# A question about perfect fit

Yea I don’t think the perfect piece and perfectly equal-sized hole could ever be made merely by drilling/cutting out the piece.

Let’s say we had a 3D printer that could build things at extremely high precision. I could make a cylinder with a 2.00000 inch round hole in it and also 3d print a 2.00000 inch round cylinder. then, perhaps, we could test it.

I was able to cut out a circle with an xacto knife from a thick piece of leather. The hole left is the same size (no kerf) as the hole. The sides of the hole and the piece cut from it are pretty straight (obviously i couldn’t hold the knife perfectly straight up the whole time). The piece just plops right into the hole. Might need a very small tap to get it in. It’s not very thick of course, maybe a little over 1/8" or so.

Another issue is how smoothly you can make the surfaces. If you essentially have no space between them, the slightest imperfection will act as block. Suppose your cylinder, for example, is a perfect 10 centimeter circle and your hole is an almost perfect 10 centimeter circle - but there’s one spot inside the hole that has a very slightly bump so the circle is actually only 9.99 centimeters at that point. If your materials have no give to them, then your cylinder won’t fit in the hole.

One problem is that if your tolerances are that high, you’ll run into cold welding. Two similar metals with perfectly mating surfaces will simply stick together when they touch. The slightest bit of oil or contamination will ruin the effect (and hence it’s actually a very rare problem in practice), but in that case you aren’t achieving the tolerances you mentioned.

Sounds like cold welding is the same sort of molecular bonding mentioned above.

Does this only happen with metal? What about plastic, glass, etc?

As far as I know, it’s only metal. According to the great Feynman (from the Wiki article)
The reason for this unexpected behavior is that when the atoms in contact are all of the same kind, there is no way for the atoms to “know” that they are in different pieces of copper. When there are other atoms, in the oxides and greases and more complicated thin surface layers of contaminants in between, the atoms “know” when they are not on the same part.

Here’s an entire thread on this topic:

Here is a really cool photo (from Wiki) of 36 gauge blocks wrung together. The description says the photo was taken 107 years ago. It’s amazing they had the precision machinery to manufacture these back then.

I was going to correct you on the spelling of gage blocks, but it’s apparently an acceptable variant. Well, not to me, but carry on.

Makes me wonder at what point the cylinder would start sticking to the hole. Say the cylinder is 6 inches long and the hole is at least 6 inches deep. perfectly smooth sides as close to being exactly the same size as possible. You put the cylinder on top of the hole and push down. How far would it go before it gets stuck? Half a mm?

What if it’s exactly the same size to within a ten thousandths of an inch but not enough to cause this sort of molecular bonding? Then would it just slide right in?

If the cylinder is 99.9999% the size of the hole, would it just slide right in then?

A very close fit means not only do your peg and hole have to be perfectly sized - they also have to be perfectly round, and they have to be perfectly straight. The closer the fit between peg and hole, the straighter they must be.

The surfaces have to be smooth and clean - no gouges resulting in raised material, and no debris.

You have to hold the peg in perfect axial alignment with the hole, and you have to apply a perfectly aligned axial force to insert it.

Real-world factors will screw things up at some point. Nothing is perfectly round, perfectly straight, perfectly clean, and perfectly aligned. At some point during insertion you will end up with localized contact between peg and hole, resulting in frictive heating (or gouging/galling). Local temperature increases result in local thermal expansion; backed by an unyielding mass of material, the warmer areas bulge outward, causing interference, resulting in more friction/heating. Now it’s a press-fit, at least until things cool down. Without lubrication, you’re likely to end up with damage if you keep advancing the peg against resistance.

I know f industries that use light interference to obtain their accuracy, such as on certain gun sights.

Its also used elsewhere, these things are hand finished - machines can’t get to that accuracy - how do you think datum plates are made.

I get that, that’s why i phrased the question to be as good as humanly possible as opposed to perfect. I don’t expect it to be atomically flat. Let’s talk about materials that can be machined to within .00001 inch or so. That’s good enough for purposes of my question. Let’s also ignore temperature changes (assume the same temp throughout) and electrical charge forces and such. The only force i’m really interested in is the friction of the sides of the hole on the sides of the cylinder.

The shape could be a square, triangle, octagon, whatever, I only use cylinder (circle) in this question for sake of simplicity and b/c i assume a perfect (as close to perfect as possible) cylinder is easier to manufacture than a perfect cube… just stick it on a lathe.

I think it might make a difference whether you’re working in an atmosphere or a vacuum at the tolerances we’re talking about. I think it would jam up really fast in a vacuum.

Well if there were a vacuum below the cylinder underneath it in the hole, yea. but assume the hole is open on the bottom, no vacuum.

The ‘home’ button on my iphone seems to fit as close to ‘perfect’ in the hole it’s in as i could possibly tell. Yet the button can still move freely. Does that necessarily mean the button is smaller than the hole by some degree? I know apple manufactures this stuff within extremely small tolerances.

The home button on an iPhone is beveled. When it is the up position, it fits snugly, but there is very little surface contact to bind. Not at all like the situation in the OP.

Like you, I’m ignoring bulk temperature changes. I’m claiming there will be local temperature changes where any slight binding (because you tilted the peg, or moved it toward one side of the hole) results in friction which results in local heating and thermal expansion, producing local dimensional changes that cause further binding.

Regardless of cross section shape, the peg (and hole) both need to be perfectly straight, or they must have perfectly matching curvature (i.e. they must both be sections of a torus with matching radii of revolution)

Maybe none of this matters: the known/demonstrable behavior of gauge blocks suggests that your perfectly-sized peg will bind in your perfectly-sized hole.

in the iphone 5s it’s actually flat, but it is still thin. Even if it’s only 1mm thick it’s still a cylinder technically speaking, just a very flat one. could the near-perfect cylinder from my OP fit 1mm down into the near-perfect same-sized hole without any force? Maybe after a few mm’s you’d need to push quite hard?

If I cut out a circle from a piece of paper with scissors or an xacto knife (no lost material), and if somehow the paper were extremely inflexible and stiff, could the circle fit through the hole I cut it from?

I mean - the atmosphere in which you’re working is going to lubricate and cushion the whole operation, even if only a little. Even if the surfaces are the theoretical perfect fit we’ve been talking about, the materials will have a bit of deformability - and this will allow air (a little bit) to get sandwiched between the objects.
It will tend to squeeze out, but will act as a lubricant to allow movement for longer than if you were working in a complete vacuum.

OK, you really need to let this go.

First of all, how do you know the 5s button has a square profile? Have you disassembled your phone and put the button under a microscope (or an optical comparator)?

You also keep talking about cutting things out with a knife on the one hand, and machining parts with impossible-to-achive precision on the other. Which is it?