How Thermal Expansion Works
When a material heats up, the atoms vibrate harder and push each other farther apart. The part gets a little bigger. When it cools, the atoms settle and the part shrinks. How much a part grows per degree of heating is called the coefficient of thermal expansion, or CTE. Every material has a different CTE.
The Formula
The change in length is the CTE times the starting length times the temperature change. Written as: ΔL = α × L × ΔT. For Al 6061-T6 (CTE 13.1 µin/in/°F), a 10 inch bar heated by 100 °F grows 0.0131 inches. That is enough to lose a press fit or shift a precision assembly.
Metal vs Plastic Expansion
Most metals have a CTE between 6 and 24 µin/in/°F. Steel is at the low end near 6.5. Aluminum is near 13. Brass and copper are around 10. Plastics are much higher, 30 to 100 µin/in/°F. That is why plastic parts need generous clearance when they mate with metal housings.
Pro tip: For tight press fits or interference fits that see temperature swings, run the numbers at both the coldest and hottest operating temperatures. A fit that works at 70 °F can go loose or bind at 0 °F or 200 °F.
Shrink-Fit Assembly
Shrink fits use thermal expansion on purpose. Heat the outer hub so the hole grows. Slip it onto the shaft while hot. Let it cool and it clamps tight. A 2 inch steel hub heated from 70 to 400 °F grows the hole about 0.0043 inches, plenty to slip over an interference-fit shaft.
Thermal Stress in Clamped Parts
A part that cannot grow freely builds up stress. The stress is CTE times elastic modulus times temperature change. For a clamped 1018 steel bar heated 100 °F, the stress is about 21,000 psi. This can yield thin sections or pop bolted joints. Always give heated parts room to move.