Engineering How Is Current Linkage Constant in a Salient Pole Motor's Amperian Loop?

[BlackMelon]

Homework Statement

I have a doubt about the current linkage, Θ_f, in figure 2.2b of a salient pole motor. In this textbook, the current linkage is expressed by ∫H⋅dl = Θ_f = ∑i. However, in the figure 2.2b between q(left) and q(right), how can the Θ_f be constant? Since, the author doesn't show how he chose the Amperian loop, how can I know how many currents are enclosed (∑i)?

2. Homework Equations
∫H⋅dl = Θ_f = ∑i

The Attempt at a Solution

I have studied the application of Ampere's law to solenoids, which have the same type of winding as that on the rotor of a salient pole machine. I was trying to assume so many Amperian paths, trying to figure the 2.2b out.

 

[Baarken]

I don't know if you solved this one or not, as I see you created this thread a while back.

If you look at page 3 in your attached pdf document the author writes:

The salient-pole windings located on the rotor or on the stator are mostly used for the DC magnetizing of a machine. The windings are then called magnetizing or sometimes excitation windings. With a direct current, they create a time-constant current linkage \theta.

So, look at my bad paint drawing below. Coils are wound around the salient pole, creating a magnetic field in the upward direction (thumb towards current direction (x inwards, dot outwards) and your hand curls in the direction of the magnetic field). And as I quoted from your pdf, the salient pole is excited using DC current, which means that the magnetic field created from the coils wound around the salient pole is constant. Therefore we have this approximately uniform magnetic field across the salient pole and hence ~uniform "current linkage" if we ignore the edge effects.Did I answer your question? I have been lurking a few months on this forum and based on my observations I believe @jim hardy would have an input on this if you need more help or I did not answer it properly.

 

[jim hardy]

Hmmmm

what he calls "current linkage" is what i call MMF ?

@Baarken got it i believe

In his example 2.1 your author simplifies things for us by considering iron to be a short circuit for magnetic flux .

There can be no circumferential MMF along the iron. It'd cause infinite flux .
Actually no radial MMF in the iron either - it's all spent in the airgap.

 

[Baarken]

what he calls "current linkage" is what i call MMF ?

That was what I assumed as well, I have not heard or used the term "current linkage" before.