Are high-end rings and rails machined with less accuracy than the lapping bar was?
As pointed out by other posters, the rings themselves, and degree of their precision, is not usually the reason to lap. The reason is the composite error of all mounting parts combined/added and their effect on ring axis alignment.
Rings of lesser precision also benefit from lapping by having sharp edges and high spots corrected.
One thing you will notice as a recurring pattern when lapping is that while the rings are machined, the thinner areas at the sides tend to deflect away from the cutter. After the cutter is retracted, that area of the rings spring back. Anyone familiar with metal machining has seen this deflection. Sharper tools deflect less, but some deflection is almost always evident. When the rings are lapped, this area is corrected and no longer grabs the scope as the scope tube enters the rings.
Lapping bars are merely round rod stock that slides between the loosely clamped rings. The diameter of the lapping bar is typically a few thousandths of an inch less that the corresponding scope tube diameter, in order that we do not loosen the fit if done properly..
We are only ensuring alignment of the ring axes, not re-cutting the bores.
How about the accuracy of the machining on the scope tube? And then there is the malleability of the aluminum scope tube vs that of the steel rings.
This is all about being kind to the scope. The scope tube, unless junk or damaged, can be assumed to be straight and cylindrical and we are using the lapping method to ensure it lies in alignment to the ring bores.
As for bedding the bases, how does the compound harden and expand so much that it is subjected to the same force as the areas of the rail and receiver that touch and pull tight?
When bedding bases, the standard practice is to lightly tighten the base screws just enough to press the base down onto the bedding compound, not squeeze the material out. Once the compound is cured, the screws are brought up to the specified torque value and nothing moves during that process.
Epoxy expansion does not affect this process, nor contribute to tightening the screws. Bedding the base normally helps with keeping the ring bores aligned and reduces the need to lap, but there are often sharp edges and/or high spots and lapping will address these.
The screws on the rings are not going to tighten exactly the same on the lapping bar as they will when you mount the scope.
This may be the source of your questions...the ring screws are NOT tightened down onto the lapping bar with any substantial force and certainly not clamped onto the bar or brought up to torque.
When I was teaching long range precision, I usually helped students with installing their scopes. Most people really don't know how to properly mount a scope and I usually saw both eye relief errors and almost always out of level. I used a Starrett 4" machinist's level to correctly level long range scopes.
I have mounted several hundred tactical/precision scopes in the following manner:
Picatinny style mounts:
The rings are set loosely onto the base, pressed forward against the face of the slot and the clamp screws lightly tightened.
The lapping bar laid onto the bottom ring halves and first used as an alignment tool.
The ring caps are lightly snugged up on the bar to align them to each other as closely as possible.
The ring clamp screws are then torqued to the base. You will not touch these clamp screws again.
The ring caps are removed.
The lapping bar is removed, loaded with lapping compound and set back into the bottom ring halves, now to be used as a lapping tool.
The ring caps are placed back on and the cap screws lightly snugged.
The bar is then slid back and forth inside the rings, using a push/pull motion with light rotation.
As the compound is exhausted and the rough/high spots worn down, chase the bar down by lightly tightening down the cap screws. At no time during lapping will the ring screws be "tight".
You will be able to feel when the lapping compound is completely exhausted and stops cutting, and you will stop at that time. One cycle is usually enough to take care of the worse of it.
Remove and clean the ring caps and lapping bar. Keep the respective ring cap both matched to the ring bottom and oriented the same. I usually index mine and students with a very small prick punch where the rings meet - one dot at the front, two dots at the back.
Clean the ring bottoms.
Inspect the condition of the ring contact surfaces. You will be able to see finish wear where material was removed. I usually go for about 50-75% contact. I do not completely remove the interior finish. Note at this time that the areas touched by the lapping bar were the high spots and pressure points against your expensive scope tube.
Once you have 50% or so contact, make sure everything is clean, loosely install the scope and ring caps, level your scope, set your eye relief and torque your ring cap screws.
Each time threads are tightened, the metal loses some of its strength properties.
Torque values are designed to deform (stretch) the screw just enough that it will return to its original shape when pressure is released. You are correct and yes, this DOES weaken the screws more and more each time, ** IF** we actually torqued them down onto the lapping bar, which we DO NOT.
Land surveyors have a term they use, "chasing dust". It may be applicable here.
If you would:
a) like to have your scope work as smoothly (magnification and parallax adjustments) as designed, and
b) like to have the best stability via increased/improved tube/ring contact, and
c) wish to eventually resell your scope without ring damage ("ring marks"), then
it's NOT "chasing dust" and *proper* lapping is a good idea.
If one doesn't care about any of that, one shouldn't bother with lapping, but also shouldn't object to those that do.
Machining round ring bores isn’t the problem. The problem is mounting two rings on an action and trying to maintain cylindricity between the ring bores.
^^^ This ^^^ ....mostly. In most cases, we will still see a slight out-of-round condition due to cutter deflection.
When moving scopes between rails, how does one lap rings to compensate for all of the possible variations? If the concept is that rails aren't true and actions aren't true, are they all identically untrue or does lapping to correct for rifle A potentially make things worse for rifles b-z?
Look at this process as matching the rings to a particular rifle/base platform.
As already pointed out, one would leave the rings with the rifle and simply swap scopes without disturbing the bottom halves of the rings.
You are correct to think that lapping rings into alignment on one rifle might make the misalignment worse on another gun.