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The Hornady LNL AP is a beefy machine, much more solid than the Dillons. IMHO it apparently does not flex as unevenly due different pressures on each side of the ram/shell plate as compared to the 550 or 650. This would explain the better run-out. But I’m no expert.
The engineer in me wants you to explain that statement. Bullet seating and thus its run-out is determined by how the bullet is set by the die and to some extent by the preparation of the brass before it accepts the bullet. The sturdiness of the ram of the press should bear little on the actual seating of the bullet, which occurs near the top of the stroke and any issues in the shell plate or ram stability minimized by simply being consistent at the top of the stroke. Are you using exactly the same dies, bullets, OAL, etc between them and making sure that the brass is flared exactly the same amount?
There are two areas in most reloading presses (single stage or progressive, other than die features/quality) that influence the straightness of sizing and expanding brass, and seating bullets: How or if dies are allowed to float independently to seek their own center relative to the case, and tightness/sturdiness of the ram in its bearing(s).
The latter is particularly critical in progressive presses, since different forces in different stations impart a tilting force on the ram, which if not sufficiently restrained will misalign the cartridges with the dies. Also, traditional compound leverage presses (with the toggle at the bottom end of the ram) have varying levels of tilting (lateral) force applied to the the bottom end of the ram during the stroke. Given equivalent manufacturing tolerances (i.e. bearing play), the sturdier, larger diameter ram of the LNL AP better resists/restrains the off-axis thrusts. In single stage presses, this is one reason many H-style presses and the Forster co-ax have excellent reputations for accuracy/concentricity.
The former (die float) issue is quite different between the two major systems of die retention in progressive presses. Dillon, Lee, and RCBS have the dies mounted rigidly in a single plate that floats in the press frame. The LNL AP has dies that individually float (to a lesser degree) in LNL bushings. As the cases advance into the dies, if one die engages (excerts pressure on) its case before others do, that one die/cartridge starts to lift its side of the tool head before the other side, causing tilt. Furthermore, each die is tilted at the same time/degree because they are all rigidly attached to the die plate. Granted, once the tool head travels to the top of its slot, it will even out consistently, but in the meantime, different cases were advancing into dies at an angle, causing problems. The LNL die retention system does not suffer from this problem.
At least one user has measurably improved the runout in ammunition loaded on their Dillon press by drilling a hole in the lock ring parallel to the die axis, and then installing a corresponding pin in the tool head that engages the hole in the lock ring. In this manner, the pin can keep the lock ring and die from turning, while still allowing the lock ring to float above the tool head, thus allowing the die to float in its threads. This is repeated for each station. Note that this modification requires the use of lock rings which can be fixed to the die via a set or clamp screw, excluding Dillon and Lee lock rings. While not perfect (conical die threads couple lateral float to angular float, which can interfere with the resulting alignment of the die to the cartridge) this is certainly an improvement over the stock arrangement.
Andy
