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

Governing standard: DIN 7190· DIN 7190-1:2017 (Lamé thick-wall, GEH burst criterion, DIN 7190-1 roughness smoothing) · ISO 286-1:2010 (H-basis tolerance fits)

How DIN 7190 works — the method explained

The MechanixCalc press fits calculator designs and verifies interference (press / shrink) fits to DIN 7190-1:2017 and ISO 286-1:2010. Enter the hub outer diameter, interface diameter, diametral interference and materials, and the tool returns the Lamé contact pressure, hub hoop stress at bore and OD (with a von Mises burst safety factor), shaft crushing stress, transmissible torque and axial capacity, plus assembly press force and thermal heating or cooling temperatures — all in one pass.

It is built for machine-design engineers who need a defensible interference-fit calculation for a gear hub, coupling, pulley, bearing ring or any press-fitted assembly, and who need to hand a reviewer a standards-cited, worked calculation rather than a rough estimate. The ISO 286-1 fit picker resolves any H7/p6, H7/s6 or similar named fit directly from the published tables of limit deviations — no interpolation, no d = 50 mm lookup scaled linearly.

What this calculator does

  • DIN 7190-1 Lamé contact pressure with GEH (von Mises) hub burst safety factor at the bore
  • ISO 286-1:2010 tolerance fit picker — published limit deviations for H7/k6, H7/p6, H7/r6, H7/s6, H7/u6 and more (H-basis, d ≤ 500 mm)
  • DIN 7190-1 roughness smoothing correction: effective interference for grip capacity = δ_min − 0.8·(Rz_shaft + Rz_hub)
  • Assembly press force and disassembly pull force, with hydraulic oil-injection assist option
  • Thermal shrink-fit temperatures — hub heating and shaft cooling required to achieve assembly clearance
  • Thermal loosening analysis — residual interference at operating temperature for dissimilar material pairs
  • Fretting fatigue safety factor at the hub edge (Goodman criterion under rotating bending)
  • Branded PDF engineering report with the full Lamé method and ISO tolerance derivation shown

Method & formulas

Lamé thick-wall contact pressure (DIN 7190-1)

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).

Lamé contact pressure
p = (δ / 1000) / [d · (C_hub + C_shaft)]

where p = 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; D = hub outer diameter (mm); E = elastic modulus (MPa); ν = Poisson's ratio

Hub burst safety factor — GEH (von Mises) criterion

DIN 7190 requires the hub to 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; DIN 7190 recommends SF_burst ≥ 2.0.

Von Mises equivalent stress at the hub bore
σ_vM = √(σ_θ² + σ_θ·p + p²)

where σ_θ = p·(D²+d²)/(D²−d²) = hub bore hoop stress (MPa); p = contact pressure (MPa); σ_r = −p at the bore (compressive); σ_z = 0 (plane stress). The recommended SF_burst ≥ 2.0 (DIN 7190-1).

Transmissible torque and thermal assembly temperatures

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.

Transmissible torque capacity
T = µ · p_min · π · d² · L / 2 / 1000

where T = transmissible torque (N·m); µ = friction coefficient (dry steel ≈ 0.10–0.15); p_min = contact pressure at minimum-material interference (MPa); d = interface diameter (mm); L = contact length (mm). The /1000 converts N·mm to N·m.

Required hub heating temperature
T_heat = T_room + (δ + δ_clearance) / (1000 · d · α)

where T_heat = hub heating temperature (°C); δ = minimum required interference (µm); δ_clearance = assembly clearance allowance (µm, typically 0.01·d in mm); d = interface diameter (mm); α = hub linear thermal expansion coefficient (°C⁻¹, e.g. 11.7 × 10⁻⁶ for steel).

Worked example

A steel gear hub (E = 210 000 MPa, ν = 0.30, Sy = 355 MPa) is pressed onto a solid steel shaft (E = 210 000 MPa, ν = 0.30) with d = 50 mm interface diameter, D = 90 mm hub OD, diametral interference δ = 40 µm and contact length L = 50 mm. Friction coefficient µ = 0.12. Find the contact pressure and transmissible torque.

Given

  • Interface diameter d50 mm
  • Hub outer diameter D90 mm
  • Contact length L50 mm
  • Diametral interference δ40 µm
  • Hub & shaft elastic modulus E210 000 MPa (steel)
  • Hub & shaft Poisson's ratio ν0.30
  • Friction coefficient µ0.12

Result

  • Contact pressure p≈ 58 MPa
  • Hub burst safety factor SF_burst≈ 2.40 (DIN 7190-1 recommends ≥ 2.0)
  • Transmissible torque T≈ 1369 N·m
  1. Compute Lamé compliance factor for the hub: C_hub = [(D²+d²)/(D²−d²) + ν] / E = [(8100+2500)/(8100−2500) + 0.30] / 210 000 = [10600/5600 + 0.30] / 210 000 = [1.893 + 0.30] / 210 000 = 2.193 / 210 000 = 1.044 × 10⁻⁵ mm/N·mm.
  2. Compute Lamé compliance factor for the solid shaft: C_shaft = (1 − ν) / E = 0.70 / 210 000 = 3.333 × 10⁻⁶ mm/N·mm.
  3. Compute the combined denominator: d · (C_hub + C_shaft) = 50 × (1.044×10⁻⁵ + 3.333×10⁻⁶) = 50 × 1.377×10⁻⁵ = 6.888×10⁻⁴ mm²/N·mm.
  4. Compute contact pressure: p = (δ / 1000) / denom = (40 / 1000) / 6.888×10⁻⁴ = 0.040 / 6.888×10⁻⁴ ≈ 58.1 MPa.
  5. Check hub burst: σ_θ at bore = p · (D²+d²)/(D²−d²) = 58.1 × 1.893 ≈ 110.0 MPa. Von Mises σ_vM = √(110.0² + 110.0×58.1 + 58.1²) = √(12100 + 6391 + 3376) = √21867 ≈ 147.9 MPa. SF_burst = 355 / 147.9 ≈ 2.40 (≥ 2.0 — acceptable per DIN 7190-1).
  6. Compute transmissible torque: T = µ · p · π · d² · L / 2 / 1000 = 0.12 × 58.1 × π × 2500 × 50 / 2 / 1000 = 0.12 × 58.1 × 196.35 / 1000 × 2500 × 50 / 2. Step-by-step: 0.12 × 58.1 = 6.972; × π = 21.905; × 2500 = 54762; × 50 = 2738100; / 2 = 1369050; / 1000 ≈ 1369 N·m.

Illustrative example with rounded inputs — verify against your actual geometry, material properties, roughness (DIN 7190-1 smoothing correction) and the ISO tolerance fit's minimum-material interference, which governs grip capacity.

Frequently asked questions

Which standard does this press fit calculator use?

Contact pressure, hub hoop stress, burst safety factor and assembly force follow DIN 7190-1:2017, which is the German standard for interference fits (Lamé thick-wall cylinder theory with the GEH / von Mises burst criterion and the surface-roughness smoothing correction). Tolerance fit limit deviations are taken directly from the published ISO 286-1:2010 tables (H-basis hole system, IT5–IT8, shaft letters h/k/m/p/r/s/u, d ≤ 500 mm). The governing method is shown in the generated PDF report.

What is the difference between press force and torque capacity in an interference fit?

The assembly press force is the axial load needed to push the shaft into the hub during cold assembly; it uses the maximum-material contact pressure (worst case for the press or hydraulic equipment). The transmissible torque and axial capacity are the loads the assembled joint can carry in service without slipping; they use the minimum-material contact pressure — the guaranteed friction grip. The ratio is governed by the friction coefficient µ and the interference tolerance band.

How does the ISO 286 tolerance fit picker work?

The calculator resolves the named fit (e.g. H7/s6 at d = 50 mm) directly from the published ISO 286-1:2010 tables of fundamental deviations and IT-grade tolerances — the same values in the standard's printed tables, not a linear interpolation from a single d = 50 mm proxy. The result is the minimum and maximum diametral interference (δ_min and δ_max) for the fit, and the DIN 7190-1 roughness smoothing loss is deducted from δ_min before computing the guaranteed grip pressure.

What heating temperature do I need for a shrink fit?

The thermal assembly panel computes the hub heating temperature (and shaft cooling temperature for liquid-nitrogen cooling) required to expand the hub enough to clear the shaft by the specified assembly clearance allowance. The required temperature rise is ΔT = (δ + δ_clearance) / (1000 · d · α), where α is the hub material's linear thermal expansion coefficient. A warning is raised if the hub temperature exceeds 300 °C (typical oven limit), in which case shaft cooling is suggested.

Is the press fit calculator free?

You can use it during a free 30-minute preview with no sign-up, and a free 14-day account trial unlocks every calculator with no credit card required. The branded PDF engineering report and saved calculations are part of a paid plan.

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