TorqueMath

Press Fit Calculator

Interference (press and shrink) fits between a shaft and a hub: contact pressure, torque and axial force the joint can hold, stresses in hub and shaft, press-in force and the temperature to heat the hub for shrink fitting. ISO 286 fits or your own interference, solid or hollow shafts, steel, cast iron, aluminium and bronze.

TorqueMath.com · Press Fit Calculator
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Method and assumptionsMethod: Lamé thick-walled cylinders, equal length, elastic (as in Shigley §3-16 and DIN 7190-1 elastic range)Basis: ISO 286-2 deviations; smoothing 0.8·(Rz shaft + Rz bore); typical material E, ν, α and yield; same μ for slip and press-in; 0.1 % assembly clearance for shrinkingLimits: No plastic design, end effects of short or stepped hubs, centrifugal loosening at high speed, fretting or temperature differences in serviceReferences: DIN 7190-1 · ISO 286-2 · Shigley's Mechanical Engineering DesignFormulas · How this calculator was checked · TorqueMath v2.1

Minimum and maximum interference

The joint must hold the torque at the smallest interference and stay elastic at the largest. Effective interference = measured interference − 0.8 × (Rz shaft + Rz bore), the peaks flattened when pressing (DIN 7190).

InterferenceEffectivePressure pTorque capacityAxial forceHub σvShaft σv

How it is calculated

Both parts are treated as thick-walled cylinders of the same length (Lamé). The interference is shared between the hub growing and the shaft shrinking, and the contact pressure is the one that makes the two radial displacements add up to the interference.

Contact pressure p = δ / ( d · [ (1/Eh)·((Do² + d²)/(Do² − d²) + νh) + (1/Es)·((d² + di²)/(d² − di²) − νs) ] ) δ = effective diametral interference Torque capacity T = μ · p · π · d · L · d/2 axial force F = μ · p · π · d · L Hub at the bore σt = p · (Do² + d²)/(Do² − d²), σr = −p, σv = √(σt² − σt·σr + σr²) Shaft (solid) σt = σr = −p → σv = p; hollow at the bore σt = −2p · d²/(d² − di²) Smoothing δ = δmeasured − 0.8 · (Rz shaft + Rz bore) (DIN 7190) Shrink fitting ΔT = (δmax + 0.001·d) / (αh · d) heat the hub until it slides on with 0.1 % clearance

Equations as in Shigley's Mechanical Engineering Design (section 3-16) and DIN 7190-1 (elastic range). ISO fits use the ISO 286-2 deviations of the fits calculator on this site. Material data are typical values: steel E 210 GPa, ν 0.30, α 11.5·10⁻⁶/K; grey cast iron EN-GJL-250 E 110 GPa, ν 0.26, α 10.5·10⁻⁶/K (brittle: limit 50 % of tensile strength); aluminium 6082-T6 E 70 GPa, ν 0.33, α 23·10⁻⁶/K; bronze CuSn12 E 100 GPa, ν 0.34, α 18·10⁻⁶/K. Friction for slip 0.10 – 0.15 dry steel on steel after pressing, higher after shrink fitting (0.14 – 0.20). Press-in force uses the same μ; real press forces scatter widely.

This calculator checks an interference fit between a shaft and a hub – a press fit or a shrink fit. Choose an ISO 286 fit (H7/p6, H7/r6, H7/s6) or enter your own interference, the diameters, fit length, materials and friction. It returns the contact pressure at the smallest and largest interference, the torque and axial force the joint can hold before it slips, the stresses in the hub and shaft against their limits, the force needed to press the parts together and the temperature to heat the hub for a shrink fit.

Worked example: steel hub on a 40 mm shaft, H7/s6

  1. Shaft Ø40 mm solid 42CrMo4, steel hub Ø80 mm outside, fit length 40 mm, H7/s6, friction μ 0.12, Rz shaft + Rz bore = 10 µm.
  2. ISO 286 at Ø40: hole H7 0/+25 µm, shaft s6 +43/+59 µm, so the interference is 43 − 25 = 18 µm to 59 − 0 = 59 µm. Pressing flattens about 0.8 × 10 = 8 µm, leaving 10 – 51 µm effective.
  3. Hub term (80² + 40²)/(80² − 40²) + 0.30 = 1.967, shaft term 1 − 0.30 = 0.70. Pressure p = 0.010 / (40 × (1.967 + 0.70)/210 000) = 19.7 MPa at the loosest fit and 100 MPa at the tightest.
  4. Torque the loosest fit holds: T = μ·p·π·d·L·d/2 = 0.12 × 19.7 × π × 40 × 40 × 0.020 = 238 N·m. The axial force it holds is 11.9 kN.
  5. At the tightest fit the hub bore hoop stress is 100 × 1.667 = 167 MPa and the von Mises stress 234 MPa, 66 % of the 355 MPa yield. Pressing on needs about 0.12 × 100 × π × 40 × 40 = 60.6 kN.
  6. For a shrink fit, heat the hub by (0.051 + 0.040)/(11.5·10⁻⁶ × 40) = 198 K, to about 218 °C, so it slides on with 0.1 % clearance.

The H7/s6 fit holds 238 N·m even at its loosest, a slip safety of 1.19 for 200 N·m, with the hub at 66 % of yield. For shock loads, use a longer hub, a tighter fit or add a key.

FAQ

How do I calculate the pressure in a press fit?

Treat the shaft and hub as thick-walled cylinders. The interference is shared between the hub expanding and the shaft compressing; the contact pressure is the one at which both displacements add up to the interference: p = δ / (d·[(1/Eh)((Do² + d²)/(Do² − d²) + νh) + (1/Es)((d² + di²)/(d² − di²) − νs)]).

How much torque can a press fit transmit?

T = μ · p · π · d · L · d/2, where μ is the friction coefficient, p the contact pressure, d the fit diameter and L the fit length. Use the smallest interference of the tolerance range, because a fit must hold even when the parts are made at the loose end.

Why is effective interference smaller than the measured one?

Machined surfaces have peaks that are flattened when the parts are pressed together. DIN 7190 takes about 0.8 × (Rz shaft + Rz bore) off the measured interference. On fine-ground surfaces the loss is small; on turned surfaces it can eat a large part of a light press fit.

What temperature do I need to shrink fit a hub?

Heat the hub until its bore grows by the maximum interference plus an assembly clearance of about 0.1 % of the diameter: ΔT = (δmax + 0.001·d) / (α·d). For steel α is about 11.5·10⁻⁶ per kelvin. Keep steel hubs below about 350 °C, or cool the shaft instead with dry ice or liquid nitrogen.

Which fit should I use for a press fit, H7/p6, H7/r6 or H7/s6?

H7/p6 is a light location press fit that may have almost no interference at the loose end; it locates parts but transmits little torque. H7/r6 is a medium press fit, and H7/s6 a heavy drive fit for permanently assembled steel parts that must carry torque. Check the result with this calculator, because the right choice depends on diameter, hub wall and load.

Can a cast iron hub be press fitted?

Yes, but grey cast iron is brittle and weak in tension, so the hoop stress at the bore must stay well below its tensile strength; this calculator limits it to about half. Use a thicker hub or a lighter fit, and avoid shrink fitting with large temperature differences.

Tools for this job

What you need to build, measure or check the result.

Induction bearing heaterHeat hubs and bearings evenly for shrink fitsView on Amazon →Arbor pressPress small fits squareView on Amazon →Outside micrometer setMeasure the real interferenceView on Amazon →Retaining compoundAdds torque capacity to a fitView on Amazon →

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Checked: 4 results compared with textbooks, standards and maker data by a separate review. See the checks →

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