dynamic equations for solenoid 1

[zekeman]

I have an application to move a .33lb mass 1 inch in and out within 35 msec so I am thinking linear solenoid which wouild require a dynamic analysis which I probably can develop but if someone out there knows of a source I would very much appreciate hearing about it. I tried Google and came up pretty empty on this and the manufacturers didn't help either.
The duty cycle is extremely low, <.1, so I can drive the solenoid into saturation which will make the math easier but I need some assurance that it will work.

 

[israelkk]

Is the solenoid needs to apply additional force too or just enough force to accelerate the mass and move the 1" in 35 msec?

 

[hydtools]

Maybe this will give you a start:

http://www.daycounter.com/Calculators/Magnets/Solenoid-Force-Calculator.phtml

or this:

http://www.mathworks.com/access/hel...&q=electromagnet+soleniod+force&aq=f&oq=&aqi=

Ted

 

[zekeman]

Thanks for your responses.
Israelkk,
You want to apply the max magnetic force to move it. There is as spring return also.

Hydtools,

Very good reference, but they make the assumption that the there is a current source, not a voltage source which would involve the electrical current equation, but I might opt for this solution which is much simpler to solve as I mentioned and can get the time out of it.

 

[israelkk]

zekeman

You need to numerically solve a set of linear and non-linear differential equations which include the magnetic circuit of the flux, electric circuit of the current build with time in the coil and the mechanical system of forces, masses, friction and spring. If it operates a valve then the pressure, sealing areas and flow of the fluid has to be taken into account too.

http://israelkk.googlepages.com/home

 

[FeX32]

The DE relating the current to voltage should be of the form"
L*di/dt+R*i=v


Fe

 

[israelkk]

FeX32

What about the back EMF from the change in the flux due to plunger movement and the non-linear B=H curve of each iron and air part of the solenoid body structure?

 

[FeX32]

Can't argue with you there. The change in flux does create a back EMF of v=d(phi)/dt.
How would you couple all these relations without making assumptions?


Fe

 

[israelkk]

FeX32

As I said in my first post, you write the magnetic circuit equations of the solenoid (including the iron parts, air gaps, etc) due to the magneto motive force, coupled with the electrical and mechanical equations. You get a set of differential equations and solve them numerically. For this you need to have a knowledge of magnetic circuit theory too. For each solenoid design the magnetic circuit will be unique due to the actual structure of the solenoid parts (plunger, pole, coil, air gaps, etc.). Recall that the flux flows in each part of the solenoid part of it in series and part of it in parallel paths.

 

[FeX32]

hmm. If I remember correctly 'accurately' this is a coupling of PDE's. The solution to coupled PDE's is only readily solvable using FE software such as comsol.
Correct me if I am mistaken.


Fe

 

[israelkk]

No. you can solve it with very good accuracy and accept the instantaneous currents, forces, and movements of the plunger as a function of time.

 

[zekeman]

Well, I looked this over again and,as I thought, going with the current source eliminates the current loop and reduces the complex set to a more manageable one; since my duty cycle is low, I can probably implement it in practice.

The equations are in the reference by Hydtools, for which I am especially grateful.

I will solve this numerically.

Many thanks to all who took the time to respond.

Zeke