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

 

[sardar]

I understand your frustration with not being able to regulate the vertical position of your magnetic levitation system. In order to address this issue, you will need to consider the forces involved in the system and how they can be manipulated.

First, let's look at the equation for the force of a magnetic field on a current-carrying wire, which is given by F = iL x B, where i is the current, L is the length of the wire, and B is the magnetic field. In your system, the electromagnet is essentially a current-carrying wire, so this equation can be applied.

To manipulate the position of the item, you will need to consider the forces acting on it. The force of gravity, Fg, will be pulling the item down, while the force of the magnetic field, Fm, will be pushing it up. The equation for the force of gravity is Fg = mg, where m is the mass of the object and g is the acceleration due to gravity. The force of the magnetic field can be calculated using the equation mentioned earlier, Fm = iL x B.

To find the relationship between current and vertical distance, we can equate these two forces and solve for x, the vertical distance. This will give us the equation Fm = Fg, which can be rearranged to solve for x: x = (mg)/(iLB). This equation shows that as the current or power to the electromagnet increases, the vertical distance will decrease.

However, keep in mind that this is a simplified equation and there may be other factors at play in your specific system. It would be best to conduct further experiments and data analysis to accurately determine the relationship between current and vertical distance in your magnetic levitation system. I wish you the best of luck in your project.