thermal expansion: hole dia shrinks when part expands?
thermal expansion: hole dia shrinks when part expands?
(OP)
Thermal expansion problem:
For a solid cilindrical part with a small concentric hole (think thickwalled tube), I've heard for the very first time today that from a certain ratio d/D (minor/major dia) the inner hole would shrink when the part is heated.
Is this true? and if so, I did learn something remarkable today.
I appreciate your opinions!
.
For a solid cilindrical part with a small concentric hole (think thickwalled tube), I've heard for the very first time today that from a certain ratio d/D (minor/major dia) the inner hole would shrink when the part is heated.
Is this true? and if so, I did learn something remarkable today.
I appreciate your opinions!
.





RE: thermal expansion: hole dia shrinks when part expands?
Engineering is not the science behind building. It is the science behind not building.
RE: thermal expansion: hole dia shrinks when part expands?
RE: thermal expansion: hole dia shrinks when part expands?
"Good to know you got shoes to wear when you find the floor." - Robert Hunter
RE: thermal expansion: hole dia shrinks when part expands?
http://www.youtube.com/watch?v=sr0yMWdWie0
RE: thermal expansion: hole dia shrinks when part expands?
rp
RE: thermal expansion: hole dia shrinks when part expands?
Without going into calculus, consider a ring cut up into 360 x 1degree segments. Now look at an individual cell along the neutral axis which has initial radius R0. For small angles let's assume this cell is a square (see attached visual aid).
The initial ID0 = 2*(R0-A0/2) where A0 is the arc length.
The circumference of this neutral axis is C0 = 2*pi*R0 but we can also represent it as C0 = 360*A0 because A0 is 1/360th of the circumference. Thus,
C0 = 360*A0 = 2*pi*R0 ... A0 = R0*2*pi/360
ID0 = 2*(R0 - (R0*2*pi/360)/2) [sub in for A0 in earlier equation]
ID0 = 2*R0*(1 - pi/360) [factor out R0]
ID0 = 2*R0*(360-pi)/360 [common denominator] ***
Now consider this cell is heated and expands in all directions. For this example, A1 = A0 * E where E is the expansion multiplier. Using the same equations as before...
C1 = 360*A1 = 2*pi*R1 ... R1 = 360*A1/(2*pi)
ID1 = 2*(R1-A1/2)
ID1 = 2*(360*A1/(2*pi) - A1/2) [sub in for R1]
ID1 = 2*A1*(360/(2*pi) - 1/2) [factor out A1]
ID1 = 2*A1*(360-pi)/(2*pi) [common denominator]
ID1 = 2*E*A0*(360-pi)/(2*pi) [sub in for A1]
ID1 = 2*E*R0*(2*pi)/360*(360-pi)/(2*pi) [sub in for A0]
ID1 = 2*E*R0*(360-pi)/360 [cancel (2*pi)] ***
Now the big question, which is bigger - ID0 or ID1? Take a look at the two marked equations and you'll see that ID1 is larger than ID0 by a factor of E. Surprise!
RE: thermal expansion: hole dia shrinks when part expands?
However EngineerTex might have a point. Point of discussion was the cupper contact piece, used for current transfer in GMAW (mig/mag) welding. although the instructor (sales manager) specifically said "from a certain ratio d/D", it is much more likely that the piece is heated unevenly, causing the wire to block and hence the need for overdimensioning.
(Inside of the piece is heated due to the current, outside is cooled by the shielding gases).
thanks again for your replies...
RE: thermal expansion: hole dia shrinks when part expands?
How could anyone argue it shrank when the teacher just got through demonstrating it expanded?
RE: thermal expansion: hole dia shrinks when part expands?
If so, forgive me.
If it is a metal bar or rod in a straight line and you heat it up, it ought to get longer. I would therefore conclude that an arclength would also get longer. In a disk with a hole in it, if the inner arclength shrunk while the outer arclength grew, then there would have to exist a "linear expansion neutral arc" which would be unaffected by heat. While it might be argued that the metal surrounding it prevented its expansion, that wouldn't make sense to me because the arcs on the outside would be moving away from it outwards from the centre and the arcs on the inside would be moving away from it towards the centre, so where would the constraint be coming from?
From this I would conclude that the hole has to get bigger.
Regards,
SNORGY.
RE: thermal expansion: hole dia shrinks when part expands?
Regards,
SNORGY.
RE: thermal expansion: hole dia shrinks when part expands?
rp
RE: thermal expansion: hole dia shrinks when part expands?
Does ID of this hole shrink or grow once the casting cools?
Not really a pure thermal expansion question but I think it plays into the details of the discussion.
RE: thermal expansion: hole dia shrinks when part expands?
Ted
RE: thermal expansion: hole dia shrinks when part expands?
RE: thermal expansion: hole dia shrinks when part expands?
SNORGY:
What would happen if your bar was rectangular, and the top was heated while the bottom was frozen. The netural axis remains netural. Do you think it would warp like a piece of badly cured wood?
Now, if this was in fact a thick walled tube with a small concentric hole, and the outside of the tube was contained--not allowed to expand, where would the expansion go? Would it make the hole smaller and increase the density of the tube?
Charlie
www.facsco.com