Analytical Modelling of the Slot Opening Function
The slot opening function, also called relative air gap permeance, is a function which, multiplied by the flux density distribution of a slotless geometry, gives the flux density distribution of a slotted configuration. Here, the magnetic field inside the air gap of a multi-slot surface facing a smo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Magnetism |
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| Online Access: | https://www.mdpi.com/2673-8724/3/4/24 |
| _version_ | 1797380241326342144 |
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| author | Antonino Di Gerlando Claudio Ricca |
| author_facet | Antonino Di Gerlando Claudio Ricca |
| author_sort | Antonino Di Gerlando |
| collection | DOAJ |
| description | The slot opening function, also called relative air gap permeance, is a function which, multiplied by the flux density distribution of a slotless geometry, gives the flux density distribution of a slotted configuration. Here, the magnetic field inside the air gap of a multi-slot surface facing a smooth one was studied, by solving the Laplace equation inside the air gap, in terms of a Fourier series. To obtain the Fourier coefficients, at first, the conformal mapping analytical solution of a single-slot configuration along the smooth surface, was considered. Then, the principle of superposition of the single-slot lost flux density distributions was applied to obtain the multi-slot distribution. The approach is valid in general, and in the case of interference among the flux density distributions of adjacent slots, where their mutual effect cannot be neglected. The field distributions obtained by using the proposed slot opening functions were compared with FEM simulations, showing satisfactory agreement. The numerical accuracy limits were also analysed and discussed. |
| first_indexed | 2024-03-08T20:34:33Z |
| format | Article |
| id | doaj.art-18fb4673bf5a413d87f7c1c871fd6c1d |
| institution | Directory Open Access Journal |
| issn | 2673-8724 |
| language | English |
| last_indexed | 2024-03-08T20:34:33Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Magnetism |
| spelling | doaj.art-18fb4673bf5a413d87f7c1c871fd6c1d2023-12-22T14:22:05ZengMDPI AGMagnetism2673-87242023-11-013430832610.3390/magnetism3040024Analytical Modelling of the Slot Opening FunctionAntonino Di Gerlando0Claudio Ricca1Department of Energy, Politecnico di Milano, Via La Masa 34, 20156 Milano, ItalyDepartment of Energy, Politecnico di Milano, Via La Masa 34, 20156 Milano, ItalyThe slot opening function, also called relative air gap permeance, is a function which, multiplied by the flux density distribution of a slotless geometry, gives the flux density distribution of a slotted configuration. Here, the magnetic field inside the air gap of a multi-slot surface facing a smooth one was studied, by solving the Laplace equation inside the air gap, in terms of a Fourier series. To obtain the Fourier coefficients, at first, the conformal mapping analytical solution of a single-slot configuration along the smooth surface, was considered. Then, the principle of superposition of the single-slot lost flux density distributions was applied to obtain the multi-slot distribution. The approach is valid in general, and in the case of interference among the flux density distributions of adjacent slots, where their mutual effect cannot be neglected. The field distributions obtained by using the proposed slot opening functions were compared with FEM simulations, showing satisfactory agreement. The numerical accuracy limits were also analysed and discussed.https://www.mdpi.com/2673-8724/3/4/24Laplace equationslot opening functionair gap relative permeance |
| spellingShingle | Antonino Di Gerlando Claudio Ricca Analytical Modelling of the Slot Opening Function Magnetism Laplace equation slot opening function air gap relative permeance |
| title | Analytical Modelling of the Slot Opening Function |
| title_full | Analytical Modelling of the Slot Opening Function |
| title_fullStr | Analytical Modelling of the Slot Opening Function |
| title_full_unstemmed | Analytical Modelling of the Slot Opening Function |
| title_short | Analytical Modelling of the Slot Opening Function |
| title_sort | analytical modelling of the slot opening function |
| topic | Laplace equation slot opening function air gap relative permeance |
| url | https://www.mdpi.com/2673-8724/3/4/24 |
| work_keys_str_mv | AT antoninodigerlando analyticalmodellingoftheslotopeningfunction AT claudioricca analyticalmodellingoftheslotopeningfunction |