Three-dimensional tool design for steady-state electrochemical machining by continuous adjoint-based shape optimization

Lu, Jinming; Riedl, Gerwin; Kiniger, Bernhard; Werner, Ewald

doi:10.1016/j.ces.2013.11.040

Cited by 19 publications

(15 citation statements)

References 45 publications

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“…Such an inverse problem emerges in various branches of engineering, for instance, in electrical impedance tomography (EIT), electrical capacitance tomography, and electrochemical tool design. Solution strategies for the inverse problem can be found, e.g., in [4][5][6][7][8] for EIT, in [9] for electrical capacitance tomography, and in [10,11] for electrochemical tool design. The solution of the inverse problem is known to be ill posed and sensitive to small errors.…”

Section: Laplace Type Of Problemsmentioning

confidence: 99%

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Geometric solution strategy of Laplace problems with free boundary

Poutala

Tarhasaari

Kettunen

2015

Numerical Meth Engineering

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This paper introduces a geometric solution strategy for Laplace problems. Our main interest and emphasis is on efficient solution of the inverse problem with a boundary with Cauchy condition and with a free boundary. This type of problem is known to be sensitive to small errors. We start from the standard Laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another. This results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of Laplace's problem. Interpretation in terms of a geometric flow will provide us with stability considerations. The approach is demonstrated with several examples.Here, the Laplace problem has become formulated as a system of ODEs. The field lines 'begin' on @ and they are forced to 'end' to @ † with condition ' D 1. Evidently, such a solution strategy for the Laplace problem is not that competitive compared with finite element kind of methods. However, our aim is not to suggest a new approach to solve the standard Laplace problem but instead to highlight the common geometric properties behind Laplace type of boundary value problems. § An example of such routine is MATLAB function bvp4c. Figure 17. The modeled phone connector in cylindrical coordinates in meters. We assume that the field lines are tangential to the surface Z D 0, which corresponds to a case when two connectors glued together through this surface are electroplated simultaneously. Figure 18. The solved field lines and equipotential surfaces.

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Section: Laplace Type Of Problemsmentioning

confidence: 99%

“…Notice also that in the general case when @ is not an equipotential, then the ordinary differential Equations (11) and (12) should also be modified to keep track of the potential along each field line. For this reason, we replace (11) and (12)…”

mentioning

confidence: 99%

Geometric solution strategy of Laplace problems with free boundary

Poutala

Tarhasaari

Kettunen

2015

Numerical Meth Engineering

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“…Research efforts have been focused on ECM process modelling and simulation, primarily concerning tool geometry prediction and workpiece shape generation [3]. In the last ten years, the research in computer simulation and process optimisation techniques to predict and control the ECM process has increased by several factors [4][5][6]. Most simulation research uses COMSOL® [7] to deal with the multiphysics aspects of the process, which despite its many advantages, seems intrinsically limited in the accuracy of its results as its electrolyte flow solutions are based on finite element method (FEM) instead of its more adequate counterpart, the finite volume method (FVM), particularly suitable when dealing with computational fluid dynamics (CFD) [8].…”

Section: Introductionmentioning

confidence: 99%

Simulation of electrolyte behaviour of industrial electrochemical machining

Moro,

Sneddon,

Gomez-Gallegos

et al. 2023

Preprint

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Development of simulation models for electrochemical machining (ECM) is a widely researched challenge to avoid the traditional trial and error process, with potential resulting advantages in terms of time, cost, and sustainability. To this objective, it is crucial to utilise software that can accurately simulate the complex multiphysics aspects of ECM without being too computationally expensive and with a fast set up. This paper investigates an alternative finite element software to model ECM for industrial production. The specific features of this software make it attractive for industrial applications, and in this work, it is validated as suitable to model the electrolyte characteristics of flow rate and pressure. The model developed is the basis for determining local changes to electrolyte conductivity, current density, and efficiency as a function of gap spacing optimisation in order to achieve the desired geometry with dimensional accuracy and assure process repeatability for industrial production. Simulation results are in agreement with the experimental ECM carried out as part of this work.

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“…McClennan et al 11 described a numerical method for tool design for two-dimensional (2D) cases based on the electric field during the ECM process. Lu et al 12 provided a numerical method for solving the design problems of 2D and 3D tools in steady-state ECM. Ernst et al 13 proposed an inverse approach based on material-specific data to improve the adaptation of the cathode and shorten the development cycle, whereby the desired vane geometry was obtained.…”

Section: Introductionmentioning

confidence: 99%

Improvement of leading-edge accuracy by optimizing the cathode design plane in electrochemical machining of a twisted blade

Zhu

Yang

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part B:

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Cathode design plays an important role in the electrochemical machining of aero engine blades and is a core issue influencing machining accuracy. Precision electrochemical machining of the leading edge of a twisted blade is particularly difficult. To improve the electrochemical machining accuracy of the leading edge, this article deals with cathode design by optimizing the design plane based on the three-dimensional potential distribution in the inter-electrode gap. A mathematical model is established according to the electrochemical machining shaping law, and the formation of the blade leading edge is simulated using ANSYS. The simulation results show that the blade leading-edge profile obtained with the optimized planar cathode is more consistent with the blade model profile. The optimized planar cathode and a non-optimized planar cathode are designed and a series of corresponding electrochemical machining experiments is carried out. The experiments show that the electrochemical machining process is stable and that the surface quality near the leading edge of the samples is slightly better than that of the body surface. Compared with the non-optimized planar cathode, the allowance difference at the leading-edge vertex is decreased by 0.062 mm. Using the optimized planar cathode allows fabrication of a workpiece whose shape is similar to that of the designed twisted blade.

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Three-dimensional tool design for steady-state electrochemical machining by continuous adjoint-based shape optimization

Cited by 19 publications

References 45 publications

Geometric solution strategy of Laplace problems with free boundary

Geometric solution strategy of Laplace problems with free boundary

Simulation of electrolyte behaviour of industrial electrochemical machining

Improvement of leading-edge accuracy by optimizing the cathode design plane in electrochemical machining of a twisted blade

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