I am unable to follow why 222 cases made from 223 cases need to be fire formed.
Depending whose drawings you take the dimensions from, both cases are within a couple of thou of an inch of being the same diameter at the neck/shoulder junction. Again depending on whose drawings are referred to, this junction is 1.260in ahead of the bolt face for the 222. It is 1.433 ahead of the bolt face for the 223, so at 1.26in ahead of the bolt face the body diameter is about 0.013 in larger than the 222 body diameter.
The usual reason for fire forming is to either reduce the body taper of a case or to move the shoulder forward – or both. When a 223 cases is re-sized to 222, the rate of body taper is increased (i.e. the diameter at the neck/shoulder junction is reduced) and the position and angle of the new shoulder is determined by the setting of the full length sizing die.
I have made 222 cases from 223 cases myself. I used a 222 form and trim die to push the 223 shoulder back to ALMOST the correct 222 length, doing it in two stages, which worked better than trying to do it in one. Then I ran the cases through my regular 222 full length sizing die, which was set up to match my rifle chamber. As expected, the finished cases measured up exactly the same as fired ‘native’ 222 cases run through the same F L die. No need for any fire forming.
I checked the neck thickness and found that with the Federal brass I was using, the neck diameter of loaded cartridges was still an easy fit in the chamber neck, so there was no need for neck turning or reaming. However, it is possible that it could be needed with other brands of 223 brass.
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