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Let's consider just one pole pair.

I know from reading my book that a pm machine will have the angular speed of its rotor equal to the speed of the rotating magnet field that the three phase winding creates.

If this was not the case then the (average?) torque would be zero.

I did some research, and it seems that this behavior is due to the fact that two magnetic fields try to align, with a torque that's proportional to the product between their magnitudes and the sin of the angle between them.

Given that I have NO idea what that law is (its name, where does it come from...to be honest it seems an elementary explanation about how two magnets attract each other), I wonder if this is the case. does the motor torque come from this phenomenon? What would be zero (if anything, later on the book it states that if the speed are different I just wouldn't get a constant torque), the ''average'' (on what? a period?) torque, or the instantaneous? I'd say it's the average over a period of the sin that appears in that formula, but it's very tricky to reconstruct it to the time domain.

I also read that a pm machine will either run at the excitation field speed or not run at all. No idea why is that, tho. and if this was the case, how would I start them? as soon as I give them a rotating field, since they are not moving they have different velocities... then the torque would be zero (from the book)? It doesn't make sense.

And what if, by any chance, when I start the machine the two fields are aligned? Would I get the minimum possible torque (around 0) or something else would happen?

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  • \$\begingroup\$ The magnetic field rotates at synchronous speed, pulling the rotor around (slightly lagging the field). Now consider if the rotor ran at any other speed, half the time it would be ahead of the field - then the field would be pulling it backwards - braking. So if it's pulled forward half the time and backwards half the time, the net torque is zero. \$\endgroup\$ – Brian Drummond Jul 9 '16 at 22:55
  • \$\begingroup\$ @BrianDrummond ok, yours is a good example. if different speed -> net torque over (some) time equal zero, clear. Then why do I have exactly that speed? I understand that I have torque (so the motor works) only if I have synchronous, but why does the motor work at all? for all I know there's nothing that forces the rotor to move at that speed and hence generate the constant torque. the problem in starting it still remains tho. (anyway, thank you a lot) \$\endgroup\$ – user3149593 Jul 9 '16 at 23:02
  • \$\begingroup\$ Now that's a good question. Synchronous motors often have other starting arrangements. Small ones may have enough power to reach synch in a couple of cycles. Larger ones may start as (asynch) induction motors, then "snap" to synch speed when they get close enough. Wiki ought to have more details. In synch operation, the rotor will lag depending on the torque. Nowadays, BLDC motors start dead slow with a low AC frequency, then increases the frequency, measuring the lag to make sure the motor keeps up, until full speed is achieved. \$\endgroup\$ – Brian Drummond Jul 10 '16 at 0:27
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it seems that this behaviour is due to the fact that two magnetic fields try to allign, with a torque that's proportional to the product between their magnitudes and the sin of the angle between them.

Magnets will try to align themselves for the strongest combined magnetic field. This phenomena is described by Lorentz Force and the Amperian loop model.

The 'sine' factor comes from having the magnet on a rotating shaft. When the magnet pole is aligned with the stator pole there is no rotational force because the field cannot get any stronger. Rotate the magnet in either direction and it will try to move back. However as it is going 'around the circle' the rotational force will decline towards zero as the rotor approaches 180°, then increase again as it completes a 360° revolution.

I also read that a pm machine will either run at the excitation field speed or not run at all. No idea why is that,

To understand why the motor must rotate at synchronous speed, imagine that the excitation frequency is zero (ie. a static stator field). The rotor will stay in one place (unless pulled away from it). Now slowly increase the frequency while allowing the rotor to be dragged around by the rotating stator field.

So long as the rotor can keep up it will stay in sync, lagging slightly behind in phase (not frequency) due to torque loading and inertia while accelerating. But if it lags too far behind it will lose torque and snap around in the other direction. If it can't keep up then it won't run at a lower frequency, but simply jitter back and forth.

how would I start them? as soon as I give them a rotating field, since they are not moving they have different velocities...

A synchronous PM motor will not start itself unless the starting frequency is low enough for the rotor to stay aligned to the rotating stator field. Since the rotor has inertia it must come into alignment and accelerate fast enough to keep up with the increasing drive frequency as it is brought up to speed. If it can manage to do that then it will be running at the same velocity (averaged over a cycle) lagging behind only in phase.

and what if, by any chance, when I start the machine the two fields are aligned?

If powered at mains frequency the rotor won't be able to accelerate fast enough to get up to speed in less than 1 cycle, so some other method of starting is required; eg. squirrel cage to create an induction drive, a separate motor to run it up to speed, or a spring that flicks the rotor in the correct direction when it starts going backwards (used in synchronous clock motors).

There is one other way to run a synchronous PM motor - electronic commutation. The rotor position is determined using Hall effect sensors or by reading back-emf off an unpowered stator coil, then the correct drive frequency and phase is synthesized by the motor controller. This operation is basically the same as for a Permanent Magnet Brushless DC (BLDC) motor.

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Depends on the class of the motor, but here are three common schemes:

DC Motor

The typical arrangement is for the rotor to have the winding and the stator to have the permanent magnet.

The brushes ensure that the rotor current is properly aligned with the PM field, so the rotor currents are aligned with the stator permanent field. There is no special starting procedure.

BLDC/PMSM Motor

The typical arrangement is to have the permanent magnet on the rotor and the windings on the stator.

The electronics commutate the stator winding with the known position of the rotor, so the stator current is controlled so that it pushes the magnet around synchronously.

Again, there is no special starting procedure required, the electronics will always know the rotor position and commutate the motor appropriately to generator torque.

AC Synchronous Motor

The AC synchronous motor is basically an AC motor with a "special" coil on the rotor.

When being started, the rotor is run like any other AC motor and is - thus - not synchronous. Once it gets close to the synchronous speed (60Hz in the US), then a DC field is applied to the rotor that will make the rotor act somewhat like a permanent magnet, and that magnet will "lock" with the stator field.

Care must be taken to not exceed the rated torque of the motor or it will begin to skip or simply resume standard AC operation with slip.

I'm sure that there are others, but this gives you a rough idea.

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  • \$\begingroup\$ There isn't just 3 common scheme's ... .and technically speaking you have only listed two. DC and Sync \$\endgroup\$ – JonRB Jul 10 '16 at 6:33
  • \$\begingroup\$ Agreed on all points! \$\endgroup\$ – slightlynybbled Jul 10 '16 at 22:54

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