Int J Mater Form (2010) 3:205–208 DOI 10.1007/s12289-009-0669-4
ORIGINAL RESEARCH
Magnetic field enhancement in electromagnetic forming systems using anisotropic materials Alireza Karimi & Kaveh Niayesh & Mohammad Amin Bahmani
Received: 29 July 2009 / Accepted: 17 November 2009 / Published online: 5 December 2009 # Springer/ESAFORM 2009
Abstract Electromagnetic Forming (EMF) is a type of high rate forming which exploits pulsed power techniques to create high intensive pulsed magnetic fields to rapidly reshape metal parts. This technique is sometimes called magnetic pulse forming. In this technique, a metal workpiece is pushed to a die and formed by a pressure created using an intensive, transient magnetic field. This magnetic field is produced by passing a pulse of electric current through a forming coil in a pulsed power circuit. Application of field shapers has been proposed to enhance the magnetic fields and consequently to increase the applied magnetic pressure at some desired regions. In this paper, 3D Finite element simulations have been applied to study the magnetic field distribution during an electromagnetic forming process with anisotropic material. Anisotropic magnetic material is described using a permeability tensor. Elements of this tensor are obtained from different magnetization curves dependent on the direction of the magnetic field. It has been shown that application of anisotropic materials with appropriate lamination directions can result in an enhancement of the magnetic field at desired points as well as in better overall efficiencies. Keywords Electromagnetic . Forming . Anisotropic . Material . Lamination . Field . Shaper A. Karimi (*) : K. Niayesh : M. A. Bahmani School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran e-mail:
[email protected]
Introduction Electromagnetic forming (EMF) is a powerful and effective high-rate forming technique with a number of advantages in contrast with other methods of high rate in terms of cleanness, cost, efficiency and productivity [1]. This technique is sometimes called magnetic pulse forming. In this technique, a metal work-piece is pushed to a die and formed by a pressure created using an intensive, transient magnetic field. This magnetic field is produced by passing a pulse of electric current through a forming coil in a pulsed power circuit [2]. In this process created magnetic forces applied to work-piece are much like uniform, but in real applications, some regions of a workpiece have to be more deformed and therefore a much greater pressure has to be applied to these regions. The field shaper is used to concentrate the magnetic fields in desired points of a metal work piece during the forming process [3]. The same principle is used to focus magnetic field in some other applications like transmission electron microscope [4] and magnetic resonance imaging [5]. The detailed finite element simulations show that an enhancement of the magnetic field in the desired regions can be achieved using an appropriately designed field shaper [6]. In this paper, 3D finite element simulations are used to calculate the magnetic field distribution applied on the work piece during the electromagnetic forming process where the work piece is a magnetically anisotropic material. It is shown that in such configurations, higher magnetic field intensities at the desired points and higher overall efficiencies can be achieved.
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Basic working principle The main principle in all of the applications of this technique is the same. Depending on the geometry of the work-piece to be modified, the geometries of the coils and other parts of the electromagnetic forming system could be different in shape. In Fig. 1, a typical system adapted to the cylindrical workpieces symmetry is sketched schematically. It can be seen that an EMF system consists of an electrical pulsed power circuit responsible for generation of the pulse current flowing through the work coil, and some parts with pure mechanical functions like matrix, which is used to determine the desired shape of the final formed work-piece. Although field shapers seem to be also a mechanical part, they play an important role in linking the electrical pulse system to the mechanical parts by modifying the magnetic field distribution generated on the work-piece [3, 6]. In this process, the electrical energy stored in capacitor bank, discharges in the coil while the switch closes cause to flow a pulsed current with significant magnitude (about several tens to hundreds kilo amperes) and high frequency (normally between 10 kHz to 100 kHz) into the coil. This current produces an intensive and transient magnetic field around the coil. As the result of the interaction of the induced currents in the surface of the work piece with the applied field, a magnetic pressure exerted on the work piece and it is consequently thrown to the die (matrix). The magnetic field distribution used to calculate the applied pressure on the workpiece is simulated by solving the Eq. 1 with finite element method. 1 ~ r A ¼ Jtot ð1Þ m
Fig. 2 Magnetic flux density distribution near work-piece in a configuration with a laminated steel work piece at the time corresponding to the first peak of the current
In this equation, ~ A is magnetic vector potential defined ~ are the using ~ B ¼ r~ A and ~ B ¼ mH, where ~ B and H magnetic flux density and the magnetic field intensity, * respectively. The total current density J contains tot displacement currents, eddy currents, conduction currents and convective currents. In case of anisotropic materials, ~ can be expressed as: the relationship between ~ B and H ~ ~ B ¼ mH where [μ] is the permeability tensor. In the present paper, the method proposed in [7] is used to simulate the magnetic field distribution in presence of anisotropic materials.
Simulation results and discussion The effect of using anisotropic material is analyzed in this section. For this purpose, the governing equations are solved using the finite element method in an EMF system as shown in Fig. 1. The high current pulse flowing through the work coil, which is responsible for the magnetic field generation, is assumed to be as follows: iðtÞ ¼ 50000 e5000t Sin ð60000 t Þ
Fig. 1 An EMF system with field shaper for compressing cylindrical work pieces
In these simulations, the work coil is made of copper, the field shaper of copper beryllium and the work piece of laminated steel. The gas filling the region between solids is air. Because of cylindrical symmetry only two permeability values µr and µz (or two B-H curves in r and z directions) are used to describe the magnetic anisotropic characteristics
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of the work piece. Figure 2 shows the magnetic flux density distribution around the anisotropic work piece at the time corresponding to the first peak of the current. It can be seen that a confinement of the magnetic field on the protrusion of the field shaper can be achieved. In Fig. 3, the maximum magnetic flux density and the maximum flux density in z direction near the surface of the field shaper are shown for different µr / µz ratios. As it can be seen, in cases where the permeability in r direction is greater, the magnetic flux density in the desired region which is also in r direction is amplified, but the magnetic flux density in z-direction is reduced. To be able to apply these results to the laminated steel, one has to take the dependence of the permeability of the laminated material in different directions on the lamination (rolling) direction. For the materials considered here, the permeability of the laminated material has its maximum in the lamination direction, decreases with the angle between the applied magnetic field and the lamination direction, reaches its minimum at the angels of about 55° and increases by further increasing the angle between the applied field and the lamination direction, as shown in Fig. 4, where reluctivity v is defined as v ¼ m1 . Therefore based on the simulation results shown in Fig. 3, the maximum magnetic flux density reaches its minimum at the lamination directions with an angle of about 55° in respect to the r-direction. Figure 5 shows the maximum magnetic flux density and the maximum magnetic flux density in z direction near the surface of the field shaper for laminated steel with different lamination directions in respect to the r-direction. As it can be seen, the magnetic flux density at the anisotropic work piece has much greater values compared to the configuration with isotropic work piece. It must be noted that the lamination direction of the steel plays a very important role in the magnetic field enhancement. In
Fig. 3 Maximum magnetic field near the work piece and the maximum magnetic field in z-direction near the field shaper in EMF system with work pieces of anisotropic materials with different µr / µz ratios
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Fig. 4 Reluctivity vs. Magnetic flux density for the laminated steel used as work piece in different lamination directions
some cases, where the relative permeability in z direction is higher than that in r direction, e.g. for the laminated steel characterized in Fig. 3 when the angle between the lamination direction and the r-direction lies in the range of 30° to 75°, the application of the anisotropic materials in electromagnetic forming systems can even lead to a reduction of the magnetic flux density in the desired region. Considering the fact that the induced surface currents on the field shaper are proportional to the tangential component of the magnetic field in z-direction, it can be seen that with appropriately laminated steel as work piece, it is possible to reduce the eddy currents on the surface of the field shaper and in this way to increase the overall efficiency of the system. For the configuration with anisotropic material with B-H curves shown in Fig. 4, a maximum 20% reduction in
Fig. 5 Maximum magnetic field near the work piece and in zdirection near the field shaper with the steel workpiece laminated steel with different lamination direction in r-direction
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Ohmic losses in field shaper can be achieved in comparison to the case with isotropic material.
Conclusion In this paper, 3-D finite element simulations have been applied to study the influence of the application of anisotropic materials on the magnetic flux density distribution in electromagnetic forming systems. The simulation results indicate that with appropriately selected anisotropic materials, an enhancement of the magnetic flux density at the desired points as well as a reduction of the losses in field shaper can be achieved. The direction of lamination of the work piece (permeability tensor) plays a significant role, so that with not appropriately selected lamination directions, even a reduction in magnetic field as well as in overall efficiency of the system is resulted.
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References 1. Oliveira DA, Warwick MJ (2003) Electromagnetic forming of aluminum Alloy sheet. J Phys IV 110:293–298 2. Batygin YV, Daehn GSK (1999) The pulse magnetic fields for progressive technologies, Columbus 3. Haiping Yu, Li C, Zhao Z, Li Z (2005) Effects of field- shaper on magnetic pressure in electromagnetic forming. J Mater Process Tech 168:245–249 4. Preikszas D, Steigerwald M, Hoffrogge P, Gnauck P United States Patent 6855938 5. Ryu JS, Yao Y, Koh CS, Shin YJ (2006) 3-D optimal shape design of pole piece in permanent magnet MRI using parameterized nonlinear design sensitivity analysis. IEEE Trans Magn 42 (4):1351–1354 6. Bahmani MA, Niayesh K, Karimi A “3-D simulation of the influence of field shaper on the magnetic field distribution in electromagnetic forming,” to be published in Journal of material processing technology 7. Lin D, Zhou P, Badics Z, Fu WN, Chen QM, Cendes ZJ (2006) A new nonlinear anisotropic model for soft magnetic material. IEEE Trans Magn 42(4):963–966
