Lecture 3. - Revision history

Marcsa at 18:52, 28 January 2020

2020-01-28T18:52:10Z

2019-11-26T15:31:39Z

‎Magnetic Vector Potential and Electric Scalar Potential

2019-03-27T19:43:55Z

‎Coupled Finite Element Method

2019-03-27T19:41:44Z

‎Coupled Finite Element Method

2019-03-27T19:38:34Z

‎Time-Dependent Magnetic Field

2019-03-27T19:17:22Z

2019-03-19T06:36:30Z

‎Electric Circuit Coupling

2019-03-19T06:34:27Z

2019-03-18T21:12:28Z

‎Rigid Body Motion

2019-03-18T20:47:16Z

‎Quasistatic Electromagnetic Field

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 | width=50% |
 '''Instructor'''
-* Dániel Marcsa (lecturer)
+* [http://wiki.maxwell.sze.hu/index.php/Marcsa Dániel Marcsa] (lecturer)
 * Lectures: Monday, 14:50 - 16:25 (D201), 16:30 - 17:15 (D105)
 * Office hours: by request

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 Substituting expression of <math>\vec{B}</math> and <math>\vec{E}</math> into Faraday's law leads to the partial differential equation
-::<math>\nabla\times\left(\frac{1}{\mu}\nabla\times\vec{A}\right)=\vec{J}_{S}-\frac{\partial\vec{A}}{\partial t}-\nabla V+\sigma\vec{v}\times\nabla\times\vec{A}</math>.
+::<math>\nabla\times\left(\frac{1}{\mu}\nabla\times\vec{A}\right)=\vec{J}_{S}-\sigma\frac{\partial\vec{A}}{\partial t}-\sigma\nabla V+\sigma\vec{v}\times\nabla\times\vec{A}</math>.
 If the velocity is a priori known, the additional term remains linear but will lead to a so-called convective term. Therefore, numerical computation will need some upwind technique for stability reasons.

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 |}
-== Coupled Finite Element Method ==
+== Coupled Finite Element Method<ref>[https://www.springer.com/gp/book/9783642090516 M. Kaltenbacher - Numerical Simulation of Mechatronic Sensors and Actuators, Springer-Verlag Berlin Heidelberg, 2007.]</ref> ==
 <blockquote>
 === Rigid Body Motion<ref>[http://maxwell.sze.hu/~marcsa/docs/Daniel-MarcsaBScThesis.pdf D. Marcsa - Induction Motors Simulation by Finite Element Method and Different Potential Formulations with Motion Voltage Term, B.Sc. Thesis, University of Győr, 2008.]</ref> ===

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 == Coupled Finite Element Method ==
 <blockquote>
-=== Rigid Body Motion ===
+=== Rigid Body Motion<ref>[http://maxwell.sze.hu/~marcsa/docs/Daniel-MarcsaBScThesis.pdf D. Marcsa - Induction Motors Simulation by Finite Element Method and Different Potential Formulations with Motion Voltage Term, B.Sc. Thesis, University of Győr, 2008.]</ref> ===
 In electromechanical systems (electric machines, actuators, etc.), the structure is subject to a rigid motion by means of the force and torque. Thus, the change on the geometry, in turn, may strongly influence the magnetic field. Further, due to the motion and time-varying magnetic field, eddy currents are generated in the conducting parts (where <math>\sigma\neq 0</math>). The so-called induced current (eddy current) in an electrically conductive body

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 </blockquote>
-== Time-Dependent Magnetic Field ==
+== Time-Dependent Magnetic Field<ref>[http://maxwell.sze.hu/docs/C4.pdf M. Kuczmann - Potential Formulations in Magnetics Applying the Finite Element Method, Lecture Note, University of Győr, 2009.]</ref> ==
 <blockquote>
 The most important case for electromagnetic equipment (sensors, actuators, motors, etc.) is the quasistatic case often referred to as the eddy current or magnetodynamic case. For quasistatic electromagnetic field, we can neglect the displacement current density term <math>\partial \vec{D}/\partial t</math>, which gives Maxwell's equations to the following form

← Older revision		Revision as of 19:17, 27 March 2019
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	where <math>\mathbf{A}</math> is the vector of unknown magnetic vector potential, <math>\mathbf{I}</math> is the vector of unknown coil currents and <math>\mathbf{U}</math> is the vector of voltage sources. <math>\mathbf{S}</math> is the matrix related to <math>\mu</math> permeability, <math>\mathbf{N}</math> is the matrix related to <math>\sigma</math> conductivity. <math>\mathbf{P}</math> is the matrix related to the current in coil and <math>\mathbf{Q}</math> is the matrix related to the coil flux linkage. <math>\mathbf{R}</math> is the diagonal matrix of coils DC resistance and <math>\mathbf{U}</math> is the vector of voltage sources.		where <math>\mathbf{A}</math> is the vector of unknown magnetic vector potential, <math>\mathbf{I}</math> is the vector of unknown coil currents and <math>\mathbf{U}</math> is the vector of voltage sources. <math>\mathbf{S}</math> is the matrix related to <math>\mu</math> permeability, <math>\mathbf{N}</math> is the matrix related to <math>\sigma</math> conductivity. <math>\mathbf{P}</math> is the matrix related to the current in coil and <math>\mathbf{Q}</math> is the matrix related to the coil flux linkage. <math>\mathbf{R}</math> is the diagonal matrix of coils DC resistance and <math>\mathbf{U}</math> is the vector of voltage sources.
−
	</blockquote>		</blockquote>

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 where <math>u(t)</math> is the voltage on the coil, <math>R</math> and <math>N</math> are the coil resistance and the number of turns, <math>\Phi(t)</math> is the magnetic flux [Wb/m] generated in the solution domain and linked by the coil.
-The equation of strongly coupled case is
+Finally, the matrix equation of strongly coupled problem is
 ::<math>\begin{bmatrix}