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# thermal expansion of ring

## thermal expansion of ring

(OP)
Hi All,

I have a doubt on the behavior of a ring during expansion,
Imagine there is a ring surrounded by another ring but of different material with less expansion coefficient, Upon increasing the temperature the rings will expand radial outwards, but after a certain point the inner ring will not be able to expand outward since the expansion is constrained by the outer ring because of its less thermal expansion coefficient, From that point onward how the inner ring behave upon increasing temperature. Whether it will expand radially inward ?

### RE: thermal expansion of ring

Well suppose inner ring were a solid disc instead. What do you think will happen?

The answer depends on the difference in CTE's and the modulus of the materials. If both rings are metal, the inner ring will likely still expand but less than if unconstrained, and the outer ring will expand more than otherwise.

If the inner ring is rubber, it will likely expand inward.

### RE: thermal expansion of ring

If they are both metal, and strong enough that yield is not an issue, then you could calculate the expanded size of each and handle it like a shrink fit calculation.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

### RE: thermal expansion of ring

Edstainless has the answer. In case the internal ring is thin and thermal load is high it may have tendency to buckle inwards.

### RE: thermal expansion of ring

Hi jobs11111

If the fit between the two rings is an interference then on heating the outer ring will expand more than that predicted, than if it was free to expand as a singular ring, this extra expansion would be due to the inner ring forcing the outer ring to expand further.The inner would be prevented from expanding by the outer ring to its normal free expansion state. This condition must occur for the stress at the ring interface to remain in equilibrium. Therefore if you keep increasing the heat both rings will expand as describe above, this is assuming these rings are of equal and robust sections of which you give no details.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: thermal expansion of ring

(OP)
Hi all,
In this case we are not looking for interference fit, at the normal case there was sufficient clearance, but upon heating the inner ring (hollow ring)made of stainless steel is expanding more compared to outer ring (made of wcc). at certain point inner ring not able to have free expansion in outside direction, so will the inner ring will expand inward or create stress?

If stress is created what is the formula to calculate.

### RE: thermal expansion of ring

Hi jobs11111

So only the inner ring is heated, in which case it will expand until it touches the outer ring, at this point the outer ring will either expand slightly due to it being forced by the inner ring expansion and any heat it absorbs during this time similar to the scenario described in my previous post
If the outer ring is more solid section compared to the inner ring then it’s likely buckling of the inner ring would probably occur as mentioned in previous posts by others, without a lot more information it’s impossible to help further and sorry I have no idea what material WWC is.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: thermal expansion of ring

Calculate the final sizes without any constraints, see how much interference develops.
Once they touch it is a pressfit situation, the OD will expand more, I ID less, and there will be tensile stress in the OD and compressive stress in the ID.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

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