2

As the title states, I am trying to find a way to measure the dipole moment(m) for my magnetorquer.

I am planning to use magnetorquers for desaturating my reaction wheels for a project. I understand that there is a relation m=nIA where m is the dipole moment, I is the current, n is the no. of turns and A is the cross sectional area of the torque rod. I intend to use that formula to calculate how much voltage to apply to my magnetorquer.

But I would also like to check that I am actually getting the correct dipole moment physically. Are there any ways to experimentally measure the dipole moment strength of my magnetorquer?

I have done some research and came across this formula on this wikipedia page:

enter image description here

https://en.wikipedia.org/wiki/Magnetic_moment

My plan is to use a magnetometer to measure the magnetic field strength at a distance r ( This would then be |r| ) away from the magnetorquer, and assume that the position vector and magnetic moment vector are parallel to simply the dot product of m and r.

Would this work?

Thanks

John
  • 413
  • 4
  • 9
  • 4
    This question might find a better home on the Physics Stack Exchange. Also, try looking at this answer: http://space.stackexchange.com/questions/2239/what-is-the-math-behind-magnetorquers?rq=1 – Phiteros Oct 08 '16 at 18:50
  • The three close votes say this is a duplicate - if there is actually a good answer to the specific question "Ways to measure dipole moment of magnetorquer" please post a link to that answer. I've posted an answer mentioning two ways to measure the dipole moment of a magnetotorquer (via magnetometer and sense coil) but I'd be happy to see that there is better answer - someone please post a link to this answer - thanks! – uhoh Oct 09 '16 at 00:28
  • @uhoh I agree that it is on-topic. However, I think that the Physics SE could provide a faster, better answer about how to calculate and measure dipole moments as this is, ultimately, physics. – Phiteros Oct 09 '16 at 00:45
  • @Phiteros Physics SE frequently closes questions because they are "engineering, and not physics". This is not a question about physics. All orbital mechanics questions here (there are many) use physics, but they are not about physics as actually defined by the physics stackexchange "community". Rocket engines use physics too. Someday I hope there will be a new Applied Physics Stackexchange (or Applied and Engineering Phys.) and that would be a great place for this question. This is a piece of standard satellite equipment and the question is how to test the equipment's function. – uhoh Oct 09 '16 at 00:57
  • 2
    @uhoh That's a pretty stupid policy of theirs. There is an Engineering SE, but it's in beta. – Phiteros Oct 09 '16 at 01:20
  • Close-voters: This is not a duplicate of the linked question. If you have another reason to think it should be closed, please leave a comment as Phiteros has. – called2voyage Oct 10 '16 at 13:50
  • @Phiteros For the record, I think that "migrate to Physics because answers there will be faster and better" is a bad reason for migration, and I cannot recall an instance where I have migrated a question from SX or Astro to Physics for that reason. – called2voyage Oct 10 '16 at 13:52
  • @Phiteros Also, see the open discussion about migration, which references migration guidelines: "If the question is on-topic for the site where it was asked, and it is answered, decline immediately. (If you feel like being generous, check if the flagger is also the answerer and migrate if this is the case.)" – called2voyage Oct 10 '16 at 13:54
  • I really like the article that you found and linked in your new question. In my answer I mentioned what the article describes as the $\theta=90°$ simplification but instead of the uniformly magnetized rod approximation I only talked about a point-dipole and the need to measure at large distances. This might be one of those times when you're best qualified to answer your own question - and that's perfectly fine! – uhoh Oct 16 '16 at 01:07
  • Ah yes, that article perfectly answers this question. But now when I'm using an air coil that's integrated into a solar panel, I don't know if the same equations apply, as technically they aren't the same thing. – John Oct 16 '16 at 01:16

2 Answers2

3

Understanding how to test and qualify systems of a satellite prototype is certainly on-topic in Space Exploration Stackexchange. Cubesat development is always conceptual at first, and you definitely need to use some physics to develop your understanding. That doesn't mean the question should be moved to Physics Stackexchange.

Measure in the plane perpendicular to the $\mathbb{m}$ direction and centered on the center of the device so that the $\mathbf{m \cdot r} $ term is zero. Then point the sensing direction of the magnetometer parallel to the $ \mathbb{m}$ direction. Now you have a scalar equation:

$$B = \mu H = \frac{4\pi \times 10^{-7}}{4\pi} \frac{m}{r^3} $$

$$B = \mu H = 10^{-7} \frac{m}{r^3} $$

$$m = 10^{7} B r^3 $$

So move the magnetometer close enough so that you are getting a good signal, then plug in the distance as $r$ and the measured $B$ and you have an approximate measurement of $m$.

A second way to do this is to drive your magnetotorquer with a low frequency sine wave and use a second small "sense coil" to measure the EMF at a distance. This can often be more accurate than a magnetometer, but it is tricky to do correctly.

Also remember that the magnetotorquer has a permeable material - the core that the coil is wrapped around that is long and skinny) and that's not necessarily going to be linear, so you should make a series of measurements at different currents. You should also make sure that $r$ is somewhat larger than the length of the rod, or measure at a few different distances. The magnetotorquer is not at all a perfect point dipole.

Also make sure there are no other ferromagnetic materials nearby.

In order to deal with the Earth's magnetic field, you can just turn the current on and off and look at the change in B.

The problem is at low fields, low cost magnetometers are not very accurate, so if you want to use an "Arduino class chip" (hobby type) or one in your phone, you may get results that are a bit off. But it could be a good sanity check or starting point at least.

This is actually not an easy measurement to do correctly. But you can get experiment with it even using an "unofficial magnetotorquer" to get a feeling for the process.

uhoh
  • 148,791
  • 53
  • 476
  • 1,473
1

Another way to measure magnetic moment is to suspend the magnetorquer (MTB) on a thread in a magnetic field. (For example, Earth's magnetic field will work). When the MTB is given a fixed DC current, it will behave like a rotational pendulum. The resonant frequency of the rotational pendulum can be used to compute the magnetic moment.

Magnetorquer Eng
  • 11
  • 1