Introduction

Working with the Tutorials

These tutorials shall allow the new user to quickly become familiar with MAGNETICS for Simcenter. Best would be to go through them in the order listed but it is also possible to start with any of them. The following three tutorials are especially convenient for beginners:

The Simcenter/NX files for these tutorials can be downloaded as a zip-archive and the download-link is given at the beginning of each section. The files of each tutorial have a folder ’complete’ that contains the files of the completed tutorial. Also a folder called ’start’ exists, that contains the files to start with when going through the exercise.

We recommend, when working through the tutorials, positioning this pdf and the Simcenter window side by side on your screen (see picture below).
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Now we wish all users a lot of success in learning and performing electromagnetic simulations with MAGNETICS for Simcenter 3D or NX.

In case of problems please write to the support address cae-support@drbinde.de and our team will be there for you.

With best wishes, your team of Dr. Binde Ingenieure

Electromagnetic Principles

This section is based on the lecture notes on ’Applied & Computational Electromagnetics’ from the University of Liège [Geuzaine 2013], on [Binde] and on [Kost].

In the context of electromagnetic fields, Maxwell’s equations are solved. Depending on the application, e.g. electrostatic or magnetodynamics, the equations are simplified or only subsets are considered. For the solution of the equations, the finite element method has been established.

In the following, we provide the usual governing electromagnetic equations, Maxwell’s equations and material relations that are the foundations of said models. We then explain which type of model is the right one for a certain application problem, and finally provide the equations that belong to the individual models.

Maxwell Equations

Let’s look at the Maxwell equations that describe the electromagnetic effects and are the basis for the models or applications listed above. Maxwell’s equations are a set of four equations.

Equation name Differential form Remarks and units
Ampere’s law \(rot \, \mathbf{H} = \nabla \times \mathbf{H} = \tfrac{\mathrm{d} \mathbf{D}}{ \mathrm{d} t} + \mathbf{J}\) Electric current \(\mathbf{J} \space [A]\) creates a
rotating magnetic field \(\mathbf{H} \space [A/m]\).
If electric fluxdensity \(\mathbf{D} \space [As/m^{2}]\)
changes with time, there will also
be a rotating magnetic field created.
Faraday’s law \(rot \, \mathbf{E} = \nabla \times \mathbf{E} = - \tfrac{\mathrm{d} \mathbf{B}}{ \mathrm{d} t}\) If magnetic fluxdensity \(\mathbf{B}\) changes
with time, there will be a rotating
electric field \(\nabla \times \mathbf{E}\) created.
Gauss’s law \(div\, \mathbf{D} = \nabla \cdot \mathbf{D} = \rho\) Electric charge \(\rho\) is a source for
electric fluxdensity \(\mathbf{D}\).
Gauss’s magnetic law \(div \, \mathbf{B} = \nabla \cdot \mathbf{B} = 0\) Magnetic fluxdensity \(\mathbf{B}\) has no sources.

Instead of the capital letters for the vector fields \(\mathbf{H}, \mathbf{B}, \mathbf{E}, \mathbf{D}, \mathbf{J}\) we will also use small letters h,b,e,d,j for them, especially when writing the formulations into the solver input file.

Material Equations

In order to properly specify the system (i.e. we have 16 unknowns from the fields and sources but only 7 equations when considering the continuity equation), additional equations are needed: the material equations. By applying material laws magnetic and electrical material properties are included in the analysis. There exist three material laws.

Equation name Form Remarks and units
Magnetic relationship \(\mathbf{B} = \mu \cdot \mathbf{H}\) Magnetic permeability \(\mu\) is the basic property.
\(\mu\) is often nonlinear. Then, a \(BH\) curve is given.
Usually \(\mu = \mu_{0} \cdot \mu_{r}\) is used.
Dielectric relationship \(\mathbf{D} = \epsilon \cdot \mathbf{E}\) Electric permittivity \(\epsilon\) is the basic property.
Ohm’s law \(\mathbf{J} = \sigma \cdot \mathbf{E}\) Electric conductivity \(\sigma \space [S/m]\) is basic property.

Electromagnetic Models

The below picture shows use cases of interest in the electromagnetic analysis area which can arise from the Maxwell equations.

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The six principle submodels that can be derived from the Maxwell equations particularly differ in the way they account for the effects capacitance, ohm resistance and inductivity. Accordingly, icons for capacitor, resistor and coil can be assigned: