So I have been running some FEMM simulations and noticed an interesting effect which others have talked about in the past, see:
http://jnaudin.free.fr/steorn/html/orboeffecten.htmBut that's all I will say about that source as to avoid having to name that cursed company
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Now where this came from is knowing that Magnetic flux is always conserved and you can say that inductance*current (L*I) is always constant for non time varying magnetic system. This can be seen as equivalent to momentum, m*v in classical mechanics which is also always conserved unless a force acts on the system to change it. We can see this by simply removing the core from a powered solenoid, the current shoots up as it will want to maintain the flux it had with the core inside. Consequently the energy of the system also rises as L*I must remain constant, since the energy of the solenoid is defined by L*I²/2, the current rising will have a quadratic relation on the energy. The obvious source of this energy gain is your muscles that jerked the core out of the solenoid, as you would notice the core would very much not like to leave the center of the solenoid.
Now that is the basic theory aside. Obviously this is nothing new. Has been discussed in the past under different names such as "parametric transformers", "parametric resonance" and so on. This research has died down since the 70's but someone in academia quite recently reignited intrest in this field:
https://www.researchgate.net/profile/Andres-Revilla-Aguilar Now this brings me to the FEMM simulation. Basically it's a toroid coil next to a magnet and in between moves a piece of iron to shield the PM field. When the shield reaches TDC the toroid is powered on, in this state the toroid has maximal inductance, now as the shield moves away and the toroid is exposed to the magnetic field, it will lose quite a bit of this inductance due to core saturation thus making the current rise to keep the flux constant inside the coil. This consequently will increase the magnetic energy, quadratically, of the coil.
Attached you also see a torque table that shows the torque difference for the shield moving to and away from the coil/magnet. What surprised me was the small difference in torque you get on the shield when the toroid being switched on and off. This may be significant as the inductance can reduce by as much as 10 folds due to the saturation of the PM field and thus end up with two orders of magnitude more energy for a very small mechanical penalty. FEMM sadly does not support such dynamic inductance calculation but this can be confirmed quite easily with a capable LCR meter. On the other hand FEMM is quite accurate at force calculations which make these results look promosing.
Sim specs:
Core: BH-curve modeled after metglass cores (attached), OD=40mm, ID=20mm
Coil: 10A, 10turns
Magnet: N55 neodymium magnet
Shield: pure iron with linear permeability
I used lua scripting in FEMM to perform the stepwise simulation.
TLDR: L*I is always constant, when you lower L, I has to rise proportionately, thus the total magnetic energy will rise quadratically due to L*I²/2. Parametric transformers have been under active research recently. FEMM simulation shows that little mechanical energy is expended for potentially large induction changes of a toroidal coil.
EDIT: Might not be obvious but there is an mp4 video showing the simulation between the attachments.
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Topic: The interesting case of mechanical induction modulation. (Read 2662 times)
