I imagine the engineering tolerances on the iPhone button are very slack compared to, say the tolerances on stuff like this (the linked article actually contains some info pertinent to the current topic, too)
Oh I’m sure. Incidentally I mentioned the repulsive Casimir Effect in one of my posts further up. I’m no expert on it though, or what materials are required to generate it (I think it only works with metals but I dunno for sure).
the casmir effect should work with all materials, it’s just easiest to perform using metal plates as you can relatively easily make them very flat
You’ve specified a precision of 1x10[sup]-12[/sup] inches. A typical small atom is about 5000 times that dimension.
So yes, this is better than the best that can be done realistically.
Good point, I was just trying to exaggerate (i actually typed twice as many zeros at first but i deleted half of them) to make a point that the two sizes are as exactly the same as possible. I wouldn’t even expect the sides to be close to being atomically flat.
As Beowulff pointed out, exact fit would lead to molecular cohesion which would prevent assembly unless considerable force is used, which would deform parts.
This is what happens when you ‘wring’ Jo (gage) blocks together. It works better than just pushing them together, as you can thus wipe oil or dirt from the mating faces of the blocks.
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When I was working, we had a system of fits for test fixtures defined by lbs, such as a 2-lb fit or a 20-lb fit. It described the size of the hammer you needed to get the parts together.
I’ll just point out that gauge blocks don’t instantly stick together when they touch, and wringing them requires twisting 90 degrees or so. That wouldn’t be possible from pushing a peg into a hole.
But even so, for purposes of my question I accept that if the cylinder and walls of the hole are perfectly smooth there will probably be some sort of molecular bonding forces that hold them together to some degree once you get the cylinder down into the hole.
But i don’t see it happening instantly. Can I push the cylinder 1 millimeter down into the hole? 1 centimeter? A few centimeters?
I’m interested in whether “the same size” hole and cylinder will be loose, tight, or something in between.
Even if molecular forces caused some sort of wringing/binding how easily would the peg fit into the hole before it got down enough for those forces to take effect?
Bottom line, friction is the only force i’m really interested in. I recognize other forces might come into play with such perfectly smooth materials touching each other, and that’s very interesting. I’d never heard of gauge blocks before, or how they can wring together. I’m dying to get my hands on some of those and try that out for myself.
The other problem is that you are a point where you need to define how you are measuring the sizes. And this is going to lead to a recursive definition of both size and fit.
We have the ability to craft solid items to several tens of atoms thickness of precision, for instance the gyro spheres in Gravity Probe B. Precision optical fabrication seems to get surface profiles down to 0.1nm on significant sized parts. That is pretty much the atomic radius of a silicon atom. So we can imagine being able to machine solid parts to one atom of precision, even if it isn’t done just now.
Down at the scales discussed you are talking about the effective surface of the electron clouds. So you start to asked the question - what do you mean by a size measure? The surface isn’t flat, nor is it solid. The electron density is probabilistic, and the profile is determined by the location of individual atoms. So where do you define the surface that you are defining the size with?
You can define the measure as something measured with an ultra-precision ruler - but any contact with the surface is done by another object that is also essentially an uneven cloud of electron density probabilities. So you need to define where on your ruler the edge is. Optical measures are also in trouble. They also measure the electron cloud, but in a different way, and you will get different answers depending upon how you do it. You can define something they measure, but how do relate this to your real world expectations, and how do you then relate this to the task of a perfect fit between two objects?
If we go back to an ultra precision ruler you are going to end up defining the nature of the interference fit by defining the measuring technique. This is because the measuring technique is going to give a result that depends upon the interaction of the two surface’s electron clouds, and how the result depends upon this depends upon how you physically perform the measure. A simple ultra precision calliper gauge applies some pressure - and thus you deform the electron clouds in a manner that is directly related to the action of performing your fitting operation. Indeed issues like cohesion apply during the measuring operation - do you define the measure in such a way the cohesion is avoided? If you do you will create a measuring protocol that results in “perfect” parts that probably are also sized so that cohesion is avoided. You will certainly get some interesting physics when you try to fit your “prefect” parts, but the exact form these take is defined by how you defined and performed the measuring process, and that depends upon same physics that controls the fit.
Francis: I think I addressed your points in one of my last posts.
Trying not to be snarky, but if you think you did, you didn’t understand what I wrote.
My position is that the question has no single useful answer, as you are actually defining the answer in the manner in which you specify the notion of “perfect fit”. The exact way you define the dimensions changes the answer.
Unless you define the way you measure the dimensions the question has no meaning, and any useful way of defining the way you measure will intrinsically depend in part on the physics that controls the nature of the fit.
You have not provided a useful definition of the measure of dimensions. How do I know I have a cylinder and hole with the “same” diameter before I try to fit them? What would you accept as a criteria for saying they are the same?
I’d say they both have diameters of 2 inches, both accurate to within, say, 1/10,000 of an inch.
I realize that means there could be a difference of less than 1/10000" but i accept the premise that it’s never going to be equivalent on an atomic level.
All I can do is say they’re “the same diameter” to within a certain tolerance. (right? or do you disagree with that?)
Say I have a really fancy 3D printer that can print to within those tolerances. I print a cylinder with a 2.0000 inch diameter and then i print a cube with a round hole in it also with a 2.0000 inch diameter. I put the cylinder on top of the hole. How hard will it be to get it in? Even just a little bit. If it’s really hard plastic and at those tolerances I don’t see molecular forces instantly binding the plastic together the second a molecule from the side of the cylinder touches the inside of the hole.
It will be impossible to get it in without a hammer.
As has been said over and over and over again in this thread.
But, might as well say it again.
Wow I leave this thread for 48 hours and it goes on and on in the same circles.
For a minute forget putting your magical perfect peg in the magical perfect hole. Think of the way gage blocks cling. All they are is two finely ground steel hunks. Something you might easily be able to get ahold of to see the same effect is two pieces of flat glass.
Lay one on the other and feel the adhesion.
Nonsense. You could easily use a mallet. Or a shoe. Or an extremely tolerant cat.
Are you really talking about some hypothetically absolutely rigid, theoretically infinitely fine-grained material?
Because all the while we’re talking about metal, plastic and glass, it seems like you’re wanting us to ignore the material properties and composition of those substances.
Interestingly, if you have a spare $500 it is possible to try it out. 0.00001" tolerance is quite achievable with commercially available parts. If you want a 1 inch diameter hole and cylinder machined to within this tolerance, buy a XXX class ring gauge and plug gauge. If you can find one, a XXXX class is even finer. (And no, XXX isn’t hard core porn, nor is XXXX a beer. XXXX isn’t even a beer in Australia, it is a sort of amber coloured bitter liquid only some Queenslander’s drink.)
However even here you discover that things are still open to interpretation. Ordering such parts requires you to specify the nature of the tolerance - you can specify plus, minus or master. Plus means that the part will not be less than the specified diameter, but may be up to 0.00001" larger. Minus, the converse, it will not be larger than specified, but may be up to 0.00001" smaller. Master is perhaps what you expect, and the part may be +/- 0.000005".
When specifying the dimension for a part you need to consider the surface finish. So a precision part will need to have a specification of surface roughness as well as dimensional tolerance. The manner in which this is specified changes with use. Optics has different criteria to a machined part.
Now the use of plug and ring gauges gets us back to the the OP in a clear manner. What are they used for? Well they are used to test other parts for size. So a newly machined cylinder will be tested by trying to insert it into a ring gauge. In practice two rings gauges may be used, one sized so that an in spec part does fit, the other so that it doesn’t. These are go/no-go gauges. Same for plug gauges - you can test a hole.
You could try a plus tolerance ring gauge and minus tolerance plug gauge, so you are guaranteed that the plug will be smaller than the hole, but anything from essentially zero, to as much as 0.00002". (Even here the guarantee is only as good as the measuring mechanism used on the part. Something like an air gauge might be used, itself calibrated against reference gauge parts.) However for even much high precision work, you might notice that the dimensions themselves are specified via a fit/no fit test, and thus again, the nature of the fit begins to specify the dimension.
Brilliant off the shelf example, how could I have forgot gage pins and rings? (What happens when I go back to a manual shop where calipers are more than good enough to measure everything.)