Hello all.

This problem has been bugging me for a while, and I really could use a little help understanding the situation. If I can be allowed to think of a permanent magnet DC motor as a magnetic dipole sitting within a constant magnetic field, then it seems to me that the following should occur. If power is applied at the terminals of the motor armature, then the the magnetic dipole should rotate at most 90 degrees before the torque goes to 0. This is because, as I see it, the flux linkage between the dipole and the field is related to the cross product between them. Therefore, simply swapping the polarity at the terminals of the armature would have no effect, as it will still be perpendicular to the field. Now, if we had 4 poles, this problem could be solved by commutating every 90 degrees.

Now, despite the logic applied here, I constantly see examples showing two bar magnets, where one is allowed to rotate 180 degrees before the torque goes to 0. But can the DC motor really be represented this way? In this example it is true that the flux of one magnetic will pass through the other and cause them to allign, but since the rotating magnetic is not sitting between two poles then it doesn't seem to represent what is going on.

Sorry about the long winded analysis, but I desperately want to understand where I am going wrong here. Thanks for any help!

 

Suppose you consider a magnetic compass in the Earths field - isn't that pretty much the same case?

You can manually apply torque to force the compass needle 180 degrees, but if you let go, the needle will experience restoring torque for the full 180 degrees until it points north again.

That shows that in a constant magnetic field, there are 180 degrees of torque on a magnet, not only 90.

But I'm not sure what you mean that "the rotating magnetic is not sitting between two poles" - why isn't it?

 

Oh, I get your point about the two bar magnets. What you probably have to think about is that magnets aren't affected by other magnets directly, magnets are affected by the magnetic field in their region of space.

It doesn't matter whether that magnetic field is generated by a single magnet at one side, or by two magnets, one on either side, or any combination of magnets. For any given configuration of magnets, a field will be set up, and if a test magnet of any shape is put in that field, the sum of all individual torques and forces will result in a single overall resulting torque on the test magnet.

Thinking about the cross-product part of the question - when the magnet is at rest, aligned with the field in its lowest energy state, like a compass needle pointing North, the vector cross product of the fields will be zero, indicating that there is no torque on the magnet.

But suppose you reverse one of the fields. The cross-product will still be zero, so there still will be no torque on the magnet, but this is now an unstable, higher potential energy state, like a pencil balanced on its point. The slightest deflection of the magnet, such as the rotation supplied by its own momentum when it is spinning, will put it in a position where there is a torque applied to it, and the torque will last for 180 degrees of rotation.

 

Most simple permanent magnet motors have a single magnet or 2 magnets arranged NS-NS with a 3 or 4 pole armature in between. Find one. Any of the cheaper Maubuchi motors should do. Take it apart slowly and look at the relationship between the magnet poles and the brushes. Record this. Then pull the armature and observe the arrangement of the commutator contacts. Finally inspect how the windings are wired to the commutator. If it's not immediately obvious to you then, report your findings and ask for further comment.

Motors exist with 3, 4, 6, 8, ... pole armatures, but the basic 3 or 4 pole job should be easier to reverse engineer.

As a follow on exercise, you can easily make a motor out of 2 nails, a couple of paper clips, a small plank of pine, 4 thumb tacks and a couple of meters of #18 magnet wire.


Edit: BTW, there is something wrong with your physics - and hence your math. Both the armature and the PM's create vector fields that do not cancel each other until they are in full opposing alignment. At (almost) any other angle, there is a force between them. Think of 3 bar magnets lined up from top to bottom. The top one and the bottom one are NS -NS. The one in the middle is at 90% (it does not matter which way):

........ N
........ |
........ S

..... N---S

........ N
........ |
........ S

In this arrangement there would be a clockwise torque on the centre magnet. If it accelerates clockwise until it aligns, and then it's polarity is made to reverse, what happens? Keep in mind that it has mass...

So, physically what is happening? Consider 180 degrees of rotation from stable alignment (NS-NS-NS) to unstable alignment (NS-SN-NS). Where would the torque be at a maximum? At a minimum? What vector product or mathematical relationship would explain this?

This is also a hint on how to make your nail and paperclip motor.

Why won't this F^%%ing website allow me to enter spaces!!!!!? POS!

 

Thank you both so much for the wonderful responses!

I think what I was failing to consider was the direction of the torque and how it will tend to align the system N-S and S-N. It was that insight that really cleared me up. I was so focused on the magnitude of the torque only. Also, I had suspected that rotor intertia could carry the system through quasi-stable points such as the S-S N-N alignment, but I was having difficulty finding a definitive answer about this.

Anyhow, thank you both so much.