Does the shielding around a solenoid actuator affect the force on the plunger?

Question

I'm looking to minimize the weight of some solenoid actuators I want to build, so I'm trying to better understand the effects of the shielding / frame commonly found on solenoid actuators.

My understanding is the force exerted on the plunger is essentially only dependent on the cross sectional area of the plunger, the permeability of the plunger, and the flux density within the plunger. If that is correct, then it seems that the shielding doesn't really affect the plunger, only the reluctance (and thus the inductance) of the overall system.

If I were to remove the shielding, it seems that I could expect a very low inductance when there was no core, so I would have to be careful not to burn out my coil, but other than that it seems like the system should be largely unaffected. Am I understanding things correctly?

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It seems like in practice there is a lot of effort taken to minimize the air gap in the system, and random forum posts state that if you don't do this your solenoid won't be as strong - however I have yet to see any math or reason to back this up or to explain how to figure out how much stronger one system is over another.

I'd be very grateful if someone could help clear this up!

Answer 1

I spent some time learning FEMM to figure this out.

The answer is yes, the case does make a notable difference in the pull on your plunger.

Without a case the pull on my sample plunger was 0.036 N

And with a case the pull was 0.047 N

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Edit: Playing with the simulations more, the effects of the case are more drastic as the plunger moves into the cavity. As the plunger approaches the other side, you'll start seeing at least an order of magnitude of difference, so not only is the case important but it is very important.