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The harmonic spectrum of the magnetic field spatial distribution in the air-gap of the doubly slotted electrical machine
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W artykule przedstawiono przykładowy stabelaryzowany rozkład przestrzenny pola magnetycznego dla obustronnie użłobkowanej maszyny wraz z wyjaśnieniem proponowanej metody jego tworzenia.
The special tables enabling us to determine the harmonic spectrum of the magnetic field in the case of the doubly slotted electrical machine was presented in this paper. The doubly slotting of the machine air-gap affects the magnetic field spatial distribution (Eqn.1). The magnetomotive force (MMF) generated by the stator winding at the point of time t as well as the reciprocal of the equivalent air-gap can be resolved in the Fourier series (Eqns 2, 3). One can notice that the harmonic spectrum of the reciprocal of the equivalent air-gap consists of: the stator permeance harmonics of the orders v(s), the rotor permeance harmonics of the orders v(r) and the differential permeance harmonics of the orders v(d). The harmonics of the orders v(s) do not move while the rotor revolves. The harmonics of the orders v(r) move with the angle theta (the angle of the rotor position). On the other hand while the rotor revolves with the rotation angle theta the harmonics of the orders v(d) move with the angel ....... (depending on the sign in the Exp. v(d) = ......). The product of the MMF (Exp. 2) and the reciprocal of the equivalent air-gap (Exp. 3), included in the Exp. 1, can be written in the form of Exp. 4. The Exp. 4. can be expressed in the different forms, depending on the presence of the harmonics fulfilling the conditions (5), (6), (7). This results in the expression describing the magnetic field spatial distribution H[alpha(s), theta, t] (Exp. 9). The summand, which does not depend on the coordinate alpha(s) (Exp. 11), occurs in the Eqn. 1 when the condition (6) is fulfilled. This summand vanishes as a result of summing with the Exp. 12. The summand (Exp. 11) does not appear when the condition (7) is fulfilled, hence in this case the magnetic field intensity distribution H[ alpha(s), theta, t] is described by the Exp. 16. The harmonic spectrum of the magnetic field intensity distribution (Exp. 9) can be shown with the help of appropriately defined tables. The numbers of rows of these tables are equal to the harmonic orders of the reciprocal of the equivalent air-gap - v((gamma), the numbers of the tables columns are equal to the harmonic orders of the MMF - v(theta). The numbers put in the table cells have a meaning of the harmonic orders of the magnetic field intensity distribution - v(H). The presented method can be helpful in the process of identification of the synchronous reluctant torques appearing in the doubly slotted electrical machine.
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Tom
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167--176
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Bibliogr. 6 poz., tab., rys.
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Bibliografia
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bwmeta1.element.baztech-article-BPS2-0014-0051