Press Fit / Interference Fit Calculator.
Calculate contact pressure, push-out force, hub stress, required interference, and shrink-fit temperature for shaft-hub press fits and shrink-fit assemblies. Based on Lamé's thick-cylinder equations.
Geometry
Materials
Chub = (Do² + Df²)/(Do² − Df²) + νh
Cshaft = (Df² + Di²)/(Df² − Di²) − νs
Faxial = π · Df · L · p · μ
Press-Fit Engineering Basics
A press-fit (also called interference fit or shrink-fit) joins two cylindrical parts by making the shaft slightly larger than the hole. Elastic deformation creates contact pressure, which provides torque transmission, axial holding, and zero backlash.
Lamé Equation for Hub Stress
Contact pressure: p = E × δ / D × [(D_o² − D²) / (2 × D_o²)]
Hub max stress (tangential at bore): σ_θ = p × (D_o² + D²) / (D_o² − D²)
Axial force: F = π × D × L × p × μ
Where δ = diametrical interference, D = bore diameter, D_o = hub OD, E = elastic modulus, μ = friction coefficient (typically 0.10-0.15 dry steel-on-steel).
Safety Factor Targets
- SF < 1.0 — Hub yields. Fit fails.
- SF 1.0 – 1.5 — Marginal. Static loads only, no thermal cycling.
- SF ≥ 2.0 — Production-acceptable. Survives manufacturing variation.
- SF ≥ 3.0 — Safety-critical applications.
Worked Press-Fit Example
Pressing a steel pin (Ø25.020) into a steel hub (Ø25.000 bore, Ø50.000 OD), 20 mm long.
- Interference δ = 0.020 mm
- E_steel = 210,000 MPa
- Contact pressure p = 210,000 × 0.020 / 25 × [(50² − 25²)/(2 × 50²)] = 168 × 0.375 ≈ 63 MPa
- Hub max stress σ = 63 × (2500 + 625)/(2500 − 625) = 63 × 1.667 ≈ 105 MPa
- If hub yield = 350 MPa → SF = 3.3 (good)
- Insertion force F = π × 25 × 20 × 63 × 0.1 ≈ 9,900 N (1 ton)
Assembly Methods
- Cold press — direct hydraulic press. Fastest for small parts, requires high force.
- Heat the hub — hub expands, fit slides in, cools to interference. Standard for bearings and large hubs.
- Cool the shaft — dry ice or LN2. Used when hub material can't be heated.
- Combined — heat hub + cool shaft. Maximum thermal differential.
Common Press-Fit Mistakes
- Ignoring temperature change in service — different CTEs can release the fit at high temperature.
- Not accounting for surface roughness — peaks crush during press, reducing effective interference by 30-50%.
- Insufficient hub wall thickness — thin hubs see disproportionate stress at bore.
- Press without lubrication — galling can occur, ruining both parts.
Related Tools
For tolerance class selection, see ISO 286 Fits Calculator. For multi-part stack-up, use Tolerance Stack-Up. For bolted alternatives, see Bolt Torque Calculator. Material properties for steels: see Hardness Conversion.