About Press Fit Calculator — ISO 286 Interference & Shrink Fits
The press fit calculator sizes interference (press and shrink) fits in two steps. First the fit: pick a nominal diameter and one of the standard hole-basis interference classes — H7/k6 and H7/n6 transition fits, H7/p6 light press, H7/s6 medium drive, H7/u6 force fit — and the tool returns the ISO 286-2:2010 limit deviations and the resulting minimum and maximum diametral interference. Every encoded deviation was verified against the published standard tables for the supported 1–200 mm range. If you already know your interference, enter it directly instead.
Then the mechanics: Lamé thick-cylinder theory turns interference into interface pressure, and friction turns pressure into holding capability — transmissible torque and axial force at the guaranteed minimum interference, plus press force, hub and shaft hoop stresses checked against yield, and the temperature change needed to shrink the hub on at the maximum interference. Elastic, preliminary sizing only: surface-finish smoothing, form error, and centrifugal loosening at speed are not modeled.
How It Works
- Pick the entry mode. Fit-class mode looks up the ISO 286-2 deviations for an H7 hole and your chosen shaft class at the nominal diameter — the interference range is shaft ei − hole ES (minimum, can be negative for the transition fits k6/n6) to shaft es (maximum). Direct mode takes one diametral interference in micrometres.
- Describe the joint geometry: hub outside diameter, shaft bore (0 for a solid shaft), and the engagement length. Thin-walled hubs and hollow shafts are more compliant — both lower the interface pressure the same interference generates.
- Set the materials: Young's modulus and Poisson's ratio for hub and shaft (steel defaults 200 GPa / 0.3), the friction coefficient (0.12 default — dry steel press fits are commonly taken at 0.1–0.15; lubricated assembly is lower), the hub yield strength for the stress check, and the thermal expansion coefficient for the shrink ΔT.
- Read the results in two columns. At the MINIMUM interference: the guaranteed transmissible torque and axial holding force — design your drive against these, because a joint at the loose end of tolerance holds least. Transition fits (H7/k6, H7/n6) can assemble with clearance, so their guaranteed capacity is zero and the tool says so.
- At the MAXIMUM interference: the highest interface pressure, the hub hoop stress compared to yield at displayed precision (the fit is elastic only if it passes), the press force an arbor press must deliver, and the hub temperature rise ΔT = δ/(αd) to slip the joint together thermally with zero force.
Worked Example
A 50 mm solid steel shaft in a steel hub with 100 mm outside diameter, 40 mm long, direct interference 50 µm (0.050 mm), E = 200 GPa, ν = 0.3, μ = 0.12. Lamé compliance: hub term (1/E)[(100² + 50²)/(100² − 50²) + 0.3] and solid-shaft term (1/E)(1 − 0.3) sum to 2.667/E, so p = (0.05/50) ÷ (2.667/200 000) = 75 MPa. Torque capacity T = 0.12 × 75 × π × 50² × 40 / 2 = 1 414 N·m; axial force F = 0.12 × 75 × π × 50 × 40 = 56.5 kN. Hub hoop stress = 75 × (100² + 50²)/(100² − 50²) = 125 MPa — comfortably below a 350 MPa yield. To shrink the hub on: ΔT = 0.05/(11.5×10⁻⁶ × 50) ≈ 87 °C above ambient.
Formulas
- Lamé interface pressure
p = (δ/d) / [ (1/E_o)((d_o² + d²)/(d_o² − d²) + ν_o) + (1/E_i)((d² + d_i²)/(d² − d_i²) − ν_i) ]- Holding capability
T = μ p π d² L / 2; F = μ p π d L- Hub hoop stress and shrink temperature
σ_t = p (d_o² + d²)/(d_o² − d²); ΔT = δ / (α d)
Standards & References
- ISO 286-2:2010, Tables of standard tolerance classes and limit deviations for holes and shafts — H7 hole (Table 6) and k6/n6/p6/s6/u6 shaft deviations (Tables 24, 25, 26, 28, 29), verified cell-by-cell for the 1–200 mm scope
- ISO 286-1:2010 — the ISO code system for tolerances on linear sizes underlying the fit designations
- Shigley's Mechanical Engineering Design, 11th ed. — press and shrink fits: Lamé pressure, torque/force capacity, and stress relations
Frequently Asked Questions
Which ISO fit should I use for a press fit?
H7/p6 is the classic light press fit for parts that transmit modest torque and may be disassembled; H7/s6 is a medium drive fit for permanent joints; H7/u6 is a heavy force/shrink fit for maximum holding power. H7/k6 and H7/n6 are transition fits — they locate precisely but can assemble with clearance at one end of tolerance, so they cannot be relied on to transmit load through friction alone.
Why does the calculator report torque at the minimum interference?
Because tolerance stacks: a batch of H7/s6 joints spans the full interference range, and the joint at the loose end grips least. The guaranteed design capacity is the torque at minimum interference; the stresses and press force must instead be checked at maximum interference, where the joint is tightest. The calculator reports both columns for exactly this reason.
Is the interference diametral or radial?
Diametral — the difference between shaft diameter and hole diameter, which is how the ISO 286 limits combine and how machinists measure. Some textbooks write the Lamé equations with radial interference (half the diametral value); this tool's formulas take δ as diametral throughout, so a 50 µm entry means the shaft measures 0.050 mm larger than the hole.
How hot do I need to heat the hub for a shrink fit?
ΔT = δ/(α·d) above ambient expands the hub bore by exactly the interference; in practice add an assembly clearance allowance (commonly the same order as the interference again) so the parts slide together freely before heat flows. For a 50 mm steel joint at 50 µm interference that is about 87 °C for zero clearance — real shop practice would heat 150–200 °C. Avoid tempering ranges of hardened parts, and remember cooling the shaft (dry ice, liquid nitrogen) is the alternative.
What friction coefficient should I use?
Dry steel-on-steel press fits are commonly designed with μ = 0.10–0.15 (0.12 default here); oiled assembly can halve that, and the value differs between pressing on (dynamic, lower) and holding (static, higher). Because capacity is proportional to μ, treat it as the least-certain input — use a conservative value and a service factor on the demanded torque.
What does the hub stress check assume?
It compares the Lamé tangential (hoop) stress at the hub bore — the largest stress in the joint — against the hub yield strength at the displayed one-decimal precision. Staying below yield keeps the fit elastic so the pressure and holding force persist. It is a preliminary check: stress concentrations at the hub edges, rotation, fatigue, and fretting are outside this calculator.