Electromagnetic Shaping Research Articles

Forming the inner flange of a rib by pulsed-magnetic field pressure

Electromagnetic flanging is a hole-protrusion of parts, a potential technology for forming sheet aluminum metal, provides rigidity, allows positioning and fixing. This paper describes the behavior of a workpiece formed by an electromagnetic flanging, in which the initial blank of annealed aluminum alloy D16AM with a circular precut hole is formed into the first part of the inner flanging (as the first operation of manufacturing a part of the rib). The purpose of this article is to assess the ability of electromagnetic shaping to produce flanges for aircraft components and to study the forming process using numerical simulation. Design of electromagnetic flanges with some elementary geometric shapes, the purpose of which is to clarify a few geometric defects encountered and to propose some solutions. The numerical model of this part was developed in the LS-DYNA computing environment. An example of the numerical simulation of electromagnetic forming of the inner flange of a rib with the obtained shape of the workpiece mesh using a clamp is given. To avoid corrugation at the corner of the workpiece, the magnetic force was increased by reducing the area of the coil adjacent to the corner.

Computation of Shape Derivatives in Electromagnetic Shaping by Algorithmic Differentiation

Computation of Shape Derivatives in Electromagnetic Shaping by Algorithmic Differentiation

Dual-band and ultra-broadband photonic spin-orbit interaction for electromagnetic shaping based on single-layer silicon metasurfaces

Achieving electromagnetic wave scattering manipulation in the multispectral and broad operation band has been a long pursuit in stealth applications. Here, we present an approach by using single-layer metasurfaces composed of space-variant amorphous silicon ridges tiled on a metallic mirror to generate high-efficiency dual-band and ultra-wideband photonic spin-orbit interaction and geometric phase. Two scattering engineered metasurfaces have been designed to reduce specular reflection; the first one can suppress both specular reflectances at 1.05–1.08 μm and 5–12 μm below 10%. The second one is designed for an ultra-broadband of 4.6–14 μm, which is actually implemented by cleverly connecting two bands of 4.6–6.1 μm and 6.1–14 μm. Furthermore, the presented structures exhibit low thermal emission at the same time due to the low absorption loss of silicon in the infrared spectrum, which can be regarded as an achievement of laser–infrared compatible camouflage. We believe the proposed strategy may open a new route to implement multispectral electromagnetic modulation and multiphysical engineering applications.

Combined process of hydroforming and electro hydraulic precision reshaping for aluminium alloy

Hydroforming has become an important process for aluminum alloy sheet forming. The advantages of this process include that it conserves mold material, energy and man power etc. However, at room temperature, due to aluminum alloy’s low plasticity and large springback after forming, the shape of the aluminum alloy parts will not meet the precision requirements, and therefore, reshaping the aluminum alloy parts to meet the precision requirements becomes a challenge. The plasticity of aluminum alloy can be improved at high speed deforming at room temperature [1]. Therefore, electromagnetic forming and electro hydraulic-forming become options. For the parts with simple shapes, it is possible to perform precise reforming with electromagnetic shaping. For the parts with complex shapes, electro hydraulic-forming becomes a better choice. Hence, combined process of hydroforming and electro hydraulic precision reshaping is a new leading process used for the precise forming of aluminum alloy sheet. This paper discusses the details of this combined process by introducing this process, analyzing the details of the parts formed, as well as providing evidence to support the superiority of this process.

Flows and mass transfers in two superimposed liquid layers in an induction furnace

In foundry, induction furnace is a well-known, clean, energy-efficient and well-controllable melting process. In order to improve its refining capacity, a salty or oxide liquid layer can be added at the surface of the liquid metal. This paper aims to simulate numerically mass transfers that occur at the liquid–liquid interface between these two liquid layers. To achieve this, the flows in both salty and metallic phases are calculated, taking into account all the present phenomena in the bulks (i.e. electromagnetic stirring, buoyancy, turbulence, heat transfer), as well as those at the interface (i.e. electromagnetic shaping, viscous shear driving). Comparison is made with literature experimental measurements.

Finite Element Method on Electromagnetic Shaping for Aluminum Alloy Sheet Parts

In this paper, the distribution of magnetic forces of uniform pressure coil and the electromagnetic shaping with die of aluminum alloy 1060 surface parts will be researched using the finite element method. The results show that: Uniform pressure coil can produce a uniform magnetic pressure on the sheet; The springback after electromagnetic aimed stamping is smaller than the springback after normal stamping; Before achieving the best results, with the discharge energy increases, springback will be smaller; with greater punch and die clearance, greater energy will be needed to achieve the best effect; Too large discharge energy will lead sheet bounce after punch, springback increases.

Inverse and direct magnetic shaping problems

In this work, we study the direct and inverse problems arising from electromagnetic shaping in applications such as continuous casting processes. The magnetic field produces a surface pressure which forces a molten metal to change its shape until it reaches an equilibrium state between the magnetic pressure and the surface tension. The arising direct problem is a free boundary problem which is to determine the shape of molten metals for a given magnetic field. On the other hand, the inverse problem is to seek a configuration of electromagnetic field generators (i.e. inductors) in order that molten metals have prescribed shapes. A level set method will be presented to determine an equilibrium shape formed by a given configuration of magnetic fields. Also a computational method as well as uniqueness results for the inverse problem will be introduced and illustrated with examples.

Suppression of Electromagnetically Induced Free‐Surface Instabilities in Liquid Metals

AbstractThe work presented is devoted to studies of foundations of the suppression techniques for electromagnetically induced instabilities of the free liquid metal surfaces. Such instabilities occur, for instance, in a number of technologies for requested refinement of materials like electron beam evaporation or levitation melting, in which the electromagnetic shaping technique is applied. The instability phenomenon in our case has following magnetohydrodynamic background. High‐frequency magnetic field causes Lorentz force density generation within so‐called skin‐layer in the liquid metal, which works as a surface pressure in turn. With increase of the electromagnetic pressure a destabilizing mechanism progresses within the liquid metal domain, which causes a bifurcation. In this paper we discuss application alternating magnetic fields to increase the bifurcation threshold by passive and active redistribution of the Lorentz force density in the near‐surface layers of the liquid metal domain. A novel stabilization system on the basis of a local electromagnetic influence on the liquid metal surface in the high frequency magnetic field is presented. The experimental results are discussed. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Inductor shape optimization for electromagnetic casting

The design of inductors in electromagnetic shaping of molten metals consists in looking for the position and the shape of a set of electric wires such that the induced electromagnetic field makes a given mass of liquid metal acquire a predefined shape. In this paper we formulate an inverse optimization problem where the position and shape of the inductors are defined by a set of design variables. In a first formulation of the inverse optimization problem we minimize the difference between the target and the equilibrium shapes while in a second approach we minimize the L 2 norm of a fictitious surface pressure that makes the target shape to be in mechanical equilibrium. Geometric constraints that prevent the inductors from penetrating the liquid metal are considered in both formulations. The optimization problems are solved using FAIPA, a line search interior-point algorithm for nonlinear optimization. Some examples are presented to show the effectiveness of the proposed approaches.

Control of free-surface instabilities during electromagnetic shaping of liquid metals

Control of free-surface instabilities during electromagnetic shaping of liquid metals

The inverse electromagnetic shaping problem

The inverse problem concerning electromagnetic casting of molten metals consists of looking for an electric current density distribution such that the induced electromagnetic field makes a given mass of liquid metal acquire a predefined shape. This problem is formulated here as an optimization problem where the positions of a finite set of inductors are the design variables. Two different formulations for this optimization problem for the two-dimensional case are proposed. The first one minimizes the difference between the target and the equilibrium shapes while the second approach minimizes the L2 norm of a fictitious surface pressure that makes the target shape to be in mechanical equilibrium. The optimization problems are solved using Feasible Arc Interior Point Algorithm, a line search interior-point algorithm for nonlinear optimization. Some examples are presented to show the effectiveness of the proposed approaches.

Radiationless electromagnetic interference shaping of evanescent cylindrical vector waves

Radiationless electromagnetic interference shaping of evanescent cylindrical vector waves

Wavelet-based boundary element methods for exterior electromagnetic shaping

In the present paper we survey on the application of shape optimization for exterior electromagnetic shaping in two and three dimensions. An energy variational approach is used to compute numerically free surfaces either of columns of molten metal or of liquid bubbles, levitating in the electromagnetic field. The cost functional and its shape gradient can be computed by boundary integrals. A wavelet-based fast boundary element method of optimal complexity is employed for the computation of the exterior magnetic field. We sketch both scalar and vector valued boundary update methods for gaining satisfactory flexibility for the class of shapes under consideration. Numerical results are carried out to illustrate our algorithms for solving such problems.

Free‐surface instabilities during electromagnetic shaping of liquid metals

AbstractElectromagnetic shaping of free surfaces of liquid metals is a well‐known EPM technology used in a couple of metallurgic processes like cold crucible melting, semi‐levitation, and electromagnetic slit sealing, among others. However, the stability of such free surfaces is the most important problem and stability control is crucial for success. Within this context we investigate experimentally the stability behavior of liquid metal free surfaces submitted to a high‐frequency magnetic field. In this case, the induced Lorentz forces act as an electromagnetic pressure directly on the free surface of the liquid met al. We consider three experimental model configurations: (i) Sessile liquid metal drop (ii) liquid metal ring, and (iii) liquid metal disc. In each model experiment, upon increasing the feeding current beyond a certain threshold value, IC, we observe that the initial surface contour becomes unstable resulting in (i) drop oscillations (ii) electromagnetic pinching and (iii) static disc deformations. In each configuration the threshold value depends in a similar manner on the frequency of the applied magnetic field. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Hölder continuity in a shape-optimization problem with perimeter

Here, we prove Hölder continuity of the state function in a shape-optimization problem arising, for instance, in the electromagnetic shaping of a liquid metal. The equilibrium state is obtained as minimizing the total energy, which is given in the form $$ \mathcal{E}_\lambda(\Omega) = J(\Omega) + P(\Omega) + \lambda ||\Omega| - m| , $$ where $\Omega$ is the domain occupied by the liquid, $P(\Omega)$ and $|\Omega|$ being respectively the perimeter and the Lebesgue measure of $\Omega$. We prove that the state function associated with the optimal shape is $\frac{1}{2}$-H\"older continuous, the main difficulty coming from the fact that the state function is not assumed to be non-negative.

Investigation on the Electromagnetic Contactless Shaping and Directional Solidification of Plates of Stainless Steel and Supperalloy under Vacuum

In this study, the distribution of electromagnetic pressure and the coupling between shaping force and temperature field are investigated in electromagnetic contactless shaping process for plates of stainless steel and superalloy. The distributions of electromagnetic pressure on outlines of melt cross sections are very different along sides than at corners. Under the vacuum, the cooling ability is not strong enough, and therefore the position of melt in inductor is too low, which causes an unbalance between electromagnetic pressure and static pressure. Experiments show the insert of a screen shell from the bottom of inductor can change the distribution of magnetic field very much and make a good and stable coupling between shaping force and temperature field.

The Electromagnetic Confinement and Shaping Process of Liquid Metal

The Electromagnetic Confinement and Shaping (EMCS) process is a crucibleless melting and mouldless shaping technology by alternating magnetic field. In this paper, stability of the shaping, effect factors of the electromagnetic force and the temperature field and the procedure of the EMCS process are systemically analyzed. The Results indicate that a good coupling of the temperature field and the electromagnetic force is important to stably shape for liquid metal, and the gravity force of liquid metal is more sensitive to change of the temperature (or the current through the inductor) than the electromagnetic force does above the melting point of the sample. Several stainless steel samples were obtained by EMCS process.

Exterior electromagnetic shaping using wavelet BEM

The present paper is devoted to exterior electromagnetic shaping in two dimensions. We model the conductors by regular densities which leads to a finite objective and allows a line-search. In order to compute the surface pressure we optimize an Augmented Lagrangian by a Newton method using a second-order approach for the Lagrange multiplier. Since the underlying state function satisfies an exterior boundary value problem, we compute first and second order derivatives of its boundary data by boundary integral equations which are numerically solved by a fast wavelet Galerkin scheme. Numerical results prove that we succeeded in finding a fast and robust algorithm for solving the considered class of problems. Copyright © 2004 John Wiley & Sons, Ltd.

Fast wavelet BEM for 3d electromagnetic shaping

In the present paper we combine an energy variational approach with shape optimization techniques to compute numerically free surfaces in electromagnetic shaping and levitation of liquid metals in three dimensions. Assuming the domains to be starshaped, the surfaces are represented via an ansatz by spherical harmonics, which generalizes the approximation by Fourier series in two dimensions. We will show that all ingredients of the shape optimization algorithm, particularly the shape gradient and the cost functional, can be computed by boundary integrals. A wavelet based fast boundary element method of optimal complexity is employed for the computation of the exterior magnetic field and its Neumann-to-Dirichlet map.

Shaping of sessile liquid metal drops using high-frequency magnetic fields

An analytical model for the electromagnetic shaping of sessile liquid metal drops in high-frequency magnetic fields is presented. We deal with both an infinitely long drop and a circular drop. In each case, the arrangement of drop and inductor is symmetric. Applying the skin depth approximation reduces the Lorentz forces induced in the liquid metal drop to a magnetic pressure on the drop surface. We neglect the coupling between drop contour and magnetic field distribution. In this case, the magnetic field can be calculated analytically applying the mirror-current method. Finally, we achieve an analytical solution of the static drop contours with the help of Green's functions. The theory is applied to three problems: (i) squeezing a drop while conserving its volume, (ii) drops with a fixed contact line, (iii) pumping up of drops. The results demonstrate the suitability of high-frequency magnetic fields for the shaping of liquid metals.