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FINITE ELEMENTS SOFTWARE FOR ELECTROMAGNETICS APPLIED TO ELECTRICAL ENGINEERING TRAINING. J. Mur, J.S. Artal, J. Letosa, A. Usón and M. Samplón Electrical Engineering Department

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Introduction Electromagnetics is difficult to learn by the student Show practical engineering examples related with the Maxwell equations Simplify the problem to avoid high-level mathematics But simplifications can lead to errors in industrial applications… Presentation of Electromagnetics theory in a more engaging manner, using a breakthrough technology as a bridge between the classical theoretical approach and real engineering applications

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Strategy to introduce the numerical simulation to the students (I) Study case: resistor with complex geometry solved with three different techniques Two of them are analytical solutions of simplified models of the resistor which can be easily solved by the student In the third one, the resistor was modelled and numerically solved using a commercial FES (Vector Fields) Graphics from FES help to understand the effect of small curvature radius in the inhomogeneous distribution of Joule power dissipation.

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Strategy to introduce the numerical simulation to the students (II) The numerical solution is compared with the results from the analytical methods. The student realize that suitable values can be obtained by analytic solutions, but better precision require sophisticated tools. Real photographs of temperature distribution during lab tests of a small automotive component. The student feels not being solving another academic problem.

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The simplified resistor: S-shape conductor sheet, with a negligible thickness, which can be considered to have only two dimensions :

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First approach (analytical) Compute the resistance as if it were a cable: Compute mean length Compute mean cross section Apply the formula of resistance of a cable (Cartesian symmetry)

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Second approach (analytical) I Split the piece in four independent resistors which can be connected in series :

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Second approach (II) The resistance of each zone can be easily computed independently:

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Third approach (numerical) I Numerical calculation of the electrical field by means of the finite element method. The visual graphs obtained help the student to discover some special features, that weren’t considered in the analytical solutions. Current density distribution at the simplified piece:

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Comparison of results for the simplified case While the first approximation predicts a constant value for | | and p in any point of the piece, the second one expects values which are dependant of the distance to the centre. The results of the second method are closer to the ones obtained by FEM, both for total values as resistance and for local values as and p. The error for the total resistance in the first method with respect to the FEM value is 4,3% and 1,2% in the second one. Note: the FEM is only used as a tool and its foundations are not explained to the students of a basic course.

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Sources of inaccuracy in the two analytical methods (I) Lines of show a transition in the zones of change of change of curvature. In the analytical solutions, this feature is not considered => the continuity law is not accomplished

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Sources of inaccuracy in the two analytical methods (II) The redistribution of current in the joins also lead to changes in equipotential lines. Graph of potential around the centre of the resistance

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Analysis of a real-case resistance The procedure to calculate the electric field and the electrical resistance is extended to cope with an industrial resistor. As the students have already understand the resolution procedure for a simplified case, they can focus in the special features of this case.

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Distribution of temperature of the resistance A high electrical current was applied to the resistor to heat it below 973 K. Colour of resistance is compared with the FEM solution. Radiation at that temperature becomes visible, and colour in each point of the surface gives an indication of the different temperature.

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Conclusions Introduction of realistic problem-solving techniques, combining basic mathematics theory and separation into elemental straightforward cases, stressing the physics behind. The accuracy of the solutions depends on several factors (temperature, skin effect...)

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