Geometry
Fit (ISO 286 / ANSI B4.2)
Interference (diametral)
Materials
Surfaces, friction, loads
Contact pressure
-Torque capacity (min interference)
-Axial holding force (min)
-Press-in force (max)
-Stresses at maximum interference
| Location | Tangential | Radial | von Mises | Safety factor |
|---|
Tension is positive. Safety factor = yield (or tensile strength) / von Mises stress.
Shrink-fit heating
Hub heated, shaft at 20 °C (68 °F). For a cooled shaft, use the same expansion with the shaft’s own α.
Interference summary
How the calculator works
The hub is a thick-walled cylinder loaded by internal pressure p and the shaft a cylinder loaded by external pressure p. For equal-length parts in plane stress, the Lamé equations give the radial change of each part, and the interference closes when the two add up to the interference:
- Contact pressure. p = (δeff/d) / [ Ch/Eh + Cs/Es ], with Ch = (D² + d²)/(D² − d²) + νh and Cs = (d² + di²)/(d² − di²) − νs. D is the hub outside diameter, d the fit diameter, di the shaft bore (0 if solid).
- Effective interference. δeff = δ − 0.4 (Rzshaft + Rzhub), because pressing flattens roughness peaks. It is evaluated at the minimum and the maximum interference of the fit.
- Capacity. Torque T = μ p π d² L / 2; axial force F = μ p π d L. The press-in force uses the maximum pressure and the pressing friction coefficient.
- Stresses at the interface. Hub bore: tangential p(D² + d²)/(D² − d²), radial −p. Shaft outside: tangential −p(d² + di²)/(d² − di²), radial −p; a hollow shaft’s bore carries −2pd²/(d² − di²). Combined with von Mises, σvm = √(σt² − σtσr + σr²).
- Interference from an ISO fit. The built-in ISO 286 engine of the limits and fits calculator gives the hole and shaft limits; minimum interference = smallest shaft − largest hole, maximum = largest shaft − smallest hole.
Limits of the method. This is the classical elastic solution for a long cylindrical hub. It ignores stress concentrations at the ends of the hub, keyways, centrifugal loss of pressure at speed, differential temperature in service and the plastic zone beyond yield. For rotating parts, thin hubs, keyed or tapered joints, or anything safety critical, use the full method of DIN 7190 or a finite element check.
Worked example: Ø1 in H7/s6 steel hub
A steel shaft (Ø25.4 mm, solid, E = 207 GPa, ν = 0.30) in a steel hub of 50.8 mm outside diameter, 38.1 mm long. H7/s6 at 25.4 mm gives an interference of 14 to 48 µm (diametral). With no roughness loss: Ch = (4 + 1)/(4 − 1) + 0.3 = 1.967, Cs = 1 − 0.3 = 0.7. Pressure at maximum interference = (0.048/25.4) / [(1.967 + 0.7)/207 000] = 146.7 MPa (21.3 ksi). At the minimum, 42.8 MPa (6.2 ksi). With μ = 0.12 the minimum torque capacity is 0.12 × 42.8 × π × 25.4² × 38.1 / 2 = 198 N·m (146 lbf·ft). The hub bore sees 244 MPa tangential tension, 342 MPa von Mises: a 350 MPa hub would have a safety factor of only 1.02 at the largest interference, which is exactly the kind of result this check is for.
New to fit codes? Read H7/g6 fit explained for what the letters and numbers mean and how common fits compare.
Questions
How do you calculate the torque a press fit can transmit?
First find the contact pressure p from the interference with the thick-walled cylinder (Lame) equations. Then the friction torque is T = μ · p · π · d² · L / 2, where d is the fit diameter, L the contact length and μ the friction coefficient. Use the minimum interference (smallest pressure) for the torque rating and the maximum interference for the stress and pressing-force checks.
What friction coefficient should I use for an interference fit?
About 0.10 to 0.15 for dry steel on steel is typical for a pressed fit; a shrink-fitted joint with a clean, dry surface is often rated with 0.12 to 0.15 once the parts have cooled. Oil on the surfaces lowers it markedly, so rate the joint for the worst surface condition you cannot rule out. The value is an input here so you can see how sensitive the result is.
Why does the calculator subtract surface roughness from the interference?
Pressing flattens the peaks of the surface roughness, so part of the nominal interference is lost and the contact pressure is lower than the drawing limits suggest. This calculator removes 0.4 × (Rz of shaft + Rz of hub) from the diametral interference, a common approximation for pressed fits. Set both roughness values to zero to see the unreduced result.
How hot do I need to heat the hub for a shrink fit?
The hub must grow by the maximum interference plus the assembly clearance you want. The temperature rise is ΔT = (δmax + clearance) / (α · d), where α is the thermal expansion coefficient. The calculator adds the rise to a 20 °C (68 °F) starting temperature. Keep the hub well below the tempering temperature of the material, and heat evenly.
Is a solid shaft ever in danger of yielding in a press fit?
A solid shaft is in a state of near-equal compression in the radial and tangential directions, so its von Mises stress equals the contact pressure and it rarely yields first. The hub is the weak part: its bore sees a tangential tension larger than the pressure, which is why the hub safety factor usually governs. A hollow shaft with a thin wall can also be critical, and the calculator checks it.
Engineering aid for guidance. Verify critical joints against DIN 7190 / ISO 286 and your own design rules, by test where possible; you remain responsible for the design. Material values are typical, check your supplier data. Nothing you enter leaves your browser except through a share link you copy yourself.