Press Fits Calculator — Lamé Contact Pressure, Assembly Force & Thermal Temperatures (DIN 7190 / ISO 286)

DIN 7190-1 models the hub as a thick-walled ring and the shaft as a solid (or hollow) cylinder under external pressure. The diametral interference δ is shared between the elastic expansion of the hub bore and the elastic compression of the shaft surface, weighted by the respective Lamé compliance factors C_hub and C_shaft. Dividing the total radial displacement at the interface by d (the diametral form) gives the contact pressure p. MechanixCalc also applies the DIN 7190-1 surface-roughness smoothing loss — 80 % of the combined 10-point roughness heights (Rz) flatten during pressing, so the capacity pressure uses the reduced effective interference δ_eff = δ_min − 0.8·(Rz_shaft + Rz_hub).

A hub should be checked against yielding at its bore, where the hoop stress is highest. MechanixCalc uses the GEH (Gestaltänderungsenergie, von Mises) equivalent stress at the bore rather than the hoop component alone, because at r = d/2 both the hoop stress σ_θ and the radial stress σ_r = −p are present. The burst safety factor SF_burst = Sy_hub / σ_vM; the tool flags SF_burst below 2.0 (review) and below 1.4 (risk) — conservative tool targets. The yield strength is read at the part's blank size where a size-banded minimum exists — 42CrMo4 from the EN 10083-3 +QT bands (900 MPa only up to 16 mm, 650 MPa at 40–100 mm, 500 MPa at 160–250 mm) and 6061-T6 from the bar minimum (240 MPa); S235 and S355 from the EN 10025-2 thickness bands (S355: 355 MPa only up to 16 mm, 315 MPa at 80–100 mm, 295 MPa at 100–150 mm), taking the bar the part is turned from (diameter plus machining stock) as the thickness; grey cast iron and grades without a banded table use their thinnest-section values, with no size reduction applied.

DIN 7190-1 checks the inner member as well as the hub. A SOLID shaft under the interface pressure sits in near-hydrostatic compression — σ_r = σ_θ = −p with σ_z = 0 — so its von Mises equivalent stress is simply p, and the crush safety factor is Sy_shaft / p.

A HOLLOW shaft behaves differently, and not in the direction intuition suggests. Boring the shaft makes it more compliant, so the same interference produces a LOWER contact pressure — but the compressive hoop stress concentrates at the free bore, reaching 2p/(1 − (d_i/d)²) there while the radial stress falls to zero. The bore governs at every bore ratio. The net effect is that the shaft's utilisation rises as the bore grows even though the contact pressure falls, so MechanixCalc evaluates the crush check at the bore whenever a hollow shaft is specified.

The transmissible torque and axial force both scale with the friction-contact area and the contact pressure at minimum-material interference (the guaranteed condition). The press assembly force uses the maximum-material contact pressure (worst case for the press). Thermal shrink-fit temperatures follow from the thermal expansion relation: the required temperature rise ΔT heats the hub until it expands by δ plus an assembly clearance allowance, determined by the hub material's linear thermal expansion coefficient α.

For dissimilar material pairs the thermal loosening panel computes the change in interference δ_thermal = d · (α_hub − α_shaft) · ΔT_operating. If the hub expands more than the shaft at service temperature the interference reduces; if the shaft expands more it tightens.