Linear Synchronous Motors, 2nd Edition

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

$\begin{matrix} F (x, t) = \frac{N_{1} \sqrt{2} I_{a}}{π p} sin(ω t) Σ_{ν = 1}^{\infty} \frac{1}{ν} k_{w 1 ν} cos(ν \frac{π}{τ} x) \\ + \frac{N_{1} \sqrt{2} I_{a}}{π p} sin(ω t - \frac{1}{m_{1}} 2 π) \sum_{ν = 1}^{\infty} \frac{1}{ν} k_{w 1} \cos ν (\frac{π}{τ} x - \frac{1}{m_{1}} 2 π) + ... \\ + \frac{N_{1} \sqrt{2} I_{a}}{π p} sin(ω t - \frac{m_{1} - 1}{m_{1}} 2 π) \sum_{ν = 1}^{\infty} \frac{1}{ν} k_{w 1 ν} \cos ν (\frac{π}{τ} x - \frac{m_{1} - 1}{m_{1}} 2 π) \\ = \frac{1}{2} \sum_{ν = 1}^{\infty} F_{m ν} {sin [(ω t - ν \frac{π}{τ} X) + (ν - 1) \frac{2 π}{m_{1}}] \\ + \sin [(ω t + ν \frac{π}{τ} x) - (ν + 1) \frac{2 π}{m_{1}}]} \end{matrix} (3.1)$

where I_a 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, k_w1ν is the winding factor, ω = 2πf is the angular frequency, τ is the pole pitch, and ...

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

3

Theory of Linear Synchronous Motors

3.1 Permanent Magnet Synchronous Motors

3.1.1 Magnetic Field of the Armature Winding

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