Uh... by dimensional analysis I get the area coefficient of expansion as
the square of the linear coefficient.  If you are looking for square
inches of hole minus square inches of shaft cross section your answer
has to be in square inches.

On the other hand if you assume they are both round and just look at the
diameter of the hole minus the diameter of the shaft the whole area
thing is moot.

I loved my high school physics teacher, but I think I annoyed him.

Sherpa Doug

> -----Original Message-----
> From: Michael Vinson [mailto:mjvinson@HOTMAIL.COM]
> Sent: Thursday, September 27, 2001 11:35 AM
> To: PICLIST@MITVMA.MIT.EDU
> Subject: Re: [OT]: Coefficient of Thermal Expansion
>
>
> Lawrence Lile wrote, in part:
> >I've got an interesting problem in thermal expansion.  We have a 304
> >stainless steel shaft running through a High Density
> Polyethylene bearing
> >block, with about 0.020" clearance. [...]
> >Once found, I'm trying to figure out what to do with it.
> Would the inside
> >of the plastic bearing contract at the:
> >
> >1.  Coefficient of expansion rate  or
> >
> >2. Coefficient of expansion times Pi or something like that,
> since it is a
> >circle?
> >
> >Hmmm.  Shouldn't have slept through Physics.
>
> As a former physics professor, I've seen more sleeping engineering
> students than I can throw a stick (or a chalkboard eraser) at. But
> now you see why your physics professor begged you to pay attention
> when you were a student (and you, like all engineering students the
> world over, scoffed, "I'll never need to know this stuff.").
>
> At any rate. To determine if a disk will fit in a circular hole
> (approximate both as 2-dimensional), you need the coefficient of
> area expansion. You may not find this listed for your materials,
> but fortunately you don't need to, because, as a simple argument
> shows (I'll spare you the physics details), the coefficient of
> area expansion is 2 times the coefficient of linear expansion, which
> you *will* find listed (this only applies to isotropic materials,
> of course). So, you measure the shaft cross-sectional area Ao at
> a reference temperature, compute the area A at your working
> temperature via A = Ao(1 + g Delta-T), where g is the coefficient
> of area expansion and delta-T is the temperature difference. Do
> the same thing for the hole, and the difference gives you the
> clearance (or overlap) in area units (sq. cm, for example). Special
> note: When you cool an object so that the material contracts, if
> it has a hole in it, does the hole get bigger (as the material
> recedes away from it) or smaller (since everything is shrinking)?
> The answer is: it gets smaller. So when you cool down your assembly,
> *both* the shaft and the hole are shrinking, but, evidently, the
> hole is shrinking faster. Do the calculation.
>
> Wake up! Class is over!
>
> Michael Vinson
>
> Thank you for reading my little posting.
>
>
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