Expanding Hole

Discussion in 'Physics & Math' started by KilljoyKlown, Apr 14, 2012.

  1. KilljoyKlown Whatever Valued Senior Member

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    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.

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  3. Read-Only Valued Senior Member

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

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    The percentage doesn't matter - that's just a red-herring in the question. <grin>
     
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  5. KilljoyKlown Whatever Valued Senior Member

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    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?
     
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  7. waitedavid137 Registered Senior Member

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    The expansion of the innermost ring of atoms.
     
  8. KilljoyKlown Whatever Valued Senior Member

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    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?
     
  9. Read-Only Valued Senior Member

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    Got back too late to answer your previous question - but can handle this one easily.

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    The distance between them increases due to the fact that they're vibrating more/faster. In fact, that's the very definition of heat.
     
  10. KilljoyKlown Whatever Valued Senior Member

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    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?
     
  11. Dinosaur Rational Skeptic Valued Senior Member

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    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.
     
  12. RealityCheck Banned Banned

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    800
    .

    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?
     
  13. Read-Only Valued Senior Member

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    "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

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    having heated HUNDREDS of parts.

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

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  15. KilljoyKlown Whatever Valued Senior Member

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    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.
     
  16. RealityCheck Banned Banned

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    Hi Read-Only!

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    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!

    .
     
  17. RealityCheck Banned Banned

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    Hi Emil!

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    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.
     
  18. KilljoyKlown Whatever Valued Senior Member

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  19. Read-Only Valued Senior Member

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    Hi, RealityCheck,

    First off, I must say you are an honest and non-pretentious individual.

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    Sadly, both of those qualities seem to be in short supply around here. So I find your response to be HIGHLY refreshing!!

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    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.
     
  20. Syne Sine qua non Valued Senior Member

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    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.
     
  21. RealityCheck Banned Banned

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    Hi Syne!

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

    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!

    .
     
  22. RealityCheck Banned Banned

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

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    .
     
  23. Syne Sine qua non Valued Senior Member

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    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.
     

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