# Magnetic decoupling torque

I have a system consisting of 4 magnets rotating at speeds between 200 and 6,000rpm, which are facing 4 other magnets with a 0.5mm gap between the two sets. The set-up looks like this:

Both sets of magnets have their noth pole facing out so that they repel each other (the 0.5mm gap is maintained by other means). The resulting effect is that when the bottom set starts spinning, the top set follows because the top magnets naturally fall (radially) between the gaps of the bottom ones.

What I'm trying to do is work out what the decoupling torque provided by this set up is. In other words, if the bottom part is spinning, how much torque do I need to provide to stop the top part from rotating?

The diameter between the centres of the magnets is 17mm, they are 90 degrees apart, and I have the following (very basic) information on the magnets themselves:

• Diameter: 6mm
• Performance: 5,900 Gauss
• Vertical pull: 1.4 kg
• Slide resistance: 0.28kg

Can anybody point me in the right direction? I have made the following attempt, but I don't think that's right:

T = 4 * (8.5e-3 * 0.28 * 9.81) = 0.093 Nm

• My hunch would be to go look at motor slip, especially in the case of a stepper motor. I would imagine whatever equations are used there would be very similar to the scenario you describe, as stepper motors work by a very similar principle, but they use electromagnets instead of permanent magnets (so they can alter which sets are "active" and thus drive/step the output shaft). Nov 15 '16 at 20:30

I think you are facing 2 different modes, depending on the difference of speed between both magnets. When both magnet are are at the same speed, the magnetic torque from one of the other is null.

Let's think on it first as a static problem, and suppose that your body1 is immobile, without any torque, the body2 make an angle of 45°. Let's rotate magnet2 from 45° to 0°. An opposite magnetic torque is created (in order to go back to the stqble position). Maximum torque would be reach at 0°. Continue to rotate, directly after position 0°, the repeal force of the magnet apply in the opposite direction (so do the torque). The magnets are pushing your system to the next stable position at -45°.

Under this maximum torque, both bodies are lightly coupled, an rotate at almost the same speed. The torque can be calculated from the repealling force between the magnets. You should calculate for one magnet the repealling effect to a second magnet depending to the distance between both magnets. Then express the force of 4 magnets from 1 body on one magnet of the second body (then multiply per 4), and deduce the torque.

Beyong this torque, both bodies are decoupled, and the magnetic torque is alternatively positive and negative. As a result, speed of both bodies are not not significantly impacted.

If you want to stop one spinning body thanks to the second, I would say, you first have to couple both (same rotating speed), then apply a torque. This torque must be under the maximum one, otherwise you decouple the bodies anew.

• "When both magnet are are at the same speed, the magnetic torque from one of the other is null." Is this correct? It sounds like confusion with an induction motor where slip is required. May 27 '18 at 16:08