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Linear Synchronous Motors, 2nd Edition by Bronislaw Tomczuk, Zbigniew J. Piech, Jacek F. Gieras

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3

Theory of Linear Synchronous Motors

3.1 Permanent Magnet Synchronous Motors

3.1.1 Magnetic Field of the Armature Winding

The time-space distribution of the magnetomotife force (MMF) of a symmetrical polyphase winding with distributed parameters fed with a balanced system of currents can be expressed as

F(x,t)=N12Iaπpsin(ωt)Σν=11νkw1νcos(νπτx)+N12Iaπpsin(ωt1m12π)ν=11νkw1cosν(πτx1m12π)+...+N12Iaπpsin(ωtm11m12π)ν=11νkw1νcosν(πτxm11m12π)=12ν=1Fmν{sin[(ωtνπτX)+(ν1)2πm1]+sin[(ωt+νπτx)(ν+1)2πm1]}(3.1)

where Ia is the armature phase current, m1 is the number of phases, p is the number of pole pairs, N1 is the number of series turns per phase, kw1ν is the winding factor, ω = 2πf is the angular frequency, τ is the pole pitch, and ...

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