03 Icee Fem for Electromagnetics

8/3/2019 03 Icee Fem for Electromagnetics

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FINITE ELEMENTS SOFTWAREFOR ELECTROMAGNETICSAPPLIED TO ELECTRICAL

ENGINEERING TRAINING.

J. Mur, J.S. Artal, J. Letosa, A. Usn

and M. SamplnElectrical Engineering Department


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Introduction

Electromagnetics is difficult to learn by thestudent

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 abridge between the classical theoretical approach and realengineering applications


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Strategy to introduce the numerical

simulation to the students (I)Study case: resistor with complex geometrysolved with three different techniques

Two of them are analytical solutions of simplified

models of the resistor which can be easily solvedby 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 inhomogeneousdistribution of Joule power dissipation.


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Strategy to introduce the numerical

simulation to the students (II)The numerical solution is compared withthe results from the analytical methods. The student realize that suitable values can be

obtained by analytic solutions, but better precisionrequire sophisticated tools.

Real photographs of temperaturedistribution during lab tests of a smallautomotive component. The student feels not being solving another academic

problem.


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The simplified resistor:S-shape conductor sheet, with a negligiblethickness, which can be considered to have onlytwo dimensions :

ba

V0

V0

Conductivity W

thickness h

c = a = 11 mm

b = 4 mm

V = 1,515 10-3; m= 0.1 mm

V0 = 15 V

c

c


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First approach (analytical)Compute the resistance as if it were acable:

Compute mean length Compute mean cross section

Apply the formula of resistance of a cable(Cartesian symmetry)

section

2 22 2 2

( - ) ( - )

mean mean

a bc

l r cR

S a b h a b h

TT

V V V

! ! !


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Second approach (analytical) I

Split the piece in four independentresistors which can be connected in

series :

R1

R2

R2

R1

R2

R1

R2

R1


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Second approach (II)

The resistance of each zone can beeasily computed independently:

Straight zone Circle

Resistance, Rsection ( )

meanl c

RS a b h

V V! !

ln

Rah

b

TV!

Current density, J

section

( )

I IJ

S a b h! !

ln

IJ

ar hb

!

Power density2

p J E J V! !

2 2

2 2 2

section( )

I Ip

a b hSV V! !

2

22 2 ln

Ipar h

b

V! -


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Third approach (numerical) INumerical calculation of the electrical fieldby means of the finite element method. The visual graphs obtained help the student to discover

some special features, that werent considered in theanalytical solutions.

Current densitydistribution atthe simplifiedpiece:


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Comparison of results for thesimplified case

While the first approximation predicts a constantvalue for | | and p in any point of the piece, thesecond one expects values which are dependant

of the distance to the centre.The results of the second method are closer tothe ones obtained by FEM, both for total valuesas resistance and for local values as and p. The

error for the total resistance in the first methodwith 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.

JT

JT


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Sources of inaccuracy in the twoanalytical methods (I)

Lines of show a transition in the zones of change of change of curvature.

N = T/2

N = T junction

at N = 0

J

In the analyticalsolutions, thisfeature is not

considered => thecontinuity law isnot accomplished

JT


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Sources of inaccuracy in the twoanalytical methods (II)

The redistribution of current in the joinsalso lead to changes in equipotential lines.

Graph of potential around the centre of the resistance


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Analysis of a real-case resistanceThe procedure to calculate the electric fieldand the electrical resistance is extended tocope with an industrial resistor. As the students have already understand the

resolution procedure for a simplified case, they canfocus in the special features of this case.


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Distribution of temperature of theresistanceA high electrical current was applied to the resistorto heat it below 973 K. Colour of resistance iscompared with the FEM solution.

Radiation at that temperature becomes visible, andcolour in each point of the surface gives an indication ofthe different temperature.


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ConclusionsIntroduction of realistic problem-solvingtechniques, combining basic mathematicstheory and separation into elementalstraightforward cases, stressing the physicsbehind.

The accuracy of the solutions depends on

several factors (temperature, skin effect...)


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Questions?

03 Icee Fem for Electromagnetics

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