This is a little brain teaser I found and thought might be an interesting post. The answer was not posted yet, but I think it's obvious the hole will get bigger.

http://i1220.photobucket.com/albums/dd456/lancewen/ExpandingHole.jpg

Larger. That's the whole basis of "heat-fitting" two metal parts. ;)

The percentage doesn't matter - that's just a red-herring in the question. <grin>

Larger. That's the whole basis of "heat-fitting" two metal parts. ;)

The percentage doesn't matter - that's just a red-herring in the question. <grin>

Yes that's true, but why? When you think about it, you might want to believe the metal will expand into the hole as well as outward. So what prevents it from doing that?

Yes that's true, but why? When you think about it, you might want to believe the metal will expand into the hole as well as outward. So what prevents it from doing that?The expansion of the innermost ring of atoms.

The expansion of the innermost ring of atoms.

Okay that sounds good, but can we actually say what happens to the atoms to cause them to expand? I mean when they heat up they must get further apart from each other. Why do they get further apart?

Okay that sounds good, but can we actually say what happens to the atoms to cause them to expand? I mean when they heat up they must get further apart from each other. Why do they get further apart?

Got back too late to answer your previous question - but can handle this one easily. :) The distance between them increases due to the fact that they're vibrating more/faster. In fact, that's the very definition of heat.

Got back too late to answer your previous question - but can handle this one easily. :) The distance between them increases due to the fact that they're vibrating more/faster. In fact, that's the very definition of heat.

That seems reasonable, but all atoms and molecules vibrate, so just vibrating faster shouldn't push them further apart. The vibrating movements must actually get larger?

My not infallible intuition tells me to consider the circumferences of the inner & outer ring.

Heat expansion should increase both circumferences & therefore both radii.

I would expect the difference between the radii (thickness of the ring) to increase. Part of the increase in the difference would be due to expansion toward the center, tending to decrease the radius of the inner circle. This decrease is overwhelmed by the increase due to increasing circumference.

BTW: The Read-Only Post provides experimental evidence that the radius of the inner circle increases.

Bonding (usually to a cylindrical rod) via heat-expansion & cooling contraction is a well known manufacturing process.

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Hi KilljoyKlown, everyone.

AFAIK, the inner surface would expand and, depending on the properties of the material, would either be under more compression stress or actually 'ripple' at the inner surface.
I think that is why when fitting a stud/bolt into a hole, it is the stud/bolt which is severely cooled and not the hole-surround material which is heated. The stud/bolt is usually machined to a diameter that is just bigger than the hole diameter would have at normal/operating temperature, then the bolt/stud is cooled by dry ice or other effective means such that, the bolt/stud having only ONE surface, its geometry is simple and just contracts inwards to reduce the diameter accordingly. The now slightly less-than-hole diameter stud/bolt is slipped into the hole, the bolt again heats up to ambient/operational temp and is fixed fast by friction.

I am not really sure, but I think the usual reason when the hole-surround material is not heated is because that is usually of greater bulk/complexity and risks cracks and misalignments developing in other parts/attachments to the hole-surround body.

As to whether heating a simple washer would also actually expand its inner surface and make the hole diameter smaller, I am not as clear myself. I suppose a very THIN RING would have very little to expand into that hole and whether the 'ring tension' comes into play more prominently compared to other forces. But as that ring thickness is incrementally increased to produce a 'washer' like material separation between inner and outer circumferences, I don't really know if there is a critical circumferential difference where the hole behaves differently under heating from 'thin ring' to 'washer' to 'hole-in-solid-body' situations. Very interesting. Does anyone have any more definite experimental data about all this?

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Hi KilljoyKlown, everyone.

AFAIK, the inner surface would expand and, depending on the properties of the material, would either be under more compression stress or actually 'ripple' at the inner surface.
I think that is why when fitting a stud/bolt into a hole, it is the stud/bolt which is severely cooled and not the hole-surround material which is heated. The stud/bolt is usually machined to a diameter that is just bigger than the hole diameter would have at normal/operating temperature, then the bolt/stud is cooled by dry ice or other effective means such that, the bolt/stud having only ONE surface, its geometry is simple and just contracts inwards to reduce the diameter accordingly. The now slightly less-than-hole diameter stud/bolt is slipped into the hole, the bolt again heats up to ambient/operational temp and is fixed fast by friction.

I am not really sure, but I think the usual reason when the hole-surround material is not heated is because that is usually of greater bulk/complexity and risks cracks and misalignments developing in other parts/attachments to the hole-surround body.

As to whether heating a simple washer would also actually expand its inner surface and make the hole diameter smaller, I am not as clear myself. I suppose a very THIN RING would have very little to expand into that hole and whether the 'ring tension' comes into play more prominently compared to other forces. But as that ring thickness is incrementally increased to produce a 'washer' like material separation between inner and outer circumferences, I don't really know if there is a critical circumferential difference where the hole behaves differently under heating from 'thin ring' to 'washer' to 'hole-in-solid-body' situations. Very interesting. Does anyone have any more definite experimental data about all this?

"Experimental data?" No. What I *DO* have is practical (real) experience from having worked in a machine shop.

I don't recall having ever chilled a single part in all those years (except for ordinary quenching in water or oil), though it certainly would have been possible. But I clearly remember :D having heated HUNDREDS of parts.

The process went by two names: Heat-fitting and friction-fitting, depending on who you were talking to.

Thermal mounting and dismounting (http://www.darex-lozyska.pl/katalogi/x33xNagrzewnia%20indukcyjna%20FAG.pdf)

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Hi KilljoyKlown, everyone.

AFAIK, the inner surface would expand and, depending on the properties of the material, would either be under more compression stress or actually 'ripple' at the inner surface.
I think that is why when fitting a stud/bolt into a hole, it is the stud/bolt which is severely cooled and not the hole-surround material which is heated. The stud/bolt is usually machined to a diameter that is just bigger than the hole diameter would have at normal/operating temperature, then the bolt/stud is cooled by dry ice or other effective means such that, the bolt/stud having only ONE surface, its geometry is simple and just contracts inwards to reduce the diameter accordingly. The now slightly less-than-hole diameter stud/bolt is slipped into the hole, the bolt again heats up to ambient/operational temp and is fixed fast by friction.

I am not really sure, but I think the usual reason when the hole-surround material is not heated is because that is usually of greater bulk/complexity and risks cracks and misalignments developing in other parts/attachments to the hole-surround body.

As to whether heating a simple washer would also actually expand its inner surface and make the hole diameter smaller, I am not as clear myself. I suppose a very THIN RING would have very little to expand into that hole and whether the 'ring tension' comes into play more prominently compared to other forces. But as that ring thickness is incrementally increased to produce a 'washer' like material separation between inner and outer circumferences, I don't really know if there is a critical circumferential difference where the hole behaves differently under heating from 'thin ring' to 'washer' to 'hole-in-solid-body' situations. Very interesting. Does anyone have any more definite experimental data about all this?

Hi RealityCheck

The washer example would work the same as if there were no hole in the middle for any size ring. If you were to take a disk and etch a circle in the middle of it then heat it the etched circle would expand exactly the same amount as a real hole of the same size.

"Experimental data?" No. What I *DO* have is practical (real) experience from having worked in a machine shop.

I don't recall having ever chilled a single part in all those years (except for ordinary quenching in water or oil), though it certainly would have been possible. But I clearly remember :D having heated HUNDREDS of parts.

The process went by two names: Heat-fitting and friction-fitting, depending on who you were talking to.


Hi Read-Only! :)

I defer to your working knowledge, mate. I confess that I only ever (a once off) cooled a stud/bolt to put in a very big block (part of an experiment) made of steel and having many attachments/instrument sensors around the hole. I avoided any problems with all those things by simply cooling the stud/bolt with dry ice and put it in. It expanded back to ambient/operating temps and stayed put thereafter.


Hi RealityCheck

The washer example would work the same as if there were no hole in the middle for any size ring. If you were to take a disk and etch a circle in the middle of it then heat it the etched circle would expand exactly the same amount as a real hole of the same size.


Yeah, I see what you mean, mate! But hang on.....since the material inside that etched circle is also expanding outward, it would naturally push the etched circle out with it. However, if no material is inside that etched circle, that circle would become a 'surface' which may be somewhat (I have no idea by how much compared to the other direction) pushed inwards by the 'outer' material also tending to expand that etched circle/surface inwards into the 'free surface' space of the hole? I admit I have no idea about the heating effects on the hole (as I mentioned to Read-Only, I have only ever once cooled a stud/bolt to accompliah the friction fit).

Is there a 'trade off' between expanding inwards and expanding outwards when it comes to the hole surface (not just circle etched on continuous-to-centre material you mentioned)? I'd be very interested if anyone had some hard figures about this.

Very interesting. Cheers!

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Thermal mounting and dismounting (http://www.darex-lozyska.pl/katalogi/x33xNagrzewnia%20indukcyjna%20FAG.pdf)

Hi Emil! :)

I nearly missed your post it was so 'one line' and sandwiched almost undetectably between Read-Only and KilljoyKlown posts!

Thanks for that info, mate.

Apparently, this is for the bearing RINGS (inner and outer separate rings). So this would be acting like the thin ring I mentioned, where there is little material in the topology/geometry to expand from the inner surfaces?

By the way, would heating the inner ring at the same time as the outer ring make the inner ring expand, but not as much as the outer ring does, so the rollers can slip out?

Interesting info. Thanks mate!

Cheers.

I pulled this off an email I get from Bigthink. This article has comments that you might find interesting. I was very interested to see if our science forum members would respond in the same way. Anybody who is interested can click the link below.:D

http://bigthink.com/ideas/the-big-enigma-6-expanding-hole?utm_source=Big+Think+Weekly+Newsletter+Subscr ibers&utm_campaign=f106e358f7-4_13_Cookie_Habit4_13_2012&utm_medium=email

Hi Read-Only! :)

I defer to your working knowledge, mate. I confess that I only ever (a once off) cooled a stud/bolt to put in a very big block (part of an experiment) made of steel and having many attachments/instrument sensors around the hole. I avoided any problems with all those things by simply cooling the stud/bolt with dry ice and put it in. It expanded back to ambient/operating temps and stayed put thereafter.




Yeah, I see what you mean, mate! But hang on.....since the material inside that etched circle is also expanding outward, it would naturally push the etched circle out with it. However, if no material is inside that etched circle, that circle would become a 'surface' which may be somewhat (I have no idea by how much compared to the other direction) pushed inwards by the 'outer' material also tending to expand that etched circle/surface inwards into the 'free surface' space of the hole? I admit I have no idea about the heating effects on the hole (as I mentioned to Read-Only, I have only ever once cooled a stud/bolt to accompliah the friction fit).

Is there a 'trade off' between expanding inwards and expanding outwards when it comes to the hole surface (not just circle etched on continuous-to-centre material you mentioned)? I'd be very interested if anyone had some hard figures about this.

Very interesting. Cheers!

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Hi, RealityCheck,

First off, I must say you are an honest and non-pretentious individual. :) Sadly, both of those qualities seem to be in short supply around here. So I find your response to be HIGHLY refreshing!! :D

Also, Let me add just bit more to the discussion. The most common application of this procedure - my guess is that it's in excess of 80% - is in the mounting of bearings. Ball, roller, tapered and needle. And the most common method of heating is by induction. Field repairs, of course, generally still employ the old torch method.

But hang on.....since the material inside that etched circle is also expanding outward, it would naturally push the etched circle out with it. However, if no material is inside that etched circle, that circle would become a 'surface' which may be somewhat (I have no idea by how much compared to the other direction) pushed inwards by the 'outer' material also tending to expand that etched circle/surface inwards into the 'free surface' space of the hole?

I can verify the practical experience that Read-Only told you. You are correct to assume the ID (inner diameter) a surface, but then you reach the completely wrong conclusion that heat could make such a surface shrink. Heat would have the same effect on the surface of the ID as it would on the overall surface of the washer. If the later expands so must the former.

I can verify the practical experience that Read-Only told you. You are correct to assume the ID (inner diameter) a surface, but then you reach the completely wrong conclusion that heat could make such a surface shrink. Heat would have the same effect on the surface of the ID as it would on the overall surface of the washer. If the later expands so must the former.

Hi Syne! :)

Sorry mate? I didn't say anything about the inner surface 'shrinking'. only the 'diameter' perhaps getting smaller. In fact, in an earlier post...




Hi KilljoyKlown, everyone.

AFAIK, the inner surface would expand and, depending on the properties of the material, would either be under more compression stress or actually 'ripple' at the inner surface.

...

I expressly surmised that the inner surface might 'expand' (ie, inner diameter get smaller) and/or be under more 'compressive strain' (ie,inner diameter remain unchanged in diameter but 'surface' itself' tending to strain together in grater density rather than actually change the surface diameter inwards....like water surface layer more dense/compressed than interior water below surface etc).

I also said I did not know for sure whether the internal diameter would change or not, having no direct experience in that area except for 'cooling' fit of a stud/bolt which involved no heating of the hole-surround case.

Sorry if I was unclear there, mate!

Cheers!

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Hi, RealityCheck,

First off, I must say you are an honest and non-pretentious individual. :) Sadly, both of those qualities seem to be in short supply around here. So I find your response to be HIGHLY refreshing!! :D

Also, Let me add just bit more to the discussion. The most common application of this procedure - my guess is that it's in excess of 80% - is in the mounting of bearings. Ball, roller, tapered and needle. And the most common method of heating is by induction. Field repairs, of course, generally still employ the old torch method.


Thanks for the extra info mate (and the kind words too. Same to you!) :)

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Sorry mate? I didn't say anything about the inner surface 'shrinking'. only the 'diameter' perhaps getting smaller.

How do you expect a diameter to get smaller without the inner surface shrinking? C=\pi\times d, so if the diameter gets smaller then the circumference, which is the surface length of the hole, must get smaller as well.

How do you expect a diameter to get smaller without the inner surface shrinking? C=\pi\times d, so if the diameter gets smaller then the circumference, which is the surface length of the hole, must get smaller as well.

Hi again, mate. :)

Sorry if I am not making myself clearer.

If the surface 'wrinkles', the surface may stay the same 'area' but its ridges effectively make the 'fitting space' smaller diameter without the actual inner surface area changing much.

Then I also said that the inner diameter may not change because the inner surface layers may be 'compressed' and made a denser layer than the material behind it.

That's all I meant mate. Cheers!

Disclaimer Again: I do not know about the 'heating fit' side of things. I've only ever used (once) the 'cooling' method for the stud/bolt to go into such a hole. :)

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To All

I've said many times that I can find a video for any occasion. If you watch the following video you will know the answer and there won't be any doubts.

http://www.bing.com/videos/search?q=Expanding+Hole&mid=2D251452FEE87BAC6A672D251452FEE87BAC6A67&view=detail&FORM=VIRE5

select the second video Conceptual physics Ball & Ring expansion

See my Post #8, where I suggested consideration of the circumference of both the inner & outer circles.

Isn't obvious that both circumferences expand as the washer is heated? If you think of the washer as made up of a large number of very thin rings, each ring would expand along the circumference.

If the inner circumference increases, the radius must increase.

I would expect the washer to get thicker (Id est: Difference between radii increases) with some expansion toward the center. I expect that expansion to be overwhelmed by the increase in circumference.

See my Post #8, where I suggested consideration of the circumference of both the inner & outer circles.

Isn't obvious that both circumferences expand as the washer is heated? If you think of the washer as made up of a large number of very thin rings, each ring would expand along the circumference.

If the inner circumference increases, the radius must increase.

I would expect the washer to get thicker (Id est: Difference between radii increases) with some expansion toward the center. I expect that expansion to be overwhelmed by the increase in circumference.

Maybe it would help to think of the hole as an arch that will dissipate any force directed towards the center around the circumference of the inner surface of the ring. Whatever, I like your example. I am somewhat surprised that so many people believed the hole would get smaller. Did anybody notice the difficulty rating on this problem was only 4 out of 10?

...so if the washer was cut through on one side and the newly-cut edges were allowed to cross over (like a ribbon) then we could expect a shrinking hole?

...so if the washer was cut through on one side and the newly-cut edges were allowed to cross over (like a ribbon) then we could expect a shrinking hole?
It's a good question.
I think whether it is cut or not, similar behave. As a photo enlargement.
Otherwise it would appear some very high tensions inside the material.
But this is only an opinion.

The material becomes molten before it expands by 1%?
The material puddles?
The hole decreases in the puddle?