Thermal Expansion of a shrink-fit collar

[akip]

Looking for some information on how a shrink fit collar actually works. I get the basic principle that you heat it, it expands, fit the collar, let it cool and it contracts and grips as a collar.
However, if you heat a material am I right in saying that it expands in all direction. If this is true, then when heating a ring, why doesn't the hole in the collar actually get smaller with expansion, i.e. the material is expanding inwards as well as outwards.

Cheers
Akip

 

[Chestermiller]

If C is the circumference of the collar and t is the thickness of the collar (t<<C), how much does C increase and how much does t increase? How much does the average radius increase? How much does the inner radius increase?

Chet