How interference fit pressure and torque are calculated
In a press or shrink fit the shaft is slightly larger than the hole. Forced together, the hub stretches and the shaft compresses. The contact pressure between them, from Lamé's thick-cylinder equations, holds the parts together by friction.
- Contact pressure:
p = δ / { d·[ (1/Eh)·((D²+d²)/(D²−d²) + νh) + (1/Es)·((d²+di²)/(d²−di²) − νs) ] } - Axial capacity:
F = μ·p·π·d·L - Torque capacity:
T = F·d/2 - Hub hoop stress:
σ = p·(D²+d²)/(D²−d²)
Worked example: gear on a 40 mm shaft
A steel hub 80 mm across on a 40 mm alloy-steel shaft, 40 mm long, with 35 µm of interference and μ = 0.15, has a contact pressure of 66 MPa. It holds 992 N·m of torque and 49.6 kN axially. The hub's hoop stress is 110 MPa (154 MPa von Mises), a safety factor of 2.3.
Good to know
- Take the interference range from your ISO fit, for example H7/s6. Check both the loosest fit for holding torque and the tightest for stress.
- Pressing flattens surface peaks and loses part of the interference. Allow for it on rough or turned surfaces.
- An aluminum hub on a steel shaft loosens as it warms, because aluminum expands twice as much. Check the fit at operating temperature.
- Pro gives the temperature to heat the hub or cool the shaft for assembly, and torque capacity across interference.