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A method of modeling permanent magnets for analytical approach to electrical machinery

Eine Methode zur Modellierung von Permanentmagneten für die analytische Behandlung elektrischer Maschinen

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Contents

A method of simulating permanent magnets in analytical approach for the transfer-matrix-method is given. The method is suited for deriving analytical expressions of the magnetic fields and electromagnetic forces in electrical machines containing permanent magnets. The method was applied to the analysis of a long-stator linear synchronous motor with permanent magnet excitation. Measurements of the forces in the 150-pole Samarium-Cobalt type linear synchronous motor for electric propulsion were used to verify this permanent magnet modeling analysis. Comparison with experimentally obtained results shows a very good agreement.

Übersicht

Eine Methode zur Simulation von Permanentmagneten für eine analytische Behandlung mit der Transfer-Matrix-Methode wird dargestellt. Die Methode ist dafür geeignet, analytische Ausdrücke von magnetischen Feldern und elektromagnetischen Kräften in elektrischen Maschinen mit Permanentmagneterregung abzuleiten. Die Methode wurde auf die Analyse eines permanentmagneterregten synchronen Langstator-Linearmotors angewandt. Messungen der Kräfte an einem synchronen Linearmotor mit 150 Seltenerden-Kobalt-Erregermagneten wurden herangezogen, um das in dieser Arbeit dargestellte analytische Berechnungsverfahren zu überprüfen. Beim Vergleich mit den experimentell ermittelten Werten zeigt sich eine gute Übereinstimmung.

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Abbreviations

A :

magnetic vector potential

B :

magnetic flux density

b :

width of the permanent magnet

H :

magnetic field intensity

H c :

coereive magnetic field intensity

h M :

height of the permanent magnet

h My :

height of the permanent magnet yoke

h Sy :

height of the stator laminated iron yoke

I m :

maximum value of the stator current

I :

unit matrix

i M :

equivalent volume-current density within the permanent magnet region

I 1 :

maximum value of the stator surface-current density

k cM :

modified Carter's coefficient

l M :

length of the permanent magnet

N :

number of turns per coil

p :

number of poles

q :

number of slots per pole per phase

T :

transfer matrix

t :

time

x, y, z :

stationary rectangular coordinates

x′, y, z :

moving rectangular coordinates

x 0 :

phase distance between the MMFs produced by the permanent magnets and by the current-carrying stator windings

w s :

width of the slot

0 :

zero matrix or vector

δ:

length of airgap

δ e =f cM ·δ:

effective length of airgap

μ My :

permeability of the permanent magnet yoke

μ Sy :

permeability of the stator laminated iron

μ0 :

permeability of free space

τ:

pole pitch

ω=2πf :

stator angular frequency

II-My, II-M, III, III′, III″, IV:

each region of six-layered model

I :

vector transpose

M :

concerning the permanent magnet

S :

concerning the stator

MS :

concerning both the permanent magnet and stator

References

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This work has been done while the first author was staying as an Alexander von Humboldt research fellow with Prof. Dr.-Ing. H. Weh, Institut für Elektrische Maschinen, Antriebe und Bahnen, Technische Universität Braunschweig. He greatfully acknowledges the support of the AvH Foundation

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Yoshida, K., Weh, H. A method of modeling permanent magnets for analytical approach to electrical machinery. Archiv f. Elektrotechnik 68, 229–239 (1985). https://doi.org/10.1007/BF01845934

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  • DOI: https://doi.org/10.1007/BF01845934

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