If you heat a ring of metal, does the inside diameter shrink or grow?

Question

Positive linear coefficient of thermal expansion would seem to make the inside and outside diameters increase (in a circle). Positive volumetric coefficient of thermal expansion would seem to make the thickness increase which would decrease the inside diameter. Which one wins?

Answer 1

It grows outward -- the O.D. wins.

The reason is fairly straightforward when you think about the geometry. To expand inward, the material on the I.D. side of the centerline would have to be forced into a smaller circle, in essence trying to compress the thing into a denser object. Think of the application of an inward uniform force along the full circumference of the ring in an attempt to compress it into a smaller ring -- damned difficult if not impossible. In 3 dimensions, it's why a sphere holds up better than other objects under uniform outside pressure.

On the other hand, it's quite easy to apply a uniform outward force to the I.D. and attempt to expand the ring into a larger space (more than likely breaking it in the process!).

So the expansion will be along the lines of least resistance, and that is most definitely outward.

This principle of heating a circular or cylindrical object to expand it is often used in an attempt to free the object from a shaft in its I.D. (e.g., old fashioned brake drums or a bearing from a shaft).
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Answer 2

It will grow according to the coefficient of linear expansion. This is done every day to fit gears and couplings onto shafts. You can also cool a metal shaft to reduce its diameter.

Answer 3

If you heat the entire ring, both the inside diameter and the outside diameters will increase.

Answer 4

I know from personal experiance that the inside and out side of a heated ring grows. If u put the same ring in the freezer it will shrink.

Answer 5

Thermostats work because of what you are kind of getting at here. The inner metal is different than the outer metal.

But if the metal is expanding, it's going to expand in every direction equally unless something prevents it from doing so. So the diameter would shrink.

Answer 6

The I.D. will increase. This principle is used in Engineering to temporarily increase the size of a shaft 'Sleeve', for example, when it's to be closely fitted onto the shaft of a pump or compressor...etc.
As it contracts, it grips the shaft extremely tightly.

Answer 7

in my opinion none of them is true . it is possible the ring will be deformed because it consist of several phases and every phase have specefic thermal expansion in addition to this external layer heats rapidly but internal layer heats slowly and this causes deformation

Answer 8

It all depends on what kind of force is present. If you heat it up and are holding it it will expand. If you heat it up and it is being compressed it will then in fact shrink in size.

Answer 9

it would definitely shrink...