Press Fit & Shrink Fit Interference Calculator

How it works

p = δ ÷ { d [ (1/E_hub)((D²+d²)/(D²−d²) + ν_hub) + (1/E_shaft)((d²+d_i²)/(d²−d_i²) − ν_shaft) ] }; hub hoop stress = p (D²+d²)/(D²−d²); press force = µ p π d L; torque = F d/2; ΔT = (δ + clearance) ÷ (α d)

An interference fit turns a shaft and hub into one part by elastic pressure: the hub is stretched and the shaft squeezed by the interference, and the thick-cylinder (Lamé) equations translate that diametral difference into a contact pressure that depends on both parts’ stiffness and geometry — a thin hub or an aluminium hub develops far less pressure than a heavy steel one for the same interference. That pressure times the contact area and friction gives the force needed to press the parts together and, at the radius, the torque the joint can carry without slipping. The hub’s bore sees the highest stress (tensile hoop plus compressive radial), so heavy fits are checked against yield. Shrink fitting — heating the hub or chilling the shaft until the bore opens past the interference — assembles the parts without force and without scoring, which also raises the effective friction.

Worked example

A steel 40 mm shaft in a steel hub 80 mm outside, 50 mm long, with 45 µm of diametral interference: contact pressure 87 MPa, hub hoop stress 146 MPa (von Mises ≈ 204 MPa, safety factor 1.7 on 350 MPa yield). Pressing needs about 82 kN at µ 0.15 and the joint transmits roughly 1,650 N·m by friction; heating the hub about 180 °C opens it enough to drop on.

Frequently asked questions