The following answers are for the negativ pole, where the spring permits the difference in legths of the batteries.
-Please can you explaien what is a CR2 battery? It is a battery with diameter 15.6 mm and length 27 mm
-How much force you want from the spring? for the smallest battery 0,5 kg (with a deflection of about 0,5 mm) and 1,0 kg with the a deflection of about 1.5 mm. The largest deflection will be about 2,2 mm when the battery is positioned in the wrong direction. These forces are suggested from a battery factory.
-What are the environmental constraint? they will be as for mobile phones.
Physical constrains:
-the diameter of the battery 15,6 mm
-in lenght about 5 mm from unbendt position to maximum deflection including support (plastic cabinet)
I´ve made some FE-analysis and the result in von Misses stress is about 1200 MPa in a bend radius of 1,5 mm and an arm about 6 mm, where the force is aplyed.
If there still are some things to be cleared, please contact me.
Regards
Lars Monroy