A question about perfect fit

Okay, say you have a cylinder with a circumference of exactly 2.00000000000000 inches (as exact as possible) and you also have a round hole also with a circumference of exactly 2.00000000000000 inches. Assume both are made of the same very hard material… steel or something that doesn’t compress easily (not marshmallow). Assume both the cylinder and the hole are perfectly round and measured as exactly as possible.

Now lets put the cylinder into the hole. If the cylinder were slightly larger than the hole obviously it would have some friction (increasing up to the point it didn’t fit at all) and if it were smaller than the hole obviously it would fit in without any friction. But what if the sizes are exactly the same, or as exact as humanly possible? (If you just cut the cylinder out of some material to make the hole at the same time, there would presumably be some lost material due to kerf making the cylinder at least marginally smaller than the hole).

If you put the cylinder into the hole, would the fit be tight? Would it slide right into place without any friction at all? Would there be a small amount of friction? If so, does the amount of friction rise or fall with the exactness of the two sizes?

I do think of ice frozen into a glass - it’s the same size - but due to the expansion of water I’d assume that is the reason it holds itself in so well… at least until it melts a bit and then slides right out (due in part to lubrication).

In practice, most materials are compressible or deformable enough that even if the plug is a bit bigger than the hole, it can be made to fit.

There are formal definitions of engineering fit. http://en.wikipedia.org/wiki/Engineering_fit

If the two holes were precisely the same size, the fit would be very, very tight.
You would have to hammer the cylinder into the hole. There is minute surface roughness, and that would cause a lot of binding.

This is called “interference fit."

Imagine a crystal, where you have a cylindrical plug* precisely removed, so that between them you had all the atoms for a single solid block. I think it would be difficult to put the plug into the hole, even if the plug were perfectly aligned, and even though they should fit perfectly. I’d expect the electrons of the plug and the hole would be interacting with each other, and forming bonds before the plug got very far into the hole.

To reduce friction, maybe you could compress the block with the hole slightly, and pull on the side of the plug that first goes into the hole, to maybe make the hole a little bigger than the plug. But not so big that any air molecules could get into the gap. Then remove the pressure, and hope the parts form a single crystal.

  • with a crystal, it might be better to have a polygon that follows the crystal shape removed, rather than a cylinder.

Beowulff: if it were very tight that seems to imply the cylinder is at least somewhat larger than the hole, requiring it to compress (to some degree) in order to fit.

That link re: interference fit seems to imply a size difference, to create the friction to hold it in.

Like a nail through wood - the hole is made by the nail so it’s technically the same size but because the wood was spread apart it was always pressing against the nail applying pressure from all sides. Thus the hole is smaller than the nail, or it would be if you took the nail out. But I could be wrong.

Here’s the deal: What’s your definition of “size?”
Remember, the surfaces aren’t perfectly smooth - so, are you taking the highest, lowest, or average distance from one side to the other?

The best machine shop in the world would be hard-pressed to make a hole (or turn a cylinder) more accurately than +/- 1/10,000 of an inch. Typical tolerances are in the 1/1,000 of an inch range.

+/- .0001" is doable, but you would need to specify the temperature as well as the dimension. Most often this would be done with a cutting process to within .002" or so of the target, then grinding or possibly honing (especially the bore) to desired fit.

Zero clearance dimensions such as the OP are rare in practice. Most things either need a running fit, or an interference fit.

Diesel injection pumps are an example of very tight bore-plunger fits. They are typically assembled submersed in fuel to bring the mating pieces to the same temperature.

Model airplane engines are often made with tapered cylinders that are extremely tight at TDC when new and cold. Materials are selected so that clearance increases as the engine heats.

One of the reasons I said same material is so that temperature differences and expansion wouldn’t make much of a difference.

Let’s just assume that it’s all kept at the same temperature as when they were made/cut out.

My definition of “size” was really given as “the same size” but if 2.000000000000 inches is not doable just the best that can be done, realistically. Not ‘to the atom’ necessarily, I don’t think that’s realistic. .00001 inch or whatever. As exact as possible. Assume temperature differences are not in effect. The hole and the cylinder were both made at 0C and have been kept at 0C and you’re putting the cylinder in the hole at 0C with a robot hand that’s also at 0C.

I know there are rings that are heated up to enlarge and then put on something and allowed to cool down and it locks on - only way to get it off is to heat it up again. But I also know that they’re made a little smaller so they’re not an example of being the same exact size.

I run a machine shop and can turn steel to .001" (called one thousandth of an inch) with a crappy tool while hung over and wishing for death.

To .0001" (One ten thousandth of an inch) If, I’m paying attention after coffee. That’s with a sharp new carbide tool and it only last a few inches along the length of the hypothetical cylinder. (Thinking on it, 2 out 3 times anyways I could hold it.)

I used to work with CNC machines that would hold a tolerance in stainless steel to about (digging back into 15 years of memory) .00005" +/- .00002 (called millionths of an inch.) This was on tiny parts the size of a pencil eraser. Slow and expensive to run machines that way.

I’m quit working with the CNC stuff (manual machines with cranks, levers and belts are so much more satisfing than pushing a button) that I’m behind on the tech. Holding parts tolerences into the millionths of an inch then isn’t unheard of, but very rare and expensive. And we are talking about exotic materials that have little or no deflection or deformation.

Even on the pacemaker parts I used to make that’s holding a tolerance so small that it’s the equivalant of using a nuclear bomb on killing a housefly.

For purposes of my question i’m trying to make the fit as exact as possible. I thought they made some jet engine parts to within tolerances of a few microns, so I don’t really know what is as exact as possible for a cylinder and a hole of the same size.

One thing I was thinking of is cutting out a piece of thick cardboard or leather with scissors (so there’s no missing kerf). Cut a circle out (even if it’s not exactly round) and the hole made will be exactly the same size as the piece. The piece will fit right back in without needing to be pushed. Would it be the same way if you could somehow cut a thick piece of steel with scissors (again, so there’s no missing material due to kerf)? Even a thin water jet or plasma cutter will cause some missing material and thus a size differential (the piece will fall right out once it’s cut free).

Yeah I lost your initial question. I know of no way on earth to cut one out of the other with no kerf. I know you are asking for the perfect answer in a vacuum with robotics and zero gravity. I got nothing there.

In reality, not theoretical machining say it’s two pieces of steel. Turning a cylinder on a lathe and boring a hole on my mill, I can measure them easily within .001" (A sheet of paper is about .003")

The cylinder can measure .001" smaller than the hole and it doesn’t ever slip fit. Sounds great but, the gap is so small getting the parts to line up is almost impossible. The teeniest tiniest angle binds. Human hands can’t make them slide together without a BFH* or a hydraulic press like what’s used to put a bearing race on a shaft.

Interesting question but I can think of no real world application. Then again, I’m being very literal, Edison didn’t have a lot of real world applications until he created them.
*Big Fucking Hammer.

I’m not even thinking about real world applications. Just a question that’s been driving me crazy.

My gut feeling is that it will have the tiniest bit of resistance but for the most part will slide right in. It might take the smallest bit of pressure. But I dunno.

Scissors cut without kerf. But they mostly cut thin material. If you were cutting thick steel with a ‘scissor’ powerful enough to do it (i know they exist at least for a small straight cut, i.e. chain cutters) it would deform the steel so you wouldn’t have a smooth 90 degree angle for the ‘cylinder’ or whatever shape you cut out.

Basically it seems like a paradox. If it’s too tight that means the shape/cutout is too big for the hole. If it slides right in, that means it’s too small. But what happens when it’s just right? What’s the middle ground between “snug” and “no friction”?

I got nothing really. It’s probably like Xeno’s paradox and it’s just a matter of how the question is phrased (to be tricky and imply something that’s not actually the case).

No, the parts will not slip together.
As was mentioned, even a part that’s slightly undersized won’t slip-fit. Two parts that are “exactly” the same size will bind, just due to molecular cohesion.

I’m not saying you’re wrong but i’d love to get some sort of cite or article or something talking about that. The article on interference fit seems to imply a size difference (the last paragraph makes that pretty clear).

Is there any example of something being so flat that it sticks to something else equally as flat? I realize a piece of paper isn’t perfectly flat but they certainly don’t stick together on a molecular level even a little bit. Well there could be some static electricity but that’s different.

There’s also the casimir effect which causes two flat plates VERY CLOSE to each other to repel. Assuming the item were made of appropriate metal would the casimir effect cause any repulsion?


Cool, thanks, that is actually informative. 1 nanometer is certainly as close to ‘perfect’ as we’re likely to ever get.

I also found this conversation for whatever it’s worth: http://www.reddit.com/r/mildlyinteresting/comments/1pgnkt/a_one_euro_coin_fits_perfectly_into_the_hole_in/

Seems to be talking about the same subject and while there’s some disagreement it seems the people who know what they’re talking about tend to think there would be some hold with a truly perfect fit.


Very little mechanical engineering knowledge.

It is my understanding that EXACT same sizes cannot fit; you aren’t going to get that nanometer-perfect peg into that nanometer perfect hole.

I have been told that the way the turbines in a hydroelectric dam are connected to the generators is by freezing the shaft (approx. 1 meter in diameter) to get it small enough to insert. The shaft is actually a few thousands of an inch larger than the holes.

Again, this is all “what I’ve heard” from people who either should have or might have known what they were talking about.

usedtobe: That’s true, i even mentioned it in my 3rd post up there (last paragraph). But those things aren’t made the same exact size. the thing that’s heated up (to expand) starts off a tiny bit smaller, so when it cools it shrinks and locks in place.

Engine cylinders are resleeved in the same manner. Back when I was a motorcycle mechanic, we would bore out the old (worn) cylinder bore until it was slightly smaller than the new cylinder sleeve with both the block and sleeve at a common temperature (i.e., at room temperature.) Then we would stick the sleeve in the freezer and heat the cylinder. The cylinder would expand and the sleeve would shrink by several thousandths of an inch (maybe 0.010-0.030"), allowing us to quickly drop the sleeve into the bore.

I think that the idea of a perfect interference fit is a practical impossibility. Boring the hole and turning the plug will leave ridges on both surfaces. These can be hone to a smoother finish, but that just means that the ridges left by honing will be smaller than those left by turning. Even if the surfaces are polished to a molecular level, the molecules will show as bumps on the surface. That said, I’m guessing that it would be a press fit for most materials in room air.