Press Fit & Interference Fit
Contact pressure, hub stress, the torque an interference fit can carry and the temperature that would open it, from the Lamé thick-walled cylinder equations.
The contact pressure from your interference, the hoop and von Mises stress at the hub bore against its yield, the torque and axial force friction can hold, and the shrink-fit temperature rise.
Example: 0.04 mm of interference on a 50 mm steel shaft gives 60 MPa of contact pressure, 100 MPa of hoop stress at the bore, and 2 121 N·m of torque at μ = 0.15.
Lamé, 1852,
and a very tight hole.
How interference becomes pressure, what that pressure can hold, and everything the elastic equations leave out.
Interference to pressure
A shaft larger than the hole it goes into squeezes both parts, and the thick-walled cylinder equations give the contact pressure from the interference, the two diameters, the hub’s outside diameter and both materials’ elastic constants. The one thing to get right before anything else is that the interference is on the *diameter*: half of it acts on the radius, and pasting a radial figure from a tolerance table doubles the answer. Once the pressure is known the hub bore is the worst-stressed place in the assembly — hoop stress tensile, radial compressive — and a thin hub multiplies pressure into hoop stress hard.
What it holds, and how to assemble it
The joint transmits torque by friction alone: T = μ·p·π·d²·L ÷ 2, with the axial push-out force from the same pressure and the same coefficient. Friction is the weakest link in the whole calculation: it depends on the surfaces, the lubricant and how the parts went together, and a shrink fit holds better than a pressed one because pressing shears the high spots off on the way in. Heating the hub is the gentler assembly — no galling — and the page gives the temperature rise that opens it by the interference plus whatever clearance you want, at the expansion coefficient you enter.
Limits
Elastic, static, uniform temperature, perfectly round and perfectly smooth. Surface roughness flattens on assembly and takes real interference with it; centrifugal load loosens a rotating fit; a temperature difference in service moves the interference either way; and once the bore yields these equations stop describing the joint at all, which is why a heavy fit is flagged. No tolerance class and no ISO 286 designation is applied — the interference you enter is the one used. Fatigue, fretting and the stress concentration at the hub ends are outside the calculation entirely, and every material constant is your input. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Lamé thick-walled cylinders for the pressure and hub stress; T = μ·p·π·d²·L ÷ 2; elastic and static only; modulus, Poisson ratio, friction and expansion are your inputs
Last reviewed 22 September 2026. How results are checked: How we verify.