FIRETEANU Virgiliu 1, POPA Monica 2, PASCA Sorin 2, TARAS Petrica 1. 1 Introduction

Transcription

1 Transversal flux scanning induction heating of magnetic nonlinear steel sheets with temperature dependent properties FIRETEANU Virgiliu 1, POPA Monica 2, PASCA Sorin 2, TARAS Petrica 1 (1. EPM_NM Laboratory, POLITEHNICA University of Bucharest, Bucharest, Romania) (2. University of Oradea, Faculty of Electrical Engineering and Information Technology, Oradea, Romania) Abstract: This paper deals with finite element study of the scanning induction heating of the magnetic steel sheets in transversal flux devices, taking into account the magnetic nonlinearity and the dependence on temperature of steel properties. The decrease of the non-uniformity of the transversal profile of sheet heating as effect of the magnetic or electromagnetic screening of the sheet lateral sides was proved. Key words: scanning induction heating; transversal flux, magnetic sheets, temperature dependent properties 1 Introduction The main issue in the scanning induction heating of metallic sheets in transversal magnetic flux inductors is the transversal non-uniformity of the sheet heating [1 5]. Besides the inductors geometry, this non-uniformity depends on the sheet thickness and speed and on the properties of the sheet material. As continuation of [6], this paper studies the heating of magnetic steel sheets taking into account the magnetic non-linearity and the dependence on temperature of the steel properties. The transversal non-uniformity of heating and the effect of magnetic or electromagnetic screening of the lateral extremities of the sheets are studied. 2. Mathematical description of phenomena in transversal flux scanning induction heating The quasi-static harmonic electromagnetic field is defined in the solid conductor regions, with the resistivity ρ and magnetic permeability µ, by the complex electric vector potential T that gives the current density J = curlt, and by the complex scalar magnetic potential Φ. These two potentials satisfies the equations curl( ρ curl T) = jω B = j ωµ ( T grad Φ ), div T = 0, div[ µ ( T grad Φ )] = 0. In the magnetic cores, which are nonconductive and no-source regions with high magnetic permeability, the potential Φ satisfies the equation div( µ grad Φ ) = 0. In the non-conductive and non-magnetic regions the magnetic field can be expressed by the formula H = H0 gradφr. The field H0 generated in the free space by the inductor currents is given by the Biot-Savart formula. The second component of the magnetic field is defined by the reduced scalar magnetic potential Φr, which satisfies the equation div(µ0gradφr) = div(µ0h0). The coupling of formulations TΦ-Φ-Φr, known as scalar formulation of the electromagnetic field, is the most advantageous variant for the finite element computation of transversal flux devices. The temperature θ (r,t) of the sheet in transversal flux heating satisfies the equation γcd θ / dt = p + div( λ grad θ ), where p(r,t) = ρj 2 is the volume density of the induced power. The temperature maps in this paper corresponds the end of step-by-step in time domain studies, when the sheet temperature with respect the inductor is time independent. The step by step study of scanning induction heating updates each time step the geometry of the computation domain. Since the magnetic non-linearity and the temperature dependence of properties, Fig. 1, are considered, the sheet properties are also updated each time step.

2 The domain of the electromagnetic and thermal fields computation contains two linear magnetic cores, Fig. 2 - length L1 = 1175 mm, width 2b1 = 600 mm, thickness a1 = 235 mm and airgap 420 mm. The total current in each of four inductor coil is 18.9 ka. Fig. 1. Magnetic nonlinearity and temperature dependence of steel properties The heating of the sheet of thickness 2a and width 2b = 1000 mm starts at 20 C. The transversal non-uniformity of the sheet heating and the influence of the magnetic non-conductive screens, Fig. 2 (b) and of the electromagnetic screens, Fig. 2 (c) are further analyzed. (a) (b) (c) Fig. 2. The main regions of the computation domain 3. Results analysis The study of the influence of the sheet thickness and speed and of the sheet screening is based on the results of a series of applications with computation data in Table 1. Here, v is the sheet speed, P is the power induced in the sheet and Q is the reactive power of the heating device. The temperatures of the sheet at the end of heating θ1, θ 2 and θ 3 are in the middle point y1 = 0, at the transversal coordinate y2 = b/2 and at the sheet lateral limit y3 = b. Table 1. Computation data and main results Applic. f [Hz] v [m/s] 2a [mm] screens P [MW] Q [MVAr] θ1[ C] θ2[ C] θ3[ C] FEA no FEA no FEA no FEA Fig.2(b) FEA Fig.2(c) The maps of the volume density of the induced power, Fig. 3, and of the sheet temperature, Fig. 4, on the half of the sheet width in case FEA1, Table 1, are practically invariables on the sheet thickness. The maps of the steel sheet properties in Fig. 5 prove that temperature dependent models of material properties were considered. Fig. 3. Volume density of induced power, FEA1 Fig. 4. Map of sheet temperature, FEA1

3 Fig. 5. Maps of the magnetic permeability, resistivity, thermal conductivity and heat capacity, FEA1 The transversal profile of the induced power density integrated along the sheet, Fig. 6 (a), is practically similar with the transversal variation of the temperature at the end of heating, Fig. 6 (b). This property is valid for high values of sheet speed. The low speed applications proved that the temperature profile non uniformity is lower than the non uniformity of the induced power. In case of FEA1 application the temperature decreases with 26.6 % from the centre of the sheet to the lateral coordinate y = 300 mm. Starting from this point, the temperature increases to the lateral extremity of the sheet, where is 3.2 % higher than in the sheet centre. (a) Fig. 6. Transversal profiles of induced power (a) and of sheet temperature (b), FEA1 (b) In comparison with FEA1, in the application FEA2 the thickness of the sheet is eight times higher and the speed is lowered in the same ratio. The map of sheet temperature, Fig. 7, and the transversal profile of this temperature, Fig. 9, clearly reflects a very non-uniform heating pattern. An important part of the sheet has a temperature under the Curie point and the lateral extremities of the sheet are strongly overheated. For a sheet speed about three times lower - application FEA3, the mean value of the sheet temperature increases more than three times, Figs. 8, 10 and the transversal non-uniformity of the temperature decreases. With respect the sheet centre, the temperature is in this case 18 % lower at y2 = b/2 and increases only 22 % to the lateral extremities. Fig. 7. Map of the sheet temperature, FEA2 Fig. 8. Map of the sheet temperature, FEA3 Fig. 9. Transversal profile of sheet temperature, FEA2 Fig. 10. Transversal profile of sheet temperature, FEA3

4 Magnetic and electromagnetic screening of the sheet lateral extremities. The induced current paths are changed in the lateral zones of the sheet in the presence of magnetic screens, Fig. 2 (b), or of solid conductor screens, Fig. 2 (c). In both cases FEA4 and FEA5, Table 1, the screens and the inductor have the same length. As Figs. 11 and 13 shows, the magnetic screens are very efficient. The strong effect of induced current pushing to the sheet centre has as result an important decrease of the temperature at the lateral extremities of the sheet. The important currents induced in the two copper plates of the electromagnetic screens affect the paths of the currents induced in the steel sheet. The comparison of the results copper screens in Figs. 12 and 14 with the results no screens in Figs. 8 and 10 reflects the decrease of the current density to the lateral sheet extremities and the increase of this density around the lateral coordinate characterizing the inner borders of screens. Fig. 11. Map of the sheet temperature, FEA4 Fig. 12. Map of the sheet temperature, FEA5 Fig. 13. Transversal profile of sheet temperature, FEA4 Fig. 14. Transversal profile of sheet temperature, FEA5 4 Conclusions While important memory and computation time are required, the consideration of the magnetic non-linearity and of the temperature dependence of the magnetic steel sheets properties is possible and represents a necessity when the transversal flux induction heating starts at usual ambient temperature and stops over the Curie point. The transversal non-uniformity of the sheet heating in the basic transversal flux devices, Fig. 2 (a), can be unacceptable in some cases. It was proved in this paper the useful effect of magnetic and electromagnetic screening of the lateral sides of the sheet to be heated. Screens with variable cross section along the sheet will be considered in a future study related the optimal design of screens for minimal transversal non-uniformity of sheet heating. References: [1] V. Fireteanu, T. Tudorache: Formulations Magnetohydrodynamiques en FLUX3D appliqués a la Modelisation d un Inducteur a Flux Transverse, FLUX Magazine Revue, [2] T. Tudorache, V. Fireteanu, J.C. Bourhis: 3D Numerical Modeling of New Structures for Transverse Flux Heating of Metallic Sheets, Proc. of ISH 98, Padua, Italy, [3] V. Fireteanu, A. Geri, T. Tudorache, G.M. Veca: Transverse Flux Induction Heating: Comparison between Numerical Models and Experimental Validation, Proc. of HIS 01, Padua, Italy, [4] V. Fireteanu, Y. Neau, B. Paya, T. Tudorache: Parameters of Transversal Non-uniformity of Induced Power in Transverse Flux Induction Heating, Proc. of OPTIM 02, Brasov, Romania, [5] F. Dughiero, S. Lupi, A. Muhlbauer, A. Nikanorov: TFH Transverse Flux Induction Heating of Non-ferrous and Precious Metal Strips. Results of a EU Research Project, COMPEL Revue, Vol. 22, 2003.

5 [6] V. Fireteanu, M. Popa, P. Taras: Magnetoharmonic - transient thermal - translating motion finite element analysis of scanning induction heating of sheets in transversal flux, Proc. of ISEF2009, Arras, France, 2009