Flux distribution on AC machines

[Caulfield]

It is a cylindrical ac machine. If we want to produce a sinusoidal voltage, we need B (magnetic density) to vary sinusoidally.
To get B vary sinusoidally, we need to get H(magnetic intensity) to vary sinusoidally.
To get H vary sinusoidal, the best way is to vary the numbers in the air gap between the rotor and the stator in a sinusoidal way.

Nc is the number of conductors at angle = 0.
nc is the number of conductors in a specific position.

The formula says: nc=Nc*cos(x)

What confuses me here is the cos(x) part. Why not sin(x)?

My logic: sin grows with angle (0 to 90). We want the H to grow in the same way. So why not put more windings at 90, and less windings at 0, and thus get bigger H at 90

 

[jim hardy]

My logic: sin grows with angle (0 to 90). We want the H to grow in the same way. So why not put more windings at 90, and less windings at 0, and thus get bigger H at 90

We don't have your textbook to look at.

So take a step back and ask yourself
"What is difference between sin and cosine ?
Where did author define zero ? "

Answering second question will probably resolve your un-ease.

 

[Hesch]

So why not put more windings at 90, and less windings at 0, and thus get bigger H at 90

That's not how an ac-motor works. We don't vary the H and B fields by choosing a proper number of windings at 0 degrees or 90 degrees, but by varying the current through the coils sinusoidally. For example we connect three coils in the stator to a three phase net. As the voltages - and therefore the currents - in the three phases are sinusoidal and individually offsetted 120 degrees one another, a magnetic vector will be induced in the motor. The length of this vector is constant, but the vector will rotate around the axis of the motor at 60 rounds per second ( 1 pole pair, USA ). In a synchronous motor, the rotor will follow this vector.

The 0 degrees / 90 degrees are electrical degrees, so where are 90 degrees located mechanically in the machine? Answer: They are rotating.

 

[jim hardy]

Caulfield might be speaking of rotor...

images courtesy these guys
http://www.generatortech.com/index.html

 

[Hesch]

Yes, could be. I don't know the name in english, but directly translated from danish, it is called an alien-magnitized motor.

I'm also aware of that in bigger motors, distributed windings may be used in the stator, and the intension is here to finetune the shape of the sine-wave (avoid higher harmonics). In smaller PM-motors it is normally done by shaping the teeths/grooves in the stator ( i.e. introduce varying magnetic "resistance" over the width of a tooth in the magnetic circuit ).