Shrink Fit
A hub that is slightly too small for its shaft can still be fitted: heat the hub until it grows over the shaft (or freeze the shaft), slide them together and let the temperatures even out. The tight grip that remains transmits torque without keys or glue.
Fitting by Temperature
Railway wheels, gear rims and bearings are often held on their shafts by nothing more than an interference fit: the hole is a few hundredths of a millimetre smaller than the shaft. Pressing them together could damage the surfaces, so instead the hub is warmed in an oven or with an induction heater until its bore is big enough — or the shaft is cooled in dry ice or liquid nitrogen.
Blacksmiths fitted iron tyres on wooden cartwheels the same way: heat the tyre red-hot, drop it over the wheel and quench it, so it shrinks and squeezes the wheel tight.
Bore Diameter vs. Hub Temperature
mmKey Relations
The bore must grow by the interference plus some clearance to slide on freely.
Thick-walled cylinder theory for a solid shaft and a hub of the same material.
Friction on the whole contact area times the shaft radius.
Sources & Verification
- R. G. Budynas & J. K. Nisbett, Shigley’s Mechanical Engineering Design, 10th ed., McGraw-Hill, 2015 — Ch. 7 (Shafts and Shaft Components).
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 18 (Temperature, Heat, and the First Law of Thermodynamics).