Analytical equation for Magnetic Levitation

[Davidk92]

Hello everyone,

So I've stumped uppon some problems during my project. It is not my homework or anything, so I didn't post it there.

I've built a magnetic levitation system, which could lift up to 2kg. The problem is, that we cannot regulate the vertical position of the item. But that can be MECHANICALY added later, it's not the main problem.

The main problem is, that we need an EQUATION or function F(i, x) - where 'x' stands for vertical distance and 'i' for the the current.

So what I want to know is, for how much does X change, if I add more current / power to the electromagnet ?

http://shrani.si/f/9/P5/3I3OPWvS/magnetna-levitacija-skic.png


Here is the scheme for easier interpretation (I apologise, it is not in English). The impotmant thing is the POSITION of the system! I don't want to have electromagnet to levitate from ground up - but too pull the item up!

I hope you understand. If not, please ask what you don't understand and I'll try to explain it better.

Kind Regards,
David

 

[mfb]

In general, it is not possible to analyze those systems analytically. You can find some approximations, you can simulate it numerically, or measure it, but there is no general formula where you just plug in your values and get the force as result.

 

[timthereaper]

mfb is right. You can't really analyze that system analytically. You can make an empirical formula by testing it a lot and doing a curve fit through your data and you'll get an equation.

 

[Davidk92]

So it's down to experimentally define it?
Honestly, I thought so too. I'll update this thread, if someone might be curious about the results for such mass to levitate - how the X and i react to each others.

Thanks.
Regards,
David