallegos, Brian Skinn, and other anonymous reviewers for their contribution to the peer review of this work.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.