Shrink Fit / Press Fit Interference Calculator
Design an interference (shrink or press) fit — contact pressure from the diametral interference, hub and shaft dimensions and moduli, torque and axial-force capacity from friction, hub hoop stress against yield, the temperature to heat the hub (or cool the shaft) for assembly, and the press force for a press fit.
How it works
p = δ ÷ { d × [ (1/E_h)((D² + d²)/(D² − d²) + ν_h) + (1/E_s)(1 − ν_s) ] } · T = p × π d L × µ × d/2 · F_axial = p × π d L × µ · σ_hoop = p (D² + d²)/(D² − d²) · ΔT = (δ + clearance) ÷ (α d)
When a hub is forced onto a slightly larger shaft, both parts deform elastically until the shaft's squeeze and the hub's stretch add up to the interference, and Lamé's thick-cylinder equations give the pressure at which that balance occurs — higher for a thick, stiff hub and a large interference. That pressure, acting over the contact area with friction, is what transmits torque and resists axial push-out, so the same equations size the fit for a drive and check that the hub's bore is not stressed past yield, which is the usual limit. Because metals expand about a hundredth of a millimetre per hundred kelvin per hundred millimetres, heating the hub by a few hundred degrees or chilling the shaft opens enough clearance to slide the parts together without a press.
Worked example
A steel hub Ø100 × 40 mm long on a Ø50 steel shaft with 0.05 mm diametral interference sees about 78 MPa of contact pressure — roughly 1,830 N·m of torque and 73 kN of axial holding at µ = 0.15 (halve both for design) — with 129 MPa of hoop stress at the bore, a safety factor of about 2.0 against 355 MPa yield. Heating the hub about 170 K (to ≈ 190 °C) opens the interference plus 0.05 mm of slip clearance.
Frequently asked questions
How much interference should I use?
Typical shrink fits run 0.0005–0.0015 mm per mm of diameter (0.025–0.075 mm on Ø50); ISO fits H7/s6 or H7/u6 land in that range. Check hub stress at the maximum and holding at the minimum of the tolerance band.
Does the shaft also stress?
A solid shaft sees the contact pressure as uniform compression — rarely critical. A hollow shaft behaves like another thick cylinder and needs its own Lamé check; the formula here assumes solid.
Related calculators
Textbook machine-design formulas (Shigley, Roark, Eurocode 3 / VDI conventions) with idealised assumptions. Use manufacturer data, material certificates and a qualified engineer's check for anything safety-related.