Analytical and Numerical Techniques for Solving Laplace and Poisson Equations in a Tubular Permanent Magnet Actuator: Part II. Schwarz-Christoffel Mapping

In Part I of the paper, we derive a semianalytical framework for the magnetic field calculation in the air gap of a tubular permanent-magnet (PM) actuator. We also make an extension for skewed topologies. However, the slotting effect and its related cogging force cannot be determined in a straightfo...

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Bibliographic Details
Published in:IEEE transactions on magnetics 2008-07, Vol.44 (7), p.1761-1767
Main Authors: Gysen, B.L.J., Lomonova, E.A., Paulides, J.J.H., Vandenput, A.J.A.
Format: Article
Language:English
Subjects:
Conformal mapping
Cross-disciplinary physics: materials science
rheology
Design optimization
Exact sciences and technology
Force control
Forging
Geometry
Hydraulic actuators
Magnetic analysis
Magnetic fields
Magnetism
Materials science
Other topics in materials science
permanent magnet
Permanent magnets
Physics
Poisson equations
tubular actuator
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Summary:In Part I of the paper, we derive a semianalytical framework for the magnetic field calculation in the air gap of a tubular permanent-magnet (PM) actuator. We also make an extension for skewed topologies. However, the slotting effect and its related cogging force cannot be determined in a straightforward way. Therefore, in Part II, we apply the Schwarz-Christoffel (SC) conformal mapping method to one pole-pair of the tubular PM actuator. This mapping allows for field calculation in a domain where standard field solutions can be used. In this way, slotting effects can be taken into account; however, skewing cannot be implemented directly. The SC-conformal mapping method is valid only for two-dimensional Cartesian domains. We therefore apply a special transformation from the cylindrical to the Cartesian coordinate system to describe the tubular actuator as a linear actuator.
ISSN:0018-9464
1941-0069
DOI:10.1109/TMAG.2008.923438