Calculation for proportional mechanical solenoid Force

[sk_astroman]

TL;DR Summary

I'm looking for calculation for proportional solenoid force - reluctance method

I'm looking for calculation for proportional solenoid force (constant force for some working stroke) using magnetic reluctance based on equivalent magnetic circuit by networking method. I was reading a book Elektromangnate by Dr Kallenbach which discussed such method but for switching solenoid. Can anyone help me how this magnetic circuit can be built for proportional solenoid?

 

[jrmichler]

I found a lot of good information using search term solenoid design. One hit, http://commons.princeton.edu/motorcycledesign/wp-content/uploads/sites/70/2018/07/solenoid.pdf, had this graph in it:

Does one of these curves describe what you are trying to accomplish?

 

[berkeman]

solenoid design. One hit, http://commons.princeton.edu/motorcycledesign/wp-content/uploads/sites/70/2018/07/solenoid.pdf,

I'd always wondered about the Yoke part of a solenoid...

 

[sk_astroman]

Thank you but i know the links you posted in the reply. Thank you!
But i am expecting building equivalent magnetic circuit for proportional solenoid with control cone geometry. if any one could help me on this topic. Thank you!