Thermal Expansion of a shrink-fit collar

AI Thread Summary
A shrink fit collar operates on the principle of thermal expansion, where heating the collar causes it to expand, allowing it to fit over a shaft. Upon cooling, the collar contracts, creating a tight grip. The discussion addresses a common question regarding the expansion of materials: while heating causes expansion in all directions, the geometry of the collar means that the inner diameter does not decrease significantly. Instead, the outer dimensions expand more than the inner dimensions, allowing for a proper fit. The conversation also touches on the mathematical relationships between the collar's circumference, thickness, and radius changes due to heating, emphasizing the need for precise calculations to understand the extent of these changes.
akip
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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
 
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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?

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