User's Guide

This library contains components for modelling of electromagnetic devices with lumped magnetic networks. Those models are suited for both rough design of the magnetic subsystem of a device as well as for efficient dynamic simulation at system level together with neighbouring subsystems. At present, components and examples for modelling of *translatory* electromagnetic and electrodynamic actuators are provided. If needed, these components can be adapted to network modelling of *rotational* electrical machines.

This user's guide gives a short introduction to the underlying concept of **magnetic flux tubes**, summarizes the calculation of magnetic **reluctance forces** from lumped magnetic network models and lists **reference literature**.

Examples illustrates the usage of magnetic network models with simple models from different fields of application.

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Name | Description |
---|---|

`Contact` | Contact |

`FluxTubeConcept` | Flux tube concept |

`Hysteresis` … | Hysteresis |

`Literature` | Literature |

`ReleaseNotes` | Release Notes |

`ReluctanceForceCalculation` | Reluctance forces |

Flux tube concept

Following below, the concept of magnetic flux tubes is outlined in short. For a detailed description of flux tube elements, please have a look at the listed literature. Magnetic flux tubes enable for modeling of magnetic fields with lumped networks. The figure below and the following equations illustrate the transition from the original magnetic field quantities described by *Maxwell*'s equations to network elements with a flow variable and an across variable:

For a region with an approximately homogeneous distribution of the magnetic field strength **H** and the magnetic flux density **B** through cross sectional area *A* at each length coordinate *s* (*A* perpendicular to the direction of the magnetic field lines), a magnetic reluctance *R _{m}* can be defined:

With the definition of the magnetic potential difference *V _{m}* as an across variable and the magnetic flux

the general formula for the calculation of a magnetic reluctance *R _{m}* from its geometric and material properties is:

For a prismatic or cylindrical volume of length *l* and cross sectional area *A* with the magnetic flux entering and leaving the region through its end planes, the above equation simplifies to:

Similar equations can be derived for other geometries. In cases where a direct integration is not possible, the reluctance can be calculated on base of average length, average cross sectional area and volume *V* respectively:

Network elements for sources of a magnetic potential difference or magnetomotive force, i.e., coils or permanent magnets can be formulated as well. The resulting magnetic network models of actuators reflect the main dimensions of these devices as well as the normally nonlinear characteristics of their magnetically active materials.

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Reluctance forces

Generally, the thrust *F* developed by a translatory electro-magneto-mechanical actuator (similar for the rotational case with torque and angular position) is equal to the change of magnetic co-energy *W _{m}^{*}* with armature position

(*Ψ* flux linkage, *i* actuator current). In lumped magnetic network models, the above equation simplifies to

where *n _{linear}* is the number of flux tube elements with constant relative permeability that change its permeance

with *Φ _{i}* being the magnetic flux through each respective flux tube element.

Flux tube elements with *non-linear* material characteristics *μ _{r}*(

The sub-package Shapes.Leakage contains flux tube shapes typical for leakage flux around prismatic or cylindrical poles. Since the permeance of these flux tubes does not change with armature position, they do not contribute to a reluctance actuator's thrust.

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Literature

**Usage of the Modelica Magnetic library is described in:**[Bö08] Bödrich, T.: *Electromagnetic Actuator Modelling with the Extended Modelica Magnetic Library*, Modelica 2008 Conference, Bielefeld, Germany,pp. 221-227, March 3-4, 2008. Download from: https://www.modelica.org/events/modelica2008/Proceedings/sessions/session2d2.pdf

**The method of magnetic flux tubes as well as derivation of the permeance of many flux tube shapes is explained in detail in:**[Ro41] Roters, H.: *Electromagnetic Devices*, New York: John Wiley & Sons 1941 (8th Printing 1961)

**Structure, properties, applications and design of electromagnetic (reluctance type) actuators are thoroughly described in:**[KEQ+12] Kallenbach, E.; Eick, R.; Quendt, P.; Ströhla, T.; Feindt, K.; Kallenbach, M.; Radler, O.: *Elektromagnete: Grundlagen, Berechnung, Entwurf und Anwendung*, 3rd ed., Wiesbaden: Vieweg Teubner 2008 (in German).[Ro00] Roschke, T.: *Entwurf geregelter elektromagnetischer Antriebe für Luftschütze*, Fortschritt-Berichte VDI, Reihe 21, Nr. 293, Düsseldorf: VDI-Verlag 2000 (in German).

**Application of the method of magnetic flux tubes to the design of rotational electrical machines is explained for example in:**[HM94] Hendershot, J.R. Jr.; Miller, T.J.E.: *Design of Brushless Permanent-Magnet Motors*, Magna Physics Publishing and Oxford University Press 1994.

**Information related to the implemented hysteresis models can be found in:**[BE01] Bergqvist, A. J.; Engdahl, S. G.: *A Homogenization Procedure of Field Quantities in Laminated Electric Steel*, IEEE Transactions on Magnetics, vol.37, no.5, pp.3329-3331, 2001.[Te98] Tellinen, J: *A simple scalar model for magnetic hysteresis*, IEEE Translation Journal on Magnetics in Japan, vol.4, no.6, pp.353-359, 1989.[Pr35] Preisach, F.: *Über die magnetische Nachwirkung*, Zeitschrift für Physik A Hadrons and Nuclei, vol. 94, pp. 277-302, 1935.[Ma03] Mayergoyz, I.: *Mathematical Models of Hysteresis and their Application*, Elsevier, 2003.[Va01] VAC Vacuumschmelze: *Soft Magnetic Cobalt-Iron-Alloys*, 2001. Download from: http://www.vacuumschmelze.com/fileadmin/docroot/medialib/documents/broschueren/htbrosch/Pht-004_e.pdf[YUY89] Yamaguchi, T.; Ueda, F.; Yamamoto, E.: *Simulation of Hysteresis Characteristics of Core Materials Using the Everett Function*, IEEE Translation Journal on Magnetics in Japan, vol.4, no.6, pp.353-359, 1989.[ZB12] Ziske, J.; Bödrich, T.: *Magnetic Hysteresis Models for Modelica*, Proc. of the 9th Modelica Conference, Munich, Germany, pp. 151-158, September 3-5, 2012. Download from: http://www.ep.liu.se/ecp/076/014/ecp12076014.pdf[ZB14] Ziske, J.; Bödrich, T.: *http://www.ep.liu.se/ecp/096/017/ecp14096017.pdf*, Proc. of the 10th Modelica Conference, Lund, Sweden, pp. 165-172, March 10-12, 2014. Download from: http://www.ep.liu.se/ecp/096/017/ecp14096017.pdf

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Release Notes

- Added package FluxTubes.UsersGuide.Hysteresis
- Added package FluxTubes.Examples.Hysteresis
- Added package FluxTubes.Shapes.HysteresisAndMagnets
- Added package FluxTubes.Material.HysteresisEverettParameter
- Added package FluxTubes.Material.HysteresisTableData
- Updated FluxTubes.Interfaces.PartialFixedShape for differentiability
- Updated FluxTubes.UsersGuide.Literature

- Added constant permeance model
- Added GenericFluxTube
- Added parameter
`useConductance`

including alternative parameterization in EddyCurrent - Added Idle
- Added Short
- Added Crossing

- Added missing initial conditions
- Fixed initial parameter values

- MagneticPort declared with MagneticPotential instead of MagneticPotentialDifference

- Added conditional heat port to EddyCurrent model

- Update and improvement for inclusion in the Modelica Standard Library

- Coupling coefficient in Basic.ElectroMagneticConverter removed
- Basic.EddyCurrent added
- Example MovingCoilActuator, especially PermeanceModel, completely revised
- Leakage coefficient replaced by coupling coefficient in Basic.LeakageWithCoefficient
- Utilities.CoilDesign: parameter U renamed to V_op,CoilDesign moved to Utilities.
- Reference direction for magnetic flux added in all sources
- degC replaced by K for compatibility with Modelica 3.0
- redeclare in Sensors for compatibility with Modelica 3.0 removed
- Partial flux tube components moved to Interfaces and basic elements moved to new package Basic

- Release of version 1.0 of the library

- First release of a Modelica magnetic library

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Contact

**Thomas Bödrich**

Dresden University of Technology

Institute of Electromechanical and Electronic Design

01062 Dresden, Germany

Phone: +49 - 351 - 463 36296

Fax: +49 - 351 - 463 37183

email: Thomas.Boedrich@tu-dresden.de

**Johannes Ziske**

Dresden University of Technology

Institute of Electromechanical and Electronic Design

01062 Dresden, Germany

Phone: +49 - 351 - 463 35250

Fax: +49 - 351 - 463 37183

email: Johannes.Ziske@tu-dresden.de

- The magnetisation characteristics of the included soft magnetic materials were compiled and measured respectively by Thomas Roschke, now with Johnson Electric. Provision of this data is highly appreciated. He also formulated the approximation function used for description of the magnetisation characteristics of these materials.
- André Klick of then Dresden University of Technology, Dresden, Germany gave valuable support on the implementation of this library. His contribution is highly appreciated, too.
- The hysteresis models of this library have been developed by Johannes Ziske and Thomas Bödrich as part of the Clean Sky JTI project; project number: 296369; Theme: JTI-CS-2011-1-SGO-02-026; MOMOLIB - Modelica Model Library Development for Media, Magnetic Systems and Wavelets. The partial financial support by the European Union for this development is highly appreciated.

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