Interference fit — pressure, force, torque and assembly temperature

Contact pressure, friction force/torque and stresses for an interference fit (Lame equations), plus the cooling/heating temperature needed for expansion/shrink-fit assembly.

✓ validated against legacyoriginal: /calculators/e6_2.htm

Interference fit — pressure, force, torque and assembly temperature — original diagram from /calculators/e6_2.htm

Inner bore of inner ring, dᵢmmInterface diameter, dmmOuter diameter of outer ring, dₒmmContact length, LmmDiametral interference ratio, δ/dFriction coefficient, µYoung’s modulus inner, EᵢGPaPoisson inner, νᵢYoung’s modulus outer, EₒGPaPoisson outer, νₒMounting interference ratio for assembly, δ/dThermal expansion coefficient, αᵢ×10⁻⁶ K⁻¹Thermal expansion coefficient, αₒ×10⁻⁶ K⁻¹

Interference pressure, p6.53667127205144 MPa

Friction force, F1.4169535328573695 kN

Transmission torque, T16.29496562785975 Nm

Stresses

σt inner ring @ dᵢ-53.61083880488703 MPa

σt inner ring @ d-47.074167532835595 MPa

σt outer ring @ d7.714630428214006 MPa

σt outer ring @ dₒ1.1779591561625655 MPa

σr inner ring @ dᵢ0 MPa

σr inner ring @ d-6.53667127205144 MPa

σr outer ring @ d-6.53667127205144 MPa

σr outer ring @ dₒ0 MPa

σe inner ring @ dᵢ53.61083880488703 MPa

σe inner ring @ d44.17009125710193 MPa

σe outer ring @ d12.356034843645773 MPa

σe outer ring @ dₒ1.1779591561625655 MPa

Assembly temperature

Cooling temperature (inner part), dTᵢ-75.00000000000001 K

Heating temperature (outer part), dTₒ125 K

Unlike the sibling press-fit calculator (e3_8), this page takes the diametral interference ratio δ/d directly as an input rather than deriving it from δ and d, and adds an independent assembly-temperature calculation for cooling the inner part / heating the outer part to reach a target mounting interference. If the entered geometry is physically invalid (interface diameter or outer diameter smaller than the bore, or a negative bore), the legacy source silently discards all three diameters and substitutes its own default set (dᵢ=20 mm, d=23 mm, dₒ=80 mm) rather than rejecting the input — preserved exactly. There is no separate output showing the diameters actually used, so an invalid combination is not obviously flagged in the results. Separately, entering dₒ=0 is a supported special case (unlike the reset above) — the legacy source treats it as an effectively infinite outer diameter (a very thick outer part with no defined outer boundary), substituting a large finite stand-in value rather than 0 itself; this is not indicated in the field label.

Method & references

Lame’s equations for thick-walled cylinders (elastic regime).
Default values represent a polymer bushing, steel hub.

ISO 286-2 hole & shaft tolerance reference tables

The computation is a literal port of the original client-side JavaScript from /calculators/e6_2.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.