Heating And Cooling Studies In Electromagnetic Forming Process Using Flux Multiphysics Models - Petrica Taras

Heating and Cooling Studies in Electromagnetic Forming Process using FLUX Multiphysics Models Petrica TARAS POLITEHNICA University of Bucharest, EPM_NM Laboratory 313 Splaiul Independentei, 060042, Bucharest, Romania [email protected] Abstract : The paper studies the transient heating of the forming coil and workpiece during the electromagnetic forming process and the cooling process that follows, when the heat sources vanish. The study uses a multiphysics coupling finite element model consisting in step by step in time evaluation of the transient electromagnetic and temperature fields. All simulations take in account the temperature dependence of all electromagnetic and thermal material properties. The results of the 2D and 3D finite element models are compared.

I. Introduction In an electromagnetic forming (EMF) process, the workpiece is forced into a desired shape by a magnetic field. The whole process implies electromagnetic, mechanical and thermal coupled phenomena. While studies regarding the first two coupled phenomena are common in the technical literature [1], [2], the thermal process was never studied. This paper offers a view of the temperature levels reached in the aluminum workpiece and copper coil, during the EMF process. It is important to have an estimation of the thermal phenomena, to see if the temperature dependent material properties should be taken into account or not. This purpose is achieved using the transient electromagnetic – transient thermal coupling multiphysics feature of FLUX® software [3]. In principle, for the process of heating, the sources of heating computed in the transient electromagnetic part of the model are exported to the thermal part of the problem; the thermal part of the model exports the temperature data on the required regions thus allowing for the electromagnetic part to update its material properties on a temperature information basis. For the process of cooling, only the thermal part of the multiphysics coupling is considered, the magnetic part being no longer required (the heating source is set to zero). The 2D multiphysics finite element model uses the “solver beta” feature of FLUX® software which basically implies solving the 2D finite element model with the FLUX 3D Solver. Through this feature, the FLUX 3D module multiphysics capability is extended to the 2D models. The entire process is piloted using Python scripts.

II. Multiphysics coupling finite element models description The study of the transient electromagnetic – transient heating coupling considers a four turns forming coil powered up by a 50 µF capacitor bank, charged at 10 kV initial voltage. The coil will act through the magnetic field upon an aluminum workpiece, thus bending it. 2D and 3D finite element studies are carried out. The 2D computation domain, Fig. 1, is of axisymmetric type, while the 3D computation domain, Fig. 2, takes into account the real geometry of the forming coil. The mesh grid for both models is shown in Fig. 3.

Symmetry axis

AIR

WORKPIECE

COIL

Fig. 1 The 2D computation domain

Fig. 2 The 3D computation domain

Fig. 3 The mesh on WORKPIECE and COIL regions (left – 2D model; right – 3D model)

The preliminary simulations show that after 100 µs, the electric current in the capacitor bank and the forming coil is practically zero and that, the cooling process of coil and workpiece begin. This process is studied over a time interval of 10 s. According to the reference [4], the workpiece motion during the EMF process has a negligible influence on the instantaneous current in the coil and respectively on the current induced in the workpiece. As a consequence the workpiece motion is not taken into account in this paper. To see the insulation effect on the heating and cooling, a region with the appropriate physical properties is added. The INSULATION region acts as support for the coil and provides both thermal and electrical insulation. The 2D computation domain, Fig. 4, shows the INSULATION region wrapped around the forming coil.

INSULATION region Fig. 4 The 2D computation domain with the INSULATION region added

The coupled electromagnetic and thermal phenomena are described by a system of equations formed with Maxwell and Fourier equations. The equations coefficients are temperature dependable. The computation domain of these equations consists of four distinctive physical regions (Figs 1-2, 4), for both 2D and 3D model version. These regions are:



AIR, a nonmagnetic (µr = 1) and nonconductive (σ = 0 S/m) region without thermal properties, were µr is the relative magnetic permeability and σ is the electric conductivity;  COIL, a solid conductor region, connected in a circuit in parallel with a capacitor bank. The COIL region material (copper) has linear temperature dependent properties like the electric resistivity ρ(T), the thermal conductivity k(T) and the volumetric heat capacity γCp(T);  WORKPIECE is a solid conductor region. However, unlike the COIL region, SHEET region does not require a circuit coupling. This region’s material (aluminum) has also linear temperature dependent properties (electric resistivity – ρ(T); thermal conductivity – k(T) and volumetric heat capacity – γCp(T));  during the insulation effect study, a nonmagnetic and nonconductive region (INSULATION) is added in the computation domain. The ceramic class material of the insulation has linear thermal properties, like the thermal conductivity k(T) and volumetric heat capacity (γCp(T)). However the thermal conductivity has a subunitary value for the considered temperature range and it will remain so on the studied temperature interval. The COIL and SHEET boundary surfaces are thermal transfer surfaces (by convection and radiation). These surfaces have a convection coefficient αc = 20 W/m/C which corresponds to a natural flow of the air near these surfaces. The thermal radiation coefficient for these surfaces has a ε = 0.9 value. In the insulation effect study, the common surfaces between the COIL / INSULATION and WORKPIECE / INSULATION are in direct thermal contact; therefore, the thermal exchange surfaces are the exterior of the INSULATION region and what is left in contact with air of the WORKPIECE region. The initial conditions are no electromagnetic field and ambient temperature everywhere in the computation domains.

III. A comparative study between the 2D and 3D models (no insulation present) Among the results of main interest for the comparison are the local temperature time variations, the time variation of the coil current and the active power through coil and workpiece. Fig. 4 shows the current density color shade, when the current through coil reaches it maximum value, in a single turn of the forming coil for both versions.

Fig. 5 The current density on a turn of the forming coil at tmax = 5 µs (on the left side– 2D model; on the right – 3D model)

Fig. 5 shows an inappropriate mesh grid on the COIL region with respect to the physical phenomena (skin effect) for the 3D model. In Fig. 6 a comparison is made between the current through forming coil obtained with 2D and 3D models. The obtained results are very close to each other.

Fig. 6 Discharge current comparison (left – 2D model; right – 3D model)

The results in Figs 7-8 show the active power time variation for the COIL and WORKPIECE regions.

Fig. 7 Active power variation through coil

Fig. 8 Active power variation through workpiece

While the 3D model obtained current and WORKPIECE induced active power, are in agreement to the results obtained with the 2D model version, the COIL active power is not. The COIL power computed with the 3D model has lower values then the one obtained with 2D model version (Fig. 7). This suggests that the local temperatures reached on the 3D model COIL region will be smaller than their counterparts from the 2D model. Fig. 9 shows the temperature color shade at the end of the heating process on regions COIL and WORKPIECE for 3D model.

Fig. 9 Temperature color shade on COIL and WORKPIECE at the heating process end (3D model)

In Figs 10-13, local time variations of the temperature are illustrated during the heating and the cooling process. In Fig. 9 are shown the points in which the local temperature time variation is computed for both coil and workpiece regions. The local computation points for the WORKPIECE region lie on the workpiece lower surface, just above their counterparts from the COIL region.

Fig. 10 Local temperature time variation on coil (2D model)

Fig. 11 Local temperature time variation on coil (3D model)

The local temperature time variations on COIL region differs between the 2D (Fig. 10) and 3D (Fig. 11) models with up to 70 % on corresponding points. On the WORKPIECE region however the results obtained with the 2D and the 3D model are very close to each other (Figs 12-13). This is a logic consequence of a similar WORKPIECE induced power time variation in the 2D/3D models. Therefore the obtained results are satisfactory at the level of the workpiece; however at the forming coil level they are not.

Fig. 12 Local temperature time variation on workpiece (2D model)

Fig. 13 Local temperature time variation on workpiece (3D model)

IV. The insulation effect (2D model comparison) If the thermal region INSULATION is included in the computation domain (Fig. 4), the heating process is affected. On the COIL region, the local temperature decreases with up to 12 % (Fig. 14)

while on the WORKPIECE the temperature decreases with up to 17 % (Fig. 15) with respect to the no insulation models. Therefore the INSULATION region affects the heating process, by absorbing the heat from the COIL and WORKPIECE regions. The 17% decrease of the local temperature on the WORKPIECE is not accurate since during the EMF process, the WORKPIECE is displaced away from the INSULATION region.

Fig. 14 Local temperature time variation on coil

Fig. 15 Local temperature time variation on workpiece

(2D Model with INSULATION region added)

(2D Model with INSULATION region added)

V. Conclusions According to the obtained results the local temperature of a forming coil can reach during the EMF process important values. This must be taken into account when the insulation material is chosen. The coil requires 100 ms to reach the ambient temperature during the cooling process (no matter if the insulation is present or not). This allows the implementation of this particular EMF configuration in a production line; however the capacitor bank requires a few seconds for recharging, thus zeroing the fast cooling process of the coil. While a resource hog, the 3D model brings little benefits in terms of results for this particular situation. The INSULATION region affects the heating and cooling process by absorbing heat from the COIL region. The introduction of this region into the computation domain is a must.

VI. References [1] N. Takatsu, M. Kato, K. Sato and T. Tobe, “High-speed forming of metal sheets by electromagnetic force”, JSME International Journal, Series III, Vol. 31, No. 1, The Japan Society of Mechanical Engineers, 1988, pp. 142-148. [2] J.P.M. Correia, M.A. Siddiqui, S. Ahzi, S. Belouettar, R. Davies, “A simple model to simulate electromagnetic sheet free bulging process”, International Journal of Mechanical Science, Elsevier, 2008, pp. 1466-1475. [3] FLUX 10 “3D Application conduction heating with multiphysics coupling” tutorial, www.cedrat.com [4] T.E. Manea, M.D. Verweij, H. Blok (2002), “The importance of velocity term in the electromagnetic forming process”, Proc. of XXVIIth General Assembly of the Int. Union of Radio, URSI 2002, Maastricht, pp. 112-115.