Heating a steel ring.

Let’s say I have a steel ring that has an outside diameter (OD) of 1 inch and an inner diameter (ID) of 3/4 inch.
If I heat this ring up does the ID get larger or smaller?
How about if this was a drilled hole in a solid piece of steel?

The hole always expands.

Imagine if you had a straight bar and heated it. It would grow a little in width, but it would grow more in length because there is more metal in that dimension. So that’s what happens with the ring, it does grow slightly in width, but it grows much more in “length” and that forces the whole ring to get bigger, including the hole in the middle.

Both the inner diameter and the outer diameter get larger as the steel expands. Conversely, freezing a ring causes both dimensions to be smaller. This method is often used for interference staking bosses in a strut or plate where welding is impactical or would cause too much distortion.


When I install ring gears on heavy duty flywheels 18" I simply heat the ring with a torch until I can gently tap it over the flywheel, once it cools it tightens right up. It doesn’t have to get all that hot to expand.

I have had a stub shaft made where the ID of the stub shaft was 5 thousands of an inch smaller that the fan shaft it was going on. Heated the stub shaft and cooled fan shaft. We aligned the two up removed the heat and cooling then slammed the stub shaft on the fan shaft. You only get one chance to get it home though. The stub shaft was solid to the fan shaft afterwards.

Imagine you have a slide projector, and you’re projecting a picture of that ring onto a screen. Then back up the projector farther away from the screen. The entire picture, and all of its parts, expands on the screen. Think of it that way.

Thanks for the replies.
What you are saying makes sense.

This is quite useful for getting pedals and cranks off of a bike, a candle will provide enough heat.

This is also part of why the second person to try to open up a stuck jar will get it open easily when the first person struggled: When the lid warms up, it gets looser.

It makes no difference, the ID still gets larger.

This was a tricky question that my Mechanics of Materials professor offered up on the first day of class 30 years ago. Surprising how many engineering students got it wrong. I actually turned to a guy who stated that the hole got smaller (pretty bright guy too) and asked him how he thought a press fit worked; he then sheepishly admitted he was incorrect. Damn that was a long time ago.

How about this:

A small hole in a large steel plate. Use a torch to quickly heat only the area around the hole. Does the hole’s diameter increase or decrease?

I expect that’s a complicated question that’ll depend on all sorts of material properties of steel, as well as how those properties vary with temperature.

Right, the answer can vary based upon material type and size. But basically this type of thing comes up in tooling modifications where a large steel die is being modified and pins being press fit into it in order to mate with another piece. In these cases the the pin holes are small compared to the overall die so there is little distortion on features far away from the were the work is happening since the heat get absorbs locally. Aluminum tooling would be a different matter.

The hole diameter will increase. The degree to which it increases depends upon the thickness of the material and the temperature gradient around the hole and through the material. From a stress standpoint, the heating one area of the plate will introduce compressive stresses between the thermally affected material and the material that is at ambient temperture which may result in other affects such as waviness of the plate, net shear flow through the thickness of the plate, initation or amplification of cracking or spallation, et cetera. These are all considerations in thermal welding where deformation from the welding process can turn a dimensionally accurate part into a warped paperweight.


If you were to do an Finite Element Analysis (FEA) of a ring , but constrained the outer dimension to not be allowed to expand, which is essentially what you are trying to do with the heated up inner material, you would see the stress levels in the material on the inner diameter rise rapidly to crazy levels. Once the stress exceeds the tensile strength of the material the material starts to plastically deform and FEA for plastically deforming materials is crazy hard.
So for a real world example, as said above, a lot depends on the materials, the properties of the constraining materials , thermal conduction etc and you would probably see some deformation in the axial direction as the radial expansion is heavily constrained and the material plastically deforms. I suspect is what you would see is the heated material expanding on the ID and bulging outwards in the axial direction.

If we are going for a spherical cow analysis and constrain perfectly in every direction except the Inward (internal diameter ) of the ring, then yes it will expand inwards as it’s the only place to go, but it will be plastic deformation (basically flowing if you like but don’t run with that too far)

The stress is a material with restricted expansion under heating is stress=Young’s mod x thermal expansion coefficient x temp difference
For 4140 - 140 ksi steel ( which is a pretty strong steel) , you would need to raise the temp by 320 degC or so to get to plastic deformation.

Another way to think about what happens to the ID of a ring under heating is to consider what happens when you continue to reduce the ID of the ring, and then get to a solid bar, which is essentially a ring with a zero ID. If a line of reasoning brings you to the ID reducing then for a solid bar you would see compressive stress on the center of the bar , ie those atoms in the middle are some how being compressed. What would happen is the stress would be redistributed throughout the steel and even out.

You could head down the route of asking what happens if you take a bar of material and constrain it perfectly in all directions and really heat it up , but that would be a question for a Stellar Physicist, not a very rusty applied physicist who has spent too much time hanging around mechanical engineers and long tubes.

I’m a big fan of using metaphor and “think about it this way” to illustrate something counter-intuitive. I at first found this post

very helpful in understanding the result, but in the final analysis this post

is the one that will stick with me. Probably because I work with projectors much more regularly than I heat up metal bars. :slight_smile: