Thermal Expansion in 4140 - Solid Disk vs Ring

Hi PM,

Maybe I should have posted this here in the first place. Metrology frequently involves temperature compensation.

Calculating thermal expansion in a 4140 HT&Q, 28-32 Rc ring: 6" OD x 4.75" ID by 1.00" Thick. Using a spreadsheet based calculator I found on line it says a 20 degree temperature differential I should compensate the ID of 4.775 by .0006" (.00057"). Is this correct?

Also I was wondering if a thin walled ring would change more, less or be the same as a solid disk of the otherwise same dimensions. Clearly the disk grows 'linearly' across the diameter. A ring is the same as a bar , right? So unroll it and you have a bar the length of the circumference. Run the calc for the bar length & rewrap it to find the delta diameter. But would one use the ring OD, ID, centerline to calc the bar length? TIA

William

A thin ring will act like a strip that has been rolled into a circle, so it is the circumference that grows or shrinks per the linear coefficient. A solid circle would grow and shrink per the volumetric coefficient which, generally being about Pi times the linear coefficient, means the diameter will grow and shrinks per the linear coefficient.

An in-between like your 6" x 4.75" ring could be expected to shrink or grow at a rate somewhere between the two cases.

HTH.

Mike

If you're talking degrees F, that expansion looks about right. My rule of thumb for steel CTE is 6 millionths inch/inch/°F. Every dimension grows uniformly: OD, ID, circumference, etc. If you want to back-of-the-envelope it for a thin ring considering the circumference straightened into a bar, use the mid-radius, but it hardly matters for a thin enough ring.

To get the growth of any dimension, just multiply the CTE x whatever dimension x temperature increase. Make sure units are consistent, i.e., the CTE has the same temperature units as the temperature change.

I dunno, but a material with isotropic CTE should expand exactly the same whether it's a ring or solid cylinder. A ring with the same OD as a cylinder would expand faster with the same amount of energy, as less mass is being heated, but at a given temperature they should both exhibit the same growth or shrinkage.

In my experience the rings grow just about the same as a solid. And yes a thin ring will grow linearly in the direction of circumference, but remember that C=π×D whether you're calculating the actual size or just the growth due to thermal expansion - so calculating for diameter of the ring will generally work just fine. The trickiest part of temperature compensation like this is being able to determine that the part has even temp throughout - most of the time that is NOT the case when a part is being roughed out and isn't left to cool before finishing - do be careful with that.