I am trying to design an efficient DC solenoid which is only 3mm across, and 5mm long. I need to choose the material for the central plunger, which would be 1mm in diameter. I also need to choose the material for the frame of the solenoid which would complete the magnetic flux circuit. The frame would be comprised of two 1mm thick end-washers, joined by a cage of four 1mm thick metal rods.
I am currently thinking that pure iron might be suitable, but there are lots of other possible alloys, and ferrite materials to choose from. The solenoid coil would essentially be a stack of tiny disks made from copper foil, providing between between 32 and copper 64 turns.
I also need to be able to calculate the pull-in force of the solenoid before manufacturing it, but I am not sure how to do this. Can anyone help?