Plunger Force of Solenoid: Am I Missing Something?

[Greg Freeman]

Maybe I'm just dense, but...

I searched for forum for "solenoid" and I still haven't found the answer that I'm looking for. Mainly, I want to know if there is a general equation for the plunger force of a solenoid-type linear actuator. I understand that the force of the plunger is related to distance in a way in the same way as a spring (but with maybe a polynomial relationship to plunger depth/distance), but I've also done some googling and I haven't found a simple general relation.

I also went through several EE books and they didn't have any descriptions of how to calculate plunger force, and then went through several E&M physics books and didn't find one with equations. In fact, the one I found that described the most about solenoids with plungers was written in 1924 (Magnets by Underhill) but doesn't really have any equations. I guess I could go through and try to derive such things, but I figure it's a solved problem and my background isn't in E&M.

Am I missing something here?

 

[Danger]

I don't know how you would calculate it. The factors involved are the magnetic and physical characteristics of the plunger itself (obviously a wooden one wouldn't have much pull), the number, gauge and arrangement of the coils, the electrical input... hmmm... I feel that I'm leaving something out, but I can't think of it right now.

 

[Greg Freeman]

Is there a general form to the solution though (neglecting specifics)? Like a R^2 or similar relation? (in this case a good approximation from the book I checked out looks like it would be the first half period of a sine wave, with no force when the plunger is centered and max force when the plunger is roughly halfway out, or maybe a shifted exp(x^2) relation)

I'm thinking back of the envelope calculations with something simple like an iron plunger (the only characteristics of the plunger would probably be its permeability and diameter) and no specifics to the coil sizes other than probably the length and wraps*current parameters for the coils. I haven't found anything even as simple as that.

Maybe an assumption that the plunger outer diameter is the same as the coil inner diameter would simplify things? Or how sensitive would the force relationship be to a plunger that doesn't completely fill the solenoid cavity. I'm just looking for any kind of relation at all, because I haven't been able to get my hands on any.

 

[Danger]

Sorry, man; somebody else is going to have to field this.

 

[marcusl]

Magnetic problems involving iron are way complicated because the permeability is non-linear and saturates at relatively low applied fields. Thus problems involve balancing turns and current (and heat) with plunger cross-section and length. You can probably make some simple assumptions like operating at weak fields to avoid saturation to get a ballpark answer, but then you aren't designing for full strength. Professionals use finite-element E&M modeling and even at that you have to increase the mesh density in areas that are prone to saturate. Commercial solenoids also include an iron frame to provide a return path for the flux.

I vaguely remember that Smythe solves for the lifting power of a horseshoe in his Static and Dynamic Electricity. Can't remember if it's permanent or electro-, if it's the latter then you'll get an overview of the equations that would be used in your case.

Is this a casual question or do you have an application (commercial or otherwise) to solve? In the first case you can experiment, or might get lucky and find someone who has worked with them before. In the second case I recommend purchasing one. Vendors will offer different models with advertised stroke, pull force, thermal properties, etc. and application data that would be hard to duplicate.