Does ISO 286 calculate interference-fit contact pressure?

No. ISO 286-1 defines the tolerance-code concepts and ISO 286-2 supplies selected limit-deviation tables. The elastic pressure equation on this page is a Lamé-Hooke engineering model and is not an ISO formula.

Which friction coefficient should I use?

There is no universal value. Use a coefficient justified for the actual material pair, surface finish, coating, lubricant, assembly process, temperature, contact pressure and life condition; otherwise leave it blank.

Can I enter H7/p6 or H7/s6 directly?

No. Determine the applicable shaft and hole limits from a controlled current source, then analyse the minimum and maximum diametral interference at a common reference or operating state.

Does this worksheet prove the fit is safe?

No. It does not evaluate yielding, plasticity, fatigue, fretting, edge effects, temperature gradients, residual stress, assembly damage, surface flattening, combined loading or a safety factor.

What interference does the model use?

It uses positive diametral interference: free shaft outside diameter minus free hub bore diameter, both defined at the same controlled state. The small diameter difference is ignored in the reference interface geometry.

Source-gated elastic screening arithmetic

Elastic Cylindrical Interference-Fit Worksheet

Ideal Lamé-Hooke contact pressure for two concentric cylinders with separate material properties and a solid or hollow shaft. Optional friction outputs are separate uniform-pressure Coulomb limits, not rated joint capacity.

Diametral interferenceOpen ends / plane stressNot an ISO pressure formula

Input unit system

Reference interface diameter d (mm)

Diametral interference δ (mm)

Shaft bore diameter Dᵢ (mm; 0 = solid)

Hub outside diameter Dₒ (mm)

Uniform contact length L (mm)

Documented friction coefficient μ (optional)

Shaft Young’s modulus Eₛ (GPa)

Shaft Poisson ratio νₛ (−1 < ν < 0.5)

Hub Young’s modulus Eₕ (GPa)

Hub Poisson ratio νₕ (−1 < ν < 0.5)

Controlled basis / source (required: dimensions and state; materials; and μ basis if used)

I confirm that δ is positive diametral interference at one controlled state; the bodies are concentric, sufficiently long away from ends, open/unrestrained axially, isotropic and linearly elastic; full contact and uniform pressure are reasonable; δ is very small relative to d; and separate yielding, hollow-shaft buckling, fatigue, fretting, thermal, tolerance and assembly checks will be made.

Ideal model results

Uniform contact pressure p

—

Interference ratio δ/d

—

Hub bore hoop stress σθ,h

—

Shaft contact hoop stress σθ,s

—

Hub diametral expansion

—

Shaft diametral contraction

—

Separate ideal axial slip limit

—

Separate ideal torque slip limit

—

Elastic compatibility

The model uses one reference interface diameter d because the free preassembly diameter difference is assumed very small. δ is diametral interference: free shaft OD minus free hub bore, evaluated at the same controlled state.

kₛ = (d² + Dᵢ²)/(d² − Dᵢ²)    kₕ = (Dₒ² + d²)/(Dₒ² − d²)
Cₛ = (kₛ − νₛ)/Eₛ    Cₕ = (kₕ + νₕ)/Eₕ
p = δ/[d(Cₛ + Cₕ)]
Δdₛ = p d Cₛ    Δdₕ = p d Cₕ    δ = Δdₛ + Δdₕ
σθ,s at contact = −p kₛ    σθ,h at bore = +p kₕ

E is in pressure units; all four diameters/lengths use one length unit. The result p and displayed hoop stresses then use the same pressure basis. These equations follow axisymmetric Lamé stresses plus plane-stress Hooke strain compatibility; they are general engineering elasticity equations, not ISO fit equations.

Optional friction arithmetic

A = πdL F_slip = μpA T_slip = μpA(d/2)

F and T are separate ideal incipient-slip limits for uniform normal pressure and constant Coulomb μ. They are not simultaneous independent capacities and contain no safety factor. Leave μ blank unless its basis is controlled for the real surfaces and service state.

Input	Definition
d	Common reference diameter at the fit interface
δ	Positive diametral interference at one state
Dᵢ	Shaft bore; zero selects the solid-shaft limit
Dₒ	Hub outside diameter
L	Length over which uniform p and μ are assumed
Eₛ Eₕ	Young’s moduli at the relevant state
νₛ νₕ	Poisson ratios for stable isotropic elasticity: −1 < ν < 0.5

No acceptance verdict: interface stresses are not a complete stress field or a yield/fatigue check. Short hubs, shoulders, grooves, keys, splines, tapers, surface asperity flattening, residual stress, plasticity, hollow-shaft external-pressure buckling, temperature gradients, centrifugal effects, fretting, assembly damage and combined axial/torque/bending loads can invalidate the uniform elastic model.

ISO fit codes do not supply this pressure formula

ISO 286-1:2010, edition 2 with Cor 1:2013, is current and was confirmed in 2026. It defines the ISO code system concepts and fit terminology. ISO 286-2:2010, edition 2 with Cor 1:2013, supplies selected limit-deviation tables; its official record is currently under systematic review. Neither public scope establishes the Lamé pressure equation or selects a fit for a load case.

Exact H7/p6, H7/s6 or other designation limits must come from the controlled applicable ISO 286-2 table and size step. They are deliberately not reconstructed here and remain NEEDS_LICENSED_SOURCE. Analyse both minimum and maximum interference after temperature, coating, surface and measurement effects.

ISO 1:2022, edition 4, defines the standard reference-temperature concept for dimensional properties. This worksheet does not convert a drawing-state interference to an operating-state interference.

Open technical sources

University of Washington ME 354, Thick Walled Cylinders, gives the same-material two-cylinder shrink-fit reduction and states the small-interference/no-axial-stress assumptions. NASA contractor report BRL 6048 (1972), Appendix F, gives the dissimilar-material radial compatibility and the ideal torque relation with a worked actuator example. Exact unit conversions use NIST SP 811 Appendix B. Sources accessed 13 July 2026.

No. ISO 286 codes and tables describe size tolerances and deviations. Pressure requires a separate structural model with geometry and material properties.

No universal dry/oiled value is supplied. Use controlled evidence for the actual pair, finish, coating, lubricant, process, pressure, temperature and life condition, or leave μ blank.

A designation alone is not one interference value. The basic size step and both shaft/hole limits determine a range, and service-state effects can change it.

No. This page reports only ideal interface quantities and no allowable. A complete multiaxial/local stress, assembly, fatigue, fretting, tolerance and service analysis is still required.