Can you help troubleshoot my solenoid issues?

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I have been working on a solenoid for different applications, but cannot find the desired output. I have a bobbin or hollow shell that houses a shaft that is split in half. At the center of this shaft is a spring, and when the solenoid is activated the spring is depressed, the two pieces of the shaft inside the bobbin come together activating a switch. Force required to activate the spring is 3 pounds, but for robust purposes, I have been using 4 lbs. I want a current between 0 and 1 Amps. The length of the bobbin is 0.12083 in. The bobbin is steel with nickel plating (this is the main suspect for the magnetic issues). I am using 30 gauge copper wire. The diameter of the solenoid is 0.375 inches.

So I have a few different concerns.

1. The nickel plating is interfering with the magnetic field.

2. I am using the wrong permeability constants for my equations.

3. The equations I am using are wrong due to the incorrect area and diameter ratios.

I have done a significant amount of research on this topic but there is just not that many in depth examples found on the internet. Many are simply theoretical, and don't apply to my applications.
 
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