Press Fit (Interference Fit) Calculator
Contact pressure, pressing force, slipping torque and hub stress for a shaft pressed into a hub with a given diametral interference — Lamé thick-cylinder theory.
Results
What this tool does
A press fit holds by the pressure that the interference squeezes into the joint: the hub stretches, the shaft shrinks, and both together take up the interference. The Lamé equations give that pressure from the diameters and the elastic constants, and friction turns it into a holding torque and an axial force. Real values come out lower than the ideal, because the peaks of the surface roughness flatten as the parts go together — measure the interference after allowing for that, and keep an eye on the hub stress, which is the one that limits how tight a fit can be. Friction of 0.1–0.2 is common for steel on steel, but it varies with surface and lubrication.
Formula
p = δ ÷ { d [ (1/E_hub)((D² + d²)/(D² − d²) + ν_hub) + (1/E_shaft)((d² + d_i²)/(d² − d_i²) − ν_shaft) ] } · F = μ p π d L · T = μ p π d² L ÷ 2
Variables
| Symbol | Meaning | Unit |
|---|---|---|
d | Nominal diameter of the fit | mm |
di | Bore of a hollow shaft (0 if solid) | mm |
dh | Outer diameter of the hub | mm |
iv | Diametral interference | µm |
es | Young's modulus of the shaft | GPa |
ns | Poisson's ratio of the shaft | — |
eh | Young's modulus of the hub | GPa |
nh | Poisson's ratio of the hub | — |
mu | Coefficient of friction between the parts | — |
l | Length of the fit | mm |
P | Contact pressure at the interface | MPa |
F | Axial force to press it in (about) | kN |
TQ | Torque the fit can carry before slipping | N·m |
HS | Hoop stress in the hub at the bore | MPa |
Worked example
- Nominal diameter of the fit50 mm
- Bore of a hollow shaft (0 if solid)0 mm
- Outer diameter of the hub90 mm
- Diametral interference40 µm
- Young's modulus of the shaft210 GPa
- Poisson's ratio of the shaft0.3
- Young's modulus of the hub210 GPa
- Poisson's ratio of the hub0.3
- Coefficient of friction between the parts0.15
- Length of the fit40 mm
- Contact pressure at the interface58.07 MPa
- Axial force to press it in (about)54.73 kN
- Torque the fit can carry before slipping1368.3 N·m
- Hoop stress in the hub at the bore109.9 MPa
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.