Shaft-Hub Interference Fit Calculator – Contact Pressure & Torque Capacity

Check	IND	US	EU	ISO
Contact pressure	implemented	—	—	—
Friction torque capacity	implemented	—	—	—

How engineers design interference fits

Interference fits connect shafts and hubs without keys or splines by relying on friction from contact pressure generated by an oversized shaft pressed or shrunk into a hub bore. The diametral interference creates radial pressure at the interface, which combined with friction provides torque capacity. The design must ensure sufficient interference for torque transmission without exceeding hub or shaft yield stress at the bore.

Fit methods and configurations

Method	Process	Application
Press fit	Hydraulic press at room temperature	Small to medium shafts
Shrink fit	Heat hub or cool shaft for assembly	Large rotors, turbine disks
Hydraulic expansion	Oil injection at interface	Large coupling hubs
Taper lock	Tapered sleeve with bolts	Adjustable, maintenance-friendly

Engineering workflow

Define the nominal shaft/hub diameter and required torque capacity.
Determine the diametral interference from ISO 286 fit designation or direct specification.
Apply Lame thick-cylinder equations to compute contact pressure.
Calculate hub bore hoop stress and verify it does not exceed yield.
Compute friction torque capacity from contact pressure, friction coefficient, and contact length.
Verify torque capacity exceeds the service torque with adequate safety factor.
Estimate press-in force or required temperature differential for assembly.

Key quantities and formulas

Contact pressure from interference (simplified, equal materials):

p = \frac{E δ}{2 r} \cdot \frac{( r _{o}^{2} - r ^{2} )}{r _{o}^{2}}

Full Lame formula for dissimilar materials:

p = \frac{δ}{\frac{r}{E _{h}} ( \frac{r _{o}^{2} + r ^{2}}{r _{o}^{2} - r ^{2}} + ν _{h} ) + \frac{r}{E _{s}} ( 1 - ν _{s} )}

Friction torque capacity:

T_{m a x} = 2 π μ p r^{2} L

Maximum hub hoop stress:

σ_{θ, m a x} = p \frac{r _{o}^{2} + r ^{2}}{r _{o}^{2} - r ^{2}}

Worked example

A 60 mm shaft with 0.04 mm diametral interference presses into a hub with 100 mm OD, contact length 50 mm. Both steel: $E = 207$ GPa, $ν = 0.3$ , $μ = 0.12$ , hub yield 350 MPa.

Contact pressure: $p \approx 207000 \times 0.04/ (2 \times 30) \times (5 0^{2} - 3 0^{2}) /5 0^{2} = 88.3$ MPa (simplified).
Hub hoop stress: $σ_{θ} = 88.3 \times (5 0^{2} + 3 0^{2}) / (5 0^{2} - 3 0^{2}) = 88.3 \times 2.125 = 187.6$ MPa — below 350 MPa yield.
Torque capacity: $T = 2 π \times 0.12 \times 88.3 \times 0.03 0^{2} \times 0.050 = 29.9$ N-m.

Common mistakes and checks

Ignoring surface roughness reduction: pressing flattens asperities, reducing effective interference by 5–15 micrometres.
Using thin-wall approximation on thick hubs: thin-wall formulas underestimate contact pressure when hub wall ratio is high.
Omitting temperature effects: thermal expansion at operating temperature changes the effective interference — verify at both assembly and service temperatures.
Friction coefficient uncertainty: $μ$ varies from 0.08 (oiled) to 0.20 (dry, rough) — this directly scales torque capacity.

FAQ

How do I choose between press fit and shrink fit?

Press fit is simpler for small shafts (under 100 mm). Shrink fit is needed for large rotors where press forces would be excessive or alignment would suffer.

What temperature differential is needed for shrink fitting?

Enough to expand the hub bore by the total interference plus assembly clearance — typically 150–300 deg C above ambient for steel hubs.

Can interference fits transmit axial loads?

Yes — the friction force resists axial sliding just as it resists torque. Axial capacity is $F = 2 π μ p r L$ .

What happens if the hub yields during assembly?

Plastic deformation at the bore reduces effective contact pressure after elastic springback. DIN 7190 provides elasto-plastic design methods for this case.

Should I combine a key with an interference fit?

Not typically — interference fits are used to eliminate keys. If both are present, the key carries most torque while the interference provides centering.

Use the PhyCalcPro calculator

Open the Shaft Hub Fits calculator to enter shaft/hub diameters, interference, material properties, contact length, and friction coefficient. The tool returns contact pressure, hub hoop stress, friction torque capacity, and utilization.

Purpose

Estimate contact pressure and friction torque capacity for interference fits between shafts and hubs.

Physics & theory

Interference fit creates radial contact pressure $p$ at the shaft-hub interface from diametral interference $δ$ . Thick-cylinder Lame equations relate interference to pressure based on elastic moduli, Poisson's ratios, and geometry. Friction torque capacity is $T = 2 π r^{2} μ p L$ . Maximum pressure must not exceed yield of hub or shaft at bore.

Governing equations

p = \frac{δ}{\frac{r}{E _{h}} ( \frac{r _{o}^{2} + r ^{2}}{r _{o}^{2} - r ^{2}} + ν _{h} ) + \frac{r}{E _{s}} ( 1 - ν _{s} )}

T_{m a x} = 2 π μ p r^{2} L

σ_{θ, m a x} = p \frac{r _{o}^{2} + r ^{2}}{r _{o}^{2} - r ^{2}}

Numerical method

Lame thick-cylinder closed-form for contact pressure from specified interference or fit tolerance. Friction torque from user $μ$ . Stress in hub bore compared to yield allowable.

Inputs

Parameter	Description
Shaft/hub diameters	Nominal and interference
Outer hub radius	Hub OD
Material $E$ , $ν$ , yield	Shaft and hub
Contact length $L$	Fit engagement length
Friction coefficient $μ$	Dry or lubricated assembly

Outputs

Contact pressure, hub hoop stress, friction torque capacity, torque utilization, minimum interference recommendation.

Design codes & checks

Indicative: Contact pressure and friction torque capacity
ISO: ISO 286 fit tolerances (with Fits module)
DIN: DIN 7190 interference fits (reference)

Assumptions & limitations

Elastic analysis; plastic deformation during press-fit not fully modeled.
Uniform pressure along length; no hub flange or step effects.
Friction coefficient highly variable with surface finish and lubricant.
Fatigue of interference joints not evaluated.

References

Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 7.
DIN 7190:2017. Interference fits — Calculation and design rules.
Roark, R. J., Young, W. C., & Budynas, R. G. Formulas for Stress and Strain, thick cylinders.
ISO 286-1:2010. Limits and fits.

Engineering guide to interference fit design for shaft-hub connections

Assumptions

Limitations

Engineering checks