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Erschienen in:

2019 | OriginalPaper | Buchkapitel

A Co-energy Based Approach to Model the Rotordynamics of Electrical Machines

verfasst von : Felix Boy, Hartmut Hetzler

Erschienen in: Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM

Verlag: Springer International Publishing

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Abstract

New technological fields of application, as for example electric vehicles and closely related lightweight design increase the sensitivity of electrical machines towards torsional and lateral rotor oscillations. The modelling of such electro-mechanical processes is a challenging multiphysical task. In this context, a vast majority of scientific publications use direct approaches to model the problem. These methods derive the equations of motion from Newton’s and Kirchhoff’s laws. In contrast to that, this work proposes a fully coupled indirect approach to the problem using Lagrange-Maxwell equations and the involved magnetic co-energy functional. Such an indirect approach provides for distinct advantages concerning energetical consistency, electro-mechanical coupling and computational effectiveness. Modelling implications like the dependency of the magnetic force on the mechanical motion are outlined and the applicability is shown for a transient simulation of a cage induction machine.

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Vorheriges Kapitel The Influence of the Vibration Suppression on the Rotor Crack Detection Performance

Nächstes Kapitel Influence of Various Control Strategies on Transient Torsional Vibrations of Rotor-Machines Driven by Asynchronous Motors

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Note that up to this point, no further restrictions have to be considered and neither magnetic saturation, nor other effects (like slotting etc.) have been excluded. Additional assumptions have to be made, when solving the magnetic field problem using a certain method (see section results). In fact, even hysteresis effects can be covered by the proposed approach, when introducing proper generalised forces.

Here in terms of forces, torque or voltages.

Usually these expressions contain dissipative effects like viscous mechanical damping, external forces, electrical resistances or external voltages.

E.g when using the Maxwell stress tensor or the definition of the flux linkage.

Concerning this point, a special case has been considered in earlier works (e.g. [2, 6]), where the eccentrical motion has been assumed to be a circular shaped foreward whirl with the same frequency of rotation as the rotor speed. If these assumptions are met and if the equations of motion are linearised with respect to \(\varvec{x}\), it is possible to define an equivalent magnetic damping constant covering the effect of the tangential magnetic force. However, it should be noted here, that such force models can only be applied, when considering a particular solution for the eccentrical motion. If transient states, or even the stability of this particular solution (in terms of a small pertubations) shall be considered, the assumptions for the definition of an equivalent magnetic damping constant are no longer met and therefore the general force model (Eq. (5)) has to be applied.

Note that support in this context does not mean the machine support. For electro-mechanical interactions only the relative motion between stator and rotor is relevant.

The forces \(\varvec{f}_\text {imb}\) are due to mechanical imbalance. They are usually assigned to the right hand side of the equations of motion, but stem from the left hand side originally.

The orbits are extracted from the simulation data for one period. Although they seem to be closed, they certainly change their shape with time from period to period and therefore are not perfectly closed.

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Titel: A Co-energy Based Approach to Model the Rotordynamics of Electrical Machines
verfasst von: Felix Boy
Hartmut Hetzler
Verlag: Springer International Publishing
Buch: Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM
Print ISBN: 978-3-319-99271-6

Electronic ISBN: 978-3-319-99272-3

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-319-99272-3_14

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