Modelling and Simulation of 3D electromagnetic metal forming processes

Unger, J.; Stiemer, Marcus; Schwarze, Marco; Svendsen, Bob; Blum, H.; Reese, Stefanie

doi:10.1007/s12289-008-0126-9

Cited by 3 publications

(2 citation statements)

References 8 publications

(8 reference statements)

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“…In this work, we investigate an inverse problem of determining the diffusion coefficient in a parabolic‐elliptic system from the final overspecified data. Problems of this type arise in a large field of engineering and industrial applications (see, eg, previous studies and references therein). One important application is from electromagnetic metal forming (see other studies).…”

Section: Introductionmentioning

confidence: 99%

An inverse problem of identifying the diffusion coefficient in a coupled parabolic‐elliptic system

Deng

Cai

Yang

2018

Math Methods in App Sciences

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This work studies a nonlinear inverse problem of reconstructing the diffusion coefficient in a parabolic-elliptic system using the final measurement data, which has important application in a large field of applied science. Being different from other works, which are governed by single partial differential equations, the underlying mathematical model in this paper is a coupled parabolic-elliptic system, which makes theoretical analysis rather difficult. On the basis of the optimal control framework, the identification problem is transformed into an optimization problem. Then the existence of the minimizer is proved, and the necessary condition that must be satisfied by the minimizer is also given. Since the optimal control problem is nonconvex, one may not expect a unique solution universally. However, the local uniqueness and stability of the minimizer are deduced in this paper. DENG ET AL 3415 coefficient problem of identification of the diffusion coefficient from the final overspecified data has been considered by several authors (see, for instance, Demir and Hasanov 22,23 ).Compared with other papers, which also deal with parameter identification problems, the results to be given in this paper have the following features. Firstly, the mathematical model proposed in this paper is a coupled parabolic-elliptic system rather than a single parabolic or elliptic equation. So this kind of problem indeed belongs to the boundary value problems of mixed type. Secondly, our task is to identify the diffusion coefficient in the coupled system, and this inverse problem generally belongs to the mathematical class of severely ill-posed problems. Furthermore, though the underlying mathematical model is linear, the corresponding inverse problem is completely nonlinear. Thirdly, since the exchange of matter and energy occurs on the interface, and after all, the connective condition is concerned with the diffusivity, the underlying mathematical model can be viewed as a nonlinear boundary-value problem combined with a nonlinear parameter-identification problem. From this point of view, such problem is rather difficult than those of single equation. Finally, the extra condition used in the paper is only imposed on the solution in the small domain rather than on the whole domain Ω. Because of the lack of measurement data, we shall carefully treat every integral to avoid using more information outside . In summary, the complexity of the inverse problem 1.2 to be introduced in following Section 3 is higher than those that are governed by single equations.In this work, we use an optimal control framework (see, eg, recent works 7,21,24,25 ) to discuss Problem 1.1 mainly from the theoretical analysis angle. As mentioned above, since the mathematical model in this paper is a coupled parabolic-elliptic system rather than the single parabolic equation in previous studies, 7,21,24,25 the major differences between them should be noted. It is well known that the properties of the solution for elliptic or parabolic system are quite different f...

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Section: Introductionmentioning

confidence: 99%

An inverse problem of identifying the diffusion coefficient in a coupled parabolic‐elliptic system

Deng

Cai

Yang

2018

Math Methods in App Sciences

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“…Electromagnetic metal forming (EMF) is an example of a high speed forming process that is determined by the dynamics of a coupled electromagnetic-mechanical system. A pulsed magnetic field is used for the high speed forming of metals with good electrical conductivity, such as aluminum or copper, whereby the magnetic field distribution is substantially influenced by the deformation of the sheet (3) . As a consequence, determination of the optimal magnetic field for forming, including the design of tool coils, cavities and power supply devices, requires further scientific research.…”

Section: Introductionmentioning

confidence: 99%

Mechanism Design of Magnetic-Assistance in Surface Finishing of End-Turning

2008

JAMDSM

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A new mechanism design using a magnetic force with high efficiency to assist discharging dregs out of the electrode gap during the electrochemical finishing on the surface finish process that follows end-turning is investigated in the current study. Through simple equipment attachment, magnetic-assistance during electrochemical finishing can follow the cutting process on the same machine. This process can be used for various end-turning operations. Among the factors affecting electrochemical finishing, the magnetic-assistance is primarily discussed. The experimental parameters are chemical composition and concentration of the electrolyte, flow rate of the electrolyte, initial gap width, current rating, on/off period of pulsed current, feed rate of workpiece, rotational speed of workpiece and electrode, magnetic strength, and distance between the two magnets. A higher current rating with magnetic-assistance reduces the finishing time and avoids the difficulty of dreg discharge. Providing a large magnetic field intensity or using a small distance between the two magnets produces a larger magnetic force and discharge ability and better finishing. A large rotational speed of the workpiece and electrode produces better finishing. Pulsed direct current can slightly promote the effect of electrochemical finishing, but the current rating needs to be increased. The magnetic-assistance during the electrochemical finishing process makes a great contribution in a short time by making the surface of the workpiece smooth and bright.

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Finite element modeling and experiment for behavior estimation of AlMn0.5Mg0.5 sheet during electromagnetic forming

Luca¹

2015

Transactions of Nonferrous Metals Society of China

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Modelling and Simulation of 3D electromagnetic metal forming processes

Cited by 3 publications

References 8 publications

An inverse problem of identifying the diffusion coefficient in a coupled parabolic‐elliptic system

An inverse problem of identifying the diffusion coefficient in a coupled parabolic‐elliptic system

Mechanism Design of Magnetic-Assistance in Surface Finishing of End-Turning

Finite element modeling and experiment for behavior estimation of AlMn0.5Mg0.5 sheet during electromagnetic forming

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