DIN 7190 Interference Fits — Lamé Contact Pressure & Assembly Force Calculator
DIN 7190 — Interference fits — Calculation and design principles
DIN 7190 is the German standard for the design and calculation of interference fits (Pressverbände) — joints in which a hub or ring is forced onto a shaft by elastic deformation, producing a contact pressure that transmits torque and axial force by friction. Part 1 (DIN 7190-1:2017) defines the Lamé thick-wall cylinder model for computing the interface contact pressure p from the diametral interference δ, the von Mises (GEH) burst criterion for the hub bore, the roughness-smoothing correction for grip capacity, the assembly press force, and the thermal temperatures required for shrink-fit assembly.
It is the standard cited by European machine designers whenever a gear hub, coupling, pulley or bearing ring is to be interference-fitted — and the one a reviewer expects to see in the calculation record. MechanixCalc implements DIN 7190-1 in full, including the ISO 286-1 tolerance fit picker that resolves H7/p6, H7/s6 and similar named fits to the published limit deviations, and produces a standards-cited PDF report that can accompany the design submission.
Calculators that implement DIN 7190
What DIN 7190 covers
- Lamé thick-wall contact pressure — diametral interference δ resolved to interface pressure p for solid and hollow shafts
- Hub burst safety factor — von Mises (GEH) equivalent stress at the bore, SF_burst ≥ 2.0 recommended by DIN 7190-1
- Surface-roughness smoothing correction — effective interference for grip capacity δ_eff = δ_min − 0.8·(Rz_shaft + Rz_hub)
- Transmissible torque and axial capacity — friction-based joint capacity at minimum-material interference
- Assembly press force and disassembly pull force — worst-case maximum-material contact pressure
- Thermal shrink-fit temperatures — hub heating and shaft cooling required to achieve assembly clearance for dissimilar or identical materials
Parts of the standard
- DIN 7190-1Interference fits — Calculation and design principles
- ISO 286-1Geometrical product specifications — Limits and fits: Part 1 — Bases of tolerances, deviations and fits (used with DIN 7190-1 for named tolerance fits)
Governing formulas
p = (δ / 1000) / [d · (C_hub + C_shaft)]where p = interface contact pressure (MPa); δ = diametral interference (µm); d = interface diameter (mm); C_hub = [(D²+d²)/(D²−d²) + ν_hub] / E_hub; C_shaft = (1 − ν_shaft) / E_shaft (solid shaft); D = hub outer diameter (mm); E = elastic modulus (MPa); ν = Poisson's ratio. For a hollow shaft the C_shaft denominator changes sign: C_shaft = [(d²+d_i²)/(d²−d_i²) − ν_shaft] / E_shaft.
σ_vM = √(σ_θ² + σ_θ·p + p²) ; SF_burst = Sy_hub / σ_vM (≥ 2.0 recommended)where σ_θ = p·(D²+d²)/(D²−d²) = hoop stress at hub bore (MPa); σ_r = −p at bore (radial compressive stress, MPa); σ_z = 0 (plane stress assumption); Sy_hub = yield strength of hub material (MPa). DIN 7190-1 recommends SF_burst ≥ 2.0.
T = µ · p_min · π · d² · L / 2 / 1000where T = transmissible torque (N·m); µ = friction coefficient (dry steel ≈ 0.10–0.15); p_min = contact pressure at minimum-material interference after roughness smoothing (MPa); d = interface diameter (mm); L = contact length (mm). The /1000 converts N·mm to N·m.
Frequently asked questions
What is DIN 7190 used for?
DIN 7190 defines the calculation method for interference fits — joints where a hub is pressed or shrunk onto a shaft. It covers: computing the interface contact pressure p from the diametral interference δ using the Lamé thick-wall cylinder model; checking the hub bore against yielding using the von Mises (GEH) burst criterion (recommended safety factor SF_burst ≥ 2.0); calculating the transmissible torque and axial force the joint can carry in service; and determining the assembly press force or the thermal temperatures needed for shrink-fit assembly. It is the standard cited in European machine design records for gear hubs, couplings, pulley bores and bearing ring fits.
How does DIN 7190-1 compute contact pressure?
DIN 7190-1 uses the Lamé thick-wall cylinder model. The hub is treated as a thick-walled ring under internal pressure and the shaft as a solid (or hollow) cylinder under external pressure. The total diametral interference δ (µm) is shared between the elastic expansion of the hub bore and the elastic compression of the shaft surface, weighted by their Lamé compliance factors C_hub and C_shaft. Dividing the interference by d·(C_hub + C_shaft) gives the contact pressure in MPa. DIN 7190-1 also subtracts a roughness-smoothing loss 0.8·(Rz_shaft + Rz_hub) from the minimum-material interference before computing the friction-grip capacity.
What safety factor does DIN 7190 require for hub burst?
DIN 7190-1 recommends a burst safety factor SF_burst = Sy_hub / σ_vM ≥ 2.0, where σ_vM is the von Mises (GEH) equivalent stress at the hub bore. At the bore both the hoop stress σ_θ and the radial stress σ_r = −p are present simultaneously, so the correct check is σ_vM = √(σ_θ² + σ_θ·p + p²) — using hoop stress alone overstates the permissible interference. The MechanixCalc press fit calculator applies the GEH form directly.
How do DIN 7190 and ISO 286 work together?
DIN 7190-1 is the calculation standard for interference fits — it converts diametral interference δ into contact pressure and capacity. ISO 286-1 is the tolerance standard that defines the limit deviations for named fits such as H7/p6, H7/s6 and H7/u6. In practice both are used together: you select the fit class from ISO 286-1 tables to get δ_min and δ_max, then apply DIN 7190-1 to verify hub burst at δ_max (worst-case stress) and torque capacity at δ_min after roughness smoothing (worst-case grip). MechanixCalc resolves H-basis fits from the published ISO 286-1:2010 tables without interpolation.
Is the DIN 7190 press fit calculator free?
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