How it works
An interference fit holds by the contact pressure created when the
shaft is forced into a slightly smaller hole. For a solid shaft pressed into a hub of
the same material, Lamé thick-cylinder theory gives that pressure
from the diametral interference δ:
p = (E · δ) / (2 · d) · (d₀² − d²) / d₀²
where d is the interface diameter, d₀ the hub outside
diameter and E Young's modulus. The hub's stiffness — set by the
(d₀² − d²)/d₀² wall-thickness term — controls how much pressure a given
interference produces.
From the contact pressure the axial assembly force is
F = π · μ · p · d · L
(μ the friction coefficient, L the engagement length), and
the friction joint's torque capacity is
T = F · d / 2. The pressure also loads the hub: the peak
tangential (hoop) stress at the bore is
σ = p · (d₀² + d²) / (d₀² − d²),
which must stay below the hub material's yield strength.
Worked example
A 50 mm shaft pressed into an 80 mm-OD hub with 0.04 mm diametral interference, 40 mm
of engagement, μ = 0.15, both steel (E = 200,000 MPa). The contact pressure is
p ≈ 48.8 MPa, the press force is
F = π × 0.15 × 48.8 × 50 × 40 ≈ 45.9 kN, and the joint transmits up to
T ≈ 1149 N·m before slipping. The hub hoop stress is
σ ≈ 111 MPa — comfortably below mild-steel yield. The calculator returns
exactly these numbers.
Frequently asked questions
- How do you calculate an interference fit?
- Start from the diametral interference δ (shaft diameter minus hole diameter) and use Lamé thick-cylinder theory to get the contact pressure: p = (E·δ)/(2·d) · (d₀²−d²)/d₀², for a solid shaft in a same-material hub. From p you get the press-in force F = π·μ·p·d·L, the torque capacity T = F·d/2, and the hub hoop stress σ = p·(d₀²+d²)/(d₀²−d²).
- How much interference do I need for a press fit?
- A common rule of thumb is about 0.001–0.002 × the interface diameter of diametral interference for a steel-on-steel press fit — so roughly 0.05–0.10 mm on a 50 mm shaft. Use the calculator to convert your chosen interference into actual pressure, force and hub stress, then back off if the hub hoop stress approaches yield.
- How much force does it take to press it together?
- The axial assembly force is F = π·μ·p·d·L, where p is the interface pressure, μ the friction coefficient, d the interface diameter and L the engagement length. Friction μ is the biggest unknown — pick it conservatively (dry steel-on-steel is typically 0.1–0.2).
- Will the hub yield?
- Check the hub hoop stress σ = p·(d₀²+d²)/(d₀²−d²) — the peak tangential stress at the bore — against the hub material yield strength. The calculator flags it when it climbs past about 250 MPa, near the yield of mild steel; a thinner hub (smaller d₀) raises this stress quickly.
- Can I use a shrink (thermal) fit instead of pressing?
- Yes — heat the hub so its bore grows by at least the interference, drop it onto the shaft, and let it cool. The required temperature rise is ΔT = δ/(α·d), where α is the coefficient of thermal expansion (≈ 12×10⁻⁶ /°C for steel) and d the interface diameter. A shrink fit avoids galling the surfaces during assembly.
- Does this work in metric and imperial?
- Yes — enter the diameters, interference and length in mm or inches and the modulus in MPa or ksi; results show in metric or imperial. The physics runs in fixed internal units, so the unit toggle never changes the answer.
Method & assumptions
- Lamé (elastic) thick-cylinder theory for a solid shaft in a hub of the same material; both parts stay below yield.
- Ignores surface-roughness flattening — real assemblies lose part of the nominal interference, so the actual pressure and force are usually a little lower.
- Ignores temperature differentials and centrifugal (rotational) effects, both of which change the effective fit in service.
- Press force and torque capacity scale directly with the friction coefficient μ, the largest source of uncertainty — choose it conservatively.
- Always check the hub hoop stress against the hub material's yield strength; a thin hub can yield well before the shaft does.
Related calculators
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- MMC Bonus Tolerance Calculator — MMC/LMC bonus tolerance from a feature’s departure from its material limit.
- Composite Position Tolerance Calculator — Two-tier PLTZF/FRTZF position check from X/Y deviation.
- Flatness Tolerance Calculator — Flatness (surface form) from measured points, with a pass/fail check.
- Hole & Shaft Fit Calculator — ISO 286 hole-basis clearance-fit limits and clearance (H7/g6, H8/f7, …).
- Cylindricity & Runout Calculator — Runout (TIR) and cylindricity zone from indicator and diameter readings.