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concentricity/ run out

I have recently begun testing concentricity on reloaded .223 & finding it to be terrible, with most measurements in the 5/1000 to 10/1000" range. I am using Dillon Carbide rifle dies. I think my dies are adjusted correctly & I take my time. Why is my bullet run out so high? I am able to correct this with another device to 1-2 thousandths but understand this is not as optimal as correct concentricity "hot off the press". What am I doing wrong?

When you set up the dies, always tighten the die lock rings with a case or cartridge up in the die. Additionally, adjust the bullet seating die with a fired case in station one. This ensures consistent upward pressure on the toolhead. Finally, what bullets are you using? Don't expect a bulk 55 grain FMJ bullet to be as concentric as a 69 grain match BTHP bullet.

My dies are set up exactly as you described. I use a variety of bullets: Armscor 62 gr, Nosler Varmageddon 62 gr, Sierra Match HPBT 69 gr & 77 gr. I don't use 55 gr bullets due to my fast twist barrel. The run out is the same with all of them. I just did a disassembly & lube of the press & used the alignment tool upon reassembly prior to this reloading session. The press functions flawlessly. I keep my dies clean. The run out measurements are very inconsistent, usually from 5-10 thousandths. Rarely, one will be 1 thousandth & sometimes as much as 13 thousandths.
I use once fired LC brass & keep it properly trimmed. All of the bullets mentioned above seat to a very consistent depth with OAL always being within 2 thousandths. I do not use compressed loads. I do note that the interior of the seating stem is not smooth & seems to have a "grainy or matte" texture. Is this normal?
Additionally, it makes no difference if I carefully align the bullet & ride it up into the seating die, or just plop it in the case mouth & don't support it as the ram is raised. I can adjust the cartridges on the Hornady Concentricity Tool easily to 1-2 thousandths but this is time consuming & tedious. It concerns me that this will adversely affect neck tension or loosen the crimp & cause bullet set back especially since I have to move the bullet so much.

Perform a couple of experiments please. First, remove the depriming assembly, and make sure the carbide expander ball can float a thousandth or so on the depriming pin. Back out the depriming pin as necessary to accomplish this. Then load a few rounds and check the runout.
Next, remove the carbide expander ball entirely and repeat. What I'm looking for is to see if the upper decap bolt is bent slightly.

I performed the test with & without the expander ball & it made no difference. The run out is still 5 to 10 thousandths. I'm beginning to wonder if it's the aftermarket screwed in tool head I'm using to keep OAL more consistent? I'm going to return to the original tool head & see if this makes a difference. I'll report back either way. Thanks for the previous suggestions & help. It is much appreciated.

As suspected, the main culprit to my run out issue was indeed a Uniquetek tool head. Once I went back to the Dillon tool head, the run out consistently decreased to 4-6 thousandths, and while not great, is certainly much improved. Interestingly, a Redding competition seating die I also have could only manage 3-5 thousandths with the bulk Armscor 62 gr FMJBT bullets I'm currently loading. The Dillon die compares very favorably to the much more expensive Redding die. I suspect the Sierra & Nosler bullets I have on hand will do much better.

Our experience has been that allowing the toolhead to float, combined with correct procedure when setting up dies, allows for more consistency.

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