A Finite Element Simulation of Nanocrystalline Tape Wound Cores

Transcription

1 A Finite Element Simulation of Nanocrystalline Tape Wound Cores Dr. Christian Scharwitz, Dr. Holger Schwenk, Dr. Johannes Beichler, Werner Loges VACUUMSCHMELZE GmbH & Co. KG, Germany Abstract In this paper a method is presented for comparing the data of numerical simulations for magnetic nanocrystalline tape wound cores with experimental results. Usually, the Finite Element Method (FEM) is applied to calculate magnetic cores with nonconductive bulk models. However, nanocrystalline material is conductive and these models do not describe the electrical behavior. The electrical eddy current behavior of genuine nanocrystalline tape is determined by its thickness of only µm. Such thin structures cannot easily implemented in FEM calculations of cores. Normally the tape dimension in core simulations is in the range of millimeters. Thus, numerical results cannot be directly compared with measurements. The method for the comparison of FEM simulations to experimental results, which is presented here, relies on an elaborated scaling of calculated data. This improves the interpretation and understanding of the experimental data. 1. Introduction With growing computational power in the last decades numerical simulation techniques got an increasing impact on driving the development in several technological areas. Fig. 1. Typical pattern of an H-field configuration. In this work the method of Finite Elements (FEM) is used to deepen the insights in phenomena related to nanocrystalline tape wound cores. Such cores (e.g. of VITROPERM ) offer superior properties for several inductive applications (e.g. common mode chokes in a rather small design or medium frequency transformers featuring high energy efficiency [1]). Typically, the FEM is used to calculate magnetic cores with nonconductive bulk models and usual results are magnetic field configurations, as shown in Figure 1. However, since the nanocrystalline tape is conductive, eddy currents and the cut-off frequency play an important role for the description of its frequency behavior. A nonconductive bulk model cannot be used to 1471

2 sufficiently describe the behavior of nanocrystalline tape wound cores. A suitable characterization should include the calculation of electric fields and eddy currents. The major challenge for the investigation of eddy current characteristics is the thin thickness of the genuine nanocrystalline tape of only µm. The need to build a mesh for the FEM impedes the implementation of such thin tapes in the simulation geometry of magnetic cores. Depending on the applied computational power, the tape dimension in calculations is normally in the range of millimeters. Thus, numerical results cannot easily compared to measurements. Here, a method is presented to compare the results of FEM calculations to experimental data of nanocrystalline tape wound cores, which relies on an elaborated scaling of the calculated data. This improves the understanding and interpretation of experimental data and helps to further shape the advantages of nanocrystalline materials for future applications. 2. General Considerations 2.1. Model Implementation To set up the model and to perform the numerical calculations, a commercial software [2] is used. Figure 2 shows an example of a typical FEM model featuring a tape wound core with an outer diameter d o = 25 mm, an inner diameter of d i = 16 mm and a height of h = 10 mm. Fig. 2. Geometry to model a nanocrystalline tape wound core. The tape structure of the core is indicated by black lines on the upside surface of the core, with ten layers implemented. For various implemented core dimensions, models with three to ten ribbon layers are calculated. Then, the thinnest tape thickness in a model is in the order of half a millimeter. The expected wavelengths at the given frequencies f sim are long compared to the geometrical settings, hence, Maxwell equations are set up and solved in quasi-static approximation. The quantities of interest, e.g. the inductance L or the eddy current losses P e, may be evaluated from the calculated results by numerical integration through, (1). (2) The boundary conditions request a source current I Source in the copper winding and electrical insulation on the appropriate interfaces. Typical values for the material parameters can be found in corresponding literature, for example [3] or [4]. 1472

3 2.2. Model Verification and Model Suitability The FEM model is applied to simulate various characteristic curves. In order to test the implementation, the results are compared to calculations with the classical eddy current theory. In figure 3 the eddy current losses P e,sim are depicted, figure 4 shows the numerically calculated real and imaginary parts of the permeability. The graphs are plotted versus the frequency f sim. Fig. 3. Calculated eddy current losses versus frequency. Fig. 4. Calculated permeability curves versus frequency. The eddy current cut-off can be clearly identified by changes of the curves gradient [3]. Furthermore, curves, which are obtained analytically with the classical eddy current theory [3], are added as black, dashed lines. The numerical simulations match the classical calculations well, the principal usability of the model is proven. However, since the model set-up features tape thicknesses in the range of millimeters, f sim reaches up to 1 khz and the eddy current losses P e,sim are located in a range of up to merely 10 mw. For measurements of genuine cores with much thinner tapes higher values for the frequency f real and the eddy current losses P e,real can be expected. Usually, the frequency range of f real starts around 1 khz and measured eddy current losses P e,real typically range from around 10 mw to more than 100 W, depending on the applied excitation. In order to compare numerical results to experimental data, a method must be prepared to deal with this different range of values. Thus, an adaption of f sim to f real and P e,sim to P e,real is needed. Furthermore, measurements must be performed to get experimental result for this comparison. 1473

4 2.3. Experimental Investigations on Genuine Cores Each of the calculated characteristic curves, which are shown in figure 3 and 4, is also suitable for an experimental determination. The eddy current losses, which are shown in figure 3, describe the large-signal behavior of magnetic cores. They cannot be directly measured. The iron losses P Fe are determined for genuine cores with a measurement set-up according to [3]. Then, the standard method of separation [3] is applied to extract the eddy current losses. The complex parts of the permeability, which are depicted in figure 4, describe the small-signal behavior of magnetic cores. On genuine cores the measurements of the permeability curves are carried out with an impedance analyzer and, at small frequencies, the standard separation method is also applied to the imaginary parts of the permeability. Experimental results can be provided, which are appropriate for a comparison to numerical calculations. However, the model set-up in figure 2 features complete, perfect insulation between the tape layers. Complete insulation may be implemented in genuine cores with some more or less minor effort, but such an implementation leads to certain disadvantages for other core parameters (e.g. mechanical stress or a reduced filling factor). Thus, in most cases considerations on a balanced core characteristic lead to the decision to apply less elaborated insulation methods. The amount of insulation clearance in genuine cores is formed and controlled by a statistical equal distribution of partially thinner covered spots. Here, a parameter D E will indicate this distribution of spots, thus, the insulation coverage. Complete insulation with full coverage should be characterized with D E = 0, most genuine cores feature D E > 0. To use the FEM for an investigation of such genuine cores, the model set-up must be adapted to an insulation with clearances Model Adaption To achieve usability of the FEM model for a sufficient description of experimental results two challenges must be dealt with. One is the different insulation coverage in the model and in genuine cores. The other is the difference in the ranges of values for the frequencies and the eddy current losses. The difference in the insulation coverage can be overcome by an introduction of clearances in the surfaces, which represent the insulation in the model set-up. Such clearances are introduced in the model as a pattern of quadratic spots on two levels, as shown in figure 5. Fig. 5. Quadratic clearances in the electrical insulation. The parameter to quantify this pattern is the insulation coverage in the model. This is the ratio F of the spots surface to the complete insulation surface. A perfect insulation coverage features F = 0 and calculations with it fix the limiting values for the characteristics of tape wound cores. The differences in the range of values can be overcome by a scaling of the frequency f sim, which can be performed by normalizing. To execute the normalizing, let f n,sim be a frequency to normalize f sim and f n,real a frequency to normalize f real. Then, the normalized frequency f n is once, for the simulation and once "#,"# for the experimental data. Assembling the two equations and resolving for f real yields "# $ %, &'() $ %,*+,. (3) Likewise, the equation 2/ μ 1 2 μ , which describes the series equivalent resistance of an inductance [3], may be used to provide a similar formula for P e,real. Here, f is 1474

5 the frequency, N is the number of turns of the winding, A Fe is the core cross sectional area and l Fe is the mean iron path length. Inserting the equation of the series equivalent resistance in equation (2) and performing some mathematical operations, which are correspondent to the ones carried out for the derivation of equation (3), yields,"# $ %,&'() 7 &'() $ %,*+,,. (4) η real is the filling factor of the genuine core in the experiment, the respective cut-off frequencies are used as f n,sim and f n,real. 3. Results With the achievements gained by the model adaption, the FEM can be used for the description and interpretation of experimental data. This will be demonstrated with two examples Large-Signal and Small-Signal Behavior Calculations for large-signal data and small-signal data are shown in figure 3 and 4. A transfer of data between large-signal analysis and small-signal analysis is not simple at any rate. While comparing such data, one should take care to avoid misinterpretation, as shown here. In figure 6 numerically calculated eddy current losses are plotted together with experimental results for a toroidal core with d o = 40 mm. One of the numerical results is shown for an insulation featuring clearances with F = S and one is plotted for an insulation with F = L. L and S are real numbers, which are determined and fixed to fit the experiment. L is more than a factor of ten greater than S. The calculation is adapted to the measurement with the equations (3) and (4). Classical theory is applied for a tape of 18 µm thickness to calculate the eddy current cut-off frequency, which is used for f n,real. The frequency, which is used for f n,sim, is determined from a simulation with perfect insulation. Fig. 6. Calculated and measured eddy current losses. Below the eddy current cut-off, the curve for F = L fits the experimental results. In this frequency range the curve for F = S is too low. For the same toroidal core with d o = 40 mm measured permeability curves are plotted together with numerically calculated curves in figure 7. The numerical results are evaluated from the same simulation as the curves in figure 6. Again one calculated result is shown for an insulation with F = S and one for an insulation with F = L. The same frequencies are used for f n,sim and f n,real to adapt the calculation to the experiment with equation (3). Both calculated curves for the real parts of the permeability fit the experimental results well below the eddy cut-off frequency. For the imaginary parts, the curve for F = S fits the experimental results well, while the curve for F = L does not fit in this frequency range. 1475

6 Fig. 7. Calculated and measured permeability curves. Since the data in both figures apply to the same genuine core, it appears, that for small-signal analysis the amount of insulation coverage is larger than for large-signal analysis. The insulation clearance is composed of partially thinner covered spots and for small signals the thinner insulation cover persists. However, for larger signals, when higher electric fields drop across the tapes, discharges may break through at some of this points. Thus, in order to tune the working point to the desired amount of insulation coverage the targeted application characteristic has to be considered thoroughly Tuning the Insulation Coverage For most genuine cores the demand of a balanced performance results in an insulation coverage with clearances and an adjusted working point. Then, to tune the working point to an optimum, an estimation of the amount of insulation clearances in correlation to the expected performance would be extremely useful. This will be investigated here. Experimentally determined eddy current losses for a toroidal core with d o = 100 mm are plotted together with numerically calculated results in figure 8. Fig. 8. Measured and calculated eddy current losses. One of the numerical results is shown for a complete insulation with F = 0 and one is depicted for an insulation featuring clearances with F = X. X is a real numbers, which is fixed to fit the experiment. The adaption of the calculation to the measurement is performed with the equations (3) and (4). The frequency f n,real is calculated with the classical theory for a tape of 18 µm thickness, the frequency f n,sim is determined from the simulation with perfect insulation. 1476

7 Below the eddy current cut-off, the curve for F = 0 is too low, while the curve for F = X fits the experimental results. For this core the eddy current losses are a factor of around 1.75 higher than the calculated losses for a core with complete insulation coverage. To estimate and tune the insulation performance, the increase of the simulated P e,sim is compared to the reference F = 0 in figure 9. The model of the toroidal core with d o = 100 mm is used for the calculation and the edge length of the quadratic clearance areas in the insulation surfaces (see figure 5) is varied. The insulation coverage changes and the percentage rise of the eddy current loss is plotted over F. The point F = X is indicate with a vertical, dashed line. Fig. 9. Calculated eddy current losses versus insulation coverage. In the depicted range of F the eddy current loss shows a non-linear behavior. With an increasing insulation coverage a decrease of the eddy current loss can be seen, while the gradient of the decrease is continuously growing. For given genuine cores such curves may be used to estimate the expected eddy current losses. Then, for example, while adjusting the working point in the design process of a nanocrystalline tape wound core, the number of genuine samples may be reduced to an inevitable minimum. 4. Summary and Outlook In this paper FEM calculations of nanocrystalline tape wound cores are presented. The numerical results are tested by analytical solutions and, moreover, compared to experimental measurements. Two drawbacks for the comparison with the experiment are identified and solved. One is the insulation design in a genuine core, which is adjusted in order to feature a balanced core characteristic. It is overcome by the introduction of a spot pattern on the insulation surfaces in the model, to adapt the set-up. The other is the different range of values for the frequencies and the eddy current losses in simulation and experiment. This drawback results from limited computational power leading to different geometrical tape thicknesses in genuine cores and in model set-ups. It is resolved by the preparation of an elaborated scaling technique for the calculated data. After solving this challenges, the numerical simulation data fit the experimental results well. FEM calculations are made suitable to describe experiments and enhance the interpretation of data. This is demonstrated on two examples. With the enhancements, which are presented in this paper, the application of FEM calculations to nanocrystalline tape wound cores will lead to various improvements. For example, the product development can receive a fundamental strengthening, especially when challenges occur in a design process, which cannot be handled with established approaches. Moreover, the potential for a suitable description of experimental data will push basic developments, especially when the data interpretation is difficult or even impossible. One example may be the treatment of cut cores. The introduction of an air gap in the magnetic 1477

8 circuit leads to various advantages [3]. As an example, a calculation of the core from figure 1 is presented in figure 10, with an air gap introduced. Fig. 10. Typical pattern of an H-field configuration for a gapped cut core. A change in the magnetic field configuration can be observed and the field strength increases. Thus, an increased amount of magnetic energy is present in the magnetic circuit and enhances potential applications. The FEM is an appropriate and helpful tool for the investigation of nanocrystalline tape wound cores and will be applied for further development and optimization. 5. References [1] H. Schwenk, J. Beichler, W. Loges, C. Scharwitz, Actual and Future Developments of Nanocrystalline Magnetic Materials for Common Mode Chokes and Transformers, PCIM Europe 2015, Conference Proceedings [2] ( ) [3] R. Hilzinger, W. Rodewald, Magnetic Materials, Publics Publishing, ISBN [4] H. Stöcker, Taschenbuch der Physik, Verlag Harri Deutsch, ISBN