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Tolerance stack and accuracy

I’m going to be doing some posts on how things are made, but before I do it’s important to make a few things clear.

One of the most critical issues in manufacturing is tolerance stack. Ordinarily this is defined as the possibility that a part can be non functional and still be within spec. I could link to Fritz Scholz, who pretty well has the science down, but it’s a classic TL: DR.

Instead, imagine a 2″ diameter shaft ten inches long. The engineer wanted grooves every inch, .100″ deep and .100″ wide. The width of the grooves isn’t critical, soo he toleranced them .100 +/- .005. Then he dimensioned the lands between the grooves .900″.

The Machinist looks at the print and determines he doesn’t have a grooving tool .100 wide, so he used one he had in his toolbox that was .104 wide. He also saw that the other dimension on the print, the .900″ one, had no stated tolerance, so he was very careful to make sure there was exactly .900″ between the grooves.

The top is “As drawn”. the bottom is “As made”

They look really close to the same, don’t they? Lets zoom in to the last groove on the right.


The addition of the extra .004″ per groove added to each segment until at the end, nine grooves later, the groove is .036″ off.

That’s tolerance stack. Proper tolerancing of engineering drawings is necesary to the manufacture of quality parts.

There’s another, less well understood kind of tolerance stack, and that is the tolerance stack of multiple fixturing. When something as simple as a bolt is made, it has one operation- it gets threaded. A shoulder bolt gets threaded, and then has the shoulder turned or ground, but even this is usually done without removing it from the machine. A pipe fitting, on the other hand, has threads on both ends, and is held in the middle to machine. So one end is cut, the fitting is turned around, and the other end is cut. The act of chucking and unchucking will cause the threads to be out of alignment, and it is the amount of “Slop” or innacuracy in the machine’s fixture that determines how far off this will be. Mostly a non issue with pipe fittings, this is a disaster in more complex manufacturing.

The upper receiver on an AR is machined in several steps, and the brilliance of the original Stoner design is that the critical dimensions are machined all in one operation. This means that the bore that houses the bolt carrier group, the mounting surface of the barrel, and the centerline of the threads are all in precise alignment, or as precise as the stated accuracy of the machine. In other words, if the bolt carrier bore is done in one op, and the part is removed from the machine and placed in a different fixture to do the threads, the liklihood of the threads not being concentric with the bore is accentuated. There are some manufacturers that do this, with varied results. This is the kind of “Tolerance stack” that is due not to bad design, or the misunderstanding of the design by the machinist, but to a failure to understand the process. The critical machining must be completed without removing the part from the machine

Here is an example of CNC machining which includes threading. This is simply a demo, but if you were to take the part out and very carefully measure it, you would find that the cylindrical surfaces are all parallel and concentric at a level that can tax the limit of the ability of the equipment to measure, because they were all cut in the same, new machine, without being removed or disrupted during manufacture. The thread roots are concentric with the shaft and cannot be otherwise.

When an AR upper is manufactured properly, the bore, the OD, the face, and the threads are cut in one operation, without removing the part from the machine, so there can be no fixture related tolerance stack. If the face is not perpendicular to the bore, it can only be because it was manufactured improperly. If the manufacturer didn’t go to the trouble to do that right, the whole thing is suspect, and if accuracy is important to you, you should purchase a properly manufactured part. If the face is not perpendicular to the bore the odds are good that the threads are off as well, and that cannot be corrected in a lathe or with some files.

Lots more on this later. Anyway, I just wanted to talk a little about tolerance stack before moving forward, it’s important to the discussion.

The AR series including the diversions off into manufacturing

Don’t know yet if they’re in a good order, they may or may not be. I think this is all of them.
This was… five years back? I had just purchased and built my very first AR and was still learning as I went.

I see there are a comment or two from Farmer Frank and Kees Kennis. G-d rest their souls. i miss those crazy, wonderful old men.

I’ve learned a lot more now, and I know that to the pros all this stuff is just common sense, but I had fun looking at it all through the eyes of a rank novice, and it filled me with admiration for Eugene.
The manufacturing stuff is still the same, the laws of physics are the laws of physics.

Ever since

tolerance stack and accuracy

CNC machining


Off the processes for a while


Putting it together

A word about the lower

The Package

CNC machining

has come a long way. When Parsons and Sikorsky decided to numerically control machines that made punches for helicopter rotor parts, they quickly realized that they didn’t know a lot about computers. MIT took the project in hand and made the first NC machines out of old Cincinnati mills. At the time, it literally was Numerical control; the circuitry took numeric instructions and made the servomotors move. Not until several years later did they actually integrate memory into the machines making them true Computer Numerical controls.

Without the CNC machine, a powerful lot of stuff the military needed could not be made, and so in concert with MIT, the Military purchased and retrofitted some machines and provided them to some of the shops they used, so they could get the stuff they needed.

The AR grew up in this time. NC and later CNC machining made the AR platform not only possible but fairly easy to build- it did for firearms what Henry Ford did to cars. It was no longer necesary to be a competent gunsmith or even machinist to make a good functioning firearm, pretty much any cletus could put a forging into a machine and a serviceable part would come out.

This was also sort of true of other firearms, like the AK, which, while it was not the child of CNC certainly benefitted by it and still does. The difference is the AK is designed to have wide open tolerances which allowed it to operate under many conditions, and withstand almost unbelievable abuse; the tradeoff is marginal accuracy, and pretty much always will be.

Unlike the AK, the AR was designed to be a precision firearm with precision fitted components, but with the ability for tolerance stack and human error removed.

Remember the post about Tolerance Stack? The brilliant thing about a CNC machine is that once a part has been verified, and tested exclusively, it can be duplicated with precise and repeatable accuracy almost infinitely. A properly cared for machine tool with appropriate tooling and careful operation has an indeterminate life; there really isn’t any way of telling how long one will last. Many of my customers are still using equipment made by Pratt Whitney and Giddings and Lewis that are now fifty or more years old. The leadscrews have automatic lubrication, they ways and gibs adjust readily and easily, and as long as they are not abused they continue to make good parts.

Stoner knew this, and he designed the components of his firearms to be easy to make with high precision. Let’s look at one of the most critical parts- though a lot of AR owners don’t even know it’s there.


You can click on the image to embiggenate.

This is the barrel adapter. Most people never see it as a separate part of their barrel, but if you look up into your receiver you should be able to see the threads that join it to the barrel inside the adapter.

This little bastard is brilliant. I mean, bloody brilliant.

In a bolt action rifle, or in other types of autos, the receiver is a solid machined piece that has the barrel screwed or pinned or sweated into the receiver face. This in itself requires a good deal of hand fitting, but the additional issue of fitting the bolt in place, making sure the bolt hits the recever lugs in the right place, and doesn’t allow excess headspace, is a good damned deal of work for even a talented gunsmith.

This little chunk of steel makes all that go away. You see, in a CNC machine, when you cut a thread, the thread always begins and ends in the same place, every single time, always. Which means that when you CNC machine a barrel, it’s threads will always start at, say, nine o’clock, and end at eleven o’clock. The threads in the barrel adapter are similarly oriented.

When the barrel adapter is made, it is machined in two operations, on a CNC machine. First, the face is squared, giving you surface A. Then the material is bored out of the center, the bottom of the hole faced, (Surface C)and the threads are cut. Then the outside of the part is machined, giving you diameter D and surface B. The part is then cut off and the secondary operations are performed. This means several things.
1: The surfaces A, B, and C are always parallel to one another, to the limit of the machine’s accuracy.
2: The surfaces A, B, and C are perpendicular to the diameter D.
3: Diameter D is concentric with the root diameter of the thread T
4: The thickness between surface A and B and the distance between surface A and surface C is predictable, repeatable, and consistent from one part to another.

Far better than can ever be done by hand in multiple operations, and far better than the average gunsmith wants to do. When JMB, God rest his soul, designed the M2 Garand (thanks Tam), he made it so the hand fitting was easy and simple. When Stoner made the M16, he made it so no hand fitting was required, period.

The upshot of this is subtle but vital. Barrels are made in a bunch of different ways, but at the end, the last thing that happens is that they get threaded and chambered. Because of CNC manufacture, threading the barrel into the barrel adapter means that the headspace is part of the barrel and adapter, and the headspace does not depend on the receiver but moves entire as a unit from receiver to receiver. Thus, a barrel/bolt that is a good accurate combination at a specific headspace can be moved from one firearm to another and the accuracy of the barrel moves with the barrel, assuming it is placed in a properly manufactured firearm. Here’s the subtle bit: No hand fitting is required to get the relationship between the barrel and the barrel adapter just right, because it’s done in CNC machines, and if done to spec it will always be just right. Sure, it’s possible to get a match grade barrel that’s headspaced as tight as a drum, but even then, you’ll see that they are sold as sets. You get the barrel, the adapter, and the bolt. Therein lies the accuracy of the firearm, and nothing else can effect it like those components can.

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